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2024/Comparing Data Augmentation Methods for End-to-End Task-Oriented Dialog Systems/6a7588fd-6217-4a89-8c21-556bca64edea_origin.pdf

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2024/Comparing Data Augmentation Methods for End-to-End Task-Oriented Dialog Systems/full.md

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+# Comparing Data Augmentation Methods for End-to-End Task-Oriented Dialog Systems
+
+Christos Vlachos<sup>1,2</sup>, Themos Stafylakis<sup>1,2,3</sup>, Ion Androutsopoulos<sup>1,3</sup>
+
+$^{1}$ Department of Informatics, Athens University of Economics and Business, Greece
+
+<sup>2</sup>Omium Natural Language Solutions Ltd. <sup>3</sup>Archimedes/Athena RC, Greece
+
+# Abstract
+
+Creating effective and reliable task-oriented dialog systems (ToDSs) is challenging, not only because of the complex structure of these systems, but also due to the scarcity of training data, especially when several modules need to be trained separately, each one with its own input/output training examples. Data augmentation (DA), whereby synthetic training examples are added to the training data, has been successful in other NLP systems, but has not been explored as extensively in ToDSs. We empirically evaluate the effectiveness of DA methods in an end-to-end ToDS setting, where a single system is trained to handle all processing stages, from user inputs to system outputs. We experiment with two ToDSs (UBAR, GALAXY) on two datasets (MultiWOZ, KVRET). We consider three types of DA methods (word-level, sentence-level, dialog-level), comparing eight DA methods that have shown promising results in ToDSs and other NLP systems. We show that all DA methods considered are beneficial, and we highlight the best ones, also providing advice to practitioners. We also introduce a more challenging few-shot cross-domain ToDS setting, reaching similar conclusions.
+
+# 1 Introduction
+
+Task-oriented dialog systems (ToDSs) aim to understand and fulfil a user's goal in a particular application domain (e.g., booking tickets, restaurant reservations) through natural language conversation (Bang et al., 2023; Zhao et al., 2022). They traditionally include several modules to handle a variety of processing stages. A natural language understanding (NLU) module typically extracts structured information from each user's utterance, usually in the form of slot-value pairs (e.g., for destination, travel date). A dialog state tracker (DST) keeps track of the information that has been revealed about the user's goal (dialog state) throughout the conversation. A policy optimizer (PO) de
+
+cides the system's next action (e.g., request information for a particular unfilled slot of the dialog state, or recommend a restaurant). A natural language generation (NLG) module realises communication actions of the system in natural language. In spoken conversations, automatic speech recognition (ASR) and text-to-speech (TTS) modules are also included (Oesterreich et al., 2023), though here we consider only written conversations.
+
+When the modules of a ToDS are trained separately, large volumes of annotated training data are needed, since each module requires its own input/output training examples. In end-to-end ToDSs (Wen et al., 2017; Lei et al., 2018), a single system is jointly trained to handle all (or most) of the processing stages, reducing (or at least harmonising) the kinds of annotated training data required, since each training example can be used by all (or most) of the modules (Deriu et al., 2021). Recent Transformer-based end-to-end ToDSs (Ham et al., 2020; Peng et al., 2021; Sun et al., 2022) aim to reduce the necessary training data further, by leveraging pre-training on unlabelled data. However, the best performance is still obtained by fine-tuning on domain-specific annotated training datasets (Hudeček and Dusek, 2023), which are costly to obtain, especially when moving to a new domain (e.g., from booking airline tickets to reserving restaurants). LLMs that promise adequate results in few- or even zero-shot settings (Radford et al., 2019; Brown et al., 2020) have been underexplored in ToDSs, and work along this direction has focused mostly on the DST module, with contradicting results (Hudeček and Dusek, 2023; Hu et al., 2022). Thus cost-effective methods to obtain or augment training sets for ToDSs are needed.
+
+We experiment with data augmentation (DA), which adds synthetic training examples to an existing annotated (possibly small) training set. DA methods have shown promising results in various NLP tasks, e.g., text classification, text generation,
+
+question answering (Feng et al., 2021; Shorten et al., 2021; Pappas et al., 2022), but have not been systematically compared in end-to-end ToDSs (Section 6). We simulate the case where the available annotated training set is limited, which is often the case with real-life ToDS applications, especially when moving to new application domains. We experiment with two end-to-end pre-trained Transformer-based TODSs, namely UBAR (Yang et al., 2021) and GALAXY (He et al., 2022b), and two English textual conversational datasets, MultiWOZ 2.0 (Budzianowski et al., 2018) and KVRET (Eric et al., 2017). We vary both the size of the initial annotated training set (e.g.,  $2\%$ ,  $10\%$ ,  $25\%$  of MultiWOZ's training set) and the expansion factor (generating one, two, or four synthetic examples from each original one, i.e., x2, x3, x5 expansion). We also introduce a more challenging few-shot cross-domain setting: in each iteration, we select a single domain as the target one, we remove from the training set all but 20 (few-shot) dialogs of the target domain, we generate synthetic training dialogs from the 20 dialogs, and evaluate only on test dialogs from the left-out target domain.<sup>1</sup>
+
+We compare eight DA methods that have shown promising results in ToDSs (mostly when training individual modules) and other NLP systems. The DA methods we consider are of three types. Word-level augmentation methods replace words of the original training examples by similar words, e.g., words that have similar word embeddings or words suggested by models that predict masked words. Sentence-level augmentation includes paraphrasing sentences of the original training data via back-translation (translating to another language and back), invoking systems trained specifically to perform paraphrasing, or by prompting Large Language Models (LLM); we also include in this type methods that rotate (swap) parts of the dependency tree of the original sentence. Finally, dialog-level augmentation methods exploit dialog-specific annotations of the original training examples (e.g., dialog states), which are available in ToDS datasets.
+
+Our contributions are: (1) We conduct a systematic comparison of DA methods in an end-to-end ToDS setting, the largest (in terms of DA methods) comparison to date in this setting. (2) We show that substantial performance gains can be obtained with DA methods, even when using pre-trained models,
+
+and we offer concrete advice to ToDS practitioners (Section 5). (3) We introduce and utilise a new few-shot cross-domain evaluation setting for DA approaches in ToDS, where we show that DA methods again boost performance.
+
+# 2 Data Augmentation Methods
+
+# 2.1 Word-level Augmentation
+
+Word-level DA methods replace words of the original training examples by similar words, e.g., words with similar word embeddings or words suggested by models that predict masked words (Wei and Zou, 2019; Wang and Yang, 2015). We experiment with word substitutions using either Word2Vec (Mikolov et al., 2013) or RoBERTa (Liu et al., 2019). Apart from boosting performance, word-level DA can generate more synthetic instances per original one, compared to other DA types considered.
+
+# 2.1.1 Word2Vec-based Word Substitution
+
+We employ Google's 300-dimensional embeddings, created using Word2Vec. We exclude stop-words or delexicalised tokens (special tokens replacing slot values) as candidates for DA. For every word in each dialog utterance, we find the 10 most similar ones in terms of cosine similarity of word embeddings. Preliminary testing showed that this may actually deteriorate performance, as some word replacements create dialog states and system actions inconsistent with the original ones, in agreement with Mi et al. (2021), who note that swapping certain words may change the original semantics. Instead, for every experiment, we train the ToDS with the original training data (the percentage available per experiment). For every word position, we test every candidate substitution from the pool of 10 most similar ones selecting at random, by passing the augmented sentence to that model. If the model's prediction (in terms of dialog state and system action) is different than the original one, the augmentation is discarded and the next word replacement from the pool is considered.
+
+# 2.1.2 LM-based Word Substitution
+
+Masking a word and using a language model (LM) to predict the masked token is a more advanced case of word substitution, previously used in numerous cases (Pantelidou et al., 2022; Kobayashi, 2018; Mi et al., 2021). We leverage the large version of an out-of-the-box RoBERTa (Liu et al., 2019).
+
+The list of candidate substitutions now comprises words that the LM deemed more likely, otherwise the method remains as in Word2Vec-based substitution, including the requirement that the dialog state and system action must remain the same.
+
+# 2.2 Sentence-level Augmentation
+
+Sentence-level augmentation includes paraphrasing (via back-translation, with systems trained specifically to perform paraphrasing, or by prompting LLMs) and fragment rotation (which moves parts of the dependency tree). These methods cannot generate as many synthetic training instances as word-level substitution, but their synthetic utterances are semantically closer to the original ones.
+
+# 2.2.1 Back-translation
+
+Back-translation has been used in many NLP tasks (Kumar et al., 2019; Huang et al., 2021; Federmann et al., 2019). It translates a piece of text (an utterance in our case) to a different (pivot) language and back to the original one. We use French as the pivot language and the Google translate API.<sup>3</sup> As explained by Ding et al. (2022), it is important to retain the original names of entities, such as attraction names and addresses. Special tokens used for delexicalisation also face the same issue. To avoid wrongly back-translating these special tokens, we apply back-translation to each utterance only after delexicalising and replacing the special tokens with special numbers (preceded by '#'), which remain unchanged during translation. The special tokens are relexicalized after DA.
+
+# 2.2.2 PEGASUS Paraphrasing
+
+The utilisation of LMs for paraphrasing was beneficial in the ToDS work of Gao et al. (2020), Hou et al. (2018), and Quan and Xiong (2019). Following Sharma et al. (2022), we leverage an instance of the Transformer-based PEGASUS (Zhang et al., 2020a), fine-tuned for paraphrasing. We set PEGASUS to generate up to two paraphrased utterances, and randomly select one, an approach that allows us the generate multiple synthetic dialogs per training instance. For each synthetic utterance, we check whether the delexicalisable tokens are preserved. If not, the augmentation is not applied.
+
+# 2.2.3 Fragment Rotation
+
+Cropping or rotating/flipping images is a popular label preserving DA approach in Computer Vision (Krizhevsky et al., 2017; Engstrom et al., 2019). An NLP analog of rotation was proposed by Şahin and Steedman (2018) and has also been tested in a ToDS setting (Louvan and Magnini, 2020, 2021). The main idea is to rotate (swap) in the dependency tree of a sentence, fragments (such as subjects/objects) around the root (usually a verb). We leverage Stanford's dependency parser (Qi et al., 2020) to generate annotations for MultiWOZ 2.0, consistent with the Universal Dependencies 2.1 (Nivre et al., 2020) in Şahin and Steedman's work. We then employ their method to generate synthetic utterances.<sup>6</sup> This may generate multiple outputs per original training instance, from which we sample uniformly. This method is a better fit for more free word-order languages, but both in Louvan and Magnini (2020) and in our experiments, it leads to substantial improvements in English too.
+
+# 2.2.4 LLM Paraphrasing
+
+LLMs have shown impressive results in tasks they have not encountered during training (Brown et al., 2020; Ouyang et al., 2022). Here we leverage ChatGPT, GPT-3.5-turbo specifically, and prompt it to generate augmented data via paraphrasing. We limit ourselves to two synthetic utterances to minimise the LLM's usage cost, randomly selecting one of the two, provided it includes all of the tokens that will be delexicalised. As a prompt we use a simple instruction and no in-context learning. $^7$
+
+# 2.3 Dialog-level Augmentation
+
+Dialog-level DA methods exploit dialog-specific annotations that ToD datasets include (e.g., dialog states, system actions). These methods can generate more synthetic data than sentence-level DA methods, but fewer than word-level ones. Also, the dialog-level DA methods considered here assume that dialog turns (user utterance–system response pairs) that have the same dialog state convey the same information, which is not always the case; hence, they may produce erroneous data.
+
+# 2.3.1 Dialog Tree
+
+The first dialog-level DA method we test was originally proposed by Aksu et al. (2022). Based on
+
+their approach, we create a tree structure containing dialogs that can be formed by combining the turns of the available training data in three steps. The first step is the creation of turn templates. Each template comprises a delexicalised turn, along with the current delexicalised dialog state  $(Cds)$  and the delexicalised dialog states of the previous  $(Pds)$  and next  $(Nds)$  turns of the dialog they originate from. If a template refers to the first dialog turn, its  $Pds$  is "Root". If a template refers to the last turn, its  $Nds$  is "Leaf". Let the set of templates created in the first step be  $T = \{r, t_1, \dots, t_n\}$ , where  $r$  is a special root template used in the second step.
+
+In the second step, templates are linked in a tree structure under a certain condition. A template  $t_j$  can be linked with a template  $t_i$  as its child node, only if  $t_i$ 's Nds matches  $t_j$ 's Cds and  $t_j$ 's Pds matches  $t_i$ 's Cds (see Fig. 7 of Appendix D for an example). All templates  $t$  that appear at the beginning of a dialog are automatically assigned as children of the special root template  $r$ . The third step is surface realisation, where delexicalised slots are filled with slot values.
+
+As the time complexity of this method increases exponentially in the number of dialogs, we sample only 50 dialogs from the original training set in the first step. We then create the tree and generate a new synthetic dialog by starting from the root and randomly selecting a child recursively until we reach a leaf. We then repeat, sampling again 50 dialogs (with replacement) from the original training set and generating another synthetic dialog.
+
+# 2.3.2 Act-Response Substitution
+
+Multi-Action Data Augmentation (MADA) is another DA approach based on dialog state matching, proposed by Zhang et al. (2020b). For every turn, they identify all other turns (of the original training dialogs) that have the same delexicalised dialog state and extract the system actions associated with the identified turns. They then train their ToDS using the original and extracted system actions per turn. Normally, a ToDS would encounter a single system action in each instance and Zhang et al. (2020b) observe that some system actions are more likely to be the ground truth actions, compared to others that may be correct as well. Instead, through MADA, the model encounters a more balanced set of system actions, helping it generate diverse responses during inference. In our case, along with valid system actions, we also store the corresponding system responses per turn, following the same
+
+principle. Then, for each dialog turn we replace the original system action and response by sampling from the set created by the process discussed.
+
+# 3 Experimental Setup
+
+In all experiments, we use three different randomly sampled training subsets (e.g., 3 different  $10\%$  subsets) and report averages.
+
+# 3.1 Main Experiments
+
+MultiWOZ: For our main experiments, we use MultiWOZ, an English human-to-human conversational dataset produced by a Wizard-of-Oz experiment, which has been used extensively in previous work (Wu et al., 2019; Heck et al., 2020; Zhao et al., 2021; Kulhánek et al., 2021; Wu et al., 2023). MultiWOZ 2.0, the most commonly used version that we also use, includes dialogs spanning 7 domains. It includes 10,438 dialogs in total, of which 1,000 are reserved for validation and another 1,000 for testing. Most dialogs fall into two or more domains making it a challenging benchmark. Of the tasks supported by MultiWOZ 2.0 (e.g., DST, intent classification, action-to-response generation) we select the response generation (RG) task, which UBAR and GALAXY can handle end-to-end.
+
+Evaluation measures: Following Budzianowski et al. (2018), we mainly report Score values for MutiWOZ. We also present Inform, Success, and BLEU results in the appendix. Inform is the percentage of dialogs where the system provided a correct recommendation based on the user's constraints (e.g., cheap hotel). Success is the percentage of dialogs where the system satisfied the user's constraints  $(\text{Inform} = 100\%)$  and provided all the requested information (Budzianowski et al., 2018; Nekvinda and Dušek, 2021). BLEU (Papineni et al., 2002) measures the word  $n$ -gram similarity between the system and the gold response. Finally,  $Score = \frac{1}{2}(\text{Inform} + \text{Success}) + \text{BLEU}$ .
+
+UBAR: For the MultiWOZ experiments, we use UBAR (Yang et al., 2021), a GPT2-based ToDS (Radford et al., 2019) that remains competitive as shown in recent studies (Nekvinda and Dušek, 2021; Sun et al., 2022), and is also easier (and much less expensive) to use compared to larger LLMs. UBAR is also based on the framework used by MADA (Zhang et al., 2020b), thus facilitating experimenting with dialog-level DA methods.
+
+MultiWOZ with all DA methods: In a first set of experiments, we reduce the size of the MultiWOZ
+
+training set to 850 dialogs ( $\sim 10\%$  of the training set) and produce an extra synthetic dialog from each original one, doubling ( $\times 2$ ) the training set.
+
+MultiWOZ with best three DA methods: In a second set of experiments, we consider only the best three DA methods of the previous experiments, but we now consider generating one, two, or four synthetic dialogs from each original dialog  $(\times 2, \times 3, \times 5)$ , using only  $\sim 2\%$  (170),  $\sim 10\%$  (850), or  $\sim 25\%$  (2,125) of the MultiWOZ training dialogs.
+
+Few-shot cross-domain experiments: Finally, we test the best three DA methods of the first set of experiments, now in a few-shot, cross-domain setting for the restaurant, hotel and attraction domains of MultiWOZ. As in the first set of experiments, we use  $10\%$  of the MultiWOZ training dialogs. Additionally, in three iterations, we leave one domain out of the training set apart from 20 (few-shot) dialogs, and we use only test (and validation) dialogs that include the left-out domain. We generate four synthetic dialogs for each few-shot dialog (x5) in these experiments, which was the augmentation size that worked best in the second set of experiments when there were very few training instances.
+
+# 3.2 Additional Experiments
+
+To ensure that our previous findings are not dataset-and model-specific, we repeat them using KVRET (Eric et al., 2017) and GALAXY (He et al., 2022b).
+
+KVRET is also an English multi-domain dataset, the domains being weather, navigation, schedule. It includes 2,424 dialogs, with 302 being reserved for validation and 304 for testing. Contrary to MultiWOZ, each dialog belongs in a single domain.
+
+Evaluation measures: Following He et al. (2022b), for KVRET we report Score (calculated using the same formula as in MultiWOZ), with slight modifications. Match is reported, which is equivalent to the Inform of MultiWOZ. Moreover, Lei et al. (2018) argues that the original Success rate favours recall, as a dialog would be considered successful if the model responded with every possible recommendation. Hence Success  $F1$  is used to balance precision and recall instead of Success.
+
+GALAXY is a more recent ToDS, pretrained using UniLM (Dong et al., 2019), currently among the best ToDSs on KVRET (He et al., 2022a).
+
+Experiments: We conduct similar experiments on KVRET as on MultiWOZ. The initial training sets (before DA) include  $\sim 5\%$  (120),  $\sim 10\%$  (250),
+
+$\sim 25\%$  (600) dialogs from KVRET's training set. We select the three best performing DA approaches on the  $5\%$  subset and conduct the same experiments using the  $10\%$  and  $25\%$  subsets, generating one, two, or four synthetic instances from each original one (x2, x3, x5). KVRET has an average dialog length of 2.5 turns, contrary to MultiWOZ's 13.68. We exclude the two dialog-level DA methods from the KVRET experiments, since they had the worst performance in the first set of experiments on MultiWOZ. As each dialog belongs in a single domain, our cross-domain evaluation setting is also not applicable to KVRET.
+
+# 4 Experimental Results and Analysis
+
+# 4.1 Results of the Main Experiments
+
+MultiWOZ with all DA methods: The results of the first set of experiments (all 8 DA methods,  $10\%$  of MultiWOZ's training set, x2 expansion) are presented in Table 1. All DA methods lead to a substantial performance boost. The three highest scores are obtained with Word2Vec substitution, PEGASUS paraphrasing and fragment rotation, improving UBAR without DA ("10% training set") by about 9 points. Surprisingly, fragment rotation is among the best DA method, even though English is not particularly free word-order (Section 2.2.3). The worst results come from the dialog-level DA methods, presumably because matching delexicalised dialog states introduces noise (Aksu et al., 2022).
+
+MultiWOZ with best three DA methods: The results of the second set of experiments (best 3 DA methods,  $2\%$ ,  $10\%$ ,  $25\%$  of original training set, expansion by x2, x3, x5) are shown in Fig. 1. For each original training set size (horizontal axis), we show the Score (vertical axis) of each DA method (curves). To save space, we show scores using the best (per DA method and training set size) expansion size (x2, x3, x5). As expected, DA methods are more beneficial when the original annotated training set is limited (e.g.  $2\%$ ,  $10\%$ ), with much smaller improvements when more annotated data are available ( $25\%$ ). Also, when the original training set is very limited ( $2\%$ ), x5 expansion leads to the best results, but when the original training set is larger ( $10\%$ ,  $25\%$ ), more conservative ( $x3$  and x2, respectively) expansion is better, presumably because it becomes more important to avoid adding multiple variants of the same original training instance. Overall, the three best DA methods lead to
+
+very similar performance boosts, in agreement with the results of the previous experiments (Table 1).
+
+Few-shot cross-domain experiments: The results of these experiments are shown in Fig. 2. All DA methods led to substantial improvements in all three few-shot domains, increasing the Score by up to 8, 9 and 10 points for the attraction, hotel and restaurant domains, respectively. Contrary to previous experiments, here PEGASUS paraphrasing was more effective overall compared to the other two DA methods.[8]
+
+<table><tr><td>DA Type</td><td>DA Method</td><td>Score</td></tr><tr><td rowspan="2">No DA</td><td>Full training set</td><td>105.1</td></tr><tr><td>10% training set</td><td>75.88</td></tr><tr><td rowspan="2">Word-level</td><td>Word2Vec replace</td><td>84.69</td></tr><tr><td>RoBERTa replace</td><td>80.11</td></tr><tr><td rowspan="4">Sentence-level</td><td>Back-translation (FR)</td><td>81.31</td></tr><tr><td>PEGASUS</td><td>83.16</td></tr><tr><td>Fragment rotation</td><td>84.59</td></tr><tr><td>LLM paraphrase</td><td>81.48</td></tr><tr><td rowspan="2">Dialog-level</td><td>Dialog Tree</td><td>79.94</td></tr><tr><td>Act-Response</td><td>80.78</td></tr></table>
+
+Table 1: MultiWOZ Score, for all 8 DA methods, using  $10\%$  of the original training dialogs, producing a single synthetic dialog from each original one (x2).
+
+![](images/fa715c3da78b2fa583cca6ea2ef9187db68f2d90289edd29a5d967267367c178.jpg)  
+Figure 1: MultiWOZ Score, for the 3 best DA methods of Table 1, using  $2\%$ ,  $10\%$ ,  $25\%$  of the original training dialogs. We report in brackets the expansion size (x2, x3, x5) that led to the best Score.
+
+# 4.2 Results of the Additional Experiments
+
+KVRET with all DA methods: GALAXY's results with all 6 applicable (to KVRET) DA methods, using  $5\%$  of KVRET's training dialogs, and x2 expansion are reported in Table 2. Word2Vec substitution and fragment rotation remain among the
+
+![](images/aa088dd48c91f99700890794c0db504e25b0e1e8d7cd38708a264baf073f709a.jpg)  
+Figure 2: MultiWOZ Score, for the 3 best DA methods of Table 1, in the few-shot cross-domain setting (domains: attraction, hotel, restaurant).
+
+top performers, with the LLM-based paraphrasing marginally overtaking PEGASUS paraphrasing.
+
+KVRET with best three DA methods: Figure 3 shows results obtained with the best three DA methods of the previous experiment, now using  $5\%$ ,  $10\%$ ,  $25\%$  of KVRET's training set, and x2, x3, x5 expansion. Interestingly, DA (any method) manages to improve performance only when  $5\%$  of KVRET's training set is used. $^{9}$  Although KVRET is smaller than MultiWOZ (2,424 dialogs in total vs. 10,438) and one would expect DA methods to be more useful in KVRET, it is also much easier than MultiWOZ, because each dialog concerns a single domain. This is evident by the fact that GALAXY with only  $25\%$  of the KVRET training set and no DA (Fig. 3, rightmost result of the red dashed line) is almost as good as GALAXY trained on the entire KVRET training set, again with no DA (horizontal dotted line). Even with only  $10\%$  of KVRET's training set, GALAXY with no DA (red dashed line) obtains a Score of 92.16, leaving very little scope for improvement. When using  $5\%$  of the original training set, where there is much larger scope for improvement (Fig. 3, left), all DA methods substantially improve performance, and the best DA method (fragment rotation) improves performance by approx. 9 points (Table 2). The results of Figures 1 and 3 also indicate that there is no universal threshold of initial annotated training instances, below which DA is beneficial; the threshold depends on the difficulty of the particular task (e.g., whether dialogs are single- or multi-domain). Instead, one should examine performance; when it is very low (e.g., with  $2\%$  of MultiWOZ or  $5\%$
+
+of KVRET), DA methods are definitely worth considering, otherwise when performance is already very high (e.g., exceeding 90 Score when using  $10\%$  or  $25\%$  of KVRET), applying DA is probably pointless. In all cases, generating more than one or two synthetic examples per original one (more than x2 or x3 expansion) is not beneficial.
+
+<table><tr><td>DA Type</td><td>DA Method</td><td>Score</td></tr><tr><td rowspan="2">No DA</td><td>Full training data</td><td>102.5</td></tr><tr><td>5% training data</td><td>73.27</td></tr><tr><td rowspan="2">Word-level</td><td>Word2Vec replace</td><td>81.44</td></tr><tr><td>RoBERTa replace</td><td>80.67</td></tr><tr><td rowspan="4">Sentence-level</td><td>Back-translation (FR)</td><td>77.83</td></tr><tr><td>PEGASUS</td><td>75.78</td></tr><tr><td>Fragment rotation</td><td>82.76</td></tr><tr><td>LLM paraphrase</td><td>82.04</td></tr></table>
+
+Table 2: KVRET Score, for 6 applicable DA methods, using  $5\%$  of original training dialogs, producing a single synthetic dialog from each original one (x2).
+
+![](images/d0db7778d9b4f7617417d601380edd828cd39d402a5b95c0ffb5b62fdea347b6.jpg)  
+Figure 3: KVRET Score, for the 3 best DA methods of Table 2, using  $5\%$ ,  $10\%$ ,  $25\%$  of the original training dialogs. We report in brackets the expansion size (x2, x3, x5) that led to the best Score.
+
+# 4.3 Response and Error Analysis
+
+In MultiWOZ dialogs the domain may change from utterance to utterance making the benchmark much more challenging, compared to KVRET. Using DA approaches have proven beneficial in terms of the overall Score, but this is not always the case with the underlying metrics Success and BLEU score that concern the generated response as seen in Figures 3 - 23. To gain a better view of the effectiveness of the DA methods tested, we present an error rate per domain category based on Success. To do so, we calculate the percentage of unsuccessful dialogs  $(Success = 0)$  per dialog category in the test set. Consider for example the case of
+
+using  $25\%$  data of the training set for DA leveraging the Word2Vec approach. A comparison of this approach when using x2 and x5 the amount of data is depicted in Figure 4. Additional comparisons for the case of PEGASUS and fragment rotations are presented in Appendix C. In the figure, "tx", "at", "re", "ho" and "tr" refer to the taxi, attraction, restaurant, hotel, and train domains respectively. Multiple domains in each category denote domain switches. It comes as no surprise that the more domain switches a dialog contains, the more errors the model makes. Using x5 the amount of training data seems to amplify this behaviour; an observation that could be attributed to the additional noise introduced mostly in terms of the synthetically generated responses. Thus, generating more than a single synthetic dialog (especially in the x5 case) may not prove as beneficial for all cases (e.g. when  $25\%$  of the MultiWOZ dialogs are available). Overall, of the three best performing methods, Word2Vec and PEGASUS seem to perform similarly, making more errors is the same dialog categories (mostly the ones including the restaurant and hotel domains). On the other hand fragment rotation straggles more mostly with dialogs involving the attraction domain. One should keep in mind that, regardless of applying DA or not, many errors made by the model are also to be blamed to the automatic evaluation as during inference the user's utterance remains static and is always in accordance with the ground truth system response, thus potentially confusing the model.
+
+After careful, manual examination of system responses on a small sample of the test set across all experimental cases, the responses themselves are fluent and informative. Generally, it is very difficult to deduce which DA method was used to train the model that generated the response. The small differences in scores could be justified by this conclusion, especially when comparing two methods that perform DA at the same level (e.g. the sentence-level PEGASUS and fragment rotation methods). Even when generating multiple synthetic dialogs per training instance (e.g. x5 DA level), the responses remain fluent even though some DA methods may alter the structure of the sentence (e.g. Figure 13). Using fragment rotation to generate four synthetic dialogs is an exception to the above observation, as in few cases the resulting responses may also feature rotated fragments of the respective dependency trees. An example of a dia
+
+![](images/dff295b487281edc4196f4abed216773289a8e1473488b3fa2a0bca2903c76fe.jpg)
+
+![](images/34280bf573b93fd762e9a1fcd11023e1539507555fee1fd5dea71848d4ed91fa.jpg)  
+Figure 4: Error rates per MultiWOZ domain category using the Word2Vec DA method and having  $25\%$  of the training data available. The upper and lower figures depict error rates when generating a single (x2) and four (x5) synthetic dialogs per instance respectively.
+
+log and its corresponding response per DA method is depicted in Figure 17 of Appendix D. Moreover, a comparison of the models' outputs when generating a single and four synthetic dialogs per training instance is depicted in Figure 18.
+
+# 5 Advice to ToDS Practitioners
+
+Based on our experiments, we provide the following advice to ToDS practitioners. (1) Although DA methods are currently not widely used in ToDS (Section 6), they can lead to very substantial gains when annotated training examples are scarce, even when using pre-trained end-to-end models. However, data scarcity depends on the difficulty of the task (e.g., whether the dialogues are single- or multi-domain), it cannot be judged using a universal threshold of initial annotated training instances, and is best assessed using performance scores. (2) Although all DA methods considered led to substantial improvements, dialog-state DA methods (at least the ones we considered) should be the last choices, as they led to a smaller performance boost and they also require dialog-specific annotations (e.g., dialog states) that are difficult to obtain in practice. (3) Among the other DA methods consid
+
+ered, the best overall performers were Word2Verb-based word substitution (Section 2.1.1), rotating parts of the dependency tree (Section 2.2.3), and paraphrasing the utterances by invoking paraphrasing models or prompting LLMs (Sections 2.2.2, 2.2.4). We recommend using any of these methods, provided that the resources they require are available; e.g., rotation requires a dependency parser for the target language, prompting requires an LLM supporting the target language and adds the cost of invoking an LLM. (4) Generating more than two synthetic instances per original one is worth considering only when the original annotated training instances are very scarce (e.g., when using only  $2\%$  of MultiWOZ's multi-domain training set).
+
+# 6 Related Work
+
+DA has been applied to a wide range of tasks from Computer Vision (Krizhevsky et al., 2017; Engstrom et al., 2019) to Speech Processing (Ko et al., 2015) and NLP (Kumar et al., 2019; Huang et al., 2021; Wei and Zou, 2019; Kobayashi, 2018).
+
+For NLP specifically, Pappas et al. (2022) carried out one of the most extensive comparisons of DA methods, in the context of biomedical QA, including Word2Vec-based word replacement (but without our semantics preserving test), LM-based word replacement, and back-translation. Word2Vec-based replacement was the most effective of the three methods, with back-translation and LM-based word replacement having similar performance.
+
+Whitehouse et al. (2023) and Sahu et al. (2022) prompt off-the-self LLMs to produce synthetic data in cross-lingual commonsense reasoning and intent classification, respectively. Mehri et al. (2022) also leverage an LLM to produce synthetic data for intent classification, slot filling, and next action prediction in a zero-shot ToDS setting, showing improvements in performance. By contrast, Hudeček and Dusek (2023) reported that relying on LLMs to directly generate belief states and system actions was not beneficial, compared to a fine-tuned model.
+
+Zhang et al. (2020b) propose the MADA (Multi-Action Data Augmentation) framework that we modified in order to include both the system actions and responses as explained in Section 2.3.2. Aksu et al. (2022) also capitalise on dialog states to produce a tree of possible dialogs (Section 2.3.1). Both of these approaches proved beneficial in our work. Similar to the approach of Aksu et al. (2022), Gritta et al. (2021) also capitalise on a graph struc
+
+ture, linking dialog states across all dialogs. In a similar spirit, Qiu et al. (2022) propose clustering dialog turns based on their dialog states. The extracted cluster structure forms the base for an augmentation approach similar to MADA.
+
+Louvan and Magnini (2020, 2021), inspired by Şahin and Steedman (2018), introduce an NLP version of image cropping and rotation, based on permutations of sentence fragments (Section 2.2.3). To improve performance on out-of-scope (OOS) dialog utterances (not represented in the training set, e.g., pertaining to new domains), Chen and Yu (2021) augment their training set by mixing OOS utterances with the ones found in their training set. Yin et al. (2020) use Reinforcement Learning to find the optimal (in terms of context) text span replacements (instead of word replacements).
+
+Paraphrasing as a form of DA was also used by Hou et al. (2018) and Gao et al. (2020) for slot-tagging (subpart of DST) and RG; they implemented their own paraphrasing model based on RNNs. Similarly, Axman et al. (2023) train a BART model (Lewis et al., 2020) for paraphrasing in an end-to-end ToD setting. Mi et al. (2021), also employ DA in a ToDS setting, by substituting masked tokens of the input using an LM (much as in Section 2.1.1). Song et al. (2021) augment their dataset by replacing slot-values with randomly generated strings to simulate references to out-of-vocabulary (OOV) words, a simple yet effective approach for models that learn to copy words from input to output by incorporating the copy-mechanism (Gu et al., 2016). Huang et al. (2022) randomly change the letter order of slot-values to improve the robustness of their ToDS. Improving robustness is also the main goal of Li et al. (2021), who generate turns with replaced slot-values not encountered in the training set.
+
+The closest previous work is that of Quan and Xiong (2019). They experiment with four DA methods in an end-to-end ToDS setting, including stopwords removal, paraphrasing, back-translation, synonym substitution (and their combination). We compare more (eight) DA methods, of three different types (word-level, sentence-level, dialog-level), while Quan and Xiong consider fewer (four) methods of the word-level and sentence-level types only. Furthermore, we also experiment with a more challenging dataset containing dialogs that may belong (the same dialog) in multiple domains (MultiWOZ), whereas Quan and Xiong use the single
+
+domain Camrest676 (Wen et al., 2017), and (like us) KVRET, which covers three domains, but each dialog pertains to a single domain. Contrary to the work of Quan and Xiong, we also experiment with several sizes of initial annotated training set (e.g.,  $2\%$ ,  $10\%$ ,  $25\%$  in MultiWOZ) and different expansions (x2, x3, x5), and we also introduce a new few-shot cross domain setting (Section 3.1).
+
+# 7 Conclusions and Future Work
+
+We performed the largest to date (in terms of methods and types) empirical comparison of DA methods in the context of end-to-end ToDSs, using two pre-trained Transformer ToDSs (UBAR, GALAXY) and two datasets (MultiWOZ, KVRET). We varied both the size of the initial annotated training set (e.g.,  $2\%$ ,  $10\%$ ,  $25\%$  of MultiWOZ's training set) and the expansion factor (generating one, two, or four synthetic instances from each original one). We also introduced a new, more challenging few-shot cross-domain evaluation setting. We showed that substantial performance gains can be obtained with DA methods, even when using pre-trained end-to-end models, and we offered concrete advice to ToDS practitioners regarding when to use DA, which DA methods to prefer, and with which expansion factors (Section 5).
+
+In future work, we plan to explore combinations of DA methods, to check if the synthetic training instances they produce are complementary. We also plan to investigate how well DA methods perform in low-resource languages (e.g., languages for which LLMs or reliable dependency parsers may not be available). Finally, we aim to measure the costs (computational, monetary) of DA methods.
+
+# 8 Limitations
+
+A major limitation of our work is based on the nature of the datasets. Most of our DA methods rely on dialog annotations to ensure that they preserve the original semantics of the dialogs (Subsection 2.1.1) or to directly generate synthetic dialogs (Subsection 2.3.1). Many ToD datasets lack such detailed annotation, as is the case with the second track of DSTC 11 (Soltau et al., 2023). $^{10}$  In real world scenarios such annotations are even harder to come by, even though there is a plethora of structured dialogs covering a wide range of topics. In
+
+such cases, DA approaches that rely on the annotations of dialogs are not guaranteed to perform as well or at all on their own, compared to the experiments presented.
+
+Another limitation of our work is the lack of detailed tuning/finetuning, in favour of a wider range of DA methods. Taking LLM-based paraphrasing as an example (Subsection 2.2.4), although we do experiment (up to a point) with different prompts during preliminary testing, a more detailed prompt tuning may have led to better results. In the same manner, for the case of PEGASUS paraphrasing (Subsection 2.2.2) or RoBERTa-based word substitution (Subsection 2.1.2), further specialised pretraining on other similar ToD datasets could have led to improved performance as shown by Wu et al. (2020). Similarly we avoid tuning the hyperparameters (e.g., learning rate, context window etc.) of the models used (UBAR and GALAXY). After all, the purpose of our work was not to achieve SOTA performance, but to compare DA methods and show their benefits under a common task (end-to-end).
+
+Finally, we only take into account DA methods that can be applied regardless of the ToDS used. ToDSs such as the ones proposed by Gao et al. (2020) and Zhang et al. (2020b) consider online DA methods, that were not covered in our work. We recognise the advantages of such methods but opt not to include them as they are ToDS specific (they are build around a specific ToDS). Instead we experiment with offline DA methods that are architecture-free and have proven beneficial in ToD and NLP in general.
+
+# 9 Ethical considerations
+
+Implementing the DA methods and training the ToDS proposed in the settings mentioned in Section 3, requires a lot of GPU processing (excluding dialog-level DA and fragment rotation). Leaving aside the cost that comes as a result of the methods' execution, such GPU usage also has environmental impact in the form of CO2 emissions. We hope to alleviate this effect by offering advice to ToDS practitioners (Section 5) and guiding them in choosing the best fit (in terms of DA methods) for their task, in order to avoid such costly experimentation in the future.
+
+# 10 Acknowledgements
+
+This work was partially supported by Omilia Natural Language Solutions Ltd; the Research Center
+
+of the Athens University of Economics and Business (AUEB-RC); and project MIS 5154714 of the National Recovery and Resilience Plan Greece 2.0, funded by the European Union under the NextGenerationEU Program. Views and opinions expressed are however those of the author(s) only and do not necessarily reflect those of the European Union or European Commission-EU. Neither the European Union nor the granting authority can be held responsible for them.
+
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+Jingqing Zhang, Yao Zhao, Mohammad Saleh, and Peter J. Liu. 2020a. Pegasus: Pre-training with extracted gap-sentences for abstractive summarization. In Proceedings of the 37th International Conference on Machine Learning, ICML'20. JMLR.org.  
+Yichi Zhang, Zhijian Ou, and Zhou Yu. 2020b. Task-oriented dialog systems that consider multiple appropriate responses under the same context. Proceedings of the AAAI Conference on Artificial Intelligence, 34(05):9604-9611.  
+Jeffrey Zhao, Raghav Gupta, Yuan Cao, Dian Yu, Mingqiu Wang, Harrison Lee, Abhinav Rastogi,
+
+Izhak Shafran, and Yonghui Wu. 2022. Description-driven task-oriented dialog modeling. ArXiv, abs/2201.08904.  
+Jeffrey Zhao, Mahdis Mahdieh, Ye Zhang, Yuan Cao, and Yonghui Wu. 2021. Effective sequence-to-sequence dialogue state tracking. In Proceedings of the 2021 Conference on Empirical Methods in Natural Language Processing, pages 7486-7493, Online and Punta Cana, Dominican Republic. Association for Computational Linguistics.
+
+# Appendix
+
+# A LLM prompting
+
+We initially construct a simplistic template prompt, without giving any in-context example paraphrases, that has the following form: "Paraphrase the following sentence twice. Maintain as much information as possible intact. The sentence to paraphrase is: {}". The "\{}" symbol denotes the placeholder for the utterance (not delexicalised) to be paraphrased. More elaborate templates were also tested (e.g. providing the LLM with the dialog history), such as "Your job is to augment the given utterance from a dialog between a user and an assistant. You will be given the dialog history as context. The user's utterances start with USER :, while the assistant's utterances with ASSISTANT .. Here is the dialog up to this point :  $\{1\}$ . Paraphrase the following sentence twice. Maintain as much information as possible intact. The sentence to paraphrase is :  $\{2\}$ ", where " $\{1\}"$  and " $\{2\}"$  denote the placeholders for the dialog history and current utterance respectively. During preliminary testing such templates did not provide a significant improvement, and as a result we opted for the more cost-efficient approach.
+
+# B More Detailed Results
+
+In this section we present the detailed results of all the experiments conducted, including the additional metrics that accompany each dataset. For MultiWOZ, we include the Inform and Success score along with BLEU score, as explained in Sub-sections 3.1. Similarly for the case of KVRET the Match, Success F1 and BLEU scores are reported. For each case, we first present the performance on the initial experiments where we select the 3 best performing DA methods followed by the results of these there methods in various other settings. From the results, we observe that the additional metrics reported tend to follow the trends of the main metric (Score), especially BLEU and Success.
+
+<table><tr><td>DA type</td><td>DA Method</td><td>Inform</td><td>Success</td><td>BLEU</td><td>Score</td></tr><tr><td rowspan="2">No DA</td><td>Full training set</td><td>95.40</td><td>80.70</td><td>17.00</td><td>105.1</td></tr><tr><td>10% training set</td><td>76.37</td><td>53.73</td><td>10.83</td><td>75.88</td></tr><tr><td rowspan="2">Word-level</td><td>Word2Vec replace</td><td>83.57</td><td>61.70</td><td>12.06</td><td>84.69</td></tr><tr><td>RoBERTa replace</td><td>81.57</td><td>55.70</td><td>11.48</td><td>80.11</td></tr><tr><td rowspan="4">Sentence-level</td><td>back-translation (FR)</td><td>80.97</td><td>58.83</td><td>11.41</td><td>81.31</td></tr><tr><td>PEGASUS paraphrase</td><td>83.33</td><td>60.87</td><td>11.06</td><td>83.16</td></tr><tr><td>Fragment rotation</td><td>83.17</td><td>61.37</td><td>12.33</td><td>84.59</td></tr><tr><td>LLM paraphrase</td><td>78.87</td><td>58.70</td><td>12.70</td><td>81.48</td></tr><tr><td rowspan="2">Dialog-level</td><td>Dialog Tree</td><td>78.83</td><td>57.23</td><td>11.90</td><td>79.94</td></tr><tr><td>Act-Response substitution</td><td>79.33</td><td>58.90</td><td>11.66</td><td>80.78</td></tr></table>
+
+Table 3: MultiWOZ metrics, for all 8 DA methods, using  $10\%$  of the original training dialogs, producing a single synthetic dialog from each original one (x2).  
+
+<table><tr><td>DA Method</td><td>Inform</td><td>Success</td><td>BLEU</td><td>Score</td></tr><tr><td>10% training set</td><td>76.37</td><td>53.73</td><td>10.83</td><td>75.88</td></tr><tr><td>Word2Vec replace</td><td>83.60</td><td>58.33</td><td>11.42</td><td>82.39</td></tr><tr><td>PEGASUS paraphrase</td><td>82.37</td><td>58.83</td><td>10.50</td><td>81.10</td></tr><tr><td>Fragment rotation</td><td>80.87</td><td>58.93</td><td>11.52</td><td>81.42</td></tr></table>
+
+Table 4: MultiWOZ metrics, for the top 3 DA methods, using  $10\%$  of the original training dialogs, producing two synthetic dialogs from each original one (x3).  
+
+<table><tr><td>DA Method</td><td>Inform</td><td>Success</td><td>BLEU</td><td>Score</td></tr><tr><td>10% training set</td><td>76.37</td><td>53.73</td><td>10.83</td><td>75.88</td></tr><tr><td>Word2Vec replace</td><td>83.67</td><td>54.67</td><td>10.45</td><td>79.62</td></tr><tr><td>PEGASUS paraphrase</td><td>82.93</td><td>58.07</td><td>9.73</td><td>80.23</td></tr><tr><td>Fragment rotation</td><td>81.73</td><td>57.47</td><td>10.10</td><td>79.70</td></tr></table>
+
+Table 5: MultiWOZ metrics, for the top 3 DA methods, using  $10\%$  of the original training dialogs, producing four synthetic dialogs from each original one (x5).  
+
+<table><tr><td>DA Method</td><td>Inform</td><td>Success</td><td>BLEU</td><td>Score</td></tr><tr><td>25% training set</td><td>88.00</td><td>69.73</td><td>13.65</td><td>92.52</td></tr><tr><td>Word2Vec replace</td><td>89.42</td><td>70.40</td><td>13.51</td><td>93.41</td></tr><tr><td>PEGASUS paraphrase</td><td>88.90</td><td>69.27</td><td>13.08</td><td>92.17</td></tr><tr><td>Fragment rotation</td><td>87.57</td><td>69.93</td><td>13.91</td><td>92.66</td></tr></table>
+
+Table 6: MultiWOZ metrics, for the top 3 DA methods, using  $25\%$  of the original training dialogs, producing a single synthetic dialog from each original one (x2).  
+
+<table><tr><td>DA Method</td><td>Inform</td><td>Success</td><td>BLEU</td><td>Score</td></tr><tr><td>25% training set</td><td>88.00</td><td>69.73</td><td>13.65</td><td>92.52</td></tr><tr><td>Word2Vec replace</td><td>89.77</td><td>70.33</td><td>13.13</td><td>93.18</td></tr><tr><td>PEGASUS paraphrase</td><td>89.00</td><td>71.03</td><td>12.37</td><td>92.38</td></tr><tr><td>Fragment rotation</td><td>88.17</td><td>69.60</td><td>13.18</td><td>92.06</td></tr></table>
+
+Table 7: MultiWOZ metrics, for the top 3 DA methods, using  $25\%$  of the original training dialogs, producing two synthetic dialogs from each original one (x3).
+
+<table><tr><td>DA Method</td><td>Inform</td><td>Success</td><td>BLEU</td><td>Score</td></tr><tr><td>25% training set</td><td>88.00</td><td>69.73</td><td>13.65</td><td>92.52</td></tr><tr><td>Word2Vec replace</td><td>88.73</td><td>66.97</td><td>12.78</td><td>90.63</td></tr><tr><td>PEGASUS paraphrase</td><td>88.20</td><td>66.13</td><td>10.92</td><td>88.08</td></tr><tr><td>Fragment rotation</td><td>88.37</td><td>67.63</td><td>11.67</td><td>89.67</td></tr></table>
+
+Table 8: MultiWOZ metrics, for the top 3 DA methods, using  $25\%$  of the original training dialogs, producing four synthetic dialogs from each original one (x5).  
+
+<table><tr><td>DA Method</td><td>Inform</td><td>Success</td><td>BLEU</td><td>Score</td></tr><tr><td>2% training set</td><td>37.20</td><td>15.60</td><td>5.62</td><td>32.02</td></tr><tr><td>Word2Vec replace</td><td>57.87</td><td>7.13</td><td>1.95</td><td>34.45</td></tr><tr><td>PEGASUS paraphrase</td><td>73.33</td><td>14.20</td><td>2.82</td><td>46.59</td></tr><tr><td>Fragment rotation</td><td>62.40</td><td>12.10</td><td>3.23</td><td>40.53</td></tr></table>
+
+Table 9: MultiWOZ metrics, for the top 3 DA methods, using  $2\%$  of the original training dialogs, producing a single synthetic dialog from each original one (x2).  
+
+<table><tr><td>DA Method</td><td>Inform</td><td>Success</td><td>BLEU</td><td>Score</td></tr><tr><td>2% training set</td><td>37.20</td><td>15.60</td><td>5.62</td><td>32.02</td></tr><tr><td>Word2Vec replace</td><td>73.93</td><td>29.93</td><td>6.27</td><td>58.20</td></tr><tr><td>PEGASUS paraphrase</td><td>73.50</td><td>34.50</td><td>7.13</td><td>61.13</td></tr><tr><td>Fragment rotation</td><td>70.37</td><td>32.43</td><td>7.14</td><td>58.54</td></tr></table>
+
+Table 10: MultiWOZ metrics, for the top 3 DA methods, using  $2\%$  of the original training dialogs, producing two synthetic dialogs from each original one (x3).  
+
+<table><tr><td>DA Method</td><td>Inform</td><td>Success</td><td>BLEU</td><td>Score</td></tr><tr><td>2% training set</td><td>37.20</td><td>15.60</td><td>5.62</td><td>32.02</td></tr><tr><td>Word2Vec replace</td><td>75.17</td><td>37.03</td><td>7.38</td><td>63.48</td></tr><tr><td>PEGASUS paraphrase</td><td>75.50</td><td>41.70</td><td>7.60</td><td>66.20</td></tr><tr><td>Fragment rotation</td><td>71.83</td><td>39.03</td><td>7.25</td><td>62.68</td></tr></table>
+
+Table 11: MultiWOZ metrics, for the top 3 DA methods, using  $2\%$  of the original training dialogs, producing four synthetic dialogs from each original one (x5).  
+
+<table><tr><td>DA Method</td><td>Inform</td><td>Success</td><td>BLEU</td><td>Score</td></tr><tr><td>10% training set</td><td>28.37</td><td>13.72</td><td>8.61</td><td>29.65</td></tr><tr><td>Word2Vec replace</td><td>33.16</td><td>17.17</td><td>8.63</td><td>33.80</td></tr><tr><td>PEGASUS paraphrase</td><td>38.30</td><td>19.53</td><td>8.64</td><td>37.56</td></tr><tr><td>Fragment rotation</td><td>33.25</td><td>17.93</td><td>8.90</td><td>34.49</td></tr></table>
+
+Table 12: MultiWOZ metrics, for the top 3 DA methods, using  $10\%$  of the original training dialogs, producing four synthetic dialogs from each original one (x5) and leaving out the attraction domain.  
+
+<table><tr><td>DA Method</td><td>Inform</td><td>Success</td><td>BLEU</td><td>Score</td></tr><tr><td>10% training set</td><td>32.15</td><td>17.43</td><td>7.62</td><td>32.41</td></tr><tr><td>Word2Vec replace</td><td>36.21</td><td>22.17</td><td>7.77</td><td>36.95</td></tr><tr><td>PEGASUS paraphrase</td><td>40.69</td><td>26.06</td><td>7.97</td><td>41.35</td></tr><tr><td>Fragment rotation</td><td>37.06</td><td>24.62</td><td>8.26</td><td>39.10</td></tr></table>
+
+Table 13: MultiWOZ metrics, for the top 3 DA methods, using  $10\%$  of the original training dialogs, producing four synthetic dialogs from each original one (x5) and leaving out the hotel domain.
+
+<table><tr><td>DA Method</td><td>Inform</td><td>Success</td><td>BLEU</td><td>Score</td></tr><tr><td>10% training set</td><td>28.37</td><td>13.65</td><td>7.17</td><td>28.19</td></tr><tr><td>Word2Vec replace</td><td>33.41</td><td>16.55</td><td>7.78</td><td>32.76</td></tr><tr><td>PEGASUS paraphrase</td><td>34.55</td><td>19.60</td><td>8.51</td><td>35.59</td></tr><tr><td>Fragment rotation</td><td>37.61</td><td>22.20</td><td>8.55</td><td>38.45</td></tr></table>
+
+Table 14: MultiWOZ metrics, for the top 3 DA methods, using  $10\%$  of the original training dialogs, producing four synthetic dialogs from each original one (x5) and leaving out the restaurant domain.  
+
+<table><tr><td>DA Type</td><td>DA Method</td><td>Match</td><td>Success F1</td><td>BLEU</td><td>Score</td></tr><tr><td rowspan="2">No DA</td><td>Full training set</td><td>81.58</td><td>81.67</td><td>20.86</td><td>102.48</td></tr><tr><td>5% training set</td><td>58.68</td><td>64.99</td><td>11.44</td><td>73.27</td></tr><tr><td rowspan="2">Word-level</td><td>Word2Vec replace</td><td>61.75</td><td>73.62</td><td>13.76</td><td>81.44</td></tr><tr><td>RoBERTa replace</td><td>61.05</td><td>73.75</td><td>13.27</td><td>80.67</td></tr><tr><td rowspan="4">Sentence-level</td><td>back-translation (FR)</td><td>60.00</td><td>72.39</td><td>11.64</td><td>77.83</td></tr><tr><td>PEGASUS paraphrase</td><td>56.49</td><td>69.81</td><td>12.63</td><td>75.78</td></tr><tr><td>Fragment rotation</td><td>64.04</td><td>73.71</td><td>13.89</td><td>82.76</td></tr><tr><td>LLM paraphrase</td><td>64.74</td><td>72.57</td><td>13.39</td><td>82.04</td></tr></table>
+
+Table 15: KVRET metrics, for all 6 DA methods, using  $5\%$  of the original training dialogs, producing a single synthetic dialog from each original one (x2).  
+
+<table><tr><td>DA Method</td><td>Match</td><td>Success F1</td><td>BLEU</td><td>Score</td></tr><tr><td>5% training set</td><td>58.68</td><td>64.99</td><td>11.44</td><td>73.27</td></tr><tr><td>Word2Vec replace</td><td>54.74</td><td>75.41</td><td>12.83</td><td>77.91</td></tr><tr><td>Fragment rotation</td><td>56.05</td><td>74.98</td><td>11.93</td><td>77.44</td></tr><tr><td>LLM paraphrase</td><td>57.89</td><td>71.87</td><td>10.82</td><td>75.70</td></tr></table>
+
+Table 16: KVRET metrics, for the top 3 DA methods, using  $5\%$  of the original training dialogs, producing two synthetic dialogs from each original one (x3).  
+
+<table><tr><td>DA Method</td><td>Match</td><td>Success F1</td><td>BLEU</td><td>Score</td></tr><tr><td>5% training set</td><td>58.68</td><td>64.99</td><td>11.44</td><td>73.27</td></tr><tr><td>Word2Vec replace</td><td>56.05</td><td>74.25</td><td>9.58</td><td>74.73</td></tr><tr><td>Fragment rotation</td><td>57.11</td><td>67.00</td><td>10.37</td><td>72.42</td></tr><tr><td>LLM paraphrase</td><td>53.16</td><td>74.10</td><td>11.35</td><td>74.97</td></tr></table>
+
+Table 17: KVRET metrics, for the top 3 DA methods, using  $5\%$  of the original training dialogs, producing four synthetic dialogs from each original one (x5).  
+
+<table><tr><td>DA Method</td><td>Match</td><td>Success F1</td><td>BLEU</td><td>Score</td></tr><tr><td>10% training set</td><td>74.21</td><td>76.69</td><td>16.70</td><td>92.16</td></tr><tr><td>Word2Vec replace</td><td>68.42</td><td>79.00</td><td>15.84</td><td>89.55</td></tr><tr><td>Fragment rotation</td><td>73.94</td><td>78.28</td><td>15.40</td><td>91.51</td></tr><tr><td>LLM paraphrase</td><td>74.47</td><td>77.42</td><td>15.96</td><td>91.91</td></tr></table>
+
+Table 18: KVRET metrics, for the top 3 DA methods, using  $10\%$  of the original training dialogs, producing a single synthetic dialog from each original one (x2).
+
+<table><tr><td>DA Method</td><td>Match</td><td>Success F1</td><td>BLEU</td><td>Score</td></tr><tr><td>10% training set</td><td>74.21</td><td>76.69</td><td>16.70</td><td>92.16</td></tr><tr><td>Word2Vec replace</td><td>71.84</td><td>76.10</td><td>13.66</td><td>87.63</td></tr><tr><td>Fragment rotation</td><td>72.90</td><td>77.93</td><td>13.82</td><td>89.22</td></tr><tr><td>LLM paraphrase</td><td>73.94</td><td>79.48</td><td>13.81</td><td>90.53</td></tr></table>
+
+Table 19: KVRET metrics, for the top 3 DA methods, using  $10\%$  of the original training dialogs, producing two synthetic dialogs from each original one (x3).  
+
+<table><tr><td>DA Method</td><td>Match</td><td>Success F1</td><td>BLEU</td><td>Score</td></tr><tr><td>10% training set</td><td>74.21</td><td>76.69</td><td>16.70</td><td>92.16</td></tr><tr><td>Word2Vec replace</td><td>69.73</td><td>77.16</td><td>13.37</td><td>86.81</td></tr><tr><td>Fragment rotation</td><td>71.58</td><td>77.17</td><td>13.79</td><td>88.16</td></tr><tr><td>LLM paraphrase</td><td>72.10</td><td>75.20</td><td>11.41</td><td>85.06</td></tr></table>
+
+Table 20: KVRET metrics, for the top 3 DA methods, using  $10\%$  of the original training dialogs, producing four synthetic dialogs from each original one (x5).  
+
+<table><tr><td>DA Method</td><td>Match</td><td>Success F1</td><td>BLEU</td><td>Score</td></tr><tr><td>25% training set</td><td>78.94</td><td>80.25</td><td>18.79</td><td>98.38</td></tr><tr><td>Word2Vec replace</td><td>78.95</td><td>79.61</td><td>18.32</td><td>97.61</td></tr><tr><td>Fragment rotation</td><td>77.11</td><td>78.16</td><td>18.09</td><td>95.72</td></tr><tr><td>LLM paraphrase</td><td>80.00</td><td>80.38</td><td>16.54</td><td>96.72</td></tr></table>
+
+Table 21: KVRET metrics, for the top 3 DA methods, using  $25\%$  of the original training dialogs, producing a single synthetic dialog from each original one (x2).  
+
+<table><tr><td>DA Method</td><td>Match</td><td>Success F1</td><td>BLEU</td><td>Score</td></tr><tr><td>25% training set</td><td>78.94</td><td>80.25</td><td>18.79</td><td>98.38</td></tr><tr><td>Word2Vec replace</td><td>76.31</td><td>80.63</td><td>17.75</td><td>96.22</td></tr><tr><td>Fragment rotation</td><td>78.42</td><td>79.77</td><td>16.95</td><td>96.04</td></tr><tr><td>LLM paraphrase</td><td>78.69</td><td>78.94</td><td>16.34</td><td>95.15</td></tr></table>
+
+Table 22: KVRET metrics, for the top 3 DA methods, using  $25\%$  of the original training dialogs, producing two synthetic dialogs from each original one (x3).  
+
+<table><tr><td>DA Method</td><td>Match</td><td>Success F1</td><td>BLEU</td><td>Score</td></tr><tr><td>25% training set</td><td>78.94</td><td>80.25</td><td>18.79</td><td>98.38</td></tr><tr><td>Word2Vec replace</td><td>75.53</td><td>78.14</td><td>14.91</td><td>91.75</td></tr><tr><td>Fragment rotation</td><td>76.58</td><td>78.68</td><td>15.19</td><td>92.81</td></tr><tr><td>LLM paraphrase</td><td>80.53</td><td>79.22</td><td>13.84</td><td>93.72</td></tr></table>
+
+Table 23: KVRET metrics, for the top 3 DA methods, using  $25\%$  of the original training dialogs, producing four synthetic dialogs from each original one (x5).
+
+# C Additional error comparisons
+
+![](images/1217628eb0cb9886746220208c967933cf8cb6d5f5eab25d443f0200f0528c8b.jpg)
+
+![](images/635569ebc1be7172c34a9649fa5774e3900afce106d4a9ebeb2d2be49e8dcf8f.jpg)  
+Figure 5: Error rates per MultiWOZ domain category using the PEGASUS DA method and having  $25\%$  of the training data available. The upper and lower figure depict error rates when generating a single (x2) and four (x5) synthetic dialogs per instance respectively.
+
+![](images/2bfe9305fbb5d316e5d52eb48d20cae5f554595b900ec65acba7a593f78d4e43.jpg)
+
+![](images/2b14da67ae18e7cef184b4e2753cb69486df0a69936be92872ae1350d15b7949.jpg)  
+Figure 6: Error rates per MultiWOZ domain category using the fragment rotation DA method and having  $25\%$  of the training data available. The upper and lower figure depict error rates when generating a single (x2) and four (x5) synthetic dialogs per instance respectively.
+
+We follow the same procedure of Section 4.3 for the cases of PEGASUS and fragment rotation. Once again, we count the number of unsuccessful dialogs Success  $= 0$  (i.e. the ToDS did not provide all the requested information or a valid recommendation), and divide by the number of dialogs belonging to each category, for the case where  $25\%$  of the training dialogs of MultiWOZ was used. We focus on Success as it features greater variance compared to BLEU and Inform, which generally remains unaffected. As was the case with Word2Vec, DA using PEGASUS or fragment rotation to generate more that one synthetic dialog reduces the overall Success. Interestingly there are a few instances where using multiple synthetic dialogs managed to increase the performance on specific, stand-alone domain categories such as "tx, ho, re" for PEGASUS and "at, tr" for fragment rotation, but such results may vary from case to case.
+
+# D Examples of synthetic and generated dialogs
+
+In this section we present an example (Fig. 7) of the template matching performed by the dialog tree DA method (Subsection 2.3.1). In this case the  $Cds$  of the first turn of pmul3825 matches the  $Pds$  of mul0665's second turn. Similarly, pmul3825's  $Nds$  matches mul0665's  $Cds$ , thus setting mul0665's turn as the continuation of pmul3825. Repeating the process until reaching a "Leaf" node (turn), creates a new synthetic dialog.
+
+Figures 9-16 depict a single delexicalised dialog (woz20572) after applying each of the DA methods, for the case of MultiWOZ. An example of the same dialog, that UBAR is trained on, without any DA is depicted in Figure 8.
+
+![](images/d4dfff3e2db9345d843374f73349e9f4d11cc6feeae66b1472c4332cb0428fce.jpg)  
+Figure 7: Two templates (from MultiWOZ dialogs pmul3825 and mul0665) are linked as they satisfy the dialog state conditions (shown in green and purple).
+
+USER: i am looking for an expensive restaurant in the south.
+
+SYSTEM: hi! we have [value_food], [value_food], [value_food], and [value_food] restaurant-s that fit the bill. do you have any preferences?
+
+USER: i do n't have any preference.
+
+SYSTEM: [value_name] is located in the [value_area] part of town and in the [value_price] price range.
+
+USER:do you have a phone number for them?
+
+SYSTEM: the number is [value_phone].
+
+USER: have a good evening.
+
+SYSTEM: have a good evening.
+
+Figure 8: Dialog  $woz20572$  of MultiWOZ, as used by Yang et al. (2021) for training UBAR, without any DA applied.
+
+USER: i am look for an expensive restaurant in the south.
+
+SYSTEM: hello! we have [value_food], [value_food], [value_food], and [value_food] restaurants that suited the legislation. do you have any preference?
+
+USER: i do ca have any preferred.
+
+SYSTEM: [value_name] is situated in the [value_area] integral part of village and in the [value_pricing] pricing ranging.
+
+USER:do you have a telephone numberfor them?
+
+SYSTEM: the number is [value_phone].
+
+USER: have a great night.
+
+SYSTEM: have a great night.
+
+Figure 9: A synthetic dialog derived from  $woz20572$  of MultiWOZ after applying our word substitution process via Word2Vec.
+
+USER: i am searching for an expensive restaurant in the south.
+
+SYSTEM: hello! we have [value_food], [value_food], [value_food], and [value_food] restaurants that fill the bill. do you have any recommendations?
+
+USER: i do not have any preference
+
+SYSTEM: [value_name] is located in the [value_area] side of city and in the [value_price] price zone.
+
+USER:do you have a contact number for them?
+
+SYSTEM: the phone is [value_phone].
+
+USER:haveagreattime.
+
+SYSTEM: have a great day.
+
+Figure 10: A synthetic dialog derived from  $woz20572$  of MultiWOZ after applying our word substitution process using RoBERTa.
+
+USER: i am looking for a restaurant expensive in the south.
+
+SYSTEM: hi! we have [value_food], [value_food], [value_food] and [value_food] restaurant-s that match your expectations. do you have any preferences?
+
+USER: i have no preference.
+
+SYSTEM: [value_name] is located in part [value_area] of the city and in the price range [value_price].
+
+USER: do you have a phone number for them?
+
+SYSTEM: the number is [value_phone].
+
+USER: have a good evening.
+
+SYSTEM: have a good evening.
+
+Figure 11: A synthetic dialog derived from woz20572 of MultiWOZ after applying back-translation.
+
+USER: i'm looking for an expensive restaurant in the south.
+
+SYSTEM: do you prefer [value_food], [value_food], [value_food], and [value_food] restaurant-s?
+
+USER: i do n't have a preference.
+
+SYSTEM: the [value_name] is located in the [value_area] part of town in the [value_price] price range.
+
+USER: do you have a phone number for them?
+
+SYSTEM: the number is [value_phone].
+
+USER: have a great evening.
+
+SYSTEM: have a great evening.
+
+Figure 12: A synthetic dialog derived from  $woz20572$  of MultiWOZ after paraphrasing using PEGASUS.
+
+USER: looking for an expensive restaurant in the south i.
+
+SYSTEM: hi! have [value_food], [value_food], [value_food], and [value_food] restaurant -s that fit the bill we. you have any preferences.
+
+USER: have any preference i.
+
+SYSTEM: [value_name] located in the [value_area] part of town and in the [value_price] price range.
+
+USER: you have a phone number for them.
+
+SYSTEM: the number is [value_phone].
+
+USER: a good evening have.
+
+SYSTEM: a good evening have.
+
+# Figure 13: A synthetic dialog derived from  $woz20572$  of MultiWOZ after applying fragment rotation.
+
+USER: my quest is to find a costly restaurant located in the south.
+
+SYSTEM: greetings! we offer restaurant-s that serve [value_food], [value_food], [value_food], and [value_food] cuisine. do you have any specific preferences?
+
+USER: i have no particular liking or inclination.
+
+SYSTEM: [value_name] can be found in the [value_area]ern area of the city and falls within the higher price bracket.
+
+USER: is there a phone number available for them?
+
+SYSTEM: [value_phone] is the numerical sequence for the phone number.
+
+USER: may your evening be enjoyable.
+
+SYSTEM: may your evening be enjoyable.
+
+# Figure 14: A synthetic dialog derived from  $woz20572$  of MultiWOZ after paraphrasing using the GPT-3.5-turbo LLM.
+
+USER: i am looking for an expensive restaurant in the south.
+
+SYSTEM: we have some very nice restaurant-s, such as [value_name], offering [value_food] cuisine, [value_name], with [value_food], and the [value_name], with [value_food] fare. what sounds good to you today?
+
+USER: i do n't have any preference.
+
+SYSTEM: alright, shall i make a reservation for the [value_name] ?
+
+USER:do you have a phone number for them?
+
+SYSTEM: the number is [value_phone].
+
+USER: have a good evening.
+
+SYSTEM: have a good evening.
+
+# Figure 15: A synthetic dialog derived from  $woz20572$  of MultiWOZ after applying our modified MADA approach.
+
+USER: i am looking for an expensive restaurant in the south.
+
+SYSTEM: hi! we have [value_food], [value_food], [value_food], and [value_food]
+
+restaurant -s that fit the bill . do you have any preferences ?
+
+USER: i want to eat thai food.
+
+SYSTEM: there are n't any [value_food] restaurant -s in that price range in the
+
+[value_area].would you like to try something else?
+
+USER: let me know about youritalian restaurant-s.
+
+SYSTEM: okay, i found [value_choice] options for you : [value_name] and [value_name].
+
+do either of those appeal to you?
+
+USER: book the 1 in the centre a table for 2 at 13:45 on thursday
+
+SYSTEM: i was able to book your table . your reference number is : [value-reference] .
+
+USER: thank you . i will also need a hotel in that same area . please , no guest house !
+
+SYSTEM: there are [value_choice] options for [value_type] in the [value_area]. there is
+
+[value_choice] [valuestars] star, 13 star and 1 [valuestars] star option . which would
+
+you prefer ?
+
+USER: yes, please. for 2 nights.
+
+SYSTEM: how many people will be staying with you and what day would you like to
+
+reserve your [value_type] room?
+
+USER: 2 for the same day . i need a taxi to commute between the 2 place -s to be sure it
+
+arrives by the booked time . the contact number and car type ?
+
+SYSTEM: your room is booked, ref# [value_reference], and a [value_car] will pick you
+
+up and get you to [valuedestination] for that reservation . contact number
+
+[value_phone].
+
+USER: thanks, those are all i need for today.
+
+SYSTEM: you are welcome. have a great day.
+
+USER: you too have a great day
+
+SYSTEM: thank you so much.
+
+Figure 16: A synthetic dialog derived from the combination of  $woz20572$  and  $pmul4652$  of MultiWOZ using the dialog tree approach.
+
+# Turn 1
+
+User : can you help me find a hotel called a and b guest house?
+
+GT : it is in the [value_area], and [value_price]. would you like to book a room?
+
+No DA : i have [value_choice] [value_type] in the [value_area] and [value_name] in the [value_area].
+
+Word2Vec : [value_name] is a [value_price] accommodation in the [value_area]. would you like me to book you a room?
+
+RoBERTa : i have [value_name] located in the [value_area] area. it is [value_price]. would you like me to book you a room?
+
+BT : [value_name] is a [value_price] [value_type] in the [value_area] with [value-stars] stars. would you like me to book you a room?
+
+PEGASUS : it is a [value_price] [value_type] in the [value_area]. it is free to enter. would you like me to book it?
+
+Rotate : it is a [value_price] [value-stars] star [value_type] in the [value_area] with free parking and internet. would you like me to book it?
+
+LLM : [value_name] is a [value_type] in the [value_area]. it is [value_price] and has [value_price] admission. would you like me to book you a room?
+
+Dialog tree : [value_name] is a [value_type] in the [value_area], it is [value_price] and has [value-stars] stars. would you like me to book it?
+
+MADA : [value_name] is a [value_type] in the [value_area] area of town. it is [value_price] and has internet. would you like me to book you a room?
+
+# Turn 2
+
+User : can i get the address and phone number, please?
+
+GT : the address is [value_address], postcode [value_postcode]. the phone number is [value_phone] . anything else ?
+
+No DA : the address is [value_address] and the phone number is [value_phone].
+
+Word2Vec : their address is [value_address] and their phone number is [value_phone].
+
+RoBERTa : the address is [value_address]. is there anything else i can help you with?
+
+BT : the address is [value_address]. is there anything else i can help you with?
+
+PEGASUS : the address is [value_address]. the phone number is [value_phone].
+
+Rotate : the address is [value_address]. the phone number is [value_phone].
+
+LLM : the address is [value_address] and the phone number is [value_phone]. is there anything else i can help you with?
+
+Dialog tree : the address is [value_address] and the phone number is [value_phone].
+
+MADA : the address is [value_address]. the phone number is [value_phone]. is there anything else i can help you with?
+
+# Turn 3
+
+User : that is all. thank you.
+
+GT :you are welcome have a great day.
+
+No DA :you are welcome. goodbye.
+
+Word2Vec : thank you goodbye
+
+RoBERTa : you are welcome. have a great day!
+
+BT :you are welcome.have a great day!
+
+PEGASUS :you are welcome.goodbye.
+
+Rotate :you are welcome.have a great day.goodbye.
+
+LLM : thank you for using our system today!
+
+Dialog tree : you are welcome, goodbye.
+
+MADA : thank you goodbye
+
+Figure 17: Dialog  $sng01386$  of MultiWOZ along with the generated responses using all the DA methods described. The models where trained using  $10\%$  of the training data and the augmentation level is  $\mathbf{x2}$ . "GT" stands for ground truth while "BT" for back-translation.
+
+```txt
+Turn 0   
+User : can you help me find a hotel called a and b guest house?   
+GT : it is in the [value_area] , and [value_price] . would you like to book a room ?   
+No DA : i have [value_choice] [value_type] in the [value_area] and [value_name] in the [value_area].   
+Word2Vec x2 : [value_name] is a [value_price] accommodation in the [value_area]. would you like me to book you a room?   
+Word2Vec x5 : it is a [value_price] [value_type] in the [value_area]. would you like me to book it?   
+PEGASUS x2 : it is a [value_price] [value_type] in the [value_area]. it is free to enter. would you like me to book it?   
+PEGASUS x5 : they are a [value_price] [value_type] in the [value_area]. would you like to make a reservation?   
+Rotate x2 : it is a [value_price] [value-stars] star [value_type] in the [value_area] with free parking and internet. would you like me to book it?   
+Rotate x5 : happy to help! that is a [value_type] in the [value_area] and is considered [value_price]. would you like to make a reservation?   
+Turn 1   
+User : can i get the address and phone number, please?   
+GT : the address is [value_address], postcode [value_postcode]. the phone number is [value_phone]. anything else ?   
+No DA : the address is [value_address] and the phone number is [value_phone].   
+Word2Vec x2 : their address is [value_address] and their phone number is [value_phone].   
+Word2Vec x5 : their address is [value_address] and their phone number is [value_phone].   
+PEGASUS x2 : the address is [value_address]. the phone number is [value_phone].   
+PEGASUS x5 : the address is [value_address] and the phone number is [value_phone].   
+Rotate x2 : the address is [value_address]. the phone number is [value_phone].   
+Rotate x5 : their phone number is [value_phone] and their address is [value_address].   
+Turn 2   
+User : that is all. thank you.   
+GT : you are welcome have a great day .   
+No DA : you are welcome. goodbye.   
+Word2Vec x2 : thank you goodbye   
+Word2Vec x5 : you are welcome, goodbye.   
+PEGASUS x2 : you are welcome. goodbye.   
+PEGASUS x5 : you are welcome, goodbye.   
+Rotate x2 : you are welcome. have a great day. goodbye.   
+Rotate x5 : you thank.
+```
+
+Figure 18: Dialog  $sng01386$  of MultiWOZ along with the generated responses using the 3 best performing DA methods and  $10\%$  of the available training dialogs. The figure depicts 2 responses per model (for x2 and x5 the amount of training data). "GT" stands for ground truth.

2024/Comparing Data Augmentation Methods for End-to-End Task-Oriented Dialog Systems/images.zip

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2024/Competition-Level Problems are Effective LLM Evaluators/65598a40-492c-43ff-8fa3-bd8222139986_origin.pdf

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2024/Competition-Level Problems are Effective LLM Evaluators/full.md

@@ -0,0 +1,394 @@
+# Competition-Level Problems are Effective LLM Evaluators
+
+Yiming Huang $^{1*†}$ , Zhenghao Lin $^{2*†}$ , Xiao Liu $^{1‡}$ , Yeyun Gong $^{1‡}$ , Shuai Lu $^{1}$ , Fangyu Lei, Yaobo Liang $^{1}$ , Yelong Shen $^{3}$ , Chen Lin $^{2‡}$ , Nan Duan $^{1}$ , Weizhu Chen $^{3‡}$
+
+<sup>1</sup> Microsoft Research Asia, <sup>2</sup> Xiamen University, <sup>3</sup> Microsoft Azure AI {xiaoliu2,yegong, wzchen}@microsoft.com, chenlin@xmu.edu.cn
+
+# Abstract
+
+Large language models (LLMs) have demonstrated impressive reasoning capabilities, yet there is ongoing debate about these abilities and the potential data contamination problem recently. This paper aims to evaluate the reasoning capacities of LLMs, specifically in solving recent competition-level programming problems in Codeforces, which are expert-crafted and unique, requiring deep understanding and robust reasoning skills. We first provide a comprehensive evaluation of GPT-4's perceived zero-shot performance on this task, considering various aspects such as problems' release time, difficulties, and types of errors encountered. Surprisingly, the perceived performance of GPT-4 has experienced a cliff like decline in problems after September 2021 consistently across all the difficulties and types of problems, which shows the potential data contamination, as well as the challenges for any existing LLM to solve unseen complex reasoning problems. We further explore various approaches such as fine-tuning, Chain-of-Thought prompting and problem description simplification. Unfortunately, none of them is able to consistently mitigate the challenges. Through our work, we emphasize the importance of this excellent data source for assessing the genuine reasoning capabilities of LLMs, and foster the development of LLMs with stronger reasoning abilities and better generalization in the future.
+
+# 1 Introduction
+
+The rise of LLMs has generated significant interest in the artificial intelligence community. These models, notably GPT-4 (OpenAI, 2023), have displayed impressive reasoning capabilities that are being harnessed in various fields (Bubeck et al., 2023). However, questions<sup>1</sup> have been raised about
+
+![](images/c898745c792e916869e3fca693637c97fa7b5cccebac65adc115573d3bfbb57d.jpg)  
+Figure 1: The perceived zero-shot performance of GPT-4 sees a sharp decline on problems of varying difficulties (D1, D2 and D3 means easy, medium and difficult, respectively) in Codeforces after September 2021.
+
+how to accurately evaluate the reasoning abilities of LLMs and the extent of data contamination issues (Mialon et al., 2023; Zhou et al., 2023).
+
+Regarding these issues, our study aims to assess the reasoning capabilities of LLMs through their ability to generate algorithms for solving competition-level programming problems. These questions are meticulously crafted by experts to form rigorous competitions. They possess high quality, are unique, and exhibit excellent discriminative ability. The testing cases are also meticulously prepared. This necessitates that LLMs deduce the solution from the presented scenario, which requires a thorough understanding of algorithms, combined reasoning and coding skills, and strong problem-solving abilities. These problems thus present a significant challenge to both human coders and LLMs. Consequently, competition-level programming problems serve as effective tools for evaluating the two issues previously discussed: they assess the reasoning abilities of LLMs and, due to the strict problem selection process in competitions, reduce the likelihood of data contamination.
+
+tion in new problems.
+
+Our research provides an in-depth analysis of the zero-shot performances of GPT-4 and other code LLMs on competition-level programming problems in Codeforces, considering factors such as release time, problem difficulty, and the types of errors encountered. The main insights of our study include: (1) GPT-4 performs significantly worse on programming problems released after September 2021, casting doubt on its actual reasoning abilities. (2) GPT-4 shows limited capability to solve difficult problems, indicating potential weaknesses in complex problem-solving. (3) GPT-4 struggles with the first test case, suggesting errors may stem from its understanding of the problem at hand. (4) The related phenomenon can be also observed in other LLMs, indicating that insufficient reasoning ability may be a common problem.
+
+To explore possible ways to enhance the zero-shot performances of these LLMs on competition-level programming problems, we investigate several methods to improve performance on unseen problems. These methods include supervised fine-tuning with code-specific LLMs, Chain-of-Thought prompting (Wei et al., 2022), and problem statement simplification. Specifically, we fine-tuned CodeLlama(Rozière et al., 2023) and DeepSeek-Coder(AI, 2023), which are specialized language models designed to handle programming-related tasks. However, none of these methods consistently mitigated the issue or resulted in noticeable performance improvements, particularly for more difficult problems. This finding indicates that difficult and unseen programming problems are effective evaluators of LLMs.
+
+Overall, the primary contributions of this study lie in proposing and validating that recent competition-level programming problems serve as an excellent data source for assessing the genuine reasoning capabilities of LLMs. We aim to foster further research in this field by innovating new approaches to address the challenge of complex reasoning problems in LLMs and by establishing reliable evaluation benchmarks for LLMs that minimize the risk of data contamination.
+
+# 2 Problem Setup
+
+# 2.1 Competition-level Programming
+
+Competition-level programming presents a unique arena for testing and developing the reasoning abilities of AI models. In competitive programming, a
+
+problem typically consists of a narrative that sets the context, which models need to understand and convert into an algorithmic problem. The challenge lies in comprehending the narrative, identifying the underlying algorithmic issues, and implementing an efficient solution in programming languages such as  $\mathrm{C + + }$  and Java. Accepted programs must satisfy stringent testing conditions, including producing outputs that exactly match with test cases, executing within memory limits, and terminating within time constraints. In contrast to prior works (Chen et al., 2021a; Austin et al., 2021; Cassano et al., 2023) focusing on basic coding abilities, competition-level programming problems require advanced reasoning and mathematical modeling skills, essential for AI.
+
+Unlike the previous works that focused on LeetCode $^{2}$  (Bubeck et al., 2023; Shen et al., 2023; Sakib et al., 2023), we follow AlphaCode (Li et al., 2022) and choose Codeforces $^{3}$ . Codeforces is universally acknowledged by competitors and enthusiasts in the International Collegiate Programming Competition $^{4}$  (ICPC) and the International Olympiad in Informatics $^{5}$  (IOI) as a popular and suitable platform for developing abilities for algorithm contests. The regular contests hosted on this platform are crafted by human experts, and contain plenty of intricate programming problems and contests of high quality. These contests come with comprehensive and robust test cases and exhibit a low degree of problem overlap. The unique nature of these contest problems makes it highly unlikely to find similar content on the internet before the competition concludes. As a result, utilizing specific time-segmented datasets, like those from contests conducted post the introduction of LLMs, serves as an effective strategy to prevent data contamination (Zhou et al., 2023).
+
+Codeforces employs the Elo rating system to rank its users and problems, categorizing all problems into 28 distinct difficulties, ranging from 800 to 3500. Compared to commonly utilized metrics such as the ratio of accepted submissions or users, this difficulty rating mechanism is more suitable as it is based on the ranking and performance of the participants during the competition.[7]
+
+2https://leetcode.com/  
+<sup>3</sup>https://codeforces.com/  
+4https://icpc.global/  
+<sup>5</sup>https://ioinformatics.org/  
+$^{6}$ https://codeforces.com/blog/entry/102  
+<sup>7</sup>https://codeforces.com/blog/entry/62865
+
+![](images/6e5e128a147f97ac27dd09c08e6653c4086034e7b0fb786115cbeafe9d82c01f.jpg)  
+Figure 2: The figure depicts the problem statement (left), comprising a problem set in a narrative context for participants to decipher, detailed input and output format specifications, and one or more example input-output pairs. In some cases, additional notes may be provided to assist competitors in understanding these example tests. This information is fed into the LLM, aiming to generate relevant code (right). The generated code is then submitted to an online judge for correctness evaluation.
+
+Hence, it is not subject to inaccuracies stemming from temporal changes, repeated submissions, plagiarism, and other potential distortions.
+
+# 2.2 Problem Definition
+
+Figure 2 presents an example of the problem statement  $\pi$ . The input of LLM is instantiated with the problem statement  $\pi$  and a prompt  $\rho$  (like  $\rho_{1}$  in Table 8). The LLM  $\Gamma$  takes the input to generate the code as  $\alpha = \Gamma (\rho (\pi))$ . The generated code  $\alpha$  is then evaluated by an online judge (OJ). The evaluation process can be summarized in the following equation:
+
+$$
+\mathrm {O J} (\alpha) = \mathrm {O J} (\Gamma (\rho (\pi))) \in \{\mathrm {A C}, \mathrm {W A}, \mathrm {C E}, \dots \}
+$$
+
+In this equation,  $\Gamma (\rho (\pi))$  denotes the code generated by LLM with the prompt  $\rho$ . The OJ platform then rigorously assesses the code for its correctness, computational efficiency, and adherence to specified input/output formats. With an extensive testing mechanism, the platform employs a wide range of test cases and hidden scenarios to ensure the code's robustness across diverse scenarios. The platform provides a spectrum of outcomes,  $\mathrm{OJ}(\Gamma (\rho (\pi)))$ , offering a holistic evaluation of the code's performance. This includes results such as Accepted
+
+(AC), Wrong Answer (WA), and Compilation Error (CE), among others.
+
+# 2.3 Dataset Collection
+
+The dataset is compiled from the Codeforces website, extracting all publicly available problem statements from completed contests spanning February 2010 through November 2023. For simplicity, problems requiring interaction, featuring non-standard input/output formats, or incompatible with C++ submission are excluded. For detailed explanations, see Appendix B.
+
+The analysis is confined to problems with difficulty levels ranging from 800 to 2400. Based on their difficulty levels, the dataset is divided into three subsets: D1 (800-1100 difficulty, 1683 problems), D2 (1200-1600 difficulty, 1821 problems), and D3 (1700-2400 difficulty, 1453 problems). These problems encompass more than 20 distinct categories of algorithms, as illustrated in Table 7. This diversity in problem types further enhances the comprehensiveness of the dataset and enables a comprehensive assessment of GPT-4's problem-solving abilities across a wide range of competition-level programming problems.
+
+<table><tr><td rowspan="2">Metric</td><td colspan="3">D1</td><td colspan="3">D2</td><td colspan="3">D3</td></tr><tr><td>Time1</td><td>Time2</td><td>Δ</td><td>Time1</td><td>Time2</td><td>Δ</td><td>Time1</td><td>Time2</td><td>Δ</td></tr><tr><td>ACC#G</td><td>81.42%</td><td>11.73%</td><td>-69.69%</td><td>43.72%</td><td>0.00%</td><td>-43.72%</td><td>11.41%</td><td>0.00%</td><td>-11.41%</td></tr><tr><td>pass@1</td><td>78.11%</td><td>10.54%</td><td>-67.57%</td><td>42.38%</td><td>0.61%</td><td>-41.77%</td><td>9.45%</td><td>0.18%</td><td>-9.27%</td></tr><tr><td>ACC1#1</td><td>78.05%</td><td>9.38%</td><td>-68.68%</td><td>43.37%</td><td>0.00%</td><td>-43.37%</td><td>8.48%</td><td>0.00%</td><td>-8.48%</td></tr><tr><td>ACC1#5</td><td>94.03%</td><td>20.09%</td><td>-73.94%</td><td>69.02%</td><td>3.06%</td><td>-65.96%</td><td>21.24%</td><td>0.88%</td><td>-20.36%</td></tr><tr><td>ACC2#5</td><td>88.34%</td><td>11.83%</td><td>-76.51%</td><td>54.41%</td><td>0.00%</td><td>-54.41%</td><td>12.36%</td><td>0.00%</td><td>-12.36%</td></tr><tr><td>ACC3#5</td><td>81.82%</td><td>9.38%</td><td>-72.44%</td><td>42.42%</td><td>0.00%</td><td>-42.42%</td><td>7.51%</td><td>0.00%</td><td>-7.51%</td></tr></table>
+
+Table 1: Performance of GPT-4 on different groups of problems: Time1 is the problems released from October 2010 to September 2021, and Time2 is the problems released from October 2021 to November 2023.  
+
+<table><tr><td>Metric</td><td>Definition</td></tr><tr><td>ACC#G</td><td>Proportion of accepted solutions using greedy sampling (temperature t = 0).</td></tr><tr><td>ACC#GN</td><td>The number of accepted solutions using greedy sampling (temperature t = 0) within the sliding window.</td></tr><tr><td>ACCK#n</td><td>Proportion of problems with k or more accepted solution with top-p samplings (t = 0.7, p = 0.95) for n times.</td></tr><tr><td>pass@k</td><td>Estimated proportion of problems with at least one accepted solution.</td></tr></table>
+
+Table 2: Definitions of evaluation metrics.
+
+# 2.4 Experiment Details
+
+In Codeforces, each problem belongs to a contest. Once the contest concludes, the problems are disclosed and become publicly summtable. Therefore, we submit the solutions to the contests that have concluded for evaluation.
+
+To evaluate the results, we employ ACC#G, ACC#GN,  $\mathrm{ACC}k\# n$  and pass@  $k$  as defined in Table 2. Specifically, for  $\mathrm{ACC}k\# n$  metric, we consider two settings: (1)  $k = n = 1$  and (2)  $k\in \{1,2,3\}$  with  $n = 5$ . Following Codex (Chen et al., 2021b), pass@  $k$  is computed as
+
+$$
+\operatorname {p a s s} @ k := \underset {\text {P r o b l e m s}} {\mathbb {E}} \left[ 1 - \frac {\binom {n - c} {k}}{\binom {n} {k}} \right]
+$$
+
+where  $n$  is defined as the total number of generated samples per problem used for evaluation, and  $c$  represents the count of correct samples out of  $n$  that have successfully passed the unit tests. Here we use  $k = 1$  and  $n = 5$  for pass@  $k$ .
+
+In our experiment, we follow the zero-shot setting. To select an appropriate prompt, we conduct preliminary experiments with three prompts,  $\rho_{1},\rho_{2}$  and  $\rho_{3}$ , as listed in Table 8, using two subsets of D1 problems: one from February to December 2010 and the other from January to October 2023, each comprising approximately 100 problems. The standard deviations are 0.015 and 0.018, respectively, indicating consistent performance. Therefore, we
+
+choose  $\rho_{1}$  as the prompt in the subsequent experiments. Furthermore, we employ a sliding window approach for all temporal analyses to smooth the data, addressing the sporadic release schedule of the problems. This ensures a sufficient number of test problems at each time point, using a window size of 51 (25 before and 25 after the time point).
+
+# 3 Insights and Implications
+
+# 3.1 Faltering on Unseen Problems
+
+In this section, we delve into a temporal analysis of GPT-4 (gpt-4-0613)'s performance on programming problems. Figure 1 illustrates GPT-4's performance using the ACC#G metric. On problems released prior to September 2021, GPT-4 exhibits minor fluctuations at different levels across problems of varying difficulty. However, for problems released after September 2021, a significant deviation from the normal fluctuation range is observed. Interestingly, this timing coincides with the cutoff date for the GPT-4 training data as announced by OpenAI $^{8}$ . We then calculate the average performance on problems before and after September 2021, as shown in Table 1. On D1 problems, GPT-4's ACC#G plummets from  $81.42\%$  to  $11.73\%$ , marking a stark decrease of  $69.69\%$ . Even more strikingly, the ACC#G drops to  $0.00\%$  on both D2 and D3 problems, from  $43.72\%$  and  $11.41\%$ , respectively. To validate the reliability of the conclusion, we also calculate the pass@1 metric, which exhibits a similar trend. This observation raises thought-provoking questions about the severity of the drop and the correlation between the data cutoff date and the performance decline.
+
+To explore the model's potential to generate correct solutions, we perform random sampling multiple times and calculate the pass rate. The average pass rate are shown in Table 1. As observed, multiple samplings can enhance the chances of gen
+
+![](images/261d909da0554d203e3101f67eb91f919981d9481cc825c12d2eecedabc9b1e5.jpg)  
+Figure 3: Random sampling enhances the probability of generating correct solutions on previously encountered problems, but offers no assistance for unseen problems.
+
+erating a correct solution. For instance, on the unseen simple D1 problems, ACC1#5 improved by  $10.71\%$  compared to ACC1#1. However, across all problems, the performance gap before and after the cut-off date is more pronounced for ACC1#5 than for both ACC1#1 and ACC#G. Figure 3 depicts the performance on D2 problems over time. A notable decline in performance metrics is observed around September 2021. This observation underscores the challenges that LLMs, including the advanced GPT-4, face in addressing unseen programming problems without similar pretraining data.
+
+The observed decline in performance on problems outside the model's training range may stem from limitations in reasoning and generalization. As highlighted by Yadlowsky et al. (2023), when confronted with problems beyond their pretraining data, transformer models exhibit various failure modes and their generalization abilities deteriorate, even for simple problems. Similarly, Lu et al. (2023) suggest that the exceptional abilities of large language models primarily stem from in-context learning, and do not necessarily reflect the emergence of reasoning abilities.
+
+The observed performance drop on unseen problems raises serious questions about GPT-4's intrinsic reasoning and generalization capabilities. This suggests a potential over-reliance on pattern recognition and reproduction from training, as opposed to grasping underlying principles and applying them to novel problems. This observation aligns with recent debates on large models' data memorization tendencies (Carlini et al., 2023; Yang et al., 2023). Therefore, future evaluations should
+
+![](images/0a666f81b79ea05c0ddaaf870be35a217b2dc7dda542d974db2090d7b4a9b05d.jpg)  
+Figure 4: For problems released before September 2021, GPT-4's ACC#G showed a negative linear correlation with difficulty, followed by consistently poor performance afterwards.
+
+prioritize the minimization of overlap between testing and training data to accurately assess a model's reasoning abilities, rather than simply its capacity for memorization. Furthermore, it's crucial to explore methods that enhance model generalization and reduce reliance on pre-training data.
+
+# 3.2 Limited Ability to Solve Difficult Problems
+
+This section provides an analysis of performance in relation to the problem difficulty. The results of ACC#G for problems with different difficulties are reported for two distinct periods: from October 2010 to September 2021, and from October 2021 to November 2023, as illustrated in Figure 4.
+
+For the results from October 2010 to September 2021, we calculate Pearson correlation coefficient  $(r = -0.97)$  and the Kendall rank correlation coefficient  $(\tau = -0.88)$ , which indicate strong linear correlations. Notably, when the difficulty level reaches 2400 (indicating greater challenge than approximately  $57\%$  of the problems on Codeforces), the ACC#G drops to zero. However, from October 2021 to November 2023, ACC#G shows a dramatic decrease across all difficulty levels.
+
+These findings reveal a significant limitation in the ability of GPT-4 to handle extremely complex problems. Despite its vast knowledge on code and algorithms, GPT-4 lacks of the competence in solving very challenging problems, particularly those with higher difficulty levels, even in the context of previously encountered problems. This indicates a potential area for further improvement and devel
+
+![](images/26ec71bd7de7b0b192d70c4586111c0a695746464fc56e582d81bc710d432786.jpg)  
+Figure 5: Error categories in GPT-4's solutions on problems released from 2010 to 2023.
+
+opment in future iterations of the model.
+
+# 3.3 Struggling with The First Test Case
+
+In this section, we gather and analyze the errors returned by GPT-4 upon submission to the Codeforces website, as outlined in Table 6. The most common error is "Wrong answer on test 1", which on average accounts for  $70\%$  of the observed errors. Test 1 is the first test case, which almost corresponds to or properly includes the example test case provided in the problem statement. This suggests that the model often struggles at the very beginning of problem-solving, possibly due to difficulties in understanding the problem's requirements or generating a correct solution based on the given test case. As depicted in Figure 5, there is a significant increase in the proportion of "Wrong answer on test 1" errors for problems released between 2021 and 2023. This suggests that GPT-4 is more likely to face challenges in understanding and reasoning during at the onset of tackling unseen problems.
+
+Other types of errors account for a smaller proportion, with an average of  $10\%$ . They have shown little variation over time. This indicates that GPT-4 demonstrates strong fundamental code-writing capabilities of generating high-quality code.
+
+# 3.4 Similar Phenomenon of Other Code LLMs
+
+We investigate whether the perceived performance degradation on unseen programming problems is observed for other popular code LLMs, such as
+
+![](images/172f47cc4b63ad6b4b323e30f4d68e9fafa6c2e9809ae3c4804e98c24acef773.jpg)  
+Figure 6: ACC#GN of CodeLlama and DeepSeekCoder on D1 problems.
+
+<table><tr><td>Problem Release Date</td><td>CodeLlama</td><td>DeepSeek-Coder</td></tr><tr><td>Before 2023.3</td><td>10.30%</td><td>32.74%</td></tr><tr><td>After 2023.3</td><td>4.52% (-5.78%)</td><td>9.03% (-23.71%)</td></tr></table>
+
+Table 3: Comparison of ACC#G between CodeLlama and DeepSeek-Coder on D1 problems before and after March 2023.
+
+CodeLlama-34B-Instruct (Rozière et al., 2023) and DeepSeek-Coder-33B-Instruct (AI, 2023).
+
+We conduct tests on CodeLlama and DeepSeek-Coder using D1 problems, following the settings in §2.3, and the results are shown in Figure 6. The experimental results indicate that CodeLlama consistently underperforms compared to DeepSeek-Coder on D1 problems. Furthermore, the performance of DeepSeek-Coder on D1 problems has been declining with the progression of the problem release date. The ACC#GN of DeepSeek-Coder has declined to a level that is on par with CodeLlama when dealing with newly released problems, as highlighted in the red area of Figure 6.
+
+To precisely and intuitively detect this phenomenon, we calculate the ACC#G of CodeLlama and DeepSeek-Coder on D1 problems, both before and after March 2023, and present the results in Table 3. The results reveal a significant difference in the average accuracy of CodeLlama and DeepSeek-Coder before and after March 2023. Regarding the magnitude of the decrease, DeepSeek-Coder, which previously exhibited superior performance, demonstrates a more pronounced decline, with acceptance rates falling below  $10\%$  after March 2023. Considering the release dates of CodeLlama and DeepSeek-Coder, we speculate that most of the programming problems after March 2023 are novel to them, which suggests that they also not be able to perform well on unseen programming problems like GPT4 does. This finding indicates that a fun
+
+![](images/ff73e55a8ec67109ef7ede637fe54cfabd04827b780cdca40b785f9621dfd994.jpg)  
+Figure 7: Comparison of ACC#GN for GPT-4 and DeepSeek-Coder on D1 problems after 2020.
+
+<table><tr><td>Model</td><td>2020.1-2021.9</td><td>2021.9-2023.10</td></tr><tr><td>GPT-4</td><td>73.19% (+50.52%)</td><td>11.53% (-0.97%)</td></tr><tr><td>DeepSeek-Coder</td><td>22.67%</td><td>12.50%</td></tr></table>
+
+Table 4: Comparison of ACC#G between GPT-4 and DeepSeek-Coder over time intervals, on D1 problems.
+
+damental limitation of current code LLMs in generalizing effectively to complex reasoning tasks.
+
+# 3.5 Evaluation Hallucination of LLMs
+
+To further analyze the phenomenon, we compare GPT-4 with DeepSeek-Coder on D1 problems as shown in Figure 7 and Table 4.
+
+It is noteworthy that while GPT-4 surpasses DeepSeek-Coder in terms of performance on problems that were released prior to September 2021, an unexpected observation is that DeepSeek-Coder exhibits a performance that is on par with GPT-4 when it comes to tackling problems that were released after September 2021. Considering the previous work (Yang et al., 2023; Zhou et al., 2023), although GPT-4 may perform particularly well on some previously seen problems due to its powerful capacity, it cannot be well generalized on unseen programming problems, and its performance is not significantly different from DeepSeek-Coder, which is specifically trained for code. This phenomenon merits attention, which is termed as "evaluation hallucination".
+
+Hence, a more equitable evaluation strategy would be to select evaluation sets that all the models have not previously encountered. However, finding such data adhering to stringent conditions is challenging, as LLMs are typically pre-trained on extensive corpora containing diverse content, leading to the potential issue of data contamination. Therefore, if we could devote more attention to the data source and timeline of the evaluation sets, such
+
+![](images/e82d3598f9421184d99cc101d9096f4644b78171a76c1faddf5c27a15deed8e4.jpg)  
+Figure 8: Comparison of ACC#GN for CodeLlama on D1 problems before and after fine-tuning.
+
+![](images/42ab4d656c5eb76deabe0fa4a636030dd8d91f4fa002b3156691c5321008d762.jpg)  
+Figure 9: Comparison of ACC#GN on D1 problems before and after fine-tuning DeepSeek-Coder.
+
+as the problems in Codeforces, it could potentially mitigate the effects of evaluation hallucination.
+
+# 4 One Step Forward
+
+In this section, we explore some approaches to mitigate the poor performance on unseen problems.
+
+# 4.1 Fine-tuning
+
+Fine-tuning is a commonly used method to improve performance on specific downstream tasks. In this study, we employ the Description2Code dataset (OpenAI and Sutskever, 2016) for fine-tuning. This dataset is compiled from three competitive programming websites: Codeforces, CodeChef, and HackerEarth, and contains problems published before 2017. CodeChef and HackerEarth, similar to Codeforces, host online coding competitions, and their problem sets are consistent in style and difficulty.
+
+The dataset includes 2128 problems from Codeforces, 2435 problems from HackerEarth, and 3201 problems from CodeChef, totaling 7764 problems. However, due to some problems lacking
+
+corresponding  $\mathrm{C + + }$  solutions, we retained a total of 7000 problems for our study. Each problem has approximately  $10\mathrm{C + + }$  solutions, resulting in 70,000 pairs of input-output sequences. These sequences are used for fine-tuning both CodeLlama and DeepSeek-Coder in a supervised manner.
+
+As shown in Figure 8 and Figure 9, we compare the performances of the models before and after fine-tuning on D1 problems. We observe that, even after fine-tuning with the same type of data, CodeLlama and DeepSeek-Coder do not exhibit improved performance on recent problems, particularly those post-2022. The significant improvement in ACC#GN before 2017 may result from the models recalling relevant or identical programming problems, rather than mastering the underlying reasoning logic, leading to their inability to adapt well to new programming challenges. Therefore, simple fine-tuning does not effectively enhance the models' performance on new programming problems.
+
+# 4.2 Chain-of-Thought Prompting
+
+In this section, we explore the application of Chain-of-Thought (CoT) prompting (Wei et al., 2022) to competition-level programming problems. CoT involves prompting GPT-4 to generate an explanation of the algorithm before coding, denoted as  $\rho_{\text{cot}}$  in Table 8. We conduct experiments on both the D1 and D3 problems released after October 2021. For D1 problems, employing CoT increases the ACC#G from  $11.54\%$  to  $16.21\%$ , demonstrating a noticeable improvement. However, for D3 problems, using CoT fails to yield any improvement, leaving the ACC#G at  $0.00\%$ . This suggests that while CoT facilitates some improvement for simple D1 problems, it is ineffective for the complex reasoning challenges presented by D3 problems.
+
+# 4.3 In-Context Learning
+
+In this section, we enhance our experimental exploration into in-context learning by integrating both fixed demonstrations and retrieval-augmented demonstrations.
+
+We use D1 problems released before September 2021 as source dataset and those released after as test data. First, we apply the same method as delineated in §4.2 to tackle the source data and validate them on Codeforces. We then retain accepted solutions, resulting in a collection of 1048 problem and CoT response pairs. A demonstration example is presented in Table 12.
+
+<table><tr><td>N-shot Prompt</td><td>CoT</td><td>Retrieval</td><td>ACC#G</td></tr><tr><td>0-shot</td><td>No</td><td>No</td><td>11.54%</td></tr><tr><td>0-shot</td><td>Yes</td><td>No</td><td>16.21%</td></tr><tr><td>3-shot</td><td>Yes</td><td>No</td><td>13.73%</td></tr><tr><td>3-shot</td><td>Yes</td><td>Yes</td><td>16.48%</td></tr></table>
+
+Table 5: Accuracy of GPT-4 on D1 problems released after September 2021 using different experimental setups
+
+In the fixed demonstration experiment, we randomly select three problems to create 3-shot prompts. In the retrieval-augmented demonstration experiment, we first generate embeddings for the statements of the source and test data problems utilizing the OpenAI text-embedding-ada-002 model. We then identify the top three problems in the source data based on cosine similarity for each test problem, incorporating them as example demonstrations within the prompts.
+
+The experimental results, summarized in Table 5, show that the retrieval-augmented 3-shot method's accuracy is nearly identical to the 0-shot CoT, while the fixed 3-shot approach is even less effective. This may be due to the highly specialized nature of competitive programming problems, which makes finding valuable references challenging. Furthermore, the model may struggle to acquire problem-solving skills through context learning alone, and inappropriate demonstrations might lead to adverse effects.
+
+# 4.4 Problem Statement Simplification
+
+Intuitively, even experienced programming competition competitors require time to understand problem statements. Therefore, we conduct a simple experiment to assess whether comprehension of problem statements hinders LLMs' ability to excel at programming problems. We first instruct GPT-4 to simplify the problem statement with  $\rho_{sip}$  and then generate the code with  $\rho_{sipgen}$  as shown in Table 8. The results are also evaluated on both the D1 and D3 problems released after October 2021. However, for D1 problems, using the simplified problem statement even brings a slight decline in ACC#G from  $11.54\%$  to  $11.14\%$ . And the ACC#G for D3 problems still remains at  $0.00\%$ . Consequently, the challenge of genuinely improving the model's reasoning ability and enhancing its performance on unseen problems represents a significant direction for future research.
+
+# 5 Related Work
+
+Code LLMs. Code intelligence is an important topic in AI research. Recently, code LLMs (Zhang et al., 2023b) have received widespread attention. Commercial LLMs (OpenAI, 2023) have achieved tremendous success. Meanwhile, research on open-source code LLMs is also thriving, such as CodeLlama (Rozière et al., 2023), StarCoder (Li et al., 2023), CodeGeeX (Zheng et al., 2023), CodeFuse (Di et al., 2023), WizardCoder (Luo et al., 2023) and Lemur (Xu et al., 2023).
+
+Reasoning on Code. Programming competition is a specialized domain within the broader landscape of programming problems. Unlike simpler tasks on code, such as HumanEval (Chen et al., 2021a), MBPP (Austin et al., 2021), MultiPLE (Cassano et al., 2023), competition-level programming problems necessitate an advanced understanding of data structures, algorithms, and problem-solving techniques. Enabling models to solve human-designed algorithmic competition problems represents a meaningful research direction, as it reflects the models' integrated capabilities in reasoning, coding, and problem-solving. AlphaCode (Li et al., 2022) simulate evaluations on 10 programming competitions on the Codeforces platform, which is the first work in this topic. ALGO (Zhang et al., 2023a) can integrate with any existing code LLMs in a model-agnostic manner, enhancing its code generation performance.
+
+Reasoning on Other Subjects. Researchers have proposed many benchmarks requiring various reasoning skills, including commonsense reasoning (Talmor et al., 2018; Geva et al., 2021), numerical reasoning (Dua et al., 2019), multi-hop reasoning (Yang et al., 2018), arithmetic reasoning (Patel et al., 2021; Cobbe et al., 2021), structured reasoning (Yu et al., 2018; Lei et al., 2023), inductive reasoning (Sinha et al., 2019) and logical reasoning (Yu et al., 2020). LLMs are also widely used in scientific research in other fields (Wang et al., 2023), such as physics (Yeadon and Halliday, 2023), chemistry (Castro Nascimento and Pimentel, 2023; Bran et al., 2023), etc.
+
+# 6 Conclusion
+
+In this study, we utilize competition-level programming problems from Codeforces to analyze the reasoning capabilities of LLMs. We find a significant
+
+decrease in perceived performance of GPT-4 on unseen problems, consistent across a range of difficulties, problem types, and experimental settings. This decrease highlights concerns of data contamination in benchmarks and the need for unseen tasks to properly assess LLMs' reasoning ability with complex challenges. Our research also extends these insights to other open-source LLMs, revealing the common difficulties these models face with complex, previously unencountered reasoning tasks. This is indicative of the LLMs' intrinsic limitations in reasoning. As a primary probe, we explore several straightforward strategies, but none of them consistently mitigated the issues. Through our work, we hope to emphasize the critical need for robust datasets to accurately evaluate LLMs' reasoning abilities and to inspire advancements in LLMs that demonstrate improved reasoning abilities.
+
+# Limitations
+
+This study identifies expertly-designed, high-quality competition-level programming problems as effective evaluation data for evaluating LLMs. However, comparing to the existing benchmarks, the quantity of such problems is limited. Constructing uncontaminated, high-quality evaluation datasets and extending them to other tasks such as mathematics still poses a challenge to researchers. The identification and creation of such datasets are crucial for enhancing our understanding of the LLMs in complex reasoning tasks. We will endeavor to achieve this goal in our future work.
+
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+Shuo Yang, Wei-Lin Chiang, Lianmin Zheng, Joseph E Gonzalez, and Ion Stoica. 2023. Rethinking benchmark and contamination for language models with rephrased samples. arXiv preprint arXiv:2311.04850.  
+Zhilin Yang, Peng Qi, Saizheng Zhang, Yoshua Bengio, William Cohen, Ruslan Salakhutdinov, and Christopher D Manning. 2018. Hotpotqa: A dataset for diverse, explainable multi-hop question answering.
+
+In Proceedings of the 2018 Conference on Empirical Methods in Natural Language Processing, pages 2369-2380.  
+Will Yeadon and Douglas P Halliday. 2023. Exploring durham university physics exams with large language models. arXiv preprint arXiv:2306.15609.  
+Tao Yu, Rui Zhang, Kai Yang, Michihiro Yasunaga, Dongxu Wang, Zifan Li, James Ma, Irene Li, Qingning Yao, Shanelle Roman, et al. 2018. Spider: A large-scale human-labeled dataset for complex and cross-domain semantic parsing and text-to-sql task. In Proceedings of the 2018 Conference on Empirical Methods in Natural Language Processing, pages 3911-3921.  
+Weihao Yu, Zihang Jiang, Yanfei Dong, and Jiashi Feng. 2020. Reclor: A reading comprehension dataset requiring logical reasoning. arXiv preprint arXiv:2002.04326.  
+Kexun Zhang, Danqing Wang, Jingtao Xia, William Yang Wang, and Lei Li. 2023a. Algo: Synthesizing algorithmic programs with generated oracle verifiers. arXiv preprint arXiv:2305.14591.  
+Ziyin Zhang, Chaoyu Chen, Bingchang Liu, Cong Liao, Zi Gong, Hang Yu, Jianguo Li, and Rui Wang. 2023b. A survey on language models for code.  
+Qinkai Zheng, Xiao Xia, Xu Zou, Yuxiao Dong, Shan Wang, Yufei Xue, Zihan Wang, Lei Shen, Andi Wang, Yang Li, et al. 2023. Codegeex: A pre-trained model for code generation with multilingual evaluations on humaneval-x. arXiv preprint arXiv:2303.17568.  
+Kun Zhou, Yutao Zhu, Zhipeng Chen, Wentong Chen, Wayne Xin Zhao, Xu Chen, Yankai Lin, Ji-Rong Wen, and Jiawei Han. 2023. Don't make your lmm an evaluation benchmark cheater. arXiv preprint arXiv:2311.01964.
+
+# A More Results with Different Versions of GPT-4 APIs
+
+In this study, we conduct an evaluation of two distinct API versions: GPT-4 and GPT-4-turbo, to assess their performance on D1 problems. The training data for GPT-4 extends up to September 2021, while that for GPT-4-turbo reaches up to April 2023. These evaluations are visually represented in Figure 10. Upon analysis of the results, it is observed that on problems prior to September 2021, the GPT-4-turbo exhibits marginally inferior performance compared to GPT-4. Between September 2021 and April 2023, GPT-4-turbo outperforms GPT-4 on D1 problems, reflecting the benefits of its more recent training data. Nonetheless, a decline in GPT-4's performance is observed for newer problems within this period, likely due to the scarcity of such recent data in its training set.
+
+Nevertheless, when faced with problems emerging after April 2023—thus unencountered during their respective training periods—both APIs demonstrate a decline in performance, albeit GPT-4-turbo marginally outperforms GPT-4. Despite this relative improvement, the performance of GPT-4-turbo on problems post-April 2023 noticeably regresses when compared to its performance on problems covered by its training data. This finding is consistent with the conclusions drawn in the §3.1 "Faltering on Unseen Problems", which elucidates the challenges faced by these models when confronted with novel questions that extend beyond their training corpus.
+
+# B Dataset Details
+
+In the context of competitive programming challenges, a "non-standard input/output format" typically refers to a situation where the program's input and output are not provided through standard methods such as reading from standard input (stdin) or writing to standard output (stdout), which are the conventional ways for programs to receive and provide data during competitions. Instead, they might involve interacting with files, graphical user interfaces, or network connections, which are not commonly used in standard programming contests (like https://codeforces.com/problems/problem/120/A). To filter out problems with non-standard input/output formats, we utilize metadata from the problem descriptions on Codeforces, which indicate whether a problem requires non-standard methods for input and output. By checking this information, we can automatically exclude such problems from our dataset to ensure the consistency of the test data.
+
+Statistics of the types of problems in D1, D2, and D3 are shown in Table 7.
+
+# C Prompt Details
+
+Prompts used in this study are shown in Table 8.
+
+# D Case Study
+
+Some examples generated by GPT4 are shown in Tables 9-13.
+
+![](images/e4348eb69dc17c80c55ad19b713f605e4065bde8eb3d1362a04c17586b31ad1a.jpg)  
+Figure 10: Comparison of ACC#G for GPT-4 and GPT-4-turbo on D1 problems.
+
+<table><tr><td>Year</td><td>WA1</td><td>WA2</td><td>WA3</td><td>WA4+</td><td>RE</td><td>CE</td><td>TLE</td><td>MLE</td></tr><tr><td>2010</td><td>0.49</td><td>0.15</td><td>0.04</td><td>0.19</td><td>0.04</td><td>0.03</td><td>0.01</td><td>0.04</td></tr><tr><td>2011</td><td>0.53</td><td>0.13</td><td>0.10</td><td>0.06</td><td>0.07</td><td>0.06</td><td>0.04</td><td>0.01</td></tr><tr><td>2012</td><td>0.55</td><td>0.14</td><td>0.05</td><td>0.12</td><td>0.04</td><td>0.04</td><td>0.03</td><td>0.02</td></tr><tr><td>2013</td><td>0.63</td><td>0.13</td><td>0.06</td><td>0.07</td><td>0.03</td><td>0.03</td><td>0.04</td><td>0.01</td></tr><tr><td>2014</td><td>0.53</td><td>0.18</td><td>0.05</td><td>0.09</td><td>0.04</td><td>0.05</td><td>0.04</td><td>0.01</td></tr><tr><td>2015</td><td>0.62</td><td>0.10</td><td>0.02</td><td>0.14</td><td>0.03</td><td>0.02</td><td>0.04</td><td>0.02</td></tr><tr><td>2016</td><td>0.68</td><td>0.09</td><td>0.02</td><td>0.10</td><td>0.02</td><td>0.05</td><td>0.04</td><td>0.00</td></tr><tr><td>2017</td><td>0.66</td><td>0.13</td><td>0.05</td><td>0.08</td><td>0.03</td><td>0.03</td><td>0.03</td><td>0.02</td></tr><tr><td>2018</td><td>0.58</td><td>0.12</td><td>0.06</td><td>0.13</td><td>0.01</td><td>0.03</td><td>0.05</td><td>0.01</td></tr><tr><td>2019</td><td>0.67</td><td>0.11</td><td>0.04</td><td>0.06</td><td>0.02</td><td>0.05</td><td>0.02</td><td>0.02</td></tr><tr><td>2020</td><td>0.77</td><td>0.06</td><td>0.01</td><td>0.01</td><td>0.05</td><td>0.06</td><td>0.03</td><td>0.01</td></tr><tr><td>2021</td><td>0.82</td><td>0.07</td><td>0.02</td><td>0.01</td><td>0.02</td><td>0.04</td><td>0.02</td><td>0.00</td></tr><tr><td>2022</td><td>0.91</td><td>0.05</td><td>0.00</td><td>0.00</td><td>0.02</td><td>0.00</td><td>0.02</td><td>0.00</td></tr><tr><td>2023</td><td>0.90</td><td>0.03</td><td>0.00</td><td>0.00</td><td>0.03</td><td>0.01</td><td>0.02</td><td>0.01</td></tr><tr><td>Average</td><td>0.70</td><td>0.10</td><td>0.03</td><td>0.06</td><td>0.03</td><td>0.03</td><td>0.03</td><td>0.01</td></tr></table>
+
+Table 6: Error category of GPT-4 from 2010 to 2023. The abbreviations stand for: WA1, WA2, WA3, and WA4+ (Wrong Answers on Test 1, 2, 3, and 4 or above), RE (Runtime Error), CE (Compilation Error), TLE (Time Limit Exceeded), and MLE (Memory Limit Exceeded).  
+
+<table><tr><td>Tag</td><td>#Problems</td><td>Tag</td><td>#Problems</td></tr><tr><td>implementation</td><td>1746</td><td>greedy</td><td>1441</td></tr><tr><td>math</td><td>1382</td><td>brute force</td><td>825</td></tr><tr><td>constructive algorithms</td><td>783</td><td>dp</td><td>577</td></tr><tr><td>sortings</td><td>514</td><td>data structures</td><td>391</td></tr><tr><td>strings</td><td>381</td><td>binary search</td><td>342</td></tr><tr><td>number theory</td><td>309</td><td>graphs</td><td>263</td></tr><tr><td>dfs and similar</td><td>244</td><td>two pointers</td><td>197</td></tr><tr><td>combinatorics</td><td>179</td><td>bitmasks</td><td>154</td></tr><tr><td>geometry</td><td>142</td><td>trees</td><td>137</td></tr><tr><td>games</td><td>87</td><td>dsu</td><td>84</td></tr><tr><td>shortest paths</td><td>66</td><td>*special</td><td>58</td></tr><tr><td>probabilities</td><td>52</td><td>hashing</td><td>48</td></tr><tr><td>divide and conquer</td><td>35</td><td>flows</td><td>24</td></tr><tr><td>graph matchings</td><td>22</td><td>ternary search</td><td>22</td></tr><tr><td>matrices</td><td>22</td><td>expression parsing</td><td>19</td></tr><tr><td>string suffix structures</td><td>10</td><td>2-sat</td><td>7</td></tr><tr><td>chinese remainder theorem</td><td>5</td><td>schedules</td><td>4</td></tr><tr><td>meet-in-the-middle</td><td>4</td><td>fft</td><td>4</td></tr></table>
+
+Table 7: Statistics of the types of problems in D1, D2, D3.
+
+<table><tr><td>ρ1</td><td>You are given a problem, you need to write a C++ solution and explain the algorithm. {promblem_name} {promblem_description} Input specification: {input_format} Output specification: {output_format} Note: {note} Memory limit: {memory_limit} Time limit: {time_limit} Example: Input: {input} Output: {output} Please provide a C++ code in ` ` `cpp\n...` ` `</td></tr><tr><td>ρ2</td><td>Read the problem, write a C++ solution and explain the algorithm. {promblem_name}: {promblem_description} Input specification is {input_format}. Output specification is {output_format}. Note that {note}. Memory limit is {memory_limit}. Time limit is {time_limit}. Example i input is {input}. Example i output is {output}. Please provide a C++ code in ` ` `cpp\n...` ` `</td></tr><tr><td>ρ3</td><td>Finish the solution of this programming problem. {promblem_name} {promblem_description} Input specification: {input_format} Output specification: {output_format} Note: {note} Memory limit: {memory_limit} Time limit: {time_limit} Example: Input: {input} Output: {output} C++ code solution: ` ` `cpp</td></tr><tr><td>ρcot</td><td>You are given an algorithm problem. First, provide a detailed explanation of the algorithm solution, including the logic behind it, the time and space complexity, and any important considerations or edge cases. Then, implement the solution in C++ code, ensuring it is clean, efficient, and well- Commented. {promblem_name} {promblem_description} Input specification: {input_format} Output specification: {output_format} Note: {note} Memory limit: {memory_limit} Time limit: {time_limit} Example: Input: {input} Output: {output} Please provide a C++ code in ` ` `cpp\n...` ` `</td></tr><tr><td>ρsip</td><td>Please extract the essential components from this algorithm problem for a C++ solution, removing any superfluous narrative or context. {promblem_name} {promblem_description} Input specification: {input_format} Output specification: {output_format} Note: {note}</td></tr><tr><td>ρsipgen</td><td>You are given a problem, you need to write a C++ solution and explain the algorithm. {promblem_simlified} Memory limit: {memory_limit} Time limit: {time_limit} Example: Input: {input} Output: {output} Please provide a C++ code in ` ` `cpp\n...` ` `</td></tr></table>
+
+Table 8: Prompts used in this study.
+
+<table><tr><td>Problem Name</td><td>1890 B: Qingshan Loves Strings Accepted</td></tr><tr><td>Problem Statement</td><td>Problem Qingshan has a string s, while Daniel has a string t. Both strings only contain 0 and 1. A string a of length k is good if and only if ai ≠ ai+1 for all i = 1, 2, ..., k-1. For example, 1, 101, 0101 are good, while 11, 1001, 001100 are not good. Qingshan wants to make s good. To do this, she can do the following operation any number of times (possibly, zero): insert t to any position of s (getting a new s). Please tell Qingshan if it is possible to make s good.
+Input Format The input consists of multiple test cases. The first line contains a single integer T (1 ≤ T ≤ 2000) — the number of test cases. The description of the test cases follows. The first line of each test case contains two integers n and m (1 ≤ n, m ≤ 50) — the length of the strings s and t, respectively. The second line of each test case contains a string s of length n. The third line of each test case contains a string t of length m. It is guaranteed that s and t only contain 0 and 1.
+Output Format For each test case, print &quot;YES&quot; (without quotes), if it is possible to make s good, and &quot;NO&quot; (without quotes) otherwise. You can print letters in any case (upper or lower).</td></tr><tr><td>Code</td><td></td></tr><tr><td>1</td><td>#include &lt;bits/&lt;stdlib.h&gt;</td></tr><tr><td>2</td><td>using namespace std;</td></tr><tr><td>3</td><td></td></tr><tr><td>4</td><td>bool isGood(string s) { 
+for (int i = 0; i &lt; s.size() - 1; i++) { 
+if (s[i] == s[i+1]) { 
+return false; 
+} 
+return true; 
+}</td></tr><tr><td>5</td><td></td></tr><tr><td>6</td><td></td></tr><tr><td>7</td><td></td></tr><tr><td>8</td><td></td></tr><tr><td>9</td><td></td></tr><tr><td>10</td><td></td></tr><tr><td>11</td><td></td></tr><tr><td>12</td><td></td></tr><tr><td>13</td><td>string solve(string s, string t) { 
+if (isGood(s)) { 
+return &quot;YES&quot;; 
+} 
+if (!isGood(t)) { 
+return &quot;NO&quot;; 
+}</td></tr><tr><td>14</td><td></td></tr><tr><td>15</td><td></td></tr><tr><td>16</td><td></td></tr><tr><td>17</td><td></td></tr><tr><td>18</td><td></td></tr><tr><td>19</td><td></td></tr><tr><td>20</td><td>for (int i = 0; i &lt; s.size() - 1; i++) { 
+if (s[i] == s[i+1] &amp;&amp; t[0] != s[i] &amp;&amp; t[t.size() - 1] != s[i+1]) { 
+s.insert(i+1, t); 
+i += t.size(); 
+}</td></tr><tr><td>21</td><td></td></tr><tr><td>22</td><td></td></tr><tr><td>23</td><td></td></tr><tr><td>24</td><td></td></tr><tr><td>25</td><td></td></tr><tr><td>26</td><td>if (isGood(s)) { 
+return &quot;YES&quot;; 
+}</td></tr><tr><td>27</td><td></td></tr><tr><td>28</td><td></td></tr><tr><td>29</td><td>return &quot;NO&quot;; 
+}</td></tr><tr><td>30</td><td></td></tr><tr><td>31</td><td></td></tr><tr><td>32</td><td>int main() { 
+int T; 
+cin &gt;&gt; T; 
+while (T--) { 
+int n, m; 
+cin &gt;&gt; n &gt;&gt; m; 
+string s, t; 
+cin &gt;&gt; s &gt;&gt; t; 
+cout &lt;&lt; solve(s, t) &lt;&lt; endl; 
+}</td></tr><tr><td>33</td><td></td></tr><tr><td>34</td><td></td></tr><tr><td>35</td><td></td></tr><tr><td>36</td><td></td></tr><tr><td>37</td><td></td></tr><tr><td>38</td><td></td></tr><tr><td>39</td><td></td></tr><tr><td>40</td><td></td></tr><tr><td>41</td><td></td></tr><tr><td>42</td><td></td></tr><tr><td>43</td><td>return 0;</td></tr></table>
+
+Table 9: An accepted example generated by GPT-4
+
+# Problem Name
+
+# 1893 A: Anonymous Informant
+
+# Wrong answer on test 1
+
+# Problem Statement
+
+Problem You are given an array  $b_{1}, b_{2}, \ldots, b_{n}$ . An anonymous informant has told you that the array  $b$  was obtained as follows: initially, there existed an array  $a_{1}, a_{2}, \ldots, a_{n}$ , after which the following two-component operation was performed  $k$  times: A fixed point  $^{\dagger} x$  of the array  $a$  was chosen. Then, the array  $a$  was cyclically shifted to the left  $^{\ddagger}$  exactly  $x$  times. As a result of  $k$  such operations, the array  $b_{1}, b_{2}, \ldots, b_{n}$  was obtained. You want to check if the words of the anonymous informant can be true or if they are guaranteed to be false.  $^{\dagger}$ A number  $x$  is called a fixed point of the array  $a_{1}, a_{2}, \ldots, a_{n}$  if  $1 \leq x \leq n$  and  $a_{x} = x$ .  $^{\ddagger}$ A cyclic left shift of the array  $a_{1}, a_{2}, \ldots, a_{n}$  is the array  $a_{2}, \ldots, a_{n}, a_{1}$ .
+
+Input Format Each test contains multiple test cases. The first line contains an integer  $t$  ( $1 \leq t \leq 10^4$ ) — the number of test cases. The description of the test cases follows. The first line of each test case contains two integers  $n, k$  ( $1 \leq n \leq 2 \cdot 10^5$ ,  $1 \leq k \leq 10^9$ ) — the length of the array  $b$  and the number of operations performed. The second line of each test case contains  $n$  integers  $b_1, b_2, \ldots, b_n$  ( $1 \leq b_i \leq 10^9$ ) — the elements of the array  $b$ . It is guaranteed that the sum of the values of  $n$  for all test cases does not exceed  $2 \cdot 10^5$ .
+
+Output Format For each test case, output "Yes" if the words of the anonymous informant can be true, and "No" if they are guaranteed to be false.
+
+# Code
+
+```cpp
+#include <bits>   
+using namespace std;   
+void solve() { int n, k; cin >> n >> k; vector<int> b(n); for (int i = 0; i < n; i++) cin >> b[i]; vector<int> prefix(n), suffix(n); prefix[0] = b[0]; suffix[n-1] = b[n-1]; for (int i = 1; i < n; i++) prefix[i] = max(prefix[i-1], b[i]); for (int i = n-2; i >= 0; i--) suffix[i] = max(prefix[i+1], b[i]); bool ok = true; for (int i = 0; i < n; i++) { if (b[i] > max((i > 0 ? prefix[i-1] : 0), (i < n-1 ? suffix[i+1] : 0))) { ok = false; break; } if (i > 0 && b[i] - b[i-1] > 1) { ok = false; break; } } if (b[0] != b[n-1]) ok = false; cout << (ok ? "Yes" : "No") << "\n";   
+}   
+int main() { ios_base::sync_with_std(false); cin.tie(NULL); int t; cin >> t; while(t-- ) solve(); return 0;   
+}
+```
+
+Table 10: An wrong example generated by GPT-4
+
+<table><tr><td>Problem Name</td><td>1893 A: Anonymous Informant</td><td>Compilation error</td></tr><tr><td>Problem Statement</td><td colspan="2">Problem You are given a set S, which contains the first n positive integers: 1,2,...,n. You can perform the following operation on S any number of times (possibly zero): Choose a positive integer k where 1 ≤ k ≤ n, such that there exists a multiple of k in S. Then, delete the smallest multiple of k from S. This operation requires a cost of k. You are given a set T, which is a subset of S. Find the minimum possible total cost of operations such that S would be transformed into T. We can show that such a transformation is always possible.Input Format The first line of the input contains a single integer t (1 ≤ t ≤ 10000) — the number of test cases. The description of the test cases follows. The first line contains a single positive integer n (1 ≤ n ≤ 10^6). The second line of each test case contains a binary string of length n, describing the set T. The i-th character of the string is &#x27;1&#x27; if and only if i is an element of T, and &#x27;0&#x27; otherwise. It is guaranteed that the sum of n over all test cases does not exceed 10^6.Output Format For each test case, output one non-negative integer — the minimum possible total cost of operations such that S would be trans-formed into T.</td></tr><tr><td>Code</td><td colspan="2"># include &lt;bits&gt; using namespace std;int main() {ios_base::sync_with_std(false);cin.tie(NULL);int t;cin &gt;&gt; t;while(t--){int n;cin &gt;&gt; n;string s;cin &gt;&gt; s;long long cost = 0, max_num = 0;for(int i = n - 1; i &gt;= 0; i--){if(s[i] == &#x27;1&#x27;) {if(i + 1 &gt; max_num) {cost += i + 1;max_num = i + 1;}else{max_num = max(max_num, i + 1);}cout &lt;&lt; cost &lt;&lt; &quot;\n&quot;;}return 0;}</td></tr></table>
+
+Table 11: An example of compilation error generated by GPT-4
+
+<table><tr><td>Problem Name</td><td>451 A: Game With Sticks Accepted</td></tr><tr><td>Problem Statement</td><td>Problem After winning gold and silver in IOI 2014, Akshit and Malvika want to have some fun. Now they are playing a game on a grid made of n horizontal and m vertical sticks. An intersection point is any point on the grid which is formed by the intersection of one horizontal stick and one vertical stick. In the grid shown below, n=3 and m=3. There are n+m=6 sticks in total (horizontal sticks are shown in red and vertical sticks are shown in green). There are n-m=9 intersection points, numbered from 1 to 9.
+The rules of the game are very simple. The players move in turns. Akshit won gold, so he makes the first move. During his/her move, a player must choose any remaining intersection point and remove from the grid all sticks which pass through this point. A player will lose the game if he/she cannot make a move (i.e. there are no intersection points remaining on the grid at his/her move). Assume that both players play optimally. Who will win the game?
+Input Format The first line of input contains two space-separated integers, n and m (1 ≤ n, m ≤ 100).
+Output Format Print a single line containing &quot;Akshit&quot; or &quot;Malvika&quot; (without the quotes), depending on the winner of the game.</td></tr><tr><td>Response</td><td>The problem can be solved using a simple observation. The game is essentially about removing rows and columns from a grid. Each move removes one row and one column. Therefore, the game ends when there are no rows or columns left, i.e., when the minimum of n and m reaches zero. Since Akshit starts the game, if the minimum of n and m is even, Malvika will make the last move and win the game. Otherwise, Akshit will make the last move and win the game.
+The time complexity of this solution is O(1) because it involves only a constant amount of computation. The space complexity is also O(1) because it uses only a constant amount of space.
+The code first reads the values of n and m. It then checks if the minimum of n and m is even. If it is, it prints &quot;Malvika&quot;. Otherwise, it prints &quot;Akshit&quot;.
+Here is the C++ code for the problem:</td></tr><tr><td>1</td><td>#include &lt;bits/&lt;stdlib.h&gt;</td></tr><tr><td>2</td><td>using namespace std;</td></tr><tr><td>3</td><td>int main() {</td></tr><tr><td>4</td><td>int n, m;</td></tr><tr><td>5</td><td>cin &gt;&gt; n &gt;&gt; m;</td></tr><tr><td>6</td><td>// If the minimum of n and m is even, Malvika wins. Otherwise, Akshit wins.</td></tr><tr><td>7</td><td>if (min(n, m) % 2 == 0) {</td></tr><tr><td>8</td><td>cout &lt;&lt; &quot;Malvika&quot;;</td></tr><tr><td>9</td><td>} else {</td></tr><tr><td>10</td><td>cout &lt;&lt; &quot;Akshit&quot;;</td></tr><tr><td>11</td><td>}</td></tr><tr><td>12</td><td>return 0;</td></tr><tr><td>13</td><td>}</td></tr><tr><td>14</td><td>}</td></tr></table>
+
+Table 12: An example generated by GPT-4 with CoT prompt.
+
+<table><tr><td>Problem Name</td><td>1890 B: Qingshan Loves Strings</td></tr><tr><td>Problem Statement</td><td>Problem Qingshan has a string s, while Daniel has a string t. Both strings only contain ∅ and 1. A string a of length k is good if and only if ai ≠ ai+1 for all i = 1, 2, ..., k-1. For example, 1, 101, 0101 are good, while 11, 1001, 001100 are not good. Qingshan wants to make s good. To do this, she can do the following operation any number of times (possibly, zero): insert t to any position of s (getting a new s). Please tell Qingshan if it is possible to make s good.Input Format The input consists of multiple test cases. The first line contains a single integer T (1 ≤ T ≤ 2000) — the number of test cases. The description of the test cases follows. The first line of each test case contains two integers n and m (1 ≤ n, m ≤ 50) — the length of the strings s and t, respectively. The second line of each test case contains a string s of length n. The third line of each test case contains a string t of length m. It is guaranteed that s and t only contain ∅ and 1.Output Format For each test case, print &quot;YES&quot; (without quotes), if it is possible to make s good, and &quot;NO&quot; (without quotes) otherwise. You can print letters in any case (upper or lower).</td></tr><tr><td>Simplified Statement</td><td>You are given a problem, you need to write a C++ solution and explain the algorithm.- You are given two strings s and t, both containing only 0s and 1s.- A string a of length k is considered good if no two consecutive characters are the same.- You can insert string t at any position in string s any number of times.- You need to determine if it is possible to make string s good.- The input consists of multiple test cases. The first line contains an integer T (1 ≤ T ≤ 2000) — the number of test cases. Each test case starts with two integers n and m (1 ≤ n, m ≤ 50) — the lengths of the strings s and t, respectively. The next two lines contain the strings s and t.- For each test case, print &quot;YES&quot; if it is possible to make s good, and &quot;NO&quot; otherwise. The output is case-insensitive.</td></tr></table>
+
+Table 13: An simplified example generated by GPT-4

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2024/Complex Logical Query Answering by Calibrating Knowledge Graph Completion Models/28987eca-6571-4ea4-b16a-06ab4319ecb4_content_list.json

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+    {
+        "type": "text",
+        "text": "Complex Logical Query Answering by Calibrating Knowledge Graph Completion Models",
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+        "type": "text",
+        "text": "Changyi Xiao $^{1*}$ , Yixin Cao $^{2}$",
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+        "type": "text",
+        "text": "<sup>1</sup>School of Data Science, University of Science and Technology of China",
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+        "type": "text",
+        "text": "$^{2}$ School of Computer Science, Fudan University",
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+        "type": "text",
+        "text": "changyi@mail.ustc.edu.cn, caoyixin2011@gmail.com",
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+    {
+        "type": "text",
+        "text": "Abstract",
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+        "type": "text",
+        "text": "Complex logical query answering (CLQA) is a challenging task that involves finding answer entities for complex logical queries over incomplete knowledge graphs (KGs). Previous research has explored the use of pre-trained knowledge graph completion (KGC) models, which can predict the missing facts in KGs, to answer complex logical queries. However, KGC models are typically evaluated using ranking evaluation metrics, which may result in values of predictions of KGC models that are not well-calibrated. In this paper, we propose a method for calibrating KGC models, namely CKGC, which enables KGC models to adapt to answering complex logical queries. Notably, CKGC is lightweight and effective. The adaptation function is simple, allowing the model to quickly converge during the adaptation process. The core concept of CKGC is to map the values of predictions of KGC models to the range [0, 1], ensuring that values associated with true facts are close to 1, while values linked to false facts are close to 0. Through experiments on three benchmark datasets, we demonstrate that our proposed calibration method can significantly boost model performance in the CLQA task. Moreover, our approach can enhance the performance of CLQA while preserving the ranking evaluation metrics of KGC models. The code is available at https://github.com/changyi7231/CKGC.",
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+    {
+        "type": "text",
+        "text": "1 Introduction",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Knowledge graphs (KGs) are composed of structured representations of facts in the form of triplets and have been widely used in various domains. One of the key tasks associated with KGs is complex logical query answering (Ren et al., 2023). Complex logical queries are typically expressed using first-order logic (FOL), which encompasses logical operations such as conjunction  $(\\wedge)$ , disjunction  $(\\lor)$ ,",
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+    {
+        "type": "text",
+        "text": "negation  $(\\neg)$ , and existential quantifier  $(\\exists)$ . For example, the query \"Which universities do the Turing Award winners not in the field of deep learning work in?\" can be formulated as a FOL query, as illustrated in Figure 1.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Many well-known knowledge graphs (KGs) suffer from incompleteness, rendering it challenging to answer complex queries through simple KG traversal. Building on the accomplishments of knowledge graph completion (KGC) methods (Bordes et al., 2013; Sun et al., 2018; Trouillon et al., 2017) in addressing one-hop KG queries, a research avenue has emerged focusing on learning embeddings for queries to handle complex logical queries (Hamilton et al., 2018; Ren et al., 2020; Zhang et al., 2021). Nonetheless, these methodologies often require extensive training on numerous complex logical queries, leading to substantial training time overhead and limited generalization to out-of-distribution query structures.",
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+        "type": "text",
+        "text": "In addressing these challenges, CQD (Aragelyan et al., 2020) introduces a method for CLQA by leveraging one-hop atom results derived from a pretrained KGC model, thereby removing the necessity for training on complex queries. CQD frames CLQA as an optimization problem and employs techniques like beam search or continuous approximation to estimate the optimal solution. Despite its effectiveness, the approximations made during the process could lead to a decrease in accuracy for CQD. Furthermore, CQD is reliant on a KGC model whose values of output might not be specifically calibrated for CLQA, potentially resulting in inaccuracies in the outcomes.",
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+    {
+        "type": "text",
+        "text": "In this paper, we introduce a method for calibrating KGC models, namely CKGC, which can make KGC models adapt to handling complex logical queries. Our method is lightweight and effective. It is lightweight, as the adaptation function is simple and the model can quickly converge in adaptation process. Moreover, it is effective in significantly",
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+    {
+        "type": "page_footnote",
+        "text": "*Corresponding author.",
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+    {
+        "type": "page_number",
+        "text": "13792",
+        "bbox": [
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+    {
+        "type": "footer",
+        "text": "Findings of the Association for Computational Linguistics: ACL 2024, pages 13792-13803 August 11-16, 2024 ©2024 Association for Computational Linguistics",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "enhancing the performance of CLQA.",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "We first represent every complex logical query as a computation graph over fuzzy sets, of which nodes represent fuzzy sets and edges represent the fuzzy set operations over fuzzy sets. To obtain the answers of a query, we traverse the computation graph and execute the fuzzy set operations through a straightforward forward propagation process, eliminating the need for optimization compared to CQD (Aragelyan et al., 2020). We define four fundamental fuzzy set operations for CLQA: projection operation, complement operation, intersection operation, and union operation, all of which require the KGC model to be calibrated.",
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+    {
+        "type": "text",
+        "text": "However, a KGC model is typically measured by the ranking metrics, which do not need it to be calibrated. Thus, we propose a calibration method for KGC models to make it adapted to CLQA. We define the adaptation function as a monotonically increasing function that preserves the ranking evaluation metrics of the KGC model. The main idea of our method is to map the values of output of a KGC model to the interval [0, 1], and makes the values corresponding to true triplets be as close as possible to 1, while the values corresponding to false triplets be as close as possible to 0.",
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+    {
+        "type": "text",
+        "text": "Our experimental evaluation on three standard datasets demonstrates the efficacy of CKGC in CLQA. The results reveal that CKGC achieves state-of-the-art performance across all datasets, showcasing an average relative improvement of  $6.7\\%$  on existential positive first-order queries and  $53.9\\%$  on negation queries compared to the prior state-of-the-art method.",
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+    {
+        "type": "text",
+        "text": "2 Related Work",
+        "text_level": 1,
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+        "type": "text",
+        "text": "Knowledge Graph Completion The task of KGC involves predicting missing triplets within a knowledge graph, which can be viewed as predicting answers for one-hop queries. Various methodologies have been proposed to address this task, encompassing embedding techniques (Bordes et al., 2013; Sun et al., 2018; Trouillon et al., 2017), reinforcement learning approaches (Xiong et al., 2017; Das et al., 2018; Hildebrandt et al., 2020; Zhang et al., 2022), rule learning strategies (Yang et al., 2017; Sadeghian et al., 2019; Qu et al., 2020), and graph neural network methodologies (Schlichtkrull et al., 2018; Vashissth et al., 2019; Teru et al., 2020). Embedding methods aim to embed entities and relations into a continuous space and de",
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "fine a scoring function based on these embeddings. Reinforcement learning methods train an agent to explore the knowledge graph to predict the missing triplets. Rule learning methods adopt a distinct approach by initially identifying confident logical rules from the knowledge graph. These rules are then utilized to infer missing triplets. Lastly, graph neural network methods utilize graph neural networks to learn representations of entities and relations by leveraging the graph structure.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Complex Logical Query Answering CLQA over KGs extends KGC to predict answers for FOL queries, which additionally requires defining relationships between sets of entities. Embedding-based methods represent sets of entities as geometric objects (Hamilton et al., 2018; Ren et al., 2020; Zhang et al., 2021) or probability distributions (Ren and Leskovec, 2020), and then minimize the distance between embeddings of queries and embeddings of their corresponding answers. However, the quality of representation of sets may be compromised when dealing with large sets. To overcome this limitation, some studies have incorporated powerful fuzzy set theory to handle FOL queries (Chen et al., 2022; Zhu et al., 2022). For instance, FuzzQE (Chen et al., 2022) embeds entities and queries into a fuzzy space and leverages fuzzy set operations to perform logical operations on the embeddings. Similarly, GNN-QE (Zhu et al., 2022) decomposes the query into relational projections operations and fuzzy set operations over fuzzy sets, and subsequently learns a graph neural network to execute relational projections.",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Nevertheless, the aforementioned methods generally necessitate training on numerous complex logical queries, resulting in significant training time overhead and limited generalization to out-of-distribution query structures. Another line of methods first pre-trains a KGC model and then integrates it with fuzzy set theory to infer answers. CQD (Aragelyan et al., 2020) formulates CLQA as an optimization problem and proposes two strategies to approximate the optimal solution: CQD-CO, which directly optimizes in the continuous space, and CQD-Beam, which utilizes beam search. Despite CQD avoiding the need to train on complex logical queries, it suffers from accuracy loss due to the approximated optimization and uncalibrated KGC models. To enhance accuracy, Bai et al. (2023) introduce QTO, which efficiently finds the theoretically optimal solution",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "page_number",
+        "text": "13793",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "through a forward-backward propagation on a tree-like computation graph. Additionally, Arakelyan et al. (2023) propose  $\\mathrm{CQD}^{\\mathcal{A}}$ , a parameter-efficient adaptation method, to calibrate KGC models. However, the KGC model for QTO is not well calibrated for complex queries, and the optimal solution for  $\\mathrm{CQD}^{\\mathcal{A}}$  is still approximated. In contrast, our proposed model not only delivers accurate solutions but also effectively calibrates the KGC models.",
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3 Background",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "In this section, we introduce the related background of our method, complex logical query answering on knowledge graphs and fuzzy sets.",
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+    {
+        "type": "text",
+        "text": "3.1 Complex Logical Query Answering on Knowledge Graphs",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "Knowledge Graphs Completion Given a set of entities  $\\mathcal{V}$  and a set of relations  $\\mathcal{R}$ , a knowledge graph  $\\mathcal{G}$  contains a set of triplets  $\\{(h,r,t)\\} \\subset \\mathcal{V} \\times \\mathcal{R} \\times \\mathcal{V}$ , where each triplet is a fact from head entity  $h$  to tail entity  $t$  with a relation type  $r$ . KGC models define scoring functions  $f(h,r,t)$  to measure the likelihood of triplets  $(h,r,t)$  based on their corresponding embeddings.",
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+    },
+    {
+        "type": "text",
+        "text": "First-Order Logic Queries Complex logical queries can be represented by FOL queries with logical operations including conjunction  $(\\wedge)$ , disjunction  $(\\vee)$ , negation  $(\\neg)$ , and existential quantifier  $(\\exists)$ . A first-order logic query  $q$  can be described in its disjunctive normal form, which consists of a set of non-variable anchor entities  $\\mathcal{V}_a \\subseteq \\mathcal{V}$ , existentially quantified bound variables  $V_1, \\ldots, V_k$  and a single target variable  $V_\\varphi$ , which provides the answers of query  $q$ . The disjunctive normal form of a logical query  $q$  is a disjunction of one or more conjunctions.",
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+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nq = V _ {j}. \\exists V _ {1}, \\dots , V _ {k}: c _ {1} \\wedge c _ {2} \\wedge , \\dots , c _ {n}.\n$$\n",
+        "text_format": "latex",
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+    {
+        "type": "text",
+        "text": "Each  $c$  represents a conjunctive query with one or more literals  $e$ , i.e.,  $c_{i} = e_{i1} \\lor e_{i2} \\lor \\dots \\lor e_{im}$ . Each literal  $e$  represents an atomic formula or its negation, i.e.,  $e_{ij} = R(v_{a}, V)$  or  $\\neg R(v_{a}, V)$  or  $\\neg R(V', V)$  or  $\\neg R(V', V)$ , where  $v_{a} \\in \\mathcal{V}_{a}$ ,  $V \\in \\{V?, V_{1}, \\ldots, V_{k}\\}$ ,  $V \\in \\{V?, V_{1}, \\ldots, V_{k}\\}$ ,  $V \\neq V'$ ,  $R(\\cdot, \\cdot)$  is a binary function  $R: \\mathcal{V} \\times \\mathcal{V} \\to \\{0, 1\\}$ . Each relation  $r \\in \\mathcal{R}$  corresponds to a binary function  $R(\\cdot, \\cdot)$ . If  $(h, r, t)$  is a true fact, then  $R(h, t) = 1$ . If  $(h, r, t)$  is a false fact, then  $R(h, t) = 0$ .",
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+    },
+    {
+        "type": "text",
+        "text": "Computation Graph Given a FOL query, we can represent it as a computation graph, of which nodes represent sets of entities and edges represent set operations over sets of entities. The set operations include the complement operation, intersection operation, union operation and projection operation. The root node represents the set of answer entities. See Figure 1 for an example. We map logical operations to set operations according to the following rules.",
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+        "list_items": [
+            "- Negation  $\\longrightarrow$  Complement Operation: Given a set of entities  $S \\subseteq \\mathcal{V}$ , the complement operator performs set complement to obtain  $\\overline{S} = \\mathcal{V} \\backslash S$ .",
+            "- Conjunction  $\\longrightarrow$  Intersection Operation: Given  $n$  sets of entities  $\\{S_1, S_2, \\ldots, S_n\\}$ , the intersection operator performs set intersection to obtain  $\\cap_{i=1}^{n} S_i$ .",
+            "- Disjunction  $\\longrightarrow$  Union Operation: Given  $n$  sets of entities  $\\{S_1, S_2, \\ldots, S_n\\}$ , the union operator performs set union to obtain  $\\cup_{i=1}^{n} S_i$ .",
+            "- Relation Projection  $\\longrightarrow$  Projection Operation: Given a set of entities  $S \\subseteq \\mathcal{V}$  and a relation  $r \\in \\mathcal{R}$ , the projection operator outputs all the adjacent entities  $\\cup_{v \\in S} N(v, r)$ , where  $N(v, r)$  is the set of entities such that  $(v, r, v')$  are true triplets for all  $v' \\in N(v, r)$ ."
+        ],
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "In order to answer a given FOL query, we can traverse the computation graph and execute the set operations. The answers of a query can be obtained by looking at the set of entities in the root node.",
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+    },
+    {
+        "type": "text",
+        "text": "3.2 Fuzzy sets",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "Definition A fuzzy set is a pair  $(U,m)$ , where  $U$  is a set and  $m:U\\to [0,1]$  is a membership function. For each  $x\\in U$ , the value  $m(x)$  measures the degree of membership of  $x$  in  $(U,m)$ . The function  $m = \\mu_{A}$  is called the membership function of the fuzzy set  $A = (U,m)$ . Classical sets are seen as special cases of fuzzy sets, if the membership functions only takes values 0 or 1.",
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Fuzzy Set Operations Fuzzy set operations are a generalization of classical set operations for fuzzy sets. The three primary fuzzy set operations are fuzzy complements, fuzzy intersections, and fuzzy unions. For a given fuzzy set  $A$ , its complement  $\\overline{A}$  is commonly defined by the following membership",
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+        "page_idx": 2
+    },
+    {
+        "type": "page_number",
+        "text": "13794",
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "First-Order Logic",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "$q = V_{?}$ .  $\\exists V$ : Win(V, Turing Award)  $\\land$  Field(V, Deep Learning)  $\\land$  University(V,  $V_{?}$ )",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Computation Graph",
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "image",
+        "img_path": "images/021c170312635a28a4cfd923c9d9b6bdd3b3d37803dc2491944602777c1cfc1d.jpg",
+        "image_caption": [
+            "Figure 1: An query, its corresponding FOL form and its corresponding computation graph."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "function:",
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+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\forall x \\in U, \\mu_ {\\overline {{A}}} (x) = 1 - \\mu_ {A} (x)\n$$\n",
+        "text_format": "latex",
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+    {
+        "type": "text",
+        "text": "Given a pair of fuzzy sets  $A, B$ , their intersection  $A \\cap B$  is defined by a t-norm  $T$  (Klement et al., 2004):",
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\forall x \\in U, \\mu_ {A \\cap B} (x) = T (\\mu_ {A} (x), \\mu_ {B} (x))\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            152,
+            448,
+            448,
+            466
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Prominent examples of t-norms include product t-norm  $T(a,b) = ab$ , Gödel t-norm  $T(a,b) = \\min \\{a,b\\}$  and so on (Klement et al., 2004). Given a t-norm  $T$  and a pair of fuzzy sets  $A, B$ , their union  $A \\cup B$  is defined by De Morgan's law:",
+        "bbox": [
+            112,
+            481,
+            487,
+            562
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\forall x \\in U, \\mu_ {A \\cup B} (x) = 1 - T \\left(1 - \\mu_ {A} (x), 1 - \\mu_ {B} (x)\\right)\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            112,
+            577,
+            500,
+            595
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "4 Method",
+        "text_level": 1,
+        "bbox": [
+            112,
+            612,
+            218,
+            627
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "We first define four fuzzy set operations over fuzzy sets in Section 4.1, and then propose a calibration method for KGC models in Section 4.2.",
+        "bbox": [
+            112,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "4.1 Fuzzy Set Operations",
+        "text_level": 1,
+        "bbox": [
+            112,
+            703,
+            329,
+            720
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "As demonstrated in Section 3.1, a query can be represented as a computation graph. To obtain the fuzzy sets of answers, it is necessary to define the fuzzy set operations utilized in computation graphs. These operations encompass the projection operation, intersection operation, union operation, and complement operation.",
+        "bbox": [
+            112,
+            726,
+            487,
+            839
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "We represent every fuzzy set of entities as a vector  $e \\in [0,1]^d$ , where  $d = |\\mathcal{V}|$  and  $e_i$  denotes the grade of membership of entity  $i$ . The anchor entity is represented by a vector with a single element set to 1 and all other elements set to 0.",
+        "bbox": [
+            112,
+            841,
+            489,
+            920
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Complement Operation: The complement operation maps a fuzzy set to the complement of the fuzzy set. We define the complement operation as",
+        "bbox": [
+            507,
+            318,
+            884,
+            367
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {C}: [ 0, 1 ] ^ {d} \\to [ 0, 1 ] ^ {d}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            621,
+            374,
+            769,
+            393
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {C} (e) = \\mathbf {1} - e\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            663,
+            395,
+            766,
+            412
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Intersection Operation: The intersection operation maps several fuzzy sets into the intersection set of these fuzzy sets. We define the intersection operation by utilizing the product t-norm, which is as follows:",
+        "bbox": [
+            507,
+            422,
+            882,
+            500
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {I}: [ 0, 1 ] ^ {n d} \\to [ 0, 1 ] ^ {d}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            591,
+            511,
+            746,
+            529
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {I} \\left(e ^ {1}, e ^ {2}, \\dots , e ^ {n}\\right) = e ^ {1} \\odot e ^ {2} \\odot \\dots \\odot e ^ {n}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            546,
+            531,
+            845,
+            550
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where  $\\{e^i\\in [0,1]^d |1\\leq i\\leq n\\}$  are vector representations of fuzzy sets and  $\\odot$  is the Hadamard product.",
+        "bbox": [
+            507,
+            560,
+            882,
+            609
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Union Operation: The union operation maps several fuzzy sets into the union set of these fuzzy sets. Due to the De Morgan's Law, we do not need to define the union operation directly. We define the union operation by utilizing the intersection operation and complement operation as follows:",
+        "bbox": [
+            507,
+            618,
+            882,
+            714
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {U}: [ 0, 1 ] ^ {n d} \\to [ 0, 1 ] ^ {d}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            636,
+            722,
+            794,
+            741
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {U} \\left(\\boldsymbol {e} ^ {1}, \\boldsymbol {e} ^ {2}, \\dots , \\boldsymbol {e} ^ {n}\\right) = \\mathcal {C} \\left(\\mathcal {I} \\left(\\mathcal {C} \\left(\\boldsymbol {e} ^ {1}\\right), \\mathcal {C} \\left(\\boldsymbol {e} ^ {2}\\right), \\dots , \\mathcal {C} \\left(\\boldsymbol {e} ^ {n}\\right)\\right)\\right)\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            507,
+            743,
+            895,
+            763
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Projection Operation: The projection operation maps a fuzzy set into another fuzzy set with a relation type  $r$ . We implement the projection operation by utilizing the G��del t-norm as follows:",
+        "bbox": [
+            507,
+            771,
+            884,
+            835
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\begin{array}{l} \\mathcal {P} _ {r}: [ 0, 1 ] ^ {d} \\to [ 0, 1 ] ^ {d} \\\\ \\mathcal{P}_{r}(\\boldsymbol {e})_{j} = 1 - \\min_{1\\leq i\\leq d}\\bigl(1 - \\boldsymbol{e}_{i}\\boldsymbol{X}_{i,r,j}\\bigr) \\\\ = \\max  _ {1 \\leq i \\leq d} e _ {i} X _ {i, r, j} \\\\ \\end{array}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            569,
+            844,
+            821,
+            917
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "header",
+        "text": "Query",
+        "bbox": [
+            179,
+            82,
+            225,
+            95
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "header",
+        "text": "Which universities do the Turing Award winners in the field of deep learning work in?",
+        "bbox": [
+            305,
+            84,
+            880,
+            99
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "page_number",
+        "text": "13795",
+        "bbox": [
+            477,
+            927,
+            524,
+            941
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where  $X\\in [0,1]^{|\\mathcal{V}|\\times |\\mathcal{R}|\\times |\\mathcal{V}|}$  is the KG tensor and  $\\pmb {X}_{i,r,j}$  denotes the likelihood of a triplet  $(i,r,j)$  which is provided by the KGC model. We do not use product t-norm here because continued product often leads to accumulated errors for large  $d$  Compared to QTO (Bai et al., 2023), we define the projection operation and the complement operation separately, which make our method more flexible.",
+        "bbox": [
+            112,
+            82,
+            487,
+            212
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "In the training process, since the value of  $X_{i,r,j}$  is constantly changed, we need to recompute the value of  $X_{i,r,j}$ . The primary bottleneck of the projection operation is the computation. We can take the nonzero entries of  $e$  and multiply them with the corresponding entries in  $\\pmb{X}$  to get results. Thus, the computational complexity of projection operation is  $\\mathcal{O}(|\\mathcal{V}||\\{e_i|e_i > 0\\})$ .",
+        "bbox": [
+            110,
+            212,
+            485,
+            341
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "In the test process, since the value of  $X_{i,r,j}$  is fixed, we pre-compute the value of  $X_{i,r,j}$  to reduce the computation. The primary bottleneck of the projection operation is the memory consumption of tensor  $X$ .  $X$  contains  $|\\mathcal{V}|^2 |\\mathcal{R}|$  entries. Due to the sparsity of the KG, most entries of  $X$  have small values, which can be filtered to 0 by a threshold  $\\epsilon > 0$  while maintaining precision (Bai et al., 2023).",
+        "bbox": [
+            112,
+            342,
+            485,
+            470
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4.2 Calibration",
+        "text_level": 1,
+        "bbox": [
+            112,
+            482,
+            252,
+            495
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Upon establishing the four fuzzy set operations, the sole requirement for computing the results of queries is a calibrated KG tensor  $\\mathbf{X}$ . The entries of a calibrated KG tensor  $\\mathbf{X}$  are expected to fall within the range of 0 to 1, with values associated with true triplets approaching 1, and those linked to false triplets nearing 0. In the event of possessing a fully calibrated KG tensor  $\\mathbf{X}$ , accurate answers of queries can be attained through the utilization of the four fuzzy set operations.",
+        "bbox": [
+            112,
+            502,
+            485,
+            663
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "The KG tensor  $X$  is furnished by a KGC model, which defines a scoring function  $f(h,r,t)$  to measure the likelihood of a triplet  $(h,r,t)$ . The ranking metrics, MRR and H@N (Bordes et al., 2013), are commonly used to evaluate KGC models. For example, the definition of MRR is as follows:",
+        "bbox": [
+            112,
+            665,
+            487,
+            760
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathrm {M R R} = \\sum_ {(h, r, t) \\in \\mathcal {G}} \\frac {1}{| \\mathcal {G} |} \\frac {1}{\\operatorname {r a n k} (h , r , t)}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            174,
+            771,
+            425,
+            812
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where  $\\mathcal{G}$  is a dataset and  $\\mathrm{rank}(h,r,t)$  is the rank of tail entity  $t$  in the predicted list for the query  $(h,r,?)$ .  $\\mathrm{rank}(h,r,t)$  is computed based on the scoring function  $f(h,r,t)$ . The ranking metrics mainly focus on ranking rather than the specific numerical value of  $f(h,r,t)$ , which is important",
+        "bbox": [
+            112,
+            824,
+            487,
+            921
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "for complex query answering. Subsequently, an illustrative example is provided to elucidate this concept.",
+        "bbox": [
+            507,
+            84,
+            880,
+            131
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "For example, supposing we have a query",
+        "bbox": [
+            526,
+            133,
+            831,
+            148
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nq = V _ {?}: R _ {1} \\left(a _ {1}, V _ {?} \\right) \\wedge R _ {2} \\left(a _ {2}, V _ {?} \\right)\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            566,
+            161,
+            820,
+            177
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where entity  $a_1$  can be represented by a vector  $\\pmb{a}_1 = [1,0,0,0]$ , entity  $a_2$  can be represented by a vector  $\\pmb{a}_2 = [0,1,0,0]$ . Assuming the KG tensor  $\\pmb{X}$  is satisfied with  $\\pmb{X}_{1,1,:} = [0.6,0.4,0.2,0.1]$  and  $\\pmb{X}_{2,2,:} = [0.5,0.7,0.2,0.1]$ . Then, we have that  $\\mathcal{P}_1(\\pmb{a}_1) = \\pmb{X}_{1,1,:} = [0.6,0.4,0.2,0.1], \\mathcal{P}_2(\\pmb{a}_2) = \\pmb{X}_{2,2,:} = [0.5,0.7,0.2,0.1]$  and the predicted answers",
+        "bbox": [
+            507,
+            190,
+            882,
+            316
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {I} \\left(\\mathcal {P} _ {1} (\\boldsymbol {a} _ {1}), \\mathcal {P} _ {2} (\\boldsymbol {a} _ {2})\\right) = [ 0. 3 0, 0. 2 8, 0. 0 4, 0. 0 1 ]\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            524,
+            331,
+            862,
+            348
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Then the largest entry in  $\\mathcal{I}(\\mathcal{P}_1(\\pmb {a}_1),\\mathcal{P}_2(\\pmb {a}_2))$  is the first entry.",
+        "bbox": [
+            507,
+            359,
+            880,
+            391
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "If we let  $\\hat{\\pmb{X}}_{1,1,:} = 0.1\\pmb{X}_{1,1,:} + 0.1$  then we have that  $\\mathcal{P}_1(\\pmb {a}_1) = \\hat{\\pmb{X}}_{1,1,:} = [0.16,0.14,0.12,0.11],$ $\\mathcal{P}_2(\\pmb {a}_2) = \\pmb {X}_{2,2,:} = [0.5,0.7,0.2,0.1]$  and the predicted answers",
+        "bbox": [
+            507,
+            392,
+            882,
+            456
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {I} \\left(\\mathcal {P} _ {1} \\left(a _ {1}\\right), \\mathcal {P} _ {2} \\left(a _ {2}\\right)\\right) = [ 0. 0 8, 0. 0 9 8, 0. 0 2 4, 0. 0 1 1 ]\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            510,
+            469,
+            875,
+            486
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Then the largest entry in  $\\mathcal{I}(\\mathcal{P}_1(\\pmb {a}_1),\\mathcal{P}_2(\\pmb {a}_2))$  is the second entry.",
+        "bbox": [
+            507,
+            498,
+            880,
+            530
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "While the aforementioned transformation does not alter the ranking metrics of KGC models, it can affect the ranking metrics of CLQA models. Hence, it is imperative to calibrate the KGC models to acquire a calibrated KG tensor  $\\mathbf{X}$  for the CLQA task.",
+        "bbox": [
+            507,
+            531,
+            882,
+            625
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "We get a calibrated KG tensor  $X$  in the following steps:",
+        "bbox": [
+            507,
+            627,
+            882,
+            659
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "list",
+        "sub_type": "text",
+        "list_items": [
+            "1. We train a KGC model to get a scoring function  $f(h, r, t)$ .",
+            "2. We use softmax function to normalize  $f(h, r, t)$  and denote the new scoring function as  $\\hat{f}(h, r, t)$ ."
+        ],
+        "bbox": [
+            522,
+            670,
+            882,
+            760
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\begin{array}{l} \\hat {f} (h, r, t) = \\min  (N \\frac {\\exp (f (h , r , t))}{\\sum_ {t ^ {\\prime} = 1} ^ {| \\mathcal {V} |} \\exp (f (h , r , t ^ {\\prime}))}, 1) \\\\ N = \\left\\{ \\begin{array}{l l} M, & M > 0 \\\\ \\alpha , & M = 0 \\end{array} \\right. \\\\ M = \\left| \\left\\{\\left(h ^ {\\prime}, r ^ {\\prime}, t ^ {\\prime}\\right) \\in \\mathcal {G} _ {\\text {t r a i n}} \\mid h ^ {\\prime} = h, r ^ {\\prime} = r \\right\\} \\right| \\\\ \\end{array}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            544,
+            771,
+            889,
+            876
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where  $\\mathcal{G}_{\\mathrm{train}}$  denotes the training set of a KG and  $\\alpha \\geq 0$  is a hyper-parameter.",
+        "bbox": [
+            544,
+            889,
+            882,
+            921
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "page_number",
+        "text": "13796",
+        "bbox": [
+            477,
+            927,
+            524,
+            940
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "image",
+        "img_path": "images/85e5d918102b5af67835c2c142aa6e15690573589e670dd915af50ba949c3aa0.jpg",
+        "image_caption": [
+            "Figure 2: Fourteen types of queries used in the datasets, where \"p\" denotes relation projection, \"i\" denotes intersection, \"u\" denotes union, and \"n\" denotes negation."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            115,
+            84,
+            884,
+            240
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "3. We adapt the KGC models to complex queries datasets.",
+        "bbox": [
+            127,
+            321,
+            485,
+            351
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\tilde {f} (h, r, t) = \\min  (\\boldsymbol {W} _ {h, r} \\hat {f} (h, r, t), 1)\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            184,
+            362,
+            450,
+            381
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "where  $\\mathbf{W} \\in (0, +\\inf)^{|\\mathcal{V}| \\times |\\mathcal{R}|}$  is a parameter matrix. For a query-answer pair  $(q, [[q]])$ , where  $[[q]]$  denotes the set of answers of query  $q$ , we optimize  $\\mathbf{W}$  by the following loss function:",
+        "bbox": [
+            149,
+            390,
+            489,
+            470
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} = - \\frac {1}{| | [ q ] | |} \\sum_ {i \\in [ [ q ] ]} \\log \\boldsymbol {a} _ {i} - \\frac {1}{| | [ q ] | |} \\sum_ {i \\in [ [ q ] ]} \\log (1 - \\boldsymbol {a} _ {i})\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            149,
+            479,
+            495,
+            521
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "where  $\\pmb{a}$  is the vector representation of predicted answers.",
+        "bbox": [
+            149,
+            531,
+            489,
+            561
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "4. We replace the values of  $\\tilde{f}(h, r, t)$  with 1 for triplets  $(h, r, t) \\in \\mathcal{G}_{\\mathrm{train}} \\cup \\mathcal{G}_{\\mathrm{validation}}$  to get the calibrated tensor  $X$ , i.e.,",
+        "bbox": [
+            127,
+            571,
+            487,
+            620
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\boldsymbol {X} _ {h, r, t} =\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            163,
+            632,
+            235,
+            649
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\left\\{ \\begin{array}{l l} 1 & (h, r, t) \\in \\mathcal {G} _ {\\text {t r a i n}} \\cup \\mathcal {G} _ {\\text {v a l i d a t i o n}} \\\\ \\tilde {f} (h, r, t) & (h, r, t) \\notin \\mathcal {G} _ {\\text {t r a i n}} \\cup \\mathcal {G} _ {\\text {v a l i d a t i o n}} \\end{array} \\right.\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            166,
+            652,
+            472,
+            694
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "where  $\\mathcal{G}_{\\mathrm{validation}}$  denotes the validation set of a KG.",
+        "bbox": [
+            149,
+            702,
+            485,
+            733
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "The first step is to get a pre-train KGC model, which lays the foundation for subsequent steps. Although any KGC model is allowed, it is better to choose a KGC model with good performance.",
+        "bbox": [
+            112,
+            744,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "The second step is to normalize the scoring function  $f(h,r,t)$  provided by the first step, which can make the values of  $\\hat{f}(h,r,t)$  between 0 and 1, and the larger the value of  $f(h,r,t)$ , the larger the value of  $\\hat{f}(h,r,t)$ . A good property of softmax function is that it is invariant under translation transformation, i.e.,  $\\operatorname{softmax}(x + c) = \\operatorname{softmax}(x)$",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "for any  $c \\in \\mathbb{R}$ . The meaning of  $N$  is the number of answer tail entities for a query  $(h, r, ?)$ . As there can be multiple answer tail entities for a query  $(h, r, ?)$ , each of their corresponding predicted values should be close to 1. Thus, we multiply  $\\text{softmax}(f(h, r, t))$  by  $N$  to make it close to 1. The operation of taking the minimum value is to prevent the value from exceeding 1. The hyperparameter  $\\alpha$  is to prevent  $\\hat{f}(h, r, t)$  from becoming 0 for the case where  $M = 0$ .",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "The third step adapts the KGC models to CLQA datasets. Since the adaptation function, linear function, is a monotonically increasing function, the new scoring function  $\\tilde{f}(h,r,t)$  have the same results of KGC ranking metrics as  $f(h,r,t)$ . Thus, our method can improve the performance of CLQA while maintaining the evaluation results of KGC. This step is lightweight because the adaptation function is simple and only the parameter matrix  $\\mathbf{W}$  is optimized.",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "The fourth step replaces the value of  $\\tilde{f}(h, r, t)$  with 1 for known true triplets to get a calibrated KG tensor  $X$ . While evaluating KGC models, the known true triplets are not typically taken into account. Nonetheless, this step is crucial for CLQA as it ensures the calibration of the tensor  $X$  for better performance.",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "5 Experiments",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "5.1 Experimental Settings",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Datasets We evaluate our method on three popular knowledge graph datasets, including FB15k (Bordes et al., 2013), FB15k-237 (Toutanova et al., 2015), NELL995 (Xiong et al., 2017). We use the standard FOL queries generated in BetaE (Ren and Leskovec, 2020), consisting of 9",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "page_number",
+        "text": "13797",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "table",
+        "img_path": "images/88291a588ac3244be3c0c83f39b177c3bdc373d5f9d402e0f7d4ff44d90d22a3.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Models</td><td>avgp</td><td>avgn</td><td>1p</td><td>2p</td><td>3p</td><td>2i</td><td>3i</td><td>pi</td><td>ip</td><td>2u</td><td>up</td><td>2in</td><td>3in</td><td>inp</td><td>pin</td><td>pni</td></tr><tr><td colspan=\"17\">FB15k</td></tr><tr><td>GQE</td><td>28.0</td><td>-</td><td>54.6</td><td>15.3</td><td>10.8</td><td>39.7</td><td>51.4</td><td>27.6</td><td>19.1</td><td>22.1</td><td>11.6</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>Q2B</td><td>38.0</td><td>-</td><td>68.0</td><td>21.0</td><td>14.2</td><td>55.1</td><td>66.5</td><td>39.4</td><td>26.1</td><td>35.1</td><td>16.7</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>BetaE</td><td>41.6</td><td>11.8</td><td>65.1</td><td>25.7</td><td>24.7</td><td>55.8</td><td>66.5</td><td>43.9</td><td>28.1</td><td>40.1</td><td>25.2</td><td>14.3</td><td>14.7</td><td>11.5</td><td>6.5</td><td>12.4</td></tr><tr><td>ConE</td><td>49.8</td><td>14.8</td><td>73.3</td><td>33.8</td><td>29.2</td><td>64.4</td><td>73.7</td><td>50.9</td><td>35.7</td><td>55.7</td><td>31.4</td><td>17.9</td><td>18.7</td><td>12.5</td><td>9.8</td><td>15.1</td></tr><tr><td>GNN-QE</td><td>72.8</td><td>38.6</td><td>88.5</td><td>69.3</td><td>58.7</td><td>79.7</td><td>83.5</td><td>69.9</td><td>70.4</td><td>74.1</td><td>61.0</td><td>44.7</td><td>41.7</td><td>42.0</td><td>30.1</td><td>34.3</td></tr><tr><td>CQD-CO</td><td>46.9</td><td>-</td><td>89.2</td><td>25.3</td><td>13.4</td><td>74.4</td><td>78.3</td><td>44.1</td><td>33.2</td><td>41.8</td><td>21.9</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>CQD-Beam</td><td>58.2</td><td>-</td><td>89.2</td><td>54.3</td><td>28.6</td><td>74.4</td><td>78.3</td><td>58.2</td><td>67.7</td><td>42.4</td><td>30.9</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>CQDA</td><td>70.4</td><td>42.8</td><td>89.2</td><td>64.5</td><td>57.9</td><td>76.1</td><td>79.4</td><td>70.0</td><td>70.6</td><td>68.4</td><td>57.9</td><td>54.7</td><td>47.1</td><td>37.6</td><td>35.3</td><td>24.6</td></tr><tr><td>QTO</td><td>74.0</td><td>49.2</td><td>89.5</td><td>67.4</td><td>58.8</td><td>80.3</td><td>83.6</td><td>75.2</td><td>74.0</td><td>76.7</td><td>61.3</td><td>61.1</td><td>61.2</td><td>47.6</td><td>48.9</td><td>27.5</td></tr><tr><td>CKGR</td><td>80.6</td><td>71.0</td><td>89.9</td><td>76.5</td><td>72.8</td><td>84.6</td><td>88.1</td><td>82.1</td><td>80.4</td><td>78.7</td><td>72.1</td><td>75.0</td><td>74.3</td><td>62.6</td><td>70.7</td><td>72.5</td></tr><tr><td colspan=\"17\">FB15k-237</td></tr><tr><td>GQE</td><td>16.3</td><td>-</td><td>35.0</td><td>7.2</td><td>5.3</td><td>23.3</td><td>34.6</td><td>16.5</td><td>10.7</td><td>8.2</td><td>5.7</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>Q2B</td><td>20.1</td><td>-</td><td>40.6</td><td>9.4</td><td>6.8</td><td>29.5</td><td>42.3</td><td>21.2</td><td>12.6</td><td>11.3</td><td>7.6</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>BetaE</td><td>20.9</td><td>5.5</td><td>39.0</td><td>10.9</td><td>10.0</td><td>28.8</td><td>42.5</td><td>22.4</td><td>12.6</td><td>12.4</td><td>9.7</td><td>5.1</td><td>7.9</td><td>7.4</td><td>3.5</td><td>3.4</td></tr><tr><td>ConE</td><td>23.4</td><td>5.9</td><td>41.8</td><td>12.8</td><td>11.0</td><td>32.6</td><td>47.3</td><td>25.5</td><td>14.0</td><td>14.5</td><td>10.8</td><td>5.4</td><td>8.6</td><td>7.8</td><td>4.0</td><td>3.6</td></tr><tr><td>FuzzQE</td><td>24.0</td><td>7.8</td><td>42.8</td><td>12.9</td><td>10.3</td><td>33.3</td><td>46.9</td><td>26.9</td><td>17.8</td><td>14.6</td><td>10.3</td><td>8.5</td><td>11.6</td><td>7.8</td><td>5.2</td><td>5.8</td></tr><tr><td>GNN-QE</td><td>26.8</td><td>10.2</td><td>42.8</td><td>14.7</td><td>11.8</td><td>38.3</td><td>54.1</td><td>31.1</td><td>18.9</td><td>16.2</td><td>13.4</td><td>10.0</td><td>16.8</td><td>9.3</td><td>7.2</td><td>7.8</td></tr><tr><td>CQD-CO</td><td>21.8</td><td>-</td><td>46.7</td><td>9.5</td><td>6.3</td><td>31.2</td><td>40.6</td><td>23.6</td><td>16.0</td><td>14.5</td><td>8.2</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>CQD-Beam</td><td>22.3</td><td>-</td><td>46.7</td><td>11.6</td><td>8.0</td><td>31.2</td><td>40.6</td><td>21.2</td><td>18.7</td><td>14.6</td><td>8.4</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>CQDA</td><td>25.7</td><td>10.7</td><td>46.7</td><td>13.6</td><td>11.4</td><td>34.5</td><td>48.3</td><td>27.4</td><td>20.9</td><td>17.6</td><td>11.4</td><td>13.6</td><td>16.8</td><td>7.9</td><td>8.9</td><td>5.8</td></tr><tr><td>QTO</td><td>33.5</td><td>15.5</td><td>49.0</td><td>21.4</td><td>21.2</td><td>43.1</td><td>56.8</td><td>38.1</td><td>28.0</td><td>22.7</td><td>21.4</td><td>16.8</td><td>26.7</td><td>15.1</td><td>13.6</td><td>5.4</td></tr><tr><td>CKGR</td><td>34.8</td><td>25.3</td><td>49.2</td><td>22.3</td><td>22.3</td><td>45.1</td><td>60.3</td><td>40.3</td><td>29.1</td><td>22.9</td><td>22.0</td><td>23.9</td><td>37.5</td><td>21.0</td><td>23.2</td><td>21.2</td></tr><tr><td colspan=\"17\">NELL995</td></tr><tr><td>GQE</td><td>18.6</td><td>-</td><td>32.8</td><td>11.9</td><td>9.6</td><td>27.5</td><td>35.2</td><td>18.4</td><td>14.4</td><td>8.5</td><td>8.8</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>Q2B</td><td>22.9</td><td>-</td><td>42.2</td><td>14.0</td><td>11.2</td><td>33.3</td><td>44.5</td><td>22.4</td><td>16.8</td><td>11.3</td><td>10.3</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>BetaE</td><td>24.6</td><td>5.9</td><td>53.0</td><td>13.0</td><td>11.4</td><td>37.6</td><td>47.5</td><td>24.1</td><td>14.3</td><td>12.2</td><td>8.5</td><td>5.1</td><td>7.8</td><td>10.0</td><td>3.1</td><td>3.5</td></tr><tr><td>ConE</td><td>27.2</td><td>6.4</td><td>53.1</td><td>16.1</td><td>13.9</td><td>40.0</td><td>50.8</td><td>26.3</td><td>17.5</td><td>15.3</td><td>11.3</td><td>5.7</td><td>8.1</td><td>10.8</td><td>3.5</td><td>3.9</td></tr><tr><td>FuzzQE</td><td>27.0</td><td>7.8</td><td>47.4</td><td>17.2</td><td>14.6</td><td>39.5</td><td>49.2</td><td>26.2</td><td>20.6</td><td>15.3</td><td>12.6</td><td>7.8</td><td>9.8</td><td>11.1</td><td>4.9</td><td>5.5</td></tr><tr><td>GNN-QE</td><td>28.9</td><td>9.7</td><td>53.3</td><td>18.9</td><td>14.9</td><td>42.4</td><td>52.5</td><td>30.8</td><td>18.9</td><td>15.9</td><td>12.6</td><td>9.9</td><td>14.6</td><td>11.4</td><td>6.3</td><td>6.3</td></tr><tr><td>CQD-CO</td><td>28.8</td><td>-</td><td>60.4</td><td>17.8</td><td>12.7</td><td>39.3</td><td>46.6</td><td>30.1</td><td>22.0</td><td>17.3</td><td>13.2</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>CQD-Beam</td><td>28.6</td><td>-</td><td>60.4</td><td>20.6</td><td>11.6</td><td>39.3</td><td>46.6</td><td>25.4</td><td>23.9</td><td>17.5</td><td>12.2</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>CQDA</td><td>32.3</td><td>13.3</td><td>60.4</td><td>22.9</td><td>16.7</td><td>43.4</td><td>52.6</td><td>32.1</td><td>26.4</td><td>20.0</td><td>17.0</td><td>15.1</td><td>18.6</td><td>15.8</td><td>10.7</td><td>6.5</td></tr><tr><td>QTO</td><td>32.9</td><td>12.9</td><td>60.7</td><td>24.1</td><td>21.6</td><td>42.5</td><td>50.6</td><td>31.3</td><td>26.5</td><td>20.4</td><td>17.9</td><td>13.8</td><td>17.9</td><td>16.9</td><td>9.9</td><td>5.9</td></tr><tr><td>CKGR</td><td>35.3</td><td>19.9</td><td>61.4</td><td>25.7</td><td>24.1</td><td>45.8</td><td>58.8</td><td>33.9</td><td>29.2</td><td>20.5</td><td>18.7</td><td>19.8</td><td>27.5</td><td>20.4</td><td>17.4</td><td>14.6</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Table 1: Complex Query Answering results on FB15k, FB15k-237 and NELL995 test sets with MRR metrics. avg  ${}_{p}$  is the average on existential positive first-order queries. avg  ${}_{n}$  is the average on queries with negation.",
+        "bbox": [
+            112,
+            445,
+            880,
+            475
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "types of existential positive first-order queries (1p/2p/3p/2i/3i/pi/ip/2u/up) and 5 types of queries with negation (2in/3in/inp/pin/pni). Specifically, \"p\", \"i\", \"u\", and \"n\" stand for \"projection\", \"intersection\", \"union\", and 'negation' in the query structure, respectively. The query types are shown in Figure 2. During adaptation, we only use queries of type 1p, 2i, 3i, 2in and 3in of the training dataset to reduce computation.",
+        "bbox": [
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+            487,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Baselines We compare our method with state-of-the-art methods on complex query answering, query embedding methods, including GQE (Hamilton et al., 2018), Q2B (Ren et al., 2020), BetaE (Ren and Leskovec, 2020)), ConE (Zhang et al., 2021), FuzzQE (Chen et al., 2022), GNN-QE Zhu et al., 2022), complex query decomposition methods, including CQD-CO (Aragelyan et al., 2020), CQD-beam (Aragelyan et al., 2020) CQD (Aragelyan et al., 2023) and QTO (Bai et al., 2023).",
+        "bbox": [
+            112,
+            665,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Evaluation Metrics We adopt the evaluation framework introduced in BetaE (Ren and Leskovec, 2020), which involves categorizing the answers to each complex query into two distinct groups: easy answers and hard answers. For validation/test",
+        "bbox": [
+            112,
+            841,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "queries, easy answers refer to entities that can be reached by edges in training/validation graph, while hard answers are those that can only be inferred by predicting missing edges in the validation/test graph. We evaluate the method on complex queries by calculating the rank for each hard answer against non-answers and computing the mean reciprocal rank (MRR) (Bordes et al., 2013).",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Implementation Details For pre-train, our method can be incorporated with any KGC model. We select a state-of-the-art KGC model, ComplEx (Trouillon et al., 2017) trained with N3 regularization (Lacroix et al., 2018) and auxiliary relation prediction task (Chen et al., 2021). We choose the hyper-parameters with the best MRR on the validation set.",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "For training of CLQA, we train at most 5 epochs. For testing of CLQA, we pre-compute the KG tensor  $X$  to make our method achieve higher efficiency compared to previous query embedding methods (Bai et al., 2023). To save the memory usage of  $X$ , we select an appropriate  $\\epsilon$  such that after filtering all entries that less than  $\\epsilon$  can be stored on a single GPU.",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "page_number",
+        "text": "13798",
+        "bbox": [
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+    },
+    {
+        "type": "table",
+        "img_path": "images/64be0e39599c09b0d00a7763f528364d0e94480dbdbf99d2c42a465c862f8aa1.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Models</td><td>\\( avg_p \\)</td><td>\\( avg_n \\)</td><td>1p</td><td>2p</td><td>3p</td><td>2i</td><td>3i</td><td>pi</td><td>ip</td><td>2u</td><td>up</td><td>2in</td><td>3in</td><td>inp</td><td>pin</td><td>pni</td></tr><tr><td colspan=\"17\">FB15k</td></tr><tr><td>S12</td><td>78.1</td><td>29.5</td><td>89.9</td><td>73.9</td><td>68.0</td><td>82.2</td><td>84.9</td><td>78.0</td><td>77.0</td><td>78.7</td><td>70.0</td><td>33.8</td><td>34.3</td><td>31.7</td><td>23.7</td><td>23.8</td></tr><tr><td>S123</td><td>78.7</td><td>45.6</td><td>89.9</td><td>74.0</td><td>68.7</td><td>83.3</td><td>86.3</td><td>79.4</td><td>77.9</td><td>78.7</td><td>69.9</td><td>51.4</td><td>50.3</td><td>45.4</td><td>39.5</td><td>41.3</td></tr><tr><td>S1234</td><td>80.6</td><td>71.0</td><td>89.9</td><td>76.5</td><td>72.8</td><td>84.6</td><td>88.1</td><td>82.1</td><td>80.4</td><td>78.7</td><td>72.1</td><td>75.0</td><td>74.3</td><td>62.6</td><td>70.7</td><td>72.5</td></tr><tr><td colspan=\"17\">FB15k-237</td></tr><tr><td>S12</td><td>32.3</td><td>9.6</td><td>49.2</td><td>20.5</td><td>19.8</td><td>41.4</td><td>54.8</td><td>35.9</td><td>26.6</td><td>22.7</td><td>19.9</td><td>9.8</td><td>16.4</td><td>10.0</td><td>7.1</td><td>4.7</td></tr><tr><td>S123</td><td>32.9</td><td>15.7</td><td>49.2</td><td>20.9</td><td>20.4</td><td>42.2</td><td>56.5</td><td>37.1</td><td>26.9</td><td>22.4</td><td>20.2</td><td>15.8</td><td>25.4</td><td>14.1</td><td>12.9</td><td>10.2</td></tr><tr><td>S1234</td><td>34.8</td><td>25.3</td><td>49.2</td><td>22.3</td><td>22.3</td><td>45.1</td><td>60.3</td><td>40.3</td><td>29.1</td><td>22.9</td><td>22.0</td><td>23.9</td><td>37.5</td><td>21.0</td><td>23.2</td><td>21.2</td></tr><tr><td colspan=\"17\">NELL995</td></tr><tr><td>S12</td><td>32.8</td><td>7.3</td><td>61.4</td><td>23.4</td><td>20.9</td><td>42.5</td><td>51.0</td><td>31.8</td><td>26.4</td><td>20.4</td><td>17.6</td><td>7.4</td><td>9.9</td><td>9.9</td><td>4.6</td><td>4.4</td></tr><tr><td>S123</td><td>33.2</td><td>11.3</td><td>61.4</td><td>23.8</td><td>21.4</td><td>43.3</td><td>52.5</td><td>32.0</td><td>26.7</td><td>20.4</td><td>17.8</td><td>12.2</td><td>16.6</td><td>13.5</td><td>8.0</td><td>6.3</td></tr><tr><td>S1234</td><td>35.3</td><td>19.9</td><td>61.4</td><td>25.7</td><td>24.1</td><td>45.8</td><td>58.8</td><td>33.9</td><td>29.2</td><td>20.5</td><td>18.7</td><td>19.8</td><td>27.5</td><td>20.4</td><td>17.4</td><td>14.6</td></tr></table>",
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+    },
+    {
+        "type": "table",
+        "img_path": "images/1c88740cd3778120fb6921c8653b61fe528bcee5e5743d6accb2b9f4d609d291.jpg",
+        "table_caption": [
+            "Table 2: Complex Query Answering results on FB15k, FB15k-237 and NELL995 test sets with different settings."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>ε</td><td>0.05</td><td>0.01</td><td>0.005</td><td>0.001</td><td>0.0005</td><td>0.0001</td><td>0.00005</td><td>0.00001</td></tr><tr><td>Memory Usage</td><td>22M</td><td>60M</td><td>103M</td><td>383M</td><td>676M</td><td>2.77G</td><td>5.99G</td><td>Out of Memory</td></tr><tr><td>Sparsity Level</td><td>99.999%</td><td>99.997%</td><td>99.995%</td><td>99.980%</td><td>99.965%</td><td>99.851%</td><td>99.678%</td><td>-</td></tr><tr><td>Running Time</td><td>290s</td><td>311s</td><td>314s</td><td>348s</td><td>373s</td><td>482s</td><td>558s</td><td>-</td></tr><tr><td>avgp</td><td>27.9</td><td>32.0</td><td>32.9</td><td>34.0</td><td>34.3</td><td>34.7</td><td>34.8</td><td>-</td></tr><tr><td>avgn</td><td>24.5</td><td>25.2</td><td>25.3</td><td>25.3</td><td>25.3</td><td>25.3</td><td>25.3</td><td>-</td></tr></table>",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Table 3: Effect of  $\\epsilon$  on memory usage, sparsity level, and  $\\mathrm{avg}_p$  and  $\\mathrm{avg}_n$ . The experiments are conducted on FB15K-237 datasets. The time is the running time on one NVIDIA A40 GPU.",
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "5.2 Results",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "See Table 1 for the results.  $\\mathrm{avg}_p$  is the average on existential positive first-order queries.  $\\mathrm{avg}_n$  is the average on queries with negation. GQE, Q2B, CKGCO, and CQD-Beam do not support queries with negation, so the corresponding entries are empty. We observe that our model significantly outperforms baseline methods across all datasets. Our model yields a relative gain of  $6.8\\%$  and  $52.3\\%$  on  $\\mathrm{avg}_p$  and  $\\mathrm{avg}_n$  compared to previous state-of-the-art model QTO. This shows that our method has better reasoning skills and superior adaptability when tackling complex query answering tasks. We attribute this improvement to our calibration method, which can adapt the KGC models to answering complex queries very well.",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "The adaptation function of CKGC is simple, making the model quickly converge during the adaptation process. We next show the training time. The running time for FB15k dataset is an average of 67 seconds per epoch, the running time for FB15k -237 dataset is an average of 32 seconds per epoch, the running time for NELL995 dataset is an average of 83 seconds per epoch. All models can converge within 5 epochs, resulting in a very short training time. In contrast, previous embedding-based models, such as BetaE, ConE, FuzzQE, GNN-QE and so on, often require hundreds of epochs to converge. For instance, BetaE",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "takes 105 epochs to converge and has an average training running time of 63 seconds per epoch on the FB15k-237 dataset. Compared to our model (32 seconds x 2 epoch = 64 seconds), these models require significantly more runtime for training. The running time is the running time on one NVIDIA A40 GPU.",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "5.3 Ablation Studies",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "As stated in Section 4.2, we obtain a calibrated knowledge graph completion model by executing four steps. To analyze the impact of each step, we obtain calibrated models by performing only a few steps. We denote the calibrated model with steps 1 and 2 as S12, the model with steps 1, step 2, and step 3 as S123, and the model with steps 1, step 2, step 3, and step 4 as S1234. S12 primarily serves as a baseline. S123 is mainly used to study the impact of adaptation (step 3). S1234 is mainly used to study the impact of calibrating the predicted values corresponding to true triplets (step 4).",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "See Table 2 for the results. S123 has an average relative improvement of  $1.3\\%$  on  $\\mathrm{avg}_p$  metric compared to S12, and S1234 has an average relative improvement of  $4.8\\%$  on  $\\mathrm{avg}_p$  metric compared to S123. S123 has an average relative improvement of  $64.8\\%$  on  $\\mathrm{avg}_n$  metric compared to S12, and S1234 has an average relative improvement of  $64.3\\%$  on  $\\mathrm{avg}_n$  metric compared to S123.",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "page_number",
+        "text": "13799",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "The results show that the  $\\mathrm{avg}_n$  metric has been significantly improved. Since step 3 calibrates both predicted values corresponding to true triplets and predicted values corresponding to false triplets, we cannot determine from this step whether the main improvement on  $\\mathrm{avg}_n$  comes from the calibration for true triplets or false triplets. Since step 4 only changes the predicted values corresponding to the true triplets, this indicates that the significant improvement on  $\\mathrm{avg}_n$  is primarily due to the more accurate calibration of the predicted values corresponding to the true triplets.",
+        "bbox": [
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+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "5.4 Hyper-parameters Analysis",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "We analyze the experimental results of our method with respect to the hyper-parameter  $\\epsilon$ . We study the changes in memory usage, sparsity level (the ratio of zero entries in the KG tensor  $X$ ),  $\\mathrm{avg}_p$  and  $\\mathrm{avg}_n$  as  $\\epsilon$  decreases.",
+        "bbox": [
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "We show the results in Table 3, which show that as  $\\epsilon$  decreases, memory usage increases, sparsity level decreases, running time increases,  $\\mathrm{avg}_p$  increases, and  $\\mathrm{avg}_n$  increases. Thus, we can select a proper  $\\epsilon$  to balance the computation or memory usage and model performance.",
+        "bbox": [
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+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "6 Conclusion",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "CLQA is one of the crucial tasks associated with KGs. In this paper, we introduce CKGC, a calibration method developed to enhance the adaptability of KGC models for CLQA. Through experimental analysis, we illustrate that the implementation of CKGC leads to a substantial improvement in model performance for the CLQA task. Therefore, the calibration of KGC models holds significant importance for the optimization of CLQA models. Moving forward, we encourage the exploration and proposal of additional calibration methods to further enhance the performance of CLQA.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Limitations",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "One limitation of our method is the space complexity and time complexity of projection operation. We use an approach to make the predicted tensor  $\\mathbf{X}$  sparse. This approach can make the model performance decreases as shown in Table 3. We plan to explore methods that can reduce the computational complexity and memory usage of the method while maintaining good performance.",
+        "bbox": [
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Acknowledgements",
+        "text_level": 1,
+        "bbox": [
+            509,
+            84,
+            684,
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "This work is supported by the National Key Research and Development Program of China (2020AAA0106000), the National Natural Science Foundation of China (U19A2079), and the CCCD Key Lab of Ministry of Culture and Tourism.",
+        "bbox": [
+            507,
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "References",
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+        ],
+        "bbox": [
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+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "page_number",
+        "text": "13801",
+        "bbox": [
+            477,
+            928,
+            522,
+            940
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "A Appendix",
+        "text_level": 1,
+        "bbox": [
+            112,
+            84,
+            238,
+            99
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "A.1 Experimental Details",
+        "text_level": 1,
+        "bbox": [
+            112,
+            109,
+            329,
+            124
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Datasets The detailed statistics for each dataset can be seen in Table 4.",
+        "bbox": [
+            112,
+            130,
+            653,
+            143
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "table",
+        "img_path": "images/3347a0fc1f7bfe8a5c27c6d1958ceb3c1a4005e9fc573dbe6284666edee5db27.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Split</td><td>Query Types</td><td>FB15k</td><td>FB15k-237</td><td>NELL995</td></tr><tr><td rowspan=\"2\">Train</td><td>1p,2p,3p,2i,3i</td><td>273,710</td><td>149,689</td><td>107,982</td></tr><tr><td>2in, 3in, inp, pin, pni</td><td>27,371</td><td>14,968</td><td>10,798</td></tr><tr><td rowspan=\"2\">Validation</td><td>1p</td><td>59,078</td><td>20,094</td><td>16,910</td></tr><tr><td>Others</td><td>8,000</td><td>5,000</td><td>4,000</td></tr><tr><td rowspan=\"2\">Test</td><td>1p</td><td>66,990</td><td>22,804</td><td>17,021</td></tr><tr><td>Others</td><td>8,000</td><td>5,000</td><td>4,000</td></tr></table>",
+        "bbox": [
+            260,
+            154,
+            732,
+            269
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Hyper-parameters Settings Table 5 shows the best hyper-parameters we searched for pre-training KGC models. Table 6 shows the best hyper-parameters we searched for CLQA.",
+        "bbox": [
+            112,
+            326,
+            880,
+            357
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "table",
+        "img_path": "images/b2a6c0b2b43fe2b7081e30e7e4842bead437ea6cf3f464f9aae6c9e8568c5c58.jpg",
+        "table_caption": [
+            "Table 4: Detailed statistics on the different types of query structures in FB15K, FB15K-237, and NELL995 datasets."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Dataset</td><td>Dimension</td><td>Epoch</td><td>Batch Size</td><td>Learning Rate</td><td>λ1</td><td>λ2</td></tr><tr><td>FB15k</td><td>2000</td><td>200</td><td>1000</td><td>0.01</td><td>0.0625</td><td>0.005</td></tr><tr><td>FB15k-237</td><td>2000</td><td>200</td><td>1000</td><td>0.1</td><td>4</td><td>0.05</td></tr><tr><td>NELL995</td><td>2000</td><td>200</td><td>1000</td><td>0.1</td><td>0.0625</td><td>0.05</td></tr></table>",
+        "bbox": [
+            183,
+            369,
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+            451
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "table",
+        "img_path": "images/8b61c4c64ac3c72c45d3f1c161e95a7bb414e0abbc8e479a67aa1b683be64ecf.jpg",
+        "table_caption": [
+            "Table 5: The hyper-parameters settings for pre-training KGC models,  $\\lambda_{1}$  is the coefficient for relation prediction loss, and  $\\lambda_{2}$  is the coefficient for regularization."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Datset</td><td>Dimension</td><td>Epoch</td><td>Batch Size</td><td>Learning Rate</td><td>α</td><td>ε</td></tr><tr><td>FB15k</td><td>2000</td><td>5</td><td>1000</td><td>0.001</td><td>0.1</td><td>0.0005</td></tr><tr><td>FB15k-237</td><td>2000</td><td>5</td><td>1000</td><td>0.001</td><td>0.1</td><td>0.00005</td></tr><tr><td>NELL995</td><td>2000</td><td>5</td><td>1000</td><td>0.001</td><td>0.1</td><td>0.00001</td></tr></table>",
+        "bbox": [
+            186,
+            523,
+            811,
+            606
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Table 6: The hyper-parameters settings for CLQA.",
+        "bbox": [
+            324,
+            615,
+            668,
+            630
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Different KGC models Our proposed method CKGC is effective for any KGC model because it relies solely on the results predicted by the KGC model. Although any KGC model is permissible, it is preferable to select a KGC model with strong performance. In Table 7, we show the results of our method with different KGC models. We select the DistMult (Yang et al., 2014), CP (Lacroix et al., 2018), SimplE (Kazemi and Poole, 2018), and ComplEx (Trouillon et al., 2017) KGC models. The results demonstrate that Step 3 (the adaptation step) can indeed enhance performance across various KGC models.",
+        "bbox": [
+            112,
+            659,
+            884,
+            758
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "page_number",
+        "text": "13802",
+        "bbox": [
+            477,
+            927,
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+            940
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "table",
+        "img_path": "images/d47bce84c171f996d5c44731eac48786071a91bb22a4e64d492d91b99a85e502.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Models</td><td>1p</td><td>avgp(S12)</td><td>avgp(S123)</td><td>avgn(S12)</td><td>avgn(S123)</td></tr><tr><td>DistMult</td><td>47.6</td><td>30.2</td><td>30.8</td><td>9.1</td><td>14.7</td></tr><tr><td>CP</td><td>46.5</td><td>29.4</td><td>30.1</td><td>8.7</td><td>13.8</td></tr><tr><td>SimpleE</td><td>46.3</td><td>29.0</td><td>29.5</td><td>8.6</td><td>13.8</td></tr><tr><td>ComplEx</td><td>49.2</td><td>32.4</td><td>32.9</td><td>9.7</td><td>15.2</td></tr></table>",
+        "bbox": [
+            223,
+            419,
+            771,
+            519
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "Table 7: The performance of complex logical quereis answering models with different KGC model, where 1p is the KGC results,  $\\mathrm{avg}_p$  is the average results of queries without negation operator,  $\\mathrm{avg}_n$  is the average results of queries with negation operator. S12 is the model using direct KGC scores. S123 is the model with adaptation.",
+        "bbox": [
+            112,
+            527,
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+            571
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "page_number",
+        "text": "13803",
+        "bbox": [
+            477,
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+        ],
+        "page_idx": 11
+    }
+]

2024/Complex Logical Query Answering by Calibrating Knowledge Graph Completion Models/28987eca-6571-4ea4-b16a-06ab4319ecb4_origin.pdf

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2024/Complex Logical Query Answering by Calibrating Knowledge Graph Completion Models/full.md

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+# Complex Logical Query Answering by Calibrating Knowledge Graph Completion Models
+
+Changyi Xiao $^{1*}$ , Yixin Cao $^{2}$
+
+<sup>1</sup>School of Data Science, University of Science and Technology of China
+
+$^{2}$ School of Computer Science, Fudan University
+
+changyi@mail.ustc.edu.cn, caoyixin2011@gmail.com
+
+# Abstract
+
+Complex logical query answering (CLQA) is a challenging task that involves finding answer entities for complex logical queries over incomplete knowledge graphs (KGs). Previous research has explored the use of pre-trained knowledge graph completion (KGC) models, which can predict the missing facts in KGs, to answer complex logical queries. However, KGC models are typically evaluated using ranking evaluation metrics, which may result in values of predictions of KGC models that are not well-calibrated. In this paper, we propose a method for calibrating KGC models, namely CKGC, which enables KGC models to adapt to answering complex logical queries. Notably, CKGC is lightweight and effective. The adaptation function is simple, allowing the model to quickly converge during the adaptation process. The core concept of CKGC is to map the values of predictions of KGC models to the range [0, 1], ensuring that values associated with true facts are close to 1, while values linked to false facts are close to 0. Through experiments on three benchmark datasets, we demonstrate that our proposed calibration method can significantly boost model performance in the CLQA task. Moreover, our approach can enhance the performance of CLQA while preserving the ranking evaluation metrics of KGC models. The code is available at https://github.com/changyi7231/CKGC.
+
+# 1 Introduction
+
+Knowledge graphs (KGs) are composed of structured representations of facts in the form of triplets and have been widely used in various domains. One of the key tasks associated with KGs is complex logical query answering (Ren et al., 2023). Complex logical queries are typically expressed using first-order logic (FOL), which encompasses logical operations such as conjunction  $(\wedge)$ , disjunction  $(\lor)$ ,
+
+negation  $(\neg)$ , and existential quantifier  $(\exists)$ . For example, the query "Which universities do the Turing Award winners not in the field of deep learning work in?" can be formulated as a FOL query, as illustrated in Figure 1.
+
+Many well-known knowledge graphs (KGs) suffer from incompleteness, rendering it challenging to answer complex queries through simple KG traversal. Building on the accomplishments of knowledge graph completion (KGC) methods (Bordes et al., 2013; Sun et al., 2018; Trouillon et al., 2017) in addressing one-hop KG queries, a research avenue has emerged focusing on learning embeddings for queries to handle complex logical queries (Hamilton et al., 2018; Ren et al., 2020; Zhang et al., 2021). Nonetheless, these methodologies often require extensive training on numerous complex logical queries, leading to substantial training time overhead and limited generalization to out-of-distribution query structures.
+
+In addressing these challenges, CQD (Aragelyan et al., 2020) introduces a method for CLQA by leveraging one-hop atom results derived from a pretrained KGC model, thereby removing the necessity for training on complex queries. CQD frames CLQA as an optimization problem and employs techniques like beam search or continuous approximation to estimate the optimal solution. Despite its effectiveness, the approximations made during the process could lead to a decrease in accuracy for CQD. Furthermore, CQD is reliant on a KGC model whose values of output might not be specifically calibrated for CLQA, potentially resulting in inaccuracies in the outcomes.
+
+In this paper, we introduce a method for calibrating KGC models, namely CKGC, which can make KGC models adapt to handling complex logical queries. Our method is lightweight and effective. It is lightweight, as the adaptation function is simple and the model can quickly converge in adaptation process. Moreover, it is effective in significantly
+
+enhancing the performance of CLQA.
+
+We first represent every complex logical query as a computation graph over fuzzy sets, of which nodes represent fuzzy sets and edges represent the fuzzy set operations over fuzzy sets. To obtain the answers of a query, we traverse the computation graph and execute the fuzzy set operations through a straightforward forward propagation process, eliminating the need for optimization compared to CQD (Aragelyan et al., 2020). We define four fundamental fuzzy set operations for CLQA: projection operation, complement operation, intersection operation, and union operation, all of which require the KGC model to be calibrated.
+
+However, a KGC model is typically measured by the ranking metrics, which do not need it to be calibrated. Thus, we propose a calibration method for KGC models to make it adapted to CLQA. We define the adaptation function as a monotonically increasing function that preserves the ranking evaluation metrics of the KGC model. The main idea of our method is to map the values of output of a KGC model to the interval [0, 1], and makes the values corresponding to true triplets be as close as possible to 1, while the values corresponding to false triplets be as close as possible to 0.
+
+Our experimental evaluation on three standard datasets demonstrates the efficacy of CKGC in CLQA. The results reveal that CKGC achieves state-of-the-art performance across all datasets, showcasing an average relative improvement of  $6.7\%$  on existential positive first-order queries and  $53.9\%$  on negation queries compared to the prior state-of-the-art method.
+
+# 2 Related Work
+
+Knowledge Graph Completion The task of KGC involves predicting missing triplets within a knowledge graph, which can be viewed as predicting answers for one-hop queries. Various methodologies have been proposed to address this task, encompassing embedding techniques (Bordes et al., 2013; Sun et al., 2018; Trouillon et al., 2017), reinforcement learning approaches (Xiong et al., 2017; Das et al., 2018; Hildebrandt et al., 2020; Zhang et al., 2022), rule learning strategies (Yang et al., 2017; Sadeghian et al., 2019; Qu et al., 2020), and graph neural network methodologies (Schlichtkrull et al., 2018; Vashissth et al., 2019; Teru et al., 2020). Embedding methods aim to embed entities and relations into a continuous space and de
+
+fine a scoring function based on these embeddings. Reinforcement learning methods train an agent to explore the knowledge graph to predict the missing triplets. Rule learning methods adopt a distinct approach by initially identifying confident logical rules from the knowledge graph. These rules are then utilized to infer missing triplets. Lastly, graph neural network methods utilize graph neural networks to learn representations of entities and relations by leveraging the graph structure.
+
+Complex Logical Query Answering CLQA over KGs extends KGC to predict answers for FOL queries, which additionally requires defining relationships between sets of entities. Embedding-based methods represent sets of entities as geometric objects (Hamilton et al., 2018; Ren et al., 2020; Zhang et al., 2021) or probability distributions (Ren and Leskovec, 2020), and then minimize the distance between embeddings of queries and embeddings of their corresponding answers. However, the quality of representation of sets may be compromised when dealing with large sets. To overcome this limitation, some studies have incorporated powerful fuzzy set theory to handle FOL queries (Chen et al., 2022; Zhu et al., 2022). For instance, FuzzQE (Chen et al., 2022) embeds entities and queries into a fuzzy space and leverages fuzzy set operations to perform logical operations on the embeddings. Similarly, GNN-QE (Zhu et al., 2022) decomposes the query into relational projections operations and fuzzy set operations over fuzzy sets, and subsequently learns a graph neural network to execute relational projections.
+
+Nevertheless, the aforementioned methods generally necessitate training on numerous complex logical queries, resulting in significant training time overhead and limited generalization to out-of-distribution query structures. Another line of methods first pre-trains a KGC model and then integrates it with fuzzy set theory to infer answers. CQD (Aragelyan et al., 2020) formulates CLQA as an optimization problem and proposes two strategies to approximate the optimal solution: CQD-CO, which directly optimizes in the continuous space, and CQD-Beam, which utilizes beam search. Despite CQD avoiding the need to train on complex logical queries, it suffers from accuracy loss due to the approximated optimization and uncalibrated KGC models. To enhance accuracy, Bai et al. (2023) introduce QTO, which efficiently finds the theoretically optimal solution
+
+through a forward-backward propagation on a tree-like computation graph. Additionally, Arakelyan et al. (2023) propose  $\mathrm{CQD}^{\mathcal{A}}$ , a parameter-efficient adaptation method, to calibrate KGC models. However, the KGC model for QTO is not well calibrated for complex queries, and the optimal solution for  $\mathrm{CQD}^{\mathcal{A}}$  is still approximated. In contrast, our proposed model not only delivers accurate solutions but also effectively calibrates the KGC models.
+
+# 3 Background
+
+In this section, we introduce the related background of our method, complex logical query answering on knowledge graphs and fuzzy sets.
+
+# 3.1 Complex Logical Query Answering on Knowledge Graphs
+
+Knowledge Graphs Completion Given a set of entities  $\mathcal{V}$  and a set of relations  $\mathcal{R}$ , a knowledge graph  $\mathcal{G}$  contains a set of triplets  $\{(h,r,t)\} \subset \mathcal{V} \times \mathcal{R} \times \mathcal{V}$ , where each triplet is a fact from head entity  $h$  to tail entity  $t$  with a relation type  $r$ . KGC models define scoring functions  $f(h,r,t)$  to measure the likelihood of triplets  $(h,r,t)$  based on their corresponding embeddings.
+
+First-Order Logic Queries Complex logical queries can be represented by FOL queries with logical operations including conjunction  $(\wedge)$ , disjunction  $(\vee)$ , negation  $(\neg)$ , and existential quantifier  $(\exists)$ . A first-order logic query  $q$  can be described in its disjunctive normal form, which consists of a set of non-variable anchor entities  $\mathcal{V}_a \subseteq \mathcal{V}$ , existentially quantified bound variables  $V_1, \ldots, V_k$  and a single target variable  $V_\varphi$ , which provides the answers of query  $q$ . The disjunctive normal form of a logical query  $q$  is a disjunction of one or more conjunctions.
+
+$$
+q = V _ {j}. \exists V _ {1}, \dots , V _ {k}: c _ {1} \wedge c _ {2} \wedge , \dots , c _ {n}.
+$$
+
+Each  $c$  represents a conjunctive query with one or more literals  $e$ , i.e.,  $c_{i} = e_{i1} \lor e_{i2} \lor \dots \lor e_{im}$ . Each literal  $e$  represents an atomic formula or its negation, i.e.,  $e_{ij} = R(v_{a}, V)$  or  $\neg R(v_{a}, V)$  or  $\neg R(V', V)$  or  $\neg R(V', V)$ , where  $v_{a} \in \mathcal{V}_{a}$ ,  $V \in \{V?, V_{1}, \ldots, V_{k}\}$ ,  $V \in \{V?, V_{1}, \ldots, V_{k}\}$ ,  $V \neq V'$ ,  $R(\cdot, \cdot)$  is a binary function  $R: \mathcal{V} \times \mathcal{V} \to \{0, 1\}$ . Each relation  $r \in \mathcal{R}$  corresponds to a binary function  $R(\cdot, \cdot)$ . If  $(h, r, t)$  is a true fact, then  $R(h, t) = 1$ . If  $(h, r, t)$  is a false fact, then  $R(h, t) = 0$ .
+
+Computation Graph Given a FOL query, we can represent it as a computation graph, of which nodes represent sets of entities and edges represent set operations over sets of entities. The set operations include the complement operation, intersection operation, union operation and projection operation. The root node represents the set of answer entities. See Figure 1 for an example. We map logical operations to set operations according to the following rules.
+
+- Negation  $\longrightarrow$  Complement Operation: Given a set of entities  $S \subseteq \mathcal{V}$ , the complement operator performs set complement to obtain  $\overline{S} = \mathcal{V} \backslash S$ .  
+- Conjunction  $\longrightarrow$  Intersection Operation: Given  $n$  sets of entities  $\{S_1, S_2, \ldots, S_n\}$ , the intersection operator performs set intersection to obtain  $\cap_{i=1}^{n} S_i$ .  
+- Disjunction  $\longrightarrow$  Union Operation: Given  $n$  sets of entities  $\{S_1, S_2, \ldots, S_n\}$ , the union operator performs set union to obtain  $\cup_{i=1}^{n} S_i$ .  
+- Relation Projection  $\longrightarrow$  Projection Operation: Given a set of entities  $S \subseteq \mathcal{V}$  and a relation  $r \in \mathcal{R}$ , the projection operator outputs all the adjacent entities  $\cup_{v \in S} N(v, r)$ , where  $N(v, r)$  is the set of entities such that  $(v, r, v')$  are true triplets for all  $v' \in N(v, r)$ .
+
+In order to answer a given FOL query, we can traverse the computation graph and execute the set operations. The answers of a query can be obtained by looking at the set of entities in the root node.
+
+# 3.2 Fuzzy sets
+
+Definition A fuzzy set is a pair  $(U,m)$ , where  $U$  is a set and  $m:U\to [0,1]$  is a membership function. For each  $x\in U$ , the value  $m(x)$  measures the degree of membership of  $x$  in  $(U,m)$ . The function  $m = \mu_{A}$  is called the membership function of the fuzzy set  $A = (U,m)$ . Classical sets are seen as special cases of fuzzy sets, if the membership functions only takes values 0 or 1.
+
+Fuzzy Set Operations Fuzzy set operations are a generalization of classical set operations for fuzzy sets. The three primary fuzzy set operations are fuzzy complements, fuzzy intersections, and fuzzy unions. For a given fuzzy set  $A$ , its complement  $\overline{A}$  is commonly defined by the following membership
+
+First-Order Logic
+
+$q = V_{?}$ .  $\exists V$ : Win(V, Turing Award)  $\land$  Field(V, Deep Learning)  $\land$  University(V,  $V_{?}$ )
+
+Computation Graph
+
+![](images/021c170312635a28a4cfd923c9d9b6bdd3b3d37803dc2491944602777c1cfc1d.jpg)  
+Figure 1: An query, its corresponding FOL form and its corresponding computation graph.
+
+function:
+
+$$
+\forall x \in U, \mu_ {\overline {{A}}} (x) = 1 - \mu_ {A} (x)
+$$
+
+Given a pair of fuzzy sets  $A, B$ , their intersection  $A \cap B$  is defined by a t-norm  $T$  (Klement et al., 2004):
+
+$$
+\forall x \in U, \mu_ {A \cap B} (x) = T (\mu_ {A} (x), \mu_ {B} (x))
+$$
+
+Prominent examples of t-norms include product t-norm  $T(a,b) = ab$ , Gödel t-norm  $T(a,b) = \min \{a,b\}$  and so on (Klement et al., 2004). Given a t-norm  $T$  and a pair of fuzzy sets  $A, B$ , their union  $A \cup B$  is defined by De Morgan's law:
+
+$$
+\forall x \in U, \mu_ {A \cup B} (x) = 1 - T \left(1 - \mu_ {A} (x), 1 - \mu_ {B} (x)\right)
+$$
+
+# 4 Method
+
+We first define four fuzzy set operations over fuzzy sets in Section 4.1, and then propose a calibration method for KGC models in Section 4.2.
+
+# 4.1 Fuzzy Set Operations
+
+As demonstrated in Section 3.1, a query can be represented as a computation graph. To obtain the fuzzy sets of answers, it is necessary to define the fuzzy set operations utilized in computation graphs. These operations encompass the projection operation, intersection operation, union operation, and complement operation.
+
+We represent every fuzzy set of entities as a vector  $e \in [0,1]^d$ , where  $d = |\mathcal{V}|$  and  $e_i$  denotes the grade of membership of entity  $i$ . The anchor entity is represented by a vector with a single element set to 1 and all other elements set to 0.
+
+Complement Operation: The complement operation maps a fuzzy set to the complement of the fuzzy set. We define the complement operation as
+
+$$
+\mathcal {C}: [ 0, 1 ] ^ {d} \to [ 0, 1 ] ^ {d}
+$$
+
+$$
+\mathcal {C} (e) = \mathbf {1} - e
+$$
+
+Intersection Operation: The intersection operation maps several fuzzy sets into the intersection set of these fuzzy sets. We define the intersection operation by utilizing the product t-norm, which is as follows:
+
+$$
+\mathcal {I}: [ 0, 1 ] ^ {n d} \to [ 0, 1 ] ^ {d}
+$$
+
+$$
+\mathcal {I} \left(e ^ {1}, e ^ {2}, \dots , e ^ {n}\right) = e ^ {1} \odot e ^ {2} \odot \dots \odot e ^ {n}
+$$
+
+where  $\{e^i\in [0,1]^d |1\leq i\leq n\}$  are vector representations of fuzzy sets and  $\odot$  is the Hadamard product.
+
+Union Operation: The union operation maps several fuzzy sets into the union set of these fuzzy sets. Due to the De Morgan's Law, we do not need to define the union operation directly. We define the union operation by utilizing the intersection operation and complement operation as follows:
+
+$$
+\mathcal {U}: [ 0, 1 ] ^ {n d} \to [ 0, 1 ] ^ {d}
+$$
+
+$$
+\mathcal {U} \left(\boldsymbol {e} ^ {1}, \boldsymbol {e} ^ {2}, \dots , \boldsymbol {e} ^ {n}\right) = \mathcal {C} \left(\mathcal {I} \left(\mathcal {C} \left(\boldsymbol {e} ^ {1}\right), \mathcal {C} \left(\boldsymbol {e} ^ {2}\right), \dots , \mathcal {C} \left(\boldsymbol {e} ^ {n}\right)\right)\right)
+$$
+
+Projection Operation: The projection operation maps a fuzzy set into another fuzzy set with a relation type  $r$ . We implement the projection operation by utilizing the Gödel t-norm as follows:
+
+$$
+\begin{array}{l} \mathcal {P} _ {r}: [ 0, 1 ] ^ {d} \to [ 0, 1 ] ^ {d} \\ \mathcal{P}_{r}(\boldsymbol {e})_{j} = 1 - \min_{1\leq i\leq d}\bigl(1 - \boldsymbol{e}_{i}\boldsymbol{X}_{i,r,j}\bigr) \\ = \max  _ {1 \leq i \leq d} e _ {i} X _ {i, r, j} \\ \end{array}
+$$
+
+where  $X\in [0,1]^{|\mathcal{V}|\times |\mathcal{R}|\times |\mathcal{V}|}$  is the KG tensor and  $\pmb {X}_{i,r,j}$  denotes the likelihood of a triplet  $(i,r,j)$  which is provided by the KGC model. We do not use product t-norm here because continued product often leads to accumulated errors for large  $d$  Compared to QTO (Bai et al., 2023), we define the projection operation and the complement operation separately, which make our method more flexible.
+
+In the training process, since the value of  $X_{i,r,j}$  is constantly changed, we need to recompute the value of  $X_{i,r,j}$ . The primary bottleneck of the projection operation is the computation. We can take the nonzero entries of  $e$  and multiply them with the corresponding entries in  $\pmb{X}$  to get results. Thus, the computational complexity of projection operation is  $\mathcal{O}(|\mathcal{V}||\{e_i|e_i > 0\})$ .
+
+In the test process, since the value of  $X_{i,r,j}$  is fixed, we pre-compute the value of  $X_{i,r,j}$  to reduce the computation. The primary bottleneck of the projection operation is the memory consumption of tensor  $X$ .  $X$  contains  $|\mathcal{V}|^2 |\mathcal{R}|$  entries. Due to the sparsity of the KG, most entries of  $X$  have small values, which can be filtered to 0 by a threshold  $\epsilon > 0$  while maintaining precision (Bai et al., 2023).
+
+# 4.2 Calibration
+
+Upon establishing the four fuzzy set operations, the sole requirement for computing the results of queries is a calibrated KG tensor  $\mathbf{X}$ . The entries of a calibrated KG tensor  $\mathbf{X}$  are expected to fall within the range of 0 to 1, with values associated with true triplets approaching 1, and those linked to false triplets nearing 0. In the event of possessing a fully calibrated KG tensor  $\mathbf{X}$ , accurate answers of queries can be attained through the utilization of the four fuzzy set operations.
+
+The KG tensor  $X$  is furnished by a KGC model, which defines a scoring function  $f(h,r,t)$  to measure the likelihood of a triplet  $(h,r,t)$ . The ranking metrics, MRR and H@N (Bordes et al., 2013), are commonly used to evaluate KGC models. For example, the definition of MRR is as follows:
+
+$$
+\mathrm {M R R} = \sum_ {(h, r, t) \in \mathcal {G}} \frac {1}{| \mathcal {G} |} \frac {1}{\operatorname {r a n k} (h , r , t)}
+$$
+
+where  $\mathcal{G}$  is a dataset and  $\mathrm{rank}(h,r,t)$  is the rank of tail entity  $t$  in the predicted list for the query  $(h,r,?)$ .  $\mathrm{rank}(h,r,t)$  is computed based on the scoring function  $f(h,r,t)$ . The ranking metrics mainly focus on ranking rather than the specific numerical value of  $f(h,r,t)$ , which is important
+
+for complex query answering. Subsequently, an illustrative example is provided to elucidate this concept.
+
+For example, supposing we have a query
+
+$$
+q = V _ {?}: R _ {1} \left(a _ {1}, V _ {?} \right) \wedge R _ {2} \left(a _ {2}, V _ {?} \right)
+$$
+
+where entity  $a_1$  can be represented by a vector  $\pmb{a}_1 = [1,0,0,0]$ , entity  $a_2$  can be represented by a vector  $\pmb{a}_2 = [0,1,0,0]$ . Assuming the KG tensor  $\pmb{X}$  is satisfied with  $\pmb{X}_{1,1,:} = [0.6,0.4,0.2,0.1]$  and  $\pmb{X}_{2,2,:} = [0.5,0.7,0.2,0.1]$ . Then, we have that  $\mathcal{P}_1(\pmb{a}_1) = \pmb{X}_{1,1,:} = [0.6,0.4,0.2,0.1], \mathcal{P}_2(\pmb{a}_2) = \pmb{X}_{2,2,:} = [0.5,0.7,0.2,0.1]$  and the predicted answers
+
+$$
+\mathcal {I} \left(\mathcal {P} _ {1} (\boldsymbol {a} _ {1}), \mathcal {P} _ {2} (\boldsymbol {a} _ {2})\right) = [ 0. 3 0, 0. 2 8, 0. 0 4, 0. 0 1 ]
+$$
+
+Then the largest entry in  $\mathcal{I}(\mathcal{P}_1(\pmb {a}_1),\mathcal{P}_2(\pmb {a}_2))$  is the first entry.
+
+If we let  $\hat{\pmb{X}}_{1,1,:} = 0.1\pmb{X}_{1,1,:} + 0.1$  then we have that  $\mathcal{P}_1(\pmb {a}_1) = \hat{\pmb{X}}_{1,1,:} = [0.16,0.14,0.12,0.11],$ $\mathcal{P}_2(\pmb {a}_2) = \pmb {X}_{2,2,:} = [0.5,0.7,0.2,0.1]$  and the predicted answers
+
+$$
+\mathcal {I} \left(\mathcal {P} _ {1} \left(a _ {1}\right), \mathcal {P} _ {2} \left(a _ {2}\right)\right) = [ 0. 0 8, 0. 0 9 8, 0. 0 2 4, 0. 0 1 1 ]
+$$
+
+Then the largest entry in  $\mathcal{I}(\mathcal{P}_1(\pmb {a}_1),\mathcal{P}_2(\pmb {a}_2))$  is the second entry.
+
+While the aforementioned transformation does not alter the ranking metrics of KGC models, it can affect the ranking metrics of CLQA models. Hence, it is imperative to calibrate the KGC models to acquire a calibrated KG tensor  $\mathbf{X}$  for the CLQA task.
+
+We get a calibrated KG tensor  $X$  in the following steps:
+
+1. We train a KGC model to get a scoring function  $f(h, r, t)$ .  
+2. We use softmax function to normalize  $f(h, r, t)$  and denote the new scoring function as  $\hat{f}(h, r, t)$ .
+
+$$
+\begin{array}{l} \hat {f} (h, r, t) = \min  (N \frac {\exp (f (h , r , t))}{\sum_ {t ^ {\prime} = 1} ^ {| \mathcal {V} |} \exp (f (h , r , t ^ {\prime}))}, 1) \\ N = \left\{ \begin{array}{l l} M, & M > 0 \\ \alpha , & M = 0 \end{array} \right. \\ M = \left| \left\{\left(h ^ {\prime}, r ^ {\prime}, t ^ {\prime}\right) \in \mathcal {G} _ {\text {t r a i n}} \mid h ^ {\prime} = h, r ^ {\prime} = r \right\} \right| \\ \end{array}
+$$
+
+where  $\mathcal{G}_{\mathrm{train}}$  denotes the training set of a KG and  $\alpha \geq 0$  is a hyper-parameter.
+
+![](images/85e5d918102b5af67835c2c142aa6e15690573589e670dd915af50ba949c3aa0.jpg)  
+Figure 2: Fourteen types of queries used in the datasets, where "p" denotes relation projection, "i" denotes intersection, "u" denotes union, and "n" denotes negation.
+
+3. We adapt the KGC models to complex queries datasets.
+
+$$
+\tilde {f} (h, r, t) = \min  (\boldsymbol {W} _ {h, r} \hat {f} (h, r, t), 1)
+$$
+
+where  $\mathbf{W} \in (0, +\inf)^{|\mathcal{V}| \times |\mathcal{R}|}$  is a parameter matrix. For a query-answer pair  $(q, [[q]])$ , where  $[[q]]$  denotes the set of answers of query  $q$ , we optimize  $\mathbf{W}$  by the following loss function:
+
+$$
+\mathcal {L} = - \frac {1}{| | [ q ] | |} \sum_ {i \in [ [ q ] ]} \log \boldsymbol {a} _ {i} - \frac {1}{| | [ q ] | |} \sum_ {i \in [ [ q ] ]} \log (1 - \boldsymbol {a} _ {i})
+$$
+
+where  $\pmb{a}$  is the vector representation of predicted answers.
+
+4. We replace the values of  $\tilde{f}(h, r, t)$  with 1 for triplets  $(h, r, t) \in \mathcal{G}_{\mathrm{train}} \cup \mathcal{G}_{\mathrm{validation}}$  to get the calibrated tensor  $X$ , i.e.,
+
+$$
+\boldsymbol {X} _ {h, r, t} =
+$$
+
+$$
+\left\{ \begin{array}{l l} 1 & (h, r, t) \in \mathcal {G} _ {\text {t r a i n}} \cup \mathcal {G} _ {\text {v a l i d a t i o n}} \\ \tilde {f} (h, r, t) & (h, r, t) \notin \mathcal {G} _ {\text {t r a i n}} \cup \mathcal {G} _ {\text {v a l i d a t i o n}} \end{array} \right.
+$$
+
+where  $\mathcal{G}_{\mathrm{validation}}$  denotes the validation set of a KG.
+
+The first step is to get a pre-train KGC model, which lays the foundation for subsequent steps. Although any KGC model is allowed, it is better to choose a KGC model with good performance.
+
+The second step is to normalize the scoring function  $f(h,r,t)$  provided by the first step, which can make the values of  $\hat{f}(h,r,t)$  between 0 and 1, and the larger the value of  $f(h,r,t)$ , the larger the value of  $\hat{f}(h,r,t)$ . A good property of softmax function is that it is invariant under translation transformation, i.e.,  $\operatorname{softmax}(x + c) = \operatorname{softmax}(x)$
+
+for any  $c \in \mathbb{R}$ . The meaning of  $N$  is the number of answer tail entities for a query  $(h, r, ?)$ . As there can be multiple answer tail entities for a query  $(h, r, ?)$ , each of their corresponding predicted values should be close to 1. Thus, we multiply  $\text{softmax}(f(h, r, t))$  by  $N$  to make it close to 1. The operation of taking the minimum value is to prevent the value from exceeding 1. The hyperparameter  $\alpha$  is to prevent  $\hat{f}(h, r, t)$  from becoming 0 for the case where  $M = 0$ .
+
+The third step adapts the KGC models to CLQA datasets. Since the adaptation function, linear function, is a monotonically increasing function, the new scoring function  $\tilde{f}(h,r,t)$  have the same results of KGC ranking metrics as  $f(h,r,t)$ . Thus, our method can improve the performance of CLQA while maintaining the evaluation results of KGC. This step is lightweight because the adaptation function is simple and only the parameter matrix  $\mathbf{W}$  is optimized.
+
+The fourth step replaces the value of  $\tilde{f}(h, r, t)$  with 1 for known true triplets to get a calibrated KG tensor  $X$ . While evaluating KGC models, the known true triplets are not typically taken into account. Nonetheless, this step is crucial for CLQA as it ensures the calibration of the tensor  $X$  for better performance.
+
+# 5 Experiments
+
+# 5.1 Experimental Settings
+
+Datasets We evaluate our method on three popular knowledge graph datasets, including FB15k (Bordes et al., 2013), FB15k-237 (Toutanova et al., 2015), NELL995 (Xiong et al., 2017). We use the standard FOL queries generated in BetaE (Ren and Leskovec, 2020), consisting of 9
+
+<table><tr><td>Models</td><td>avgp</td><td>avgn</td><td>1p</td><td>2p</td><td>3p</td><td>2i</td><td>3i</td><td>pi</td><td>ip</td><td>2u</td><td>up</td><td>2in</td><td>3in</td><td>inp</td><td>pin</td><td>pni</td></tr><tr><td colspan="17">FB15k</td></tr><tr><td>GQE</td><td>28.0</td><td>-</td><td>54.6</td><td>15.3</td><td>10.8</td><td>39.7</td><td>51.4</td><td>27.6</td><td>19.1</td><td>22.1</td><td>11.6</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>Q2B</td><td>38.0</td><td>-</td><td>68.0</td><td>21.0</td><td>14.2</td><td>55.1</td><td>66.5</td><td>39.4</td><td>26.1</td><td>35.1</td><td>16.7</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>BetaE</td><td>41.6</td><td>11.8</td><td>65.1</td><td>25.7</td><td>24.7</td><td>55.8</td><td>66.5</td><td>43.9</td><td>28.1</td><td>40.1</td><td>25.2</td><td>14.3</td><td>14.7</td><td>11.5</td><td>6.5</td><td>12.4</td></tr><tr><td>ConE</td><td>49.8</td><td>14.8</td><td>73.3</td><td>33.8</td><td>29.2</td><td>64.4</td><td>73.7</td><td>50.9</td><td>35.7</td><td>55.7</td><td>31.4</td><td>17.9</td><td>18.7</td><td>12.5</td><td>9.8</td><td>15.1</td></tr><tr><td>GNN-QE</td><td>72.8</td><td>38.6</td><td>88.5</td><td>69.3</td><td>58.7</td><td>79.7</td><td>83.5</td><td>69.9</td><td>70.4</td><td>74.1</td><td>61.0</td><td>44.7</td><td>41.7</td><td>42.0</td><td>30.1</td><td>34.3</td></tr><tr><td>CQD-CO</td><td>46.9</td><td>-</td><td>89.2</td><td>25.3</td><td>13.4</td><td>74.4</td><td>78.3</td><td>44.1</td><td>33.2</td><td>41.8</td><td>21.9</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>CQD-Beam</td><td>58.2</td><td>-</td><td>89.2</td><td>54.3</td><td>28.6</td><td>74.4</td><td>78.3</td><td>58.2</td><td>67.7</td><td>42.4</td><td>30.9</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>CQDA</td><td>70.4</td><td>42.8</td><td>89.2</td><td>64.5</td><td>57.9</td><td>76.1</td><td>79.4</td><td>70.0</td><td>70.6</td><td>68.4</td><td>57.9</td><td>54.7</td><td>47.1</td><td>37.6</td><td>35.3</td><td>24.6</td></tr><tr><td>QTO</td><td>74.0</td><td>49.2</td><td>89.5</td><td>67.4</td><td>58.8</td><td>80.3</td><td>83.6</td><td>75.2</td><td>74.0</td><td>76.7</td><td>61.3</td><td>61.1</td><td>61.2</td><td>47.6</td><td>48.9</td><td>27.5</td></tr><tr><td>CKGR</td><td>80.6</td><td>71.0</td><td>89.9</td><td>76.5</td><td>72.8</td><td>84.6</td><td>88.1</td><td>82.1</td><td>80.4</td><td>78.7</td><td>72.1</td><td>75.0</td><td>74.3</td><td>62.6</td><td>70.7</td><td>72.5</td></tr><tr><td colspan="17">FB15k-237</td></tr><tr><td>GQE</td><td>16.3</td><td>-</td><td>35.0</td><td>7.2</td><td>5.3</td><td>23.3</td><td>34.6</td><td>16.5</td><td>10.7</td><td>8.2</td><td>5.7</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>Q2B</td><td>20.1</td><td>-</td><td>40.6</td><td>9.4</td><td>6.8</td><td>29.5</td><td>42.3</td><td>21.2</td><td>12.6</td><td>11.3</td><td>7.6</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>BetaE</td><td>20.9</td><td>5.5</td><td>39.0</td><td>10.9</td><td>10.0</td><td>28.8</td><td>42.5</td><td>22.4</td><td>12.6</td><td>12.4</td><td>9.7</td><td>5.1</td><td>7.9</td><td>7.4</td><td>3.5</td><td>3.4</td></tr><tr><td>ConE</td><td>23.4</td><td>5.9</td><td>41.8</td><td>12.8</td><td>11.0</td><td>32.6</td><td>47.3</td><td>25.5</td><td>14.0</td><td>14.5</td><td>10.8</td><td>5.4</td><td>8.6</td><td>7.8</td><td>4.0</td><td>3.6</td></tr><tr><td>FuzzQE</td><td>24.0</td><td>7.8</td><td>42.8</td><td>12.9</td><td>10.3</td><td>33.3</td><td>46.9</td><td>26.9</td><td>17.8</td><td>14.6</td><td>10.3</td><td>8.5</td><td>11.6</td><td>7.8</td><td>5.2</td><td>5.8</td></tr><tr><td>GNN-QE</td><td>26.8</td><td>10.2</td><td>42.8</td><td>14.7</td><td>11.8</td><td>38.3</td><td>54.1</td><td>31.1</td><td>18.9</td><td>16.2</td><td>13.4</td><td>10.0</td><td>16.8</td><td>9.3</td><td>7.2</td><td>7.8</td></tr><tr><td>CQD-CO</td><td>21.8</td><td>-</td><td>46.7</td><td>9.5</td><td>6.3</td><td>31.2</td><td>40.6</td><td>23.6</td><td>16.0</td><td>14.5</td><td>8.2</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>CQD-Beam</td><td>22.3</td><td>-</td><td>46.7</td><td>11.6</td><td>8.0</td><td>31.2</td><td>40.6</td><td>21.2</td><td>18.7</td><td>14.6</td><td>8.4</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>CQDA</td><td>25.7</td><td>10.7</td><td>46.7</td><td>13.6</td><td>11.4</td><td>34.5</td><td>48.3</td><td>27.4</td><td>20.9</td><td>17.6</td><td>11.4</td><td>13.6</td><td>16.8</td><td>7.9</td><td>8.9</td><td>5.8</td></tr><tr><td>QTO</td><td>33.5</td><td>15.5</td><td>49.0</td><td>21.4</td><td>21.2</td><td>43.1</td><td>56.8</td><td>38.1</td><td>28.0</td><td>22.7</td><td>21.4</td><td>16.8</td><td>26.7</td><td>15.1</td><td>13.6</td><td>5.4</td></tr><tr><td>CKGR</td><td>34.8</td><td>25.3</td><td>49.2</td><td>22.3</td><td>22.3</td><td>45.1</td><td>60.3</td><td>40.3</td><td>29.1</td><td>22.9</td><td>22.0</td><td>23.9</td><td>37.5</td><td>21.0</td><td>23.2</td><td>21.2</td></tr><tr><td colspan="17">NELL995</td></tr><tr><td>GQE</td><td>18.6</td><td>-</td><td>32.8</td><td>11.9</td><td>9.6</td><td>27.5</td><td>35.2</td><td>18.4</td><td>14.4</td><td>8.5</td><td>8.8</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>Q2B</td><td>22.9</td><td>-</td><td>42.2</td><td>14.0</td><td>11.2</td><td>33.3</td><td>44.5</td><td>22.4</td><td>16.8</td><td>11.3</td><td>10.3</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>BetaE</td><td>24.6</td><td>5.9</td><td>53.0</td><td>13.0</td><td>11.4</td><td>37.6</td><td>47.5</td><td>24.1</td><td>14.3</td><td>12.2</td><td>8.5</td><td>5.1</td><td>7.8</td><td>10.0</td><td>3.1</td><td>3.5</td></tr><tr><td>ConE</td><td>27.2</td><td>6.4</td><td>53.1</td><td>16.1</td><td>13.9</td><td>40.0</td><td>50.8</td><td>26.3</td><td>17.5</td><td>15.3</td><td>11.3</td><td>5.7</td><td>8.1</td><td>10.8</td><td>3.5</td><td>3.9</td></tr><tr><td>FuzzQE</td><td>27.0</td><td>7.8</td><td>47.4</td><td>17.2</td><td>14.6</td><td>39.5</td><td>49.2</td><td>26.2</td><td>20.6</td><td>15.3</td><td>12.6</td><td>7.8</td><td>9.8</td><td>11.1</td><td>4.9</td><td>5.5</td></tr><tr><td>GNN-QE</td><td>28.9</td><td>9.7</td><td>53.3</td><td>18.9</td><td>14.9</td><td>42.4</td><td>52.5</td><td>30.8</td><td>18.9</td><td>15.9</td><td>12.6</td><td>9.9</td><td>14.6</td><td>11.4</td><td>6.3</td><td>6.3</td></tr><tr><td>CQD-CO</td><td>28.8</td><td>-</td><td>60.4</td><td>17.8</td><td>12.7</td><td>39.3</td><td>46.6</td><td>30.1</td><td>22.0</td><td>17.3</td><td>13.2</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>CQD-Beam</td><td>28.6</td><td>-</td><td>60.4</td><td>20.6</td><td>11.6</td><td>39.3</td><td>46.6</td><td>25.4</td><td>23.9</td><td>17.5</td><td>12.2</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>CQDA</td><td>32.3</td><td>13.3</td><td>60.4</td><td>22.9</td><td>16.7</td><td>43.4</td><td>52.6</td><td>32.1</td><td>26.4</td><td>20.0</td><td>17.0</td><td>15.1</td><td>18.6</td><td>15.8</td><td>10.7</td><td>6.5</td></tr><tr><td>QTO</td><td>32.9</td><td>12.9</td><td>60.7</td><td>24.1</td><td>21.6</td><td>42.5</td><td>50.6</td><td>31.3</td><td>26.5</td><td>20.4</td><td>17.9</td><td>13.8</td><td>17.9</td><td>16.9</td><td>9.9</td><td>5.9</td></tr><tr><td>CKGR</td><td>35.3</td><td>19.9</td><td>61.4</td><td>25.7</td><td>24.1</td><td>45.8</td><td>58.8</td><td>33.9</td><td>29.2</td><td>20.5</td><td>18.7</td><td>19.8</td><td>27.5</td><td>20.4</td><td>17.4</td><td>14.6</td></tr></table>
+
+Table 1: Complex Query Answering results on FB15k, FB15k-237 and NELL995 test sets with MRR metrics. avg  ${}_{p}$  is the average on existential positive first-order queries. avg  ${}_{n}$  is the average on queries with negation.
+
+types of existential positive first-order queries (1p/2p/3p/2i/3i/pi/ip/2u/up) and 5 types of queries with negation (2in/3in/inp/pin/pni). Specifically, "p", "i", "u", and "n" stand for "projection", "intersection", "union", and 'negation' in the query structure, respectively. The query types are shown in Figure 2. During adaptation, we only use queries of type 1p, 2i, 3i, 2in and 3in of the training dataset to reduce computation.
+
+Baselines We compare our method with state-of-the-art methods on complex query answering, query embedding methods, including GQE (Hamilton et al., 2018), Q2B (Ren et al., 2020), BetaE (Ren and Leskovec, 2020)), ConE (Zhang et al., 2021), FuzzQE (Chen et al., 2022), GNN-QE Zhu et al., 2022), complex query decomposition methods, including CQD-CO (Aragelyan et al., 2020), CQD-beam (Aragelyan et al., 2020) CQD (Aragelyan et al., 2023) and QTO (Bai et al., 2023).
+
+Evaluation Metrics We adopt the evaluation framework introduced in BetaE (Ren and Leskovec, 2020), which involves categorizing the answers to each complex query into two distinct groups: easy answers and hard answers. For validation/test
+
+queries, easy answers refer to entities that can be reached by edges in training/validation graph, while hard answers are those that can only be inferred by predicting missing edges in the validation/test graph. We evaluate the method on complex queries by calculating the rank for each hard answer against non-answers and computing the mean reciprocal rank (MRR) (Bordes et al., 2013).
+
+Implementation Details For pre-train, our method can be incorporated with any KGC model. We select a state-of-the-art KGC model, ComplEx (Trouillon et al., 2017) trained with N3 regularization (Lacroix et al., 2018) and auxiliary relation prediction task (Chen et al., 2021). We choose the hyper-parameters with the best MRR on the validation set.
+
+For training of CLQA, we train at most 5 epochs. For testing of CLQA, we pre-compute the KG tensor  $X$  to make our method achieve higher efficiency compared to previous query embedding methods (Bai et al., 2023). To save the memory usage of  $X$ , we select an appropriate  $\epsilon$  such that after filtering all entries that less than  $\epsilon$  can be stored on a single GPU.
+
+<table><tr><td>Models</td><td>\( avg_p \)</td><td>\( avg_n \)</td><td>1p</td><td>2p</td><td>3p</td><td>2i</td><td>3i</td><td>pi</td><td>ip</td><td>2u</td><td>up</td><td>2in</td><td>3in</td><td>inp</td><td>pin</td><td>pni</td></tr><tr><td colspan="17">FB15k</td></tr><tr><td>S12</td><td>78.1</td><td>29.5</td><td>89.9</td><td>73.9</td><td>68.0</td><td>82.2</td><td>84.9</td><td>78.0</td><td>77.0</td><td>78.7</td><td>70.0</td><td>33.8</td><td>34.3</td><td>31.7</td><td>23.7</td><td>23.8</td></tr><tr><td>S123</td><td>78.7</td><td>45.6</td><td>89.9</td><td>74.0</td><td>68.7</td><td>83.3</td><td>86.3</td><td>79.4</td><td>77.9</td><td>78.7</td><td>69.9</td><td>51.4</td><td>50.3</td><td>45.4</td><td>39.5</td><td>41.3</td></tr><tr><td>S1234</td><td>80.6</td><td>71.0</td><td>89.9</td><td>76.5</td><td>72.8</td><td>84.6</td><td>88.1</td><td>82.1</td><td>80.4</td><td>78.7</td><td>72.1</td><td>75.0</td><td>74.3</td><td>62.6</td><td>70.7</td><td>72.5</td></tr><tr><td colspan="17">FB15k-237</td></tr><tr><td>S12</td><td>32.3</td><td>9.6</td><td>49.2</td><td>20.5</td><td>19.8</td><td>41.4</td><td>54.8</td><td>35.9</td><td>26.6</td><td>22.7</td><td>19.9</td><td>9.8</td><td>16.4</td><td>10.0</td><td>7.1</td><td>4.7</td></tr><tr><td>S123</td><td>32.9</td><td>15.7</td><td>49.2</td><td>20.9</td><td>20.4</td><td>42.2</td><td>56.5</td><td>37.1</td><td>26.9</td><td>22.4</td><td>20.2</td><td>15.8</td><td>25.4</td><td>14.1</td><td>12.9</td><td>10.2</td></tr><tr><td>S1234</td><td>34.8</td><td>25.3</td><td>49.2</td><td>22.3</td><td>22.3</td><td>45.1</td><td>60.3</td><td>40.3</td><td>29.1</td><td>22.9</td><td>22.0</td><td>23.9</td><td>37.5</td><td>21.0</td><td>23.2</td><td>21.2</td></tr><tr><td colspan="17">NELL995</td></tr><tr><td>S12</td><td>32.8</td><td>7.3</td><td>61.4</td><td>23.4</td><td>20.9</td><td>42.5</td><td>51.0</td><td>31.8</td><td>26.4</td><td>20.4</td><td>17.6</td><td>7.4</td><td>9.9</td><td>9.9</td><td>4.6</td><td>4.4</td></tr><tr><td>S123</td><td>33.2</td><td>11.3</td><td>61.4</td><td>23.8</td><td>21.4</td><td>43.3</td><td>52.5</td><td>32.0</td><td>26.7</td><td>20.4</td><td>17.8</td><td>12.2</td><td>16.6</td><td>13.5</td><td>8.0</td><td>6.3</td></tr><tr><td>S1234</td><td>35.3</td><td>19.9</td><td>61.4</td><td>25.7</td><td>24.1</td><td>45.8</td><td>58.8</td><td>33.9</td><td>29.2</td><td>20.5</td><td>18.7</td><td>19.8</td><td>27.5</td><td>20.4</td><td>17.4</td><td>14.6</td></tr></table>
+
+Table 2: Complex Query Answering results on FB15k, FB15k-237 and NELL995 test sets with different settings.  
+
+<table><tr><td>ε</td><td>0.05</td><td>0.01</td><td>0.005</td><td>0.001</td><td>0.0005</td><td>0.0001</td><td>0.00005</td><td>0.00001</td></tr><tr><td>Memory Usage</td><td>22M</td><td>60M</td><td>103M</td><td>383M</td><td>676M</td><td>2.77G</td><td>5.99G</td><td>Out of Memory</td></tr><tr><td>Sparsity Level</td><td>99.999%</td><td>99.997%</td><td>99.995%</td><td>99.980%</td><td>99.965%</td><td>99.851%</td><td>99.678%</td><td>-</td></tr><tr><td>Running Time</td><td>290s</td><td>311s</td><td>314s</td><td>348s</td><td>373s</td><td>482s</td><td>558s</td><td>-</td></tr><tr><td>avgp</td><td>27.9</td><td>32.0</td><td>32.9</td><td>34.0</td><td>34.3</td><td>34.7</td><td>34.8</td><td>-</td></tr><tr><td>avgn</td><td>24.5</td><td>25.2</td><td>25.3</td><td>25.3</td><td>25.3</td><td>25.3</td><td>25.3</td><td>-</td></tr></table>
+
+Table 3: Effect of  $\epsilon$  on memory usage, sparsity level, and  $\mathrm{avg}_p$  and  $\mathrm{avg}_n$ . The experiments are conducted on FB15K-237 datasets. The time is the running time on one NVIDIA A40 GPU.
+
+# 5.2 Results
+
+See Table 1 for the results.  $\mathrm{avg}_p$  is the average on existential positive first-order queries.  $\mathrm{avg}_n$  is the average on queries with negation. GQE, Q2B, CKGCO, and CQD-Beam do not support queries with negation, so the corresponding entries are empty. We observe that our model significantly outperforms baseline methods across all datasets. Our model yields a relative gain of  $6.8\%$  and  $52.3\%$  on  $\mathrm{avg}_p$  and  $\mathrm{avg}_n$  compared to previous state-of-the-art model QTO. This shows that our method has better reasoning skills and superior adaptability when tackling complex query answering tasks. We attribute this improvement to our calibration method, which can adapt the KGC models to answering complex queries very well.
+
+The adaptation function of CKGC is simple, making the model quickly converge during the adaptation process. We next show the training time. The running time for FB15k dataset is an average of 67 seconds per epoch, the running time for FB15k -237 dataset is an average of 32 seconds per epoch, the running time for NELL995 dataset is an average of 83 seconds per epoch. All models can converge within 5 epochs, resulting in a very short training time. In contrast, previous embedding-based models, such as BetaE, ConE, FuzzQE, GNN-QE and so on, often require hundreds of epochs to converge. For instance, BetaE
+
+takes 105 epochs to converge and has an average training running time of 63 seconds per epoch on the FB15k-237 dataset. Compared to our model (32 seconds x 2 epoch = 64 seconds), these models require significantly more runtime for training. The running time is the running time on one NVIDIA A40 GPU.
+
+# 5.3 Ablation Studies
+
+As stated in Section 4.2, we obtain a calibrated knowledge graph completion model by executing four steps. To analyze the impact of each step, we obtain calibrated models by performing only a few steps. We denote the calibrated model with steps 1 and 2 as S12, the model with steps 1, step 2, and step 3 as S123, and the model with steps 1, step 2, step 3, and step 4 as S1234. S12 primarily serves as a baseline. S123 is mainly used to study the impact of adaptation (step 3). S1234 is mainly used to study the impact of calibrating the predicted values corresponding to true triplets (step 4).
+
+See Table 2 for the results. S123 has an average relative improvement of  $1.3\%$  on  $\mathrm{avg}_p$  metric compared to S12, and S1234 has an average relative improvement of  $4.8\%$  on  $\mathrm{avg}_p$  metric compared to S123. S123 has an average relative improvement of  $64.8\%$  on  $\mathrm{avg}_n$  metric compared to S12, and S1234 has an average relative improvement of  $64.3\%$  on  $\mathrm{avg}_n$  metric compared to S123.
+
+The results show that the  $\mathrm{avg}_n$  metric has been significantly improved. Since step 3 calibrates both predicted values corresponding to true triplets and predicted values corresponding to false triplets, we cannot determine from this step whether the main improvement on  $\mathrm{avg}_n$  comes from the calibration for true triplets or false triplets. Since step 4 only changes the predicted values corresponding to the true triplets, this indicates that the significant improvement on  $\mathrm{avg}_n$  is primarily due to the more accurate calibration of the predicted values corresponding to the true triplets.
+
+# 5.4 Hyper-parameters Analysis
+
+We analyze the experimental results of our method with respect to the hyper-parameter  $\epsilon$ . We study the changes in memory usage, sparsity level (the ratio of zero entries in the KG tensor  $X$ ),  $\mathrm{avg}_p$  and  $\mathrm{avg}_n$  as  $\epsilon$  decreases.
+
+We show the results in Table 3, which show that as  $\epsilon$  decreases, memory usage increases, sparsity level decreases, running time increases,  $\mathrm{avg}_p$  increases, and  $\mathrm{avg}_n$  increases. Thus, we can select a proper  $\epsilon$  to balance the computation or memory usage and model performance.
+
+# 6 Conclusion
+
+CLQA is one of the crucial tasks associated with KGs. In this paper, we introduce CKGC, a calibration method developed to enhance the adaptability of KGC models for CLQA. Through experimental analysis, we illustrate that the implementation of CKGC leads to a substantial improvement in model performance for the CLQA task. Therefore, the calibration of KGC models holds significant importance for the optimization of CLQA models. Moving forward, we encourage the exploration and proposal of additional calibration methods to further enhance the performance of CLQA.
+
+# Limitations
+
+One limitation of our method is the space complexity and time complexity of projection operation. We use an approach to make the predicted tensor  $\mathbf{X}$  sparse. This approach can make the model performance decreases as shown in Table 3. We plan to explore methods that can reduce the computational complexity and memory usage of the method while maintaining good performance.
+
+# Acknowledgements
+
+This work is supported by the National Key Research and Development Program of China (2020AAA0106000), the National Natural Science Foundation of China (U19A2079), and the CCCD Key Lab of Ministry of Culture and Tourism.
+
+# References
+
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+Komal Teru, Etienne Denis, and Will Hamilton. 2020. Inductive relation prediction by subgraph reasoning. In International Conference on Machine Learning, pages 9448-9457. PMLR.  
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+Théo Trouillon, Christopher R Dance, Éric Gaussier, Johannes Welbl, Sebastian Riedel, and Guillaume Bouchard. 2017. Knowledge graph completion via complex tensor factorization. Journal of Machine Learning Research, 18:1-38.  
+Shikhar Vashishth, Soumya Sanyal, Vikram Nitin, and Partha Talukdar. 2019. Composition-based multi-relational graph convolutional networks. In International Conference on Learning Representations.  
+Wenhan Xiong, Thien Hoang, and William Yang Wang. 2017. Deeppath: A reinforcement learning method for knowledge graph reasoning. In Proceedings of the 2017 Conference on Empirical Methods in Natural Language Processing, pages 564-573.  
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+
+# A Appendix
+
+# A.1 Experimental Details
+
+Datasets The detailed statistics for each dataset can be seen in Table 4.
+
+<table><tr><td>Split</td><td>Query Types</td><td>FB15k</td><td>FB15k-237</td><td>NELL995</td></tr><tr><td rowspan="2">Train</td><td>1p,2p,3p,2i,3i</td><td>273,710</td><td>149,689</td><td>107,982</td></tr><tr><td>2in, 3in, inp, pin, pni</td><td>27,371</td><td>14,968</td><td>10,798</td></tr><tr><td rowspan="2">Validation</td><td>1p</td><td>59,078</td><td>20,094</td><td>16,910</td></tr><tr><td>Others</td><td>8,000</td><td>5,000</td><td>4,000</td></tr><tr><td rowspan="2">Test</td><td>1p</td><td>66,990</td><td>22,804</td><td>17,021</td></tr><tr><td>Others</td><td>8,000</td><td>5,000</td><td>4,000</td></tr></table>
+
+Hyper-parameters Settings Table 5 shows the best hyper-parameters we searched for pre-training KGC models. Table 6 shows the best hyper-parameters we searched for CLQA.
+
+Table 4: Detailed statistics on the different types of query structures in FB15K, FB15K-237, and NELL995 datasets.  
+
+<table><tr><td>Dataset</td><td>Dimension</td><td>Epoch</td><td>Batch Size</td><td>Learning Rate</td><td>λ1</td><td>λ2</td></tr><tr><td>FB15k</td><td>2000</td><td>200</td><td>1000</td><td>0.01</td><td>0.0625</td><td>0.005</td></tr><tr><td>FB15k-237</td><td>2000</td><td>200</td><td>1000</td><td>0.1</td><td>4</td><td>0.05</td></tr><tr><td>NELL995</td><td>2000</td><td>200</td><td>1000</td><td>0.1</td><td>0.0625</td><td>0.05</td></tr></table>
+
+Table 5: The hyper-parameters settings for pre-training KGC models,  $\lambda_{1}$  is the coefficient for relation prediction loss, and  $\lambda_{2}$  is the coefficient for regularization.  
+
+<table><tr><td>Datset</td><td>Dimension</td><td>Epoch</td><td>Batch Size</td><td>Learning Rate</td><td>α</td><td>ε</td></tr><tr><td>FB15k</td><td>2000</td><td>5</td><td>1000</td><td>0.001</td><td>0.1</td><td>0.0005</td></tr><tr><td>FB15k-237</td><td>2000</td><td>5</td><td>1000</td><td>0.001</td><td>0.1</td><td>0.00005</td></tr><tr><td>NELL995</td><td>2000</td><td>5</td><td>1000</td><td>0.001</td><td>0.1</td><td>0.00001</td></tr></table>
+
+Table 6: The hyper-parameters settings for CLQA.
+
+Different KGC models Our proposed method CKGC is effective for any KGC model because it relies solely on the results predicted by the KGC model. Although any KGC model is permissible, it is preferable to select a KGC model with strong performance. In Table 7, we show the results of our method with different KGC models. We select the DistMult (Yang et al., 2014), CP (Lacroix et al., 2018), SimplE (Kazemi and Poole, 2018), and ComplEx (Trouillon et al., 2017) KGC models. The results demonstrate that Step 3 (the adaptation step) can indeed enhance performance across various KGC models.
+
+<table><tr><td>Models</td><td>1p</td><td>avgp(S12)</td><td>avgp(S123)</td><td>avgn(S12)</td><td>avgn(S123)</td></tr><tr><td>DistMult</td><td>47.6</td><td>30.2</td><td>30.8</td><td>9.1</td><td>14.7</td></tr><tr><td>CP</td><td>46.5</td><td>29.4</td><td>30.1</td><td>8.7</td><td>13.8</td></tr><tr><td>SimpleE</td><td>46.3</td><td>29.0</td><td>29.5</td><td>8.6</td><td>13.8</td></tr><tr><td>ComplEx</td><td>49.2</td><td>32.4</td><td>32.9</td><td>9.7</td><td>15.2</td></tr></table>
+
+Table 7: The performance of complex logical quereis answering models with different KGC model, where 1p is the KGC results,  $\mathrm{avg}_p$  is the average results of queries without negation operator,  $\mathrm{avg}_n$  is the average results of queries with negation operator. S12 is the model using direct KGC scores. S123 is the model with adaptation.

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+    {
+        "type": "text",
+        "text": "Compositional Generalization with Grounded Language Models",
+        "text_level": 1,
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+            89,
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+        ],
+        "page_idx": 0
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+    {
+        "type": "text",
+        "text": "Sondre Wold, Étienne Simon, Lucas Georges Gabriel Charpentier, Egor V. Kostylev, Erik Velldal, Lilja Øvrelid  \nUniversity of Oslo",
+        "bbox": [
+            211,
+            143,
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Abstract",
+        "text_level": 1,
+        "bbox": [
+            260,
+            260,
+            339,
+            275
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Grounded language models use external sources of information, such as knowledge graphs, to meet some of the general challenges associated with pre-training. By extending previous work on compositional generalization in semantic parsing, we allow for a controlled evaluation of the degree to which these models learn and generalize from patterns in knowledge graphs. We develop a procedure for generating natural language questions paired with knowledge graphs that targets different aspects of compositionality and further avoids grounding the language models in information already encoded implicitly in their weights. We evaluate existing methods for combining language models with knowledge graphs and find them to struggle with generalization to sequences of unseen lengths and to novel combinations of seen base components. While our experimental results provide some insight into the expressive power of these models, we hope our work and released datasets motivate future research on how to better combine language models with structured knowledge representations.",
+        "bbox": [
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+            286,
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+        "page_idx": 0
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+    {
+        "type": "text",
+        "text": "1 Introduction",
+        "text_level": 1,
+        "bbox": [
+            114,
+            638,
+            260,
+            653
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Language models (LMs) acquire latent representations of text through their pre-training. One drawback of this paradigm is the implicit encoding of knowledge in a large parameter space, which can lead to factual hallucinations in model outputs. To reduce this effect, there has recently been a widespread interest in what is sometimes referred to as grounded language models, which are LMs grounded in external information sources, such as knowledge graphs (KGs). These approaches typically attempt to enable reasoning over KGs by combining the LM outputs with that of a separate graph encoder, such as a graph neural network (GNN; Lin et al., 2019; Zhang et al., 2022; Sun et al., 2022; Yasunaga et al., 2022; Yu et al., 2022). It can be difficult to determine to what extent grounded models",
+        "bbox": [
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "exhibit any structured reasoning, or what precisely would constitute reasoning in this context, as the information contained in these KGs often targets the same domain as the corpora used for LM pretraining. One example of this is the overlap in information between Wikidata, often used as the KG in previous work on grounded LMs, and Wikipedia, which is a common corpus for pre-training.",
+        "bbox": [
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+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Central to human reasoning is the ability to form novel combinations from seen components, often referred to as compositional generalization. Studies on compositionality have a long tradition within many fields of study, such as linguistics (Partee et al., 1995), philosophy (Pagin and Westerstahl, 2010), and cognitive science (Churchland, 1990), and determining to what degree neural networks capture compositionality is a long-standing research problem in machine learning, with debates going back several decades (Fodor and Pylyshyn, 1988; Smolensky, 1987). Recent studies in NLP have primarily used semantic parsing of synthetic utterances as a testbed for investigating to what extent neural networks combine syntactic elements to form new complex expressions (Hosseini et al., 2022). One of the most well-known examples of this is from Lake and Baroni (2018), who found seq2seq models to struggle both with systematic compositional skills and generalization to longer sequences than seen during training – abilities that are often taken to be central to compositional generalization. Some of these shortcomings were recently mitigated using a meta-learning framework (Lake and Baroni, 2023), but it is still not clear under what circumstances neural networks can consistently demonstrate compositional generalization, or if they can at all (Dziri et al., 2024).",
+        "bbox": [
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+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "In this work, we investigate to what extent grounded language models exhibit compositional generalization by combining two orthogonal research directions: compositionality in neural networks and the grounding of LMs in KGs.",
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+        "type": "page_number",
+        "text": "3447",
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+    {
+        "type": "footer",
+        "text": "Findings of the Association for Computational Linguistics: ACL 2024, pages 3447-3460 August 11-16, 2024 ©2024 Association for Computational Linguistics",
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+    {
+        "type": "text",
+        "text": "Using question answering as a task, we train models to recognize the relation between certain patterns in a synthetic KG and natural language questions. We develop a data generation procedure that targets three aspects of compositionality from Hupkes et al. (2020): substitutivity, productivity, and systematicity. In our experiments, we evaluate LMs that interact with KGs through the use of a GNN, an approach previously proven effective for tasks such as question answering (Lin et al., 2019; Zhang et al., 2022; Sun et al., 2022) and pre-training (Yasunaga et al., 2022).",
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+    {
+        "type": "text",
+        "text": "Our work targets two key limitations from the literature: Firstly, by extending existing work on compositional generalization to question answering over KGs, we can assess the capabilities of these models for structured reasoning over natural language questions of varying complexities; and secondly, by using a synthetic knowledge graph we do not run the risk of grounding a language model in a knowledge source containing information that already exists implicitly in the models' weights. The contribution of our work is three-fold: i) We provide the first experimental study on the expressive power of grounded LMs with respect to compositional generalization ii) We develop a procedure for generating dataset samples that target three theoretically motivated aspects of compositionality, and iii) We release a series of generated datasets using this procedure, together with all code and data related to our experiments, which can be used to benchmark grounded language models in a controlled environment.",
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+    {
+        "type": "text",
+        "text": "2 Compositionality",
+        "text_level": 1,
+        "bbox": [
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+        "type": "text",
+        "text": "In what follows we discuss three aspects of compositionality that have been established as tests of compositionality in previous work (Hupkes et al., 2020): substitutivity, systematicity, and productivity. We also describe how we ground these notions to be applicable for our setting, where data consists of both text and KGs. We refer an interested reader to the overview by Szabó (2022) for a more extensive introduction to these terms.",
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+        "type": "text",
+        "text": "Substitutivity One of the most well-known definitions of compositionality is the principle of compositionality from Partee et al. (1995): \"The meaning of a compound expression is a function of the",
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+    {
+        "type": "text",
+        "text": "meanings of its parts and of the way they are syntactically combined\". Closely related to this principle is the notion of substitutivity, which states that any change to a complex expression that maintains the meaning of individual parts also maintains the meaning of the whole expression. On the one hand, in the context of natural languages, this definition is not without controversy. Languages often have elements that do not adhere strictly to such a principle, for example through the use of idioms (Dankers et al., 2022a). On the other hand, in our setting, we can exploit the observation that if an atomic expression in natural language has a node in a graph as its reference, then we can substitute this reference with a compounded expression referencing the same node without changing the meaning of the whole expression. As the principle of compositionality is not committed to any specific theory of semantics, we can use reference as the qualification for semantic equivalence, a theory sometimes referred to as the compositionality of reference (Szabó, 2022). For example, given the KG in Figure 1, we can ask ourselves whether \"Paper2 was authored by Professor2\". We can then replace \"Professor2\" with a compounded reference, such as \"the supervisor of GraduateStudent5\", which gives rise to the question: \"Was Paper2 authored by the supervisor of GraduateStudent5?\" Following the compositionality of reference, we do not change the meaning of the overall question, since we still enquire about the same node in the graph, even though we have substituted a 1-hop reference with a 2-hop reference. Consequently, by constructing highly compositional questions in natural language, we can test whether or not neural networks can learn the mapping between constituents in text and paths in a graph.",
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+    {
+        "type": "text",
+        "text": "Productivity Closely related to substitutivity, productivity refers to the ability to construct seemingly infinite constructions using a finite capacity. As Hupkes et al. (2020) point out, this view on the open-endedness of language is typically associated with generative linguistics, and in the context of neural networks, the most direct way of testing for this ability is to test models on generalization to sequences of lengths not seen during training. In our case, we can train models on questions that require reasoning over  $k$ -hop paths, for several  $k$ , in a graph, and then test on  $j$ -hop paths, for various  $j$  different from the  $k$ 's used in training.",
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+    {
+        "type": "page_footnote",
+        "text": "1https://github.com/ltgoslo/text-graph-generalization",
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+    {
+        "type": "page_number",
+        "text": "3448",
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+    },
+    {
+        "type": "image",
+        "img_path": "images/d008a6a40165247a751788512afa4e90410d15a303cd357e2fe93e3f8fb02c25.jpg",
+        "image_caption": [
+            "Figure 1: An example KG illustrating the relationship between entities from the LUBM inventory."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Systematicity One of the most tested properties of compositionality is systematicity, which was popularized as a term by Fodor and Pylyshyn (1988). Systematicity can loosely be described as the ability to combine seen parts and rules to form new combinations, an ability that has a long tradition within linguistics. In the context of neural networks, tests of systematicity typically involve exposing models to a finite set of items and combinations during training and then evaluating the same models on a test set containing the same set of items, but combined in ways not seen during training. Lake and Baroni (2018) use the example of a person that knows the meaning and usage of words such as \"twice,\" \"and,\" and \"again,\" which upon learning the new verb \"to dax\" can generalize to new constructions such as \"dax twice and then dax again,\" something they find neural networks to struggle with. Recently, there have also been some attempts to formalize and quantify systematic generalization in neural networks (Keysers et al., 2020; Ram et al., 2023). In our setting, we can use the typed relations of the edges in a graph, such as the one illustrated in Figure 1, to test for systematicity. If a model has seen the relations TEACHES, HAS-STUDENT, and ADVISOR in numerous 3-hop paths, but never in this order, a display of systematicity would require generalization to this unseen order.",
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+    {
+        "type": "text",
+        "text": "3 Dataset Generation",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "3.1 Overview",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "To target the compositional abilities specified above, we generate several datasets consisting of",
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+    {
+        "type": "text",
+        "text": "pairs of KGs and yes/no questions in natural language, all of which are about the information in these graphs. This section explains the properties of these datasets and how they are created.",
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+        "text": "A KG over a set  $\\mathcal{T}$  of types and a set  $\\mathcal{R}$  of relations is a directed labeled multi-graph  $(\\mathcal{V},\\mathcal{L},\\mathcal{E})$  with nodes  $\\nu$ , called entities in this context, set  $\\mathcal{L}$  of node labelings, each of which is of the form  $(v,t)$  where  $v$  is an entity in  $\\mathcal{V}$  and  $t$  a type in  $\\mathcal{T}$ , and set  $\\mathcal{E}$  of edges, each of which is of the form  $(v,r,v')$ , where  $v$  and  $v'$  are entities from  $\\nu$ , and  $r$  is a relation from  $\\mathcal{R}$ . In this work, we only concentrate on graphs from the Lehigh University Benchmark (LUBM; Guo et al., 2005), which is a synthetic KG benchmark popular for evaluating various aspects of knowledge graph repositories. In particular, we exploit LUBM's KG generator of customizable and repeatable synthetic data, which can produce KGs of a user-specified size describing a fictitious university domain and committing to a realistic ontology over sets  $\\mathcal{T}_{\\text{LUBM}}$  and  $\\mathcal{R}_{\\text{LUBM}}$  of university-related types and relations. We generate several graphs with an average number of 685 entities, each labeled by a single type, and 4949 edges, each labeled by a single relation.",
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+    {
+        "type": "text",
+        "text": "Each of the natural language questions targets two entities in the corresponding generated LUBM graph  $\\mathcal{G}$  and a chain of relations from  $\\mathcal{R}_{\\text{LUBM}}$  and inverses of such relations that is to hold between these entities. In particular, for a number of hops (i.e., chain length)  $k$ , the questions are semimanually created by first mapping each unique  $k$ -hop combination (i.e., chain of length  $k$ ) of relations from a selected subset of  $\\mathcal{R}_{\\text{LUBM}}$  and their inverses to a natural language template with two parameters, and then substituting these parameters by two entities from  $\\mathcal{V}$  as arguments. As a result, the answer to the question is TRUE if there exists a path between the two entities in  $\\mathcal{G}$  as prompted by the  $k$ -hop combination of the question template, and FALSE otherwise. We create templates for 2, 3, and 4 hops, with 5 relations from  $\\mathcal{R}_{\\text{LUBM}}$  and their inverses as  $\\mathcal{R}_{\\text{LUBM}}'$ . This makes for over 280 unique templates (while the number of questions depends on  $\\mathcal{G}$ ). To illustrate our dataset creation we concentrate on an example and a discussion of a key step, sampling of positive and negative question-graph pairs, in the next two subsections. We refer to Appendix A for further details.",
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+        "type": "page_footnote",
+        "text": "2The ontology is specified in Web Ontology Language OWL (https://www.w3.org/OWL/).",
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+        "text": "3449",
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+    {
+        "type": "text",
+        "text": "3.2 Example",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "Given the KG in Figure 1, we can create the following templates, for an increasing number of hops, where the “—” superscript denotes the inverse of the relation:",
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+        "sub_type": "text",
+        "list_items": [
+            "2 hops: [TEACHES, TAKES COURSE $^{-}$ ]  $\\rightarrow$  Does  $s$  teach a course that has a student named  $e$ ?",
+            "3 hops: [TEACHES, TAKESCOURSE $^{-}$ , ADVISOR]  $\\rightarrow$  Does  $s$  teach a course that has a student supervised by  $e$ ?",
+            "4 hops: [TEACHES, TAKESCOURSE $^{-}$ , ADVISOR, PUBLICATIONAUTHOR]  $\\rightarrow$  Does  $s$  teach a course that has a student supervised by an author of  $e$ ?"
+        ],
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+    {
+        "type": "text",
+        "text": "To create questions from these templates that we label TRUE we can use PROFESSOR7 and GRADSTUDENT9 as arguments substituting parameters  $s$  and  $e$ , respectively, in the 2-hop case, PROFESSOR7 and PROFESSOR2 for the 3-hop case, and PROFESSOR7 and PAPER2 for the 4-hop case. Creating examples labeled as FALSE for these templates then involves sampling two entities to use as  $s$  and  $e$  that are not connected by the chains of relations, but are similarly connected in the graph as the entities in the positive examples. We describe this negative sampling in the next section.",
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+    {
+        "type": "text",
+        "text": "3.3 Sampling Procedure",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "As mentioned, we create each question-graph pair by sampling pairs of entities and the relations on the edges that are to hold between them in the graph  $\\mathcal{G}$ . The key requirement to this procedure is to guarantee that the  $k$  relations and their inverses in every sampled  $k$ -hop combination are as likely to be labeled TRUE as they are to be labeled FALSE; failing to do so introduces distributional bias. This means that our sampling procedure must ensure two important properties:  $i$  it must be impossible for a text-only model to associate a question template (i.e., all questions produced from this template) to the TRUE or FALSE label, and  $ii$  it must be impossible for a graph-only model to associate the presence of a specific set of relations in graph  $\\mathcal{G}$  with a specific label.",
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+        "type": "text",
+        "text": "We ensure property  $i$  ) by creating the same number of questions labeled TRUE as FALSE for every unique  $k$ -hop combination of relations. We ensure ii) by sampling  $k$ -hop relation paths from  $\\mathcal{G}$  symmetrically: We first sample i.i.d. two pairs of",
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+    {
+        "type": "text",
+        "text": "different entities,  $s_{+}, e_{+}$  and  $s_{-}, e_{-}$ , such that  $s_{+}$  and  $s_{-}$  are of the same entity type, and  $e_{+}$  and  $e_{-}$  are also of the same entity type. We then identify a  $k$ -hop combination over  $\\mathcal{R}_{\\text{LUBM}}'$  that exists between  $s_{+}$  and  $e_{+}$  but not between  $s_{-}$  and  $e_{-}$ , as well as verify that there exists another (different)  $k$ -hop combination over  $\\mathcal{R}_{\\text{LUBM}}'$  between  $s_{-}$  and  $e_{-}$ . If all this succeeds, the pair  $s_{+}, e_{+}$  with the question corresponding to the template becomes a positive example, and the pair  $s_{-}, e_{-}$  with the same template a negative one. Further details of the sampling procedure can be found in Appendix A.",
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+        "type": "text",
+        "text": "4 Modeling",
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+        "type": "text",
+        "text": "For all experiments, each data point includes a natural language question  $q$  and a graph  $\\mathcal{G}$ . Following previous work on combining language models with KGs (Lin et al., 2019; Zhang et al., 2020; Yasunaga et al., 2021; Zhang et al., 2022; Kaur et al., 2022; Sun et al., 2022; Yasunaga et al., 2022), we use separate encoders for  $q$  and  $\\mathcal{G}$  to obtain representations of both modalities. Section 4.1 outlines these encoders and Section 4.2 how we combine them to produce the final output prediction  $\\hat{y} \\in \\{\\mathrm{TRUE},\\mathrm{FALSE}\\}$ .",
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+        "type": "text",
+        "text": "4.1 Encoders",
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+        "text": "Text encoder We obtain representations of  $q$  by using the special sentence representation token at the last layer of a pre-trained language model, as per Devlin et al. (2019):  $z_{\\mathrm{text}} = \\mathrm{BERT}(q)$ .",
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+        "type": "text",
+        "text": "Graph encoder As a graph encoder, we use the relational graph convolution model, R-GCN, from Schlichtkrull et al. (2018):",
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+        "type": "equation",
+        "text": "\n$$\nh _ {i} ^ {\\ell + 1} = \\sigma \\left(\\sum_ {r \\in \\mathcal {R}} \\sum_ {j \\in \\mathcal {N} _ {i} ^ {r}} \\frac {1}{| \\mathcal {N} _ {i} ^ {r} |} W _ {r} ^ {\\ell} h _ {j} ^ {\\ell} + W _ {0} ^ {\\ell} h _ {i} ^ {\\ell}\\right),\n$$\n",
+        "text_format": "latex",
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+    {
+        "type": "text",
+        "text": "where  $h_i^\\ell$  is the hidden state of a node  $i$  in layer  $\\ell$ ,  $\\sigma$  is the ReLU function and  $\\mathcal{N}_i^r$  is the set of neighborhood vertices of node  $i$  under relation  $r$ .",
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+    {
+        "type": "text",
+        "text": "4.2 Final models",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "Inspired by previous work on combining text and graph encoders, we experiment with different approaches to integrating the two modalities and apply them using the above-mentioned encoders and our experimental setup. Figure 2 provides an overview of the differences between these approaches.",
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+        "text": "3450",
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+    {
+        "type": "image",
+        "img_path": "images/ec18fa16804874f13ff9aebbbd1e49525cca7b331dd9c610365ee46cbfc0c157.jpg",
+        "image_caption": [
+            "Figure 2: Overview of the different approaches to combining the two encoders. Purple nodes are initialized at random while green and blue nodes are initialized using a frozen BERT model."
+        ],
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+    {
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+        "img_path": "images/fd948d5a75f87705b416757955ce0fc44d15465ce54663ca4268cef329b3c2ad.jpg",
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+        "img_path": "images/b3e03ba17858afb26c81f618dbe7f1b15345b076ddf6df120396084a033a49ed.jpg",
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+    },
+    {
+        "type": "image",
+        "img_path": "images/87a300401d078159659e972953cdee172d11c7d8c7cdaec8f2e1130b6ba66d0f.jpg",
+        "image_caption": [],
+        "image_footnote": [],
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+    {
+        "type": "text",
+        "text": "Disjoint The simplest way of having the two modalities interact is to initialize and run both encoders separately before conjoining their outputs in a final classification layer. This keeps the encoders disjoint, essentially making a \"two-tower architecture\" – conceptually similar to approaches such as Wang et al. (2019).",
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+    {
+        "type": "text",
+        "text": "To get a final representation of the graph,  $z_{\\mathrm{graph}}$ , we take the embedding of the head and tail node targeted by the question after  $L$  rounds of message passing:  $z_{\\mathrm{graph}} = h_s^L \\oplus h_e^L$ , where  $s$  and  $e$  are the indices of the head and tail node and  $\\oplus$  is vector concatenation. We initialize these nodes by creating two distinct embeddings,  $E_s$  and  $E_e$ , with  $E_s, E_e \\sim \\mathcal{N}(0,1)$ . We keep these static throughout training and testing and use them for all head and tail nodes targeted by the questions. The initialization of remaining nodes in each graph is discussed in more detail in Section 4.3.",
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+    {
+        "type": "text",
+        "text": "For the question, we take the output of the text encoder without any modifications. The final output prediction is then obtained by the following:  $f(z_{\\mathrm{text}} \\oplus z_{\\mathrm{graph}})$ , where  $f$  is a two-layered MLP with a ReLU activation function.",
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+        "type": "text",
+        "text": "Grounded For this model, we concatenate the original question string from  $q$  with both the head and tail entity strings, respectively, using a separation token. This is then used as input to the text encoder, obtaining a representation of the head and tail nodes:",
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+    {
+        "type": "equation",
+        "text": "\n$$\n\\begin{array}{l} h _ {s} ^ {0} = \\operatorname {B E R T} (q <   \\text {S E P} > \\text {h e a d s u r f a c e f o r m}), \\\\ h _ {e} ^ {0} = \\operatorname {B E R T} (q <   \\text {S E P} > \\text {t a i l s u r f a c e f o r m}). \\\\ \\end{array}\n$$\n",
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+    {
+        "type": "text",
+        "text": "These are then used to initialize the embeddings for the nodes pertaining to these entities in the graph. This is done in a pre-processing step before the text encoder is fine-tuned on our datasets. The final output prediction is calculated in the same way as with the disjoint model.",
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+    {
+        "type": "text",
+        "text": "Unidirectional In this model, we add a unidirectional interaction between the encoders, inspired by works such as Yasunaga et al. (2021). For each question-graph pair,  $(q,\\mathcal{G})$ , we introduce a new special context node,  $u$ , and connect  $u$  to each node in  $\\mathcal{G}$ . This special node is connected using two new relations, one for each direction, and its embedding is initialized using the text encoder representation of the question,  $\\mathrm{BERT}(q)$ . In Figure 2,  $u$  is marked as a blue node. For each  $\\mathcal{G}$ , we perform global pooling over the hidden states:",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nz _ {\\text {g r a p h}} = \\frac {1}{| \\mathcal {V} |} \\sum_ {v \\in \\mathcal {V} ^ {\\prime}} h _ {v} ^ {L},\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+            650,
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where  $\\mathcal{V}'$  is the set containing the head, tail, and special context nodes. We do not consider the set of all nodes due to the zero-initialization of the remaining nodes in  $\\mathcal{G}$  (see Section 4.3). The head and tail nodes are initialized as in the grounded model, using the text encoder representations. We also take the embedding of the special node at the last layer,  $h_u^L$ , as a representation of  $\\mathcal{G}$ . The final output prediction is then given by:  $f(z_{\\mathrm{text}} \\oplus z_{\\mathrm{graph}} \\oplus h_u^L)$ , where  $f$  is a two-layered MLP with a ReLU activation function.",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Bidirectional We also develop a model inspired by the interaction approach used in works such as",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "page_number",
+        "text": "3451",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Zhang et al. (2022) and Yasunaga et al. (2022) to allow for a bidirectional interaction between the two encoders. We keep the special context node  $u$  as described in the unidirectional model, but we add a special interaction token,  $t$ , to the question  $q$ .  $t$  is set to be the representation of the special context node  $u$  after  $L$  layers of message passing:  $t = h_u^L$ . This is done after the embedding of  $q$  in the text encoder. We produce the final output prediction using the same method as in the unidirectional model.",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Baseline We use a sole graph encoder as a baseline. Theoretically, it should not be possible to solve the tasks without having access to both the text and the graph. By using a graph-only system as a baseline we therefore get both a sanity check and an upper bound on the noise produced by the sampling. As the natural language questions are not sampled, but rather constructed deterministically from the paths sampled from our graphs, one positive and one negative, the performance of a text-only encoder will by design be equal to a random classifier. The output of the baseline is calculated the same way as for the disjoint model, taking the representations of the head and tail entity.",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "4.3 Node initialization",
+        "text_level": 1,
+        "bbox": [
+            112,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Except for the head and tail nodes targeted by each question, and the special context node  $u$ , all nodes are initialized as zero-vectors. This means that we leak the position of the head and tail entity in  $\\mathcal{G}$  for each sample in the dataset, making any pruning of  $\\mathcal{G}$  redundant. It is often necessary to reduce the computational complexity of combining language models and large knowledge graphs using mechanisms such as subgraph retrieval and entity linking, but these steps are also known to be error-prone (Wold et al., 2023). This initialization ensures that we further isolate the application of compositional generalization rules, as opposed to evaluating the performance of a pipeline model with numerous error-prone components.",
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+    },
+    {
+        "type": "text",
+        "text": "5 Experiments and results",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "table",
+        "img_path": "images/7a94b94650d0a9ebfeaa94940c0974261d2d851a0633f2facc69d7f4cf7863dc.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Hops</td><td>#relation-paths</td><td>N</td></tr><tr><td>2</td><td>23</td><td>1043±1941</td></tr><tr><td>3</td><td>73</td><td>328±449</td></tr><tr><td>4</td><td>188</td><td>127±260</td></tr></table>",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Table 1: The mean number of occurrences of the relation paths across 24000 generated graphs per hop  $k$  .",
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+    {
+        "type": "text",
+        "text": "In this section, we test our suite of models on data specifically targeting substitutivity (Section 5.1), productivity (Section 5.2), and systematicity (Section 5.3), going test by test. For all experiments, the distribution between the two classes is perfectly balanced. Statistics on the diversity of the generated graphs with respect to relation paths can be found in Table 1. Details on the selection of hyperparameters can be found in Appendix B.",
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+    {
+        "type": "text",
+        "text": "5.1 Substitutivity",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "In our first test, we evaluate to what extent the five model configurations can answer questions targeting substitutivity, as defined in Section 2. Success at this task requires recognizing the mapping between the presence of certain relations in the graph and phrases in the natural language questions. Substitutivity is the most basic setting of our experiments and the results on this task demonstrate the general difficulty of the task.",
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+        "type": "text",
+        "text": "Test design We generate 12000 question-graph pairs using our generation procedure. We do this for 2, 3 and 4-hops. Each experiment targets one of the hop lengths, i.e., both training and evaluating on the same number of hops. For all experiments, we use 10000 samples for training and 2000 for testing. All results are reported using mean accuracy and standard deviation from five randomly seeded runs.",
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+    {
+        "type": "text",
+        "text": "Results The results of the substitutivity tests can be seen in Table 2. There is a strong generalization in the 2-hop case for all models. In the 3-hop case, performance drops significantly and the variance also increases for most models. There is a further loss in generalization when moving to the 4-hop case, where there is little difference between the models. Figure 3 shows that there is a positive correlation between test accuracy on a specific question type and the frequency of the corresponding relation path in the training data for the 3-hop case. For the 2-hop and 4-hop cases, where the performance is closer to perfect and random classification, respectively, the relationship flattens. This aligns with the increase in unique combinations of relation paths as the number of hops increases, as shown in Table 1. For 2-hops there is either a high number of examples per relation path combination, which enables learning, or very few, which makes the performance on these relation paths negligible on the overall accuracy. For 4-hops, on the other hand, there is too much of a long tail on the dis",
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+    },
+    {
+        "type": "page_number",
+        "text": "3452",
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+    {
+        "type": "table",
+        "img_path": "images/6d2c7ba0005804248ba85716a9a3a4334e8378de9d433468b73f5b6c0f1f5606.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Model</td><td>2-hop</td><td>3-hop</td><td>4-hop</td></tr><tr><td>Baseline</td><td>48.88±1.00</td><td>49.8±0.64</td><td>49.36±0.44</td></tr><tr><td>Disjoint</td><td>98.17±0.39</td><td>83.08±0.96</td><td>67.86±1.89</td></tr><tr><td>Grounded</td><td>92.46±0.49</td><td>84.91±0.38</td><td>69.32±1.96</td></tr><tr><td>Unidirectional</td><td>91.78±0.72</td><td>70.88±3.53</td><td>62.0±3.97</td></tr><tr><td>Bidirectional</td><td>92.44±0.23</td><td>73.66±1.04</td><td>63.24±3.36</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "ribution of number of samples per combination, making learning difficult. For 3-hops, however, there is a balance, which is reflected in the results. See Figure 4 in Appendix A for an illustration of the relative percentage of each unique combination to the total for each hop.",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "These results show that the models struggle to generalize to the long tail of the training distribution, which is a known attribute of neural networks. However, single relation types are reused extensively throughout our training data, as there are only 10 unique relations of length 1. This means that the distribution only has a long tail if one considers each 4-hop combination to be a single unique type, as opposed to being composed of four individual relations that are individually high-frequent. We argue that these results indicate that these models do not create internal representations of each 1-hop path together with a function for composing them into compounded expressions, but rather learn individual representations for each compound. This also explains why the performance drops as the complexity increases and the number of samples per relation decreases, making such a strategy less viable. This explanation is further explored in the systematicity tests. We also note that there is little difference between the models, indicating that an increase in model complexity does not add any benefits to this task.",
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "5.2 Productivity",
+        "text_level": 1,
+        "bbox": [
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+            709,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "In our next test, we evaluate to what extent models can answer  $k$ -hop questions when trained on  $j$ -hops, with  $k \\neq j$ . We define experiments requiring extrapolation and interpolation for different values of  $k$  and  $j$ . Success at this task requires generalization to sequences with a different length than those seen during training.",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Test design In our first experiment, we use an even amount of 2 and 3-hop questions for training while using 4-hop questions for testing, targeting extrapolation. In our second experiment, we tar",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "table",
+        "img_path": "images/7277cc17c798e46391a7c20f8c0f5a0c3d144123159a3627754dc39cc65d33a3.jpg",
+        "table_caption": [
+            "Table 2: Substitutivity results."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Experiment</td><td>Acc.</td></tr><tr><td colspan=\"2\">TRAIN: 2 AND 3-HOP. TEST: 4-HOP</td></tr><tr><td>Baseline</td><td>49.92±0.82</td></tr><tr><td>Disjoint</td><td>59.42±2.07</td></tr><tr><td>Grounded</td><td>61.79±0.52</td></tr><tr><td>Unidirectional</td><td>62.40±1.02</td></tr><tr><td>Bidirectional</td><td>62.05±0.91</td></tr><tr><td colspan=\"2\">TRAIN: 2 AND 4-HOP. TEST: 3-HOP</td></tr><tr><td>Baseline</td><td>51.19±0.31</td></tr><tr><td>Disjoint</td><td>63.87±2.24</td></tr><tr><td>Grounded</td><td>66.10±2.02</td></tr><tr><td>Unidirectional</td><td>66.65±2.24</td></tr><tr><td>Bidirectional</td><td>66.29±1.25</td></tr><tr><td colspan=\"2\">TRAIN: 3 AND 4-HOP. TEST: 2-HOP</td></tr><tr><td>Baseline</td><td>50.98±0.25</td></tr><tr><td>Disjoint</td><td>60.34±3.25</td></tr><tr><td>Grounded</td><td>62.32±1.98</td></tr><tr><td>Unidirectional</td><td>64.04±4.47</td></tr><tr><td>Bidirectional</td><td>63.03±3.76</td></tr></table>",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Table 3: Productivity results.",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "get interpolation by training on an even amount of 2 and 4-hop questions while testing on 3-hops. For our last experiment, we target extrapolation to lower values, using a training split with an even amount of 3 and 4-hop questions while testing on 2-hops. For all three experiments, we generate 10 000 samples for training and 2 000 for testing.",
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+    {
+        "type": "text",
+        "text": "Results The results of the productivity tests can be seen in Table 3. In general, we observe that all models struggle to extrapolate to both shorter and longer hops. We observe some generalization for the interpolation test, where the model has seen sequences both shorter and longer during training, but the overall absolute performance is still poor. This aligns with previous work, such as Lake and Baroni (2018) and Hupkes et al. (2020). We observe a tiny increase in performance with the more complex models compared to the simpler, disjoint model, but given the overall low scores and the variance, we do not think these results are significant. This indicates that adding a more complex interaction between the encoders does not provide any added benefit for extrapolation or interpolation.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "5.3 Systematicity",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "In our last test, we evaluate to what extent our models can generalize systematically. This means that all unique 1-hop relations are seen during training in some  $k$ -hop combination, but in the test data, we only include unseen combinations. For example, during training the models might see samples using the relations TAKES COURSE and",
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+        "text": "3453",
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+        "page_idx": 6
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+    {
+        "type": "image",
+        "img_path": "images/10738a4e76ea540b1acc4de1b4e5248ec075dcaa6fd4343d2f1fa343585b795e.jpg",
+        "image_caption": [
+            "Figure 3: Relationship between frequency of a  $k$ -hop relation and the performance of the Disjoint model on these during testing. Each blue point corresponds to a tuple of  $k$  relations for  $k = 1,2,3$ . The orange lines are the linear regressions for each setting showing positive correlations between frequencies of  $k$ -hop relations and performances of the Disjoint model."
+        ],
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+        "page_idx": 7
+    },
+    {
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+        "img_path": "images/4fbdf814a10ededda6e908da8f49d0346c3c26da0b9aa37c372be46a513722dc.jpg",
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+    },
+    {
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+        "img_path": "images/a75cd526d4e524697f521864c00404708a8917440e5ebf1da827813bcdf89ef7.jpg",
+        "image_caption": [],
+        "image_footnote": [],
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+    {
+        "type": "text",
+        "text": "HASTEACHINGASSISTANT, and the 2-hop combination [TAKESCOURSE, HASTEACHINGASSISTANT], but in the test we target [HASTEACHINGASSISTANT, TAKESCOURSE]. Success at this task requires the model to learn that a 3-hop question, for example, consists of three individual parts that are combined, as opposed to encoding the entire sequence as one entity.",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Test design With  $k$  being 2, 3, or 4, we generate question-graph pairs with length  $k$ . Then, for each  $k$ , we randomly select a fraction of the available  $k$ -length combinations of relations as our test combinations. We then separate the generated pairs into two parts: those who use the test combinations and those who do not. The former is saved as the test set. We note that the use of test combinations is not limited to the relations on the path between the head and tail entities targeted by the question, but any  $k$ -hop path that exists between these entities. For the training set, we split the remaining possible combinations into five chunks and collect all samples that use these combinations. This leaves us with five different folds of the training set. Models are then trained on each fold independently, but evaluated on the same test set. We do this to control for the fact that some combinations of relations might have a similar distribution of samples as the relations picked out for the test set, making them better fits for that particular split.",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "As this tests out-of-distribution generalization, we argue that folding is better suited for finding the true performance and variance of the models than the more straightforward evaluation method used for our substitutivity and productivity experiments. The results are reported as the mean accuracy over all five folds.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Results The results of the systematicity tests can be seen in Table 4. As with the productivity tests, we see that there is no consistent display of generalization for any of the models across hops. We see, however, that for the 3-hops setting the two simpler models achieve some success on the task. As these models had the highest performance on the substitutivity test, we take this to indicate that additional architectural complexity does not provide any performance benefit for this type of generalization. We also note that it is possible that these experiments are sensible to the hyperparameters, and that the two simpler models happened to have a better fit for the 3-hop setting. We did not do a specific hyperparameter search per model for the systematicity experiments but relied on those from the initial hyperparameter search.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Overall, these results might come from undersampling, or it might be the case, as is reported in Hupkes et al. (2020), that the models are not able to construct useful representations of smaller syntactic units. We argue that our results further support the intuition from the substitutivity experiments: the models do not learn to create representations that correspond to each 1-hop relation, together with a function for combining them, but rather rely on memorization of whole combinations of relation types. For short-tailed distributions and some settings of hyperparameters this works, but it is not a robust solution to the general problem of matching the text questions to certain patterns in the graphs, illustrated by the significant drop in performance in these results.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "We also see adjacent work on assessing compositional generalizations in LLMs to provide possible explanations for our results. Dziri et al. (2024) hypothesize that transformer-based models try to solve a highly compositional problem, like ours, by",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "page_number",
+        "text": "3454",
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+    },
+    {
+        "type": "table",
+        "img_path": "images/da03381620c851168d0fb8528d11c7e81f477a1e7c91fa0058370326f669c35e.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Model</td><td>2-hop</td><td>3-hop</td><td>4-hop</td></tr><tr><td>Baseline</td><td>49.50±0.24</td><td>49.40±0.33</td><td>49.92±1.01</td></tr><tr><td>Disjoint</td><td>53.62±8.39</td><td>74.05±3.42</td><td>62.18±1.20</td></tr><tr><td>Grounded</td><td>60.02±3.22</td><td>75.68±3.27</td><td>64.96±1.39</td></tr><tr><td>Unidir.</td><td>64.24±0.75</td><td>57.12±1.81</td><td>64.10±3.62</td></tr><tr><td>Bidir.</td><td>64.15±1.10</td><td>60.37±2.31</td><td>63.72±3.63</td></tr></table>",
+        "bbox": [
+            131,
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Table 4: Systematicity results.",
+        "bbox": [
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "reducing it into linearized path matching. If this is the case, models do not learn the compositional rule needed to solve the task. If the samples from the test distribution only resemble the training distribution superficially, this pattern matching approach is not a viable solution for out-of-distribution generalization in both our productivity and systematicity experiments. In these experiments, the mapping from the input samples to output labels cannot be based on surface-form frequency, due to our balanced sampling, which could then explain the collapse in performance we are observing for these experiments.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "6 Previous work",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "There have been numerous works on compositional generalization in neural networks (Andreas, 2019; Lake and Baroni, 2018; Kim and Linzen, 2020; Hupkes et al., 2020; Dankers et al., 2022b; Lake and Baroni, 2023; Dziri et al., 2024). Most similar to our work is Gu et al. (2021), which develops a large-scale dataset targeting aspects of compositional generalization using question answering over Wikidata. Both this work and similar efforts reformulate the problem of integrating the KG to a seq2seq task where the questions are first translated into an intermediate logical form, such as SPARQL, which can be executed over the KG (Shu et al., 2022). Under the same framework, Ravishankar et al. (2022) explicitly tests generalization to unseen combinations of relations in a similar fashion to our systematicity test. They too find that the performance tends to drop significantly for this setting.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "The mapping from natural language to logical form can also use techniques from semantic parsing, a topic where compositionality is of special interest (Lindemann et al., 2023). Our work, however, is the first to target compositionality in a setup where the models learn representations of both text and graphs directly, without any logical form as an intermediate step. In contrast to previous work on grounded language models (Lin et al., 2019; Zhang",
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+    },
+    {
+        "type": "text",
+        "text": "et al., 2020; Yasunaga et al., 2021; Zhang et al., 2022; Kaur et al., 2022; Sun et al., 2022), our methods can also more precisely quantify the effect of combining LMs with GNNs, as our sampling procedure ensures that the encoders can not achieve above random performance on their own, a property which we believe is unique to our approach.",
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+    {
+        "type": "text",
+        "text": "7 Conclusion",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Research on compositional generalization in neural networks has a long history. To the best of our knowledge, we provide the first experimental evaluation of compositional generalization in grounded LMs, using question answering over KGs as a task. Our results indicate that these models  $i$  ) require large sample sizes and quickly lose generalization power as the complexity of the compositional structure increases,  $ii$  ) struggle with extrapolation and interpolation to sequences of lengths not seen during training, and  $iii$  ) cannot systematically generalize from seen base components to novel compositions given the sample sizes used in our experiments. We show this across a set of model architectures inspired by the literature. Our results are in line with previous work on compositional generalization in other domains and for other types of neural architectures. Overall, we believe our results show that grounded LMs do not display signs of structured reasoning over KGs and that there is still much to be done on the improvement of models that try to exploit external information stored as symbolic objects. This is the case not only for knowledge graphs but also for other types of data representations, such as tabular data. We hope our generation procedure and released datasets can help motivate future efforts at overcoming these challenges.",
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+    {
+        "type": "text",
+        "text": "Limitations",
+        "text_level": 1,
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+    },
+    {
+        "type": "text",
+        "text": "Models Our models are inspired by previous work. However, since our experimental setup differs from the original settings these models were implemented to work in, we had to make multiple simplifications. Consequently, we are not able to conclude anything about the abilities of the specific models from the literature, but rather about the general interaction approach they propose.",
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+    {
+        "type": "text",
+        "text": "Question variety The questions in our dataset are formulated in English, and although they have more linguistic variety than similar studies from semantic parsing, such as Lake and Baroni (2018)",
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+    {
+        "type": "page_number",
+        "text": "3455",
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+    {
+        "type": "text",
+        "text": "and Hupkes et al. (2020), we still use a rather limited version of the language, which is by design devoid of any metaphors, idioms, analogies and other constructs that would make compositionality more difficult to measure. It is not given that our results transfer to real language data.",
+        "bbox": [
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+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Acknowledgments",
+        "text_level": 1,
+        "bbox": [
+            114,
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+            212
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "We acknowledge Sigma2, Norway, for awarding this project access to the LUMI supercomputer, owned by the EuroHPC Joint Undertaking, hosted by CSC (Finland) and the LUMI consortium.",
+        "bbox": [
+            112,
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+    },
+    {
+        "type": "text",
+        "text": "References",
+        "text_level": 1,
+        "bbox": [
+            114,
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+            331
+        ],
+        "page_idx": 9
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+        ],
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+        "page_idx": 10
+    },
+    {
+        "type": "page_number",
+        "text": "3457",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "A Dataset generation",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "A.1 LUBM",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "We use the LUBM UBA to generate knowledge graphs on the fly. We limit our graphs to the following entity types: Professor, AssociateProfessor, UndergraduateStudent, GraduateStudent, TeachingAssistant, Publication, Course; and the following relations: PUBLICATIONAUTHOR, TEACHEROF, ADVISOR, TAKESCOURSE, TEACHINGASSISTANTOF. We also add reverse edges with reverse relations for all of these to create more diverse question types in our final dataset, making  $|\\mathcal{R}_{LUBM}^{\\prime}| = 10$ . We remove all literals. Using a sample size of approximately 14000, we create graphs that have  $\\mu = 685$ ,  $\\sigma = 77.16$  nodes and  $\\mu = 4949$ ,  $\\sigma = 532$  edges after processing.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "A.2 Statistics",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 11
+    },
+    {
+        "type": "image",
+        "img_path": "images/81adfba236d19aa9a51be36fad045a472638f20f1d072b1b532033d949364823.jpg",
+        "image_caption": [
+            "Figure 4: The relative percentage of each unique relation path to the total for 2, 3, and 4-hops."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "The number of possible combinations of relations on the edges in a  $k$ -hop path increases with the number of hops. As our sampling procedure uses 10 distinct relations we have  $10^{k}$  theoretical combinations of relations for any  $k$ -hop path. As our graphs are committed to the LUBM ontology the number of relations that hold between two entity types is much lower.",
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+    },
+    {
+        "type": "page_footnote",
+        "text": "<sup>3</sup>https://swat.cse.lehigh.edu/projects/lubm/",
+        "bbox": [
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+    },
+    {
+        "type": "page_number",
+        "text": "3458",
+        "bbox": [
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+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "A.3 Sampling procedure",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "Given a directed multigraph  $G = (\\mathcal{V}, \\mathcal{E})$  with labeled entities  $v_i \\in \\mathcal{V}$  and labeled edges  $(v_i, r, v_j) \\in \\mathcal{E}$  where  $r \\in \\mathcal{R}$  is a relation, we sample a positive and negative example for a  $k$ -hop path using the following procedure:",
+        "bbox": [
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+        "page_idx": 12
+    },
+    {
+        "type": "list",
+        "sub_type": "text",
+        "list_items": [
+            "1. Sample two pairs of nodes  $(s_{+}$  and  $e_+$ ) and  $(s_{-}$  and  $e_{-})$  from  $\\mathcal{V}$  with uniform probability, making sure that  $s_{+} \\neq s_{-}$  or  $e_{+} \\neq e_{-}$ , that  $s_{+}$  and  $s_{-}$  are of the same entity type, and that  $e_{+}$  and  $e_{-}$  are of the same entity type.",
+            "2. Let  $R_{+}$  be the set of all relation paths of length  $k$  from  $s_{+}$  to  $e_{+}$ .",
+            "3. Let  $R_{-}$  be the set of all relation paths of length  $k$  from  $s_{-}$  to  $e_{-}$ .",
+            "4. Let  $P_{+}$  be the set  $R_{+} \\setminus R_{-}$",
+            "5. Let  $P_{-}$  be the set  $R_{-} \\setminus R_{+}$",
+            "6. If  $P_{+} \\neq \\emptyset$  and  $P_{-} \\neq \\emptyset$ :"
+        ],
+        "bbox": [
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+            181,
+            878,
+            359
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "list",
+        "sub_type": "text",
+        "list_items": [
+            "(a) Sample a relation path  $q\\colon q\\sim \\mathcal{U}(P_{+})$",
+            "(b) Return the triple  $(q, s_{+}, e_{+})$  as a positive example and  $(q, s_{-}, e_{-})$  as a negative example."
+        ],
+        "bbox": [
+            156,
+            367,
+            842,
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+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "This procedure returns a  $k$ -hop relation path,  $q$ , that holds between  $s_{+}$  and  $e_{+}$  but not between  $s_{-}$  and  $e_{-}$ . However, we also make sure that there are paths that hold between  $s_{-}$  and  $e_{-}$  but not  $s_{+}$  and  $e_{+}$ , ensuring symmetry.",
+        "bbox": [
+            112,
+            420,
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+            469
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "In addition, we shuffle entities labels while preserving entity types before running this procedure since the LUBM generator introduces problematic patterns with its entity numbering. For example, in the original graph, Professor1 is more likely to author Paper1 than Paper5. By randomly exchanging the labels of Paper1 and Paper5, we ensure the models cannot exploit this regularity.",
+        "bbox": [
+            112,
+            478,
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+            542
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "B Models",
+        "text_level": 1,
+        "bbox": [
+            114,
+            563,
+            216,
+            577
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "B.1 Parameters",
+        "text_level": 1,
+        "bbox": [
+            114,
+            596,
+            253,
+            611
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "All our combined models have a total of  $\\approx 141000000$  parameters, with the majority of them coming from the language model. Our baseline has  $\\approx 30000000$ .",
+        "bbox": [
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+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "B.2 Computation infrastructure",
+        "text_level": 1,
+        "bbox": [
+            114,
+            678,
+            384,
+            694
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "All the experiments ran on the LUMI supercomputer, using a single AMD MI250X GPU. Running all the experiments reported in the paper has a total computing budget of approximately 150 hours.",
+        "bbox": [
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+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "B.3 Hyperparameters",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "We tune the learning rate for the text encoder from  $\\{1 \\times 10^{-6}, 1 \\times 10^{-5}, 2 \\times 10^{-5}, 3 \\times 10^{-5}, 5 \\times 10^{-5}\\}$ , the graph encoder module from  $\\{2 \\times 10^{-4}, 5 \\times 10^{-4}, 1 \\times 10^{-3}, 2 \\times 10^{-3}, 1 \\times 10^{-5}\\}$ , and the MLP module from  $\\{1 \\times 10^{-4}, 1 \\times 10^{-5}\\}$ ; the dropout value from  $\\{0.1, 0.2, 0.3\\}$  and the epochs from  $\\{5, 8, 10\\}$ , with no early stopping. The hyperparameters are tuned on a development set targeting the substitutivity task with an equal mix of 2, 3, and 4-hop questions. We run 60 trials for each of the five model configurations and sample a random combination of these parameters for each trial, selecting the best combination for our experiments. We find that all models perform the best with no decay on the learning rate.",
+        "bbox": [
+            112,
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+            884,
+            902
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "page_footnote",
+        "text": "<sup>4</sup>https://www.lumi-supercomputer.eu/sustainable-future/",
+        "bbox": [
+            134,
+            906,
+            547,
+            920
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "page_number",
+        "text": "3459",
+        "bbox": [
+            480,
+            928,
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+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "table",
+        "img_path": "images/528e1207b4f20688a0d2a4ce16f4af2cf37c15d54a1fe8757ad53db1d3043be4.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Hyperparameter</td><td>BASELINE</td><td>DISJOINT</td><td>GROUNDED</td><td>UNIDIRECTIONAL</td><td>BIDIRECTIONAL</td></tr><tr><td>LM lr</td><td>-</td><td>0.00001</td><td>0.00001</td><td>0.00001</td><td>0.00001</td></tr><tr><td>GNN lr</td><td>0.00001</td><td>0.0005</td><td>0.0005</td><td>0.00005</td><td>0.0005</td></tr><tr><td>MLP lr</td><td>0.00001</td><td>0.0001</td><td>0.0001</td><td>0.0001</td><td>0.0001</td></tr><tr><td>Dropout</td><td>0.3</td><td>0.3</td><td>0.3</td><td>0.3</td><td>0.3</td></tr><tr><td>Epochs</td><td>5</td><td>8</td><td>8</td><td>8</td><td>8</td></tr></table>",
+        "bbox": [
+            179,
+            215,
+            815,
+            315
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "table",
+        "img_path": "images/bffe4a9925265a1287eba5b6ab6e239d2088f54c8228d76f8d299729ccf5a5a7.jpg",
+        "table_caption": [
+            "Table 5: Variable training hyperparameters for all five model configurations"
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Hyperparameter</td><td>Value</td></tr><tr><td>Pre-trained LM</td><td>bert-base-uncased (Devlin et al., 2019)</td></tr><tr><td>LM hidden size</td><td>768</td></tr><tr><td>GNN hidden size</td><td>768</td></tr><tr><td>GNN layers</td><td>4</td></tr><tr><td>Batch size</td><td>16</td></tr><tr><td>Sequence length</td><td>64</td></tr><tr><td>Learning rate decay</td><td>constant</td></tr><tr><td>Optimizer</td><td>AdamW</td></tr></table>",
+        "bbox": [
+            307,
+            615,
+            690,
+            758
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "Table 6: Constant training hyperparameters for all five model configurations",
+        "bbox": [
+            238,
+            768,
+            756,
+            783
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "page_number",
+        "text": "3460",
+        "bbox": [
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+        ],
+        "page_idx": 13
+    }
+]

2024/Compositional Generalization with Grounded Language Models/5b07d1a5-aacb-474d-988a-7cd18a966725_origin.pdf

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2024/Compositional Generalization with Grounded Language Models/full.md

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+# Compositional Generalization with Grounded Language Models
+
+Sondre Wold, Étienne Simon, Lucas Georges Gabriel Charpentier, Egor V. Kostylev, Erik Velldal, Lilja Øvrelid  
+University of Oslo
+
+# Abstract
+
+Grounded language models use external sources of information, such as knowledge graphs, to meet some of the general challenges associated with pre-training. By extending previous work on compositional generalization in semantic parsing, we allow for a controlled evaluation of the degree to which these models learn and generalize from patterns in knowledge graphs. We develop a procedure for generating natural language questions paired with knowledge graphs that targets different aspects of compositionality and further avoids grounding the language models in information already encoded implicitly in their weights. We evaluate existing methods for combining language models with knowledge graphs and find them to struggle with generalization to sequences of unseen lengths and to novel combinations of seen base components. While our experimental results provide some insight into the expressive power of these models, we hope our work and released datasets motivate future research on how to better combine language models with structured knowledge representations.
+
+# 1 Introduction
+
+Language models (LMs) acquire latent representations of text through their pre-training. One drawback of this paradigm is the implicit encoding of knowledge in a large parameter space, which can lead to factual hallucinations in model outputs. To reduce this effect, there has recently been a widespread interest in what is sometimes referred to as grounded language models, which are LMs grounded in external information sources, such as knowledge graphs (KGs). These approaches typically attempt to enable reasoning over KGs by combining the LM outputs with that of a separate graph encoder, such as a graph neural network (GNN; Lin et al., 2019; Zhang et al., 2022; Sun et al., 2022; Yasunaga et al., 2022; Yu et al., 2022). It can be difficult to determine to what extent grounded models
+
+exhibit any structured reasoning, or what precisely would constitute reasoning in this context, as the information contained in these KGs often targets the same domain as the corpora used for LM pretraining. One example of this is the overlap in information between Wikidata, often used as the KG in previous work on grounded LMs, and Wikipedia, which is a common corpus for pre-training.
+
+Central to human reasoning is the ability to form novel combinations from seen components, often referred to as compositional generalization. Studies on compositionality have a long tradition within many fields of study, such as linguistics (Partee et al., 1995), philosophy (Pagin and Westerstahl, 2010), and cognitive science (Churchland, 1990), and determining to what degree neural networks capture compositionality is a long-standing research problem in machine learning, with debates going back several decades (Fodor and Pylyshyn, 1988; Smolensky, 1987). Recent studies in NLP have primarily used semantic parsing of synthetic utterances as a testbed for investigating to what extent neural networks combine syntactic elements to form new complex expressions (Hosseini et al., 2022). One of the most well-known examples of this is from Lake and Baroni (2018), who found seq2seq models to struggle both with systematic compositional skills and generalization to longer sequences than seen during training – abilities that are often taken to be central to compositional generalization. Some of these shortcomings were recently mitigated using a meta-learning framework (Lake and Baroni, 2023), but it is still not clear under what circumstances neural networks can consistently demonstrate compositional generalization, or if they can at all (Dziri et al., 2024).
+
+In this work, we investigate to what extent grounded language models exhibit compositional generalization by combining two orthogonal research directions: compositionality in neural networks and the grounding of LMs in KGs.
+
+Using question answering as a task, we train models to recognize the relation between certain patterns in a synthetic KG and natural language questions. We develop a data generation procedure that targets three aspects of compositionality from Hupkes et al. (2020): substitutivity, productivity, and systematicity. In our experiments, we evaluate LMs that interact with KGs through the use of a GNN, an approach previously proven effective for tasks such as question answering (Lin et al., 2019; Zhang et al., 2022; Sun et al., 2022) and pre-training (Yasunaga et al., 2022).
+
+Our work targets two key limitations from the literature: Firstly, by extending existing work on compositional generalization to question answering over KGs, we can assess the capabilities of these models for structured reasoning over natural language questions of varying complexities; and secondly, by using a synthetic knowledge graph we do not run the risk of grounding a language model in a knowledge source containing information that already exists implicitly in the models' weights. The contribution of our work is three-fold: i) We provide the first experimental study on the expressive power of grounded LMs with respect to compositional generalization ii) We develop a procedure for generating dataset samples that target three theoretically motivated aspects of compositionality, and iii) We release a series of generated datasets using this procedure, together with all code and data related to our experiments, which can be used to benchmark grounded language models in a controlled environment.
+
+# 2 Compositionality
+
+In what follows we discuss three aspects of compositionality that have been established as tests of compositionality in previous work (Hupkes et al., 2020): substitutivity, systematicity, and productivity. We also describe how we ground these notions to be applicable for our setting, where data consists of both text and KGs. We refer an interested reader to the overview by Szabó (2022) for a more extensive introduction to these terms.
+
+Substitutivity One of the most well-known definitions of compositionality is the principle of compositionality from Partee et al. (1995): "The meaning of a compound expression is a function of the
+
+meanings of its parts and of the way they are syntactically combined". Closely related to this principle is the notion of substitutivity, which states that any change to a complex expression that maintains the meaning of individual parts also maintains the meaning of the whole expression. On the one hand, in the context of natural languages, this definition is not without controversy. Languages often have elements that do not adhere strictly to such a principle, for example through the use of idioms (Dankers et al., 2022a). On the other hand, in our setting, we can exploit the observation that if an atomic expression in natural language has a node in a graph as its reference, then we can substitute this reference with a compounded expression referencing the same node without changing the meaning of the whole expression. As the principle of compositionality is not committed to any specific theory of semantics, we can use reference as the qualification for semantic equivalence, a theory sometimes referred to as the compositionality of reference (Szabó, 2022). For example, given the KG in Figure 1, we can ask ourselves whether "Paper2 was authored by Professor2". We can then replace "Professor2" with a compounded reference, such as "the supervisor of GraduateStudent5", which gives rise to the question: "Was Paper2 authored by the supervisor of GraduateStudent5?" Following the compositionality of reference, we do not change the meaning of the overall question, since we still enquire about the same node in the graph, even though we have substituted a 1-hop reference with a 2-hop reference. Consequently, by constructing highly compositional questions in natural language, we can test whether or not neural networks can learn the mapping between constituents in text and paths in a graph.
+
+Productivity Closely related to substitutivity, productivity refers to the ability to construct seemingly infinite constructions using a finite capacity. As Hupkes et al. (2020) point out, this view on the open-endedness of language is typically associated with generative linguistics, and in the context of neural networks, the most direct way of testing for this ability is to test models on generalization to sequences of lengths not seen during training. In our case, we can train models on questions that require reasoning over  $k$ -hop paths, for several  $k$ , in a graph, and then test on  $j$ -hop paths, for various  $j$  different from the  $k$ 's used in training.
+
+![](images/d008a6a40165247a751788512afa4e90410d15a303cd357e2fe93e3f8fb02c25.jpg)  
+Figure 1: An example KG illustrating the relationship between entities from the LUBM inventory.
+
+Systematicity One of the most tested properties of compositionality is systematicity, which was popularized as a term by Fodor and Pylyshyn (1988). Systematicity can loosely be described as the ability to combine seen parts and rules to form new combinations, an ability that has a long tradition within linguistics. In the context of neural networks, tests of systematicity typically involve exposing models to a finite set of items and combinations during training and then evaluating the same models on a test set containing the same set of items, but combined in ways not seen during training. Lake and Baroni (2018) use the example of a person that knows the meaning and usage of words such as "twice," "and," and "again," which upon learning the new verb "to dax" can generalize to new constructions such as "dax twice and then dax again," something they find neural networks to struggle with. Recently, there have also been some attempts to formalize and quantify systematic generalization in neural networks (Keysers et al., 2020; Ram et al., 2023). In our setting, we can use the typed relations of the edges in a graph, such as the one illustrated in Figure 1, to test for systematicity. If a model has seen the relations TEACHES, HAS-STUDENT, and ADVISOR in numerous 3-hop paths, but never in this order, a display of systematicity would require generalization to this unseen order.
+
+# 3 Dataset Generation
+
+# 3.1 Overview
+
+To target the compositional abilities specified above, we generate several datasets consisting of
+
+pairs of KGs and yes/no questions in natural language, all of which are about the information in these graphs. This section explains the properties of these datasets and how they are created.
+
+A KG over a set  $\mathcal{T}$  of types and a set  $\mathcal{R}$  of relations is a directed labeled multi-graph  $(\mathcal{V},\mathcal{L},\mathcal{E})$  with nodes  $\nu$ , called entities in this context, set  $\mathcal{L}$  of node labelings, each of which is of the form  $(v,t)$  where  $v$  is an entity in  $\mathcal{V}$  and  $t$  a type in  $\mathcal{T}$ , and set  $\mathcal{E}$  of edges, each of which is of the form  $(v,r,v')$ , where  $v$  and  $v'$  are entities from  $\nu$ , and  $r$  is a relation from  $\mathcal{R}$ . In this work, we only concentrate on graphs from the Lehigh University Benchmark (LUBM; Guo et al., 2005), which is a synthetic KG benchmark popular for evaluating various aspects of knowledge graph repositories. In particular, we exploit LUBM's KG generator of customizable and repeatable synthetic data, which can produce KGs of a user-specified size describing a fictitious university domain and committing to a realistic ontology over sets  $\mathcal{T}_{\text{LUBM}}$  and  $\mathcal{R}_{\text{LUBM}}$  of university-related types and relations. We generate several graphs with an average number of 685 entities, each labeled by a single type, and 4949 edges, each labeled by a single relation.
+
+Each of the natural language questions targets two entities in the corresponding generated LUBM graph  $\mathcal{G}$  and a chain of relations from  $\mathcal{R}_{\text{LUBM}}$  and inverses of such relations that is to hold between these entities. In particular, for a number of hops (i.e., chain length)  $k$ , the questions are semimanually created by first mapping each unique  $k$ -hop combination (i.e., chain of length  $k$ ) of relations from a selected subset of  $\mathcal{R}_{\text{LUBM}}$  and their inverses to a natural language template with two parameters, and then substituting these parameters by two entities from  $\mathcal{V}$  as arguments. As a result, the answer to the question is TRUE if there exists a path between the two entities in  $\mathcal{G}$  as prompted by the  $k$ -hop combination of the question template, and FALSE otherwise. We create templates for 2, 3, and 4 hops, with 5 relations from  $\mathcal{R}_{\text{LUBM}}$  and their inverses as  $\mathcal{R}_{\text{LUBM}}'$ . This makes for over 280 unique templates (while the number of questions depends on  $\mathcal{G}$ ). To illustrate our dataset creation we concentrate on an example and a discussion of a key step, sampling of positive and negative question-graph pairs, in the next two subsections. We refer to Appendix A for further details.
+
+# 3.2 Example
+
+Given the KG in Figure 1, we can create the following templates, for an increasing number of hops, where the “—” superscript denotes the inverse of the relation:
+
+2 hops: [TEACHES, TAKES COURSE $^{-}$ ]  $\rightarrow$  Does  $s$  teach a course that has a student named  $e$ ?  
+3 hops: [TEACHES, TAKESCOURSE $^{-}$ , ADVISOR]  $\rightarrow$  Does  $s$  teach a course that has a student supervised by  $e$ ?  
+4 hops: [TEACHES, TAKESCOURSE $^{-}$ , ADVISOR, PUBLICATIONAUTHOR]  $\rightarrow$  Does  $s$  teach a course that has a student supervised by an author of  $e$ ?
+
+To create questions from these templates that we label TRUE we can use PROFESSOR7 and GRADSTUDENT9 as arguments substituting parameters  $s$  and  $e$ , respectively, in the 2-hop case, PROFESSOR7 and PROFESSOR2 for the 3-hop case, and PROFESSOR7 and PAPER2 for the 4-hop case. Creating examples labeled as FALSE for these templates then involves sampling two entities to use as  $s$  and  $e$  that are not connected by the chains of relations, but are similarly connected in the graph as the entities in the positive examples. We describe this negative sampling in the next section.
+
+# 3.3 Sampling Procedure
+
+As mentioned, we create each question-graph pair by sampling pairs of entities and the relations on the edges that are to hold between them in the graph  $\mathcal{G}$ . The key requirement to this procedure is to guarantee that the  $k$  relations and their inverses in every sampled  $k$ -hop combination are as likely to be labeled TRUE as they are to be labeled FALSE; failing to do so introduces distributional bias. This means that our sampling procedure must ensure two important properties:  $i$  it must be impossible for a text-only model to associate a question template (i.e., all questions produced from this template) to the TRUE or FALSE label, and  $ii$  it must be impossible for a graph-only model to associate the presence of a specific set of relations in graph  $\mathcal{G}$  with a specific label.
+
+We ensure property  $i$  ) by creating the same number of questions labeled TRUE as FALSE for every unique  $k$ -hop combination of relations. We ensure ii) by sampling  $k$ -hop relation paths from  $\mathcal{G}$  symmetrically: We first sample i.i.d. two pairs of
+
+different entities,  $s_{+}, e_{+}$  and  $s_{-}, e_{-}$ , such that  $s_{+}$  and  $s_{-}$  are of the same entity type, and  $e_{+}$  and  $e_{-}$  are also of the same entity type. We then identify a  $k$ -hop combination over  $\mathcal{R}_{\text{LUBM}}'$  that exists between  $s_{+}$  and  $e_{+}$  but not between  $s_{-}$  and  $e_{-}$ , as well as verify that there exists another (different)  $k$ -hop combination over  $\mathcal{R}_{\text{LUBM}}'$  between  $s_{-}$  and  $e_{-}$ . If all this succeeds, the pair  $s_{+}, e_{+}$  with the question corresponding to the template becomes a positive example, and the pair  $s_{-}, e_{-}$  with the same template a negative one. Further details of the sampling procedure can be found in Appendix A.
+
+# 4 Modeling
+
+For all experiments, each data point includes a natural language question  $q$  and a graph  $\mathcal{G}$ . Following previous work on combining language models with KGs (Lin et al., 2019; Zhang et al., 2020; Yasunaga et al., 2021; Zhang et al., 2022; Kaur et al., 2022; Sun et al., 2022; Yasunaga et al., 2022), we use separate encoders for  $q$  and  $\mathcal{G}$  to obtain representations of both modalities. Section 4.1 outlines these encoders and Section 4.2 how we combine them to produce the final output prediction  $\hat{y} \in \{\mathrm{TRUE},\mathrm{FALSE}\}$ .
+
+# 4.1 Encoders
+
+Text encoder We obtain representations of  $q$  by using the special sentence representation token at the last layer of a pre-trained language model, as per Devlin et al. (2019):  $z_{\mathrm{text}} = \mathrm{BERT}(q)$ .
+
+Graph encoder As a graph encoder, we use the relational graph convolution model, R-GCN, from Schlichtkrull et al. (2018):
+
+$$
+h _ {i} ^ {\ell + 1} = \sigma \left(\sum_ {r \in \mathcal {R}} \sum_ {j \in \mathcal {N} _ {i} ^ {r}} \frac {1}{| \mathcal {N} _ {i} ^ {r} |} W _ {r} ^ {\ell} h _ {j} ^ {\ell} + W _ {0} ^ {\ell} h _ {i} ^ {\ell}\right),
+$$
+
+where  $h_i^\ell$  is the hidden state of a node  $i$  in layer  $\ell$ ,  $\sigma$  is the ReLU function and  $\mathcal{N}_i^r$  is the set of neighborhood vertices of node  $i$  under relation  $r$ .
+
+# 4.2 Final models
+
+Inspired by previous work on combining text and graph encoders, we experiment with different approaches to integrating the two modalities and apply them using the above-mentioned encoders and our experimental setup. Figure 2 provides an overview of the differences between these approaches.
+
+![](images/ec18fa16804874f13ff9aebbbd1e49525cca7b331dd9c610365ee46cbfc0c157.jpg)  
+Figure 2: Overview of the different approaches to combining the two encoders. Purple nodes are initialized at random while green and blue nodes are initialized using a frozen BERT model.
+
+![](images/fd948d5a75f87705b416757955ce0fc44d15465ce54663ca4268cef329b3c2ad.jpg)
+
+![](images/b3e03ba17858afb26c81f618dbe7f1b15345b076ddf6df120396084a033a49ed.jpg)
+
+![](images/87a300401d078159659e972953cdee172d11c7d8c7cdaec8f2e1130b6ba66d0f.jpg)
+
+Disjoint The simplest way of having the two modalities interact is to initialize and run both encoders separately before conjoining their outputs in a final classification layer. This keeps the encoders disjoint, essentially making a "two-tower architecture" – conceptually similar to approaches such as Wang et al. (2019).
+
+To get a final representation of the graph,  $z_{\mathrm{graph}}$ , we take the embedding of the head and tail node targeted by the question after  $L$  rounds of message passing:  $z_{\mathrm{graph}} = h_s^L \oplus h_e^L$ , where  $s$  and  $e$  are the indices of the head and tail node and  $\oplus$  is vector concatenation. We initialize these nodes by creating two distinct embeddings,  $E_s$  and  $E_e$ , with  $E_s, E_e \sim \mathcal{N}(0,1)$ . We keep these static throughout training and testing and use them for all head and tail nodes targeted by the questions. The initialization of remaining nodes in each graph is discussed in more detail in Section 4.3.
+
+For the question, we take the output of the text encoder without any modifications. The final output prediction is then obtained by the following:  $f(z_{\mathrm{text}} \oplus z_{\mathrm{graph}})$ , where  $f$  is a two-layered MLP with a ReLU activation function.
+
+Grounded For this model, we concatenate the original question string from  $q$  with both the head and tail entity strings, respectively, using a separation token. This is then used as input to the text encoder, obtaining a representation of the head and tail nodes:
+
+$$
+\begin{array}{l} h _ {s} ^ {0} = \operatorname {B E R T} (q <   \text {S E P} > \text {h e a d s u r f a c e f o r m}), \\ h _ {e} ^ {0} = \operatorname {B E R T} (q <   \text {S E P} > \text {t a i l s u r f a c e f o r m}). \\ \end{array}
+$$
+
+These are then used to initialize the embeddings for the nodes pertaining to these entities in the graph. This is done in a pre-processing step before the text encoder is fine-tuned on our datasets. The final output prediction is calculated in the same way as with the disjoint model.
+
+Unidirectional In this model, we add a unidirectional interaction between the encoders, inspired by works such as Yasunaga et al. (2021). For each question-graph pair,  $(q,\mathcal{G})$ , we introduce a new special context node,  $u$ , and connect  $u$  to each node in  $\mathcal{G}$ . This special node is connected using two new relations, one for each direction, and its embedding is initialized using the text encoder representation of the question,  $\mathrm{BERT}(q)$ . In Figure 2,  $u$  is marked as a blue node. For each  $\mathcal{G}$ , we perform global pooling over the hidden states:
+
+$$
+z _ {\text {g r a p h}} = \frac {1}{| \mathcal {V} |} \sum_ {v \in \mathcal {V} ^ {\prime}} h _ {v} ^ {L},
+$$
+
+where  $\mathcal{V}'$  is the set containing the head, tail, and special context nodes. We do not consider the set of all nodes due to the zero-initialization of the remaining nodes in  $\mathcal{G}$  (see Section 4.3). The head and tail nodes are initialized as in the grounded model, using the text encoder representations. We also take the embedding of the special node at the last layer,  $h_u^L$ , as a representation of  $\mathcal{G}$ . The final output prediction is then given by:  $f(z_{\mathrm{text}} \oplus z_{\mathrm{graph}} \oplus h_u^L)$ , where  $f$  is a two-layered MLP with a ReLU activation function.
+
+Bidirectional We also develop a model inspired by the interaction approach used in works such as
+
+Zhang et al. (2022) and Yasunaga et al. (2022) to allow for a bidirectional interaction between the two encoders. We keep the special context node  $u$  as described in the unidirectional model, but we add a special interaction token,  $t$ , to the question  $q$ .  $t$  is set to be the representation of the special context node  $u$  after  $L$  layers of message passing:  $t = h_u^L$ . This is done after the embedding of  $q$  in the text encoder. We produce the final output prediction using the same method as in the unidirectional model.
+
+Baseline We use a sole graph encoder as a baseline. Theoretically, it should not be possible to solve the tasks without having access to both the text and the graph. By using a graph-only system as a baseline we therefore get both a sanity check and an upper bound on the noise produced by the sampling. As the natural language questions are not sampled, but rather constructed deterministically from the paths sampled from our graphs, one positive and one negative, the performance of a text-only encoder will by design be equal to a random classifier. The output of the baseline is calculated the same way as for the disjoint model, taking the representations of the head and tail entity.
+
+# 4.3 Node initialization
+
+Except for the head and tail nodes targeted by each question, and the special context node  $u$ , all nodes are initialized as zero-vectors. This means that we leak the position of the head and tail entity in  $\mathcal{G}$  for each sample in the dataset, making any pruning of  $\mathcal{G}$  redundant. It is often necessary to reduce the computational complexity of combining language models and large knowledge graphs using mechanisms such as subgraph retrieval and entity linking, but these steps are also known to be error-prone (Wold et al., 2023). This initialization ensures that we further isolate the application of compositional generalization rules, as opposed to evaluating the performance of a pipeline model with numerous error-prone components.
+
+# 5 Experiments and results
+
+<table><tr><td>Hops</td><td>#relation-paths</td><td>N</td></tr><tr><td>2</td><td>23</td><td>1043±1941</td></tr><tr><td>3</td><td>73</td><td>328±449</td></tr><tr><td>4</td><td>188</td><td>127±260</td></tr></table>
+
+Table 1: The mean number of occurrences of the relation paths across 24000 generated graphs per hop  $k$  .
+
+In this section, we test our suite of models on data specifically targeting substitutivity (Section 5.1), productivity (Section 5.2), and systematicity (Section 5.3), going test by test. For all experiments, the distribution between the two classes is perfectly balanced. Statistics on the diversity of the generated graphs with respect to relation paths can be found in Table 1. Details on the selection of hyperparameters can be found in Appendix B.
+
+# 5.1 Substitutivity
+
+In our first test, we evaluate to what extent the five model configurations can answer questions targeting substitutivity, as defined in Section 2. Success at this task requires recognizing the mapping between the presence of certain relations in the graph and phrases in the natural language questions. Substitutivity is the most basic setting of our experiments and the results on this task demonstrate the general difficulty of the task.
+
+Test design We generate 12000 question-graph pairs using our generation procedure. We do this for 2, 3 and 4-hops. Each experiment targets one of the hop lengths, i.e., both training and evaluating on the same number of hops. For all experiments, we use 10000 samples for training and 2000 for testing. All results are reported using mean accuracy and standard deviation from five randomly seeded runs.
+
+Results The results of the substitutivity tests can be seen in Table 2. There is a strong generalization in the 2-hop case for all models. In the 3-hop case, performance drops significantly and the variance also increases for most models. There is a further loss in generalization when moving to the 4-hop case, where there is little difference between the models. Figure 3 shows that there is a positive correlation between test accuracy on a specific question type and the frequency of the corresponding relation path in the training data for the 3-hop case. For the 2-hop and 4-hop cases, where the performance is closer to perfect and random classification, respectively, the relationship flattens. This aligns with the increase in unique combinations of relation paths as the number of hops increases, as shown in Table 1. For 2-hops there is either a high number of examples per relation path combination, which enables learning, or very few, which makes the performance on these relation paths negligible on the overall accuracy. For 4-hops, on the other hand, there is too much of a long tail on the dis
+
+<table><tr><td>Model</td><td>2-hop</td><td>3-hop</td><td>4-hop</td></tr><tr><td>Baseline</td><td>48.88±1.00</td><td>49.8±0.64</td><td>49.36±0.44</td></tr><tr><td>Disjoint</td><td>98.17±0.39</td><td>83.08±0.96</td><td>67.86±1.89</td></tr><tr><td>Grounded</td><td>92.46±0.49</td><td>84.91±0.38</td><td>69.32±1.96</td></tr><tr><td>Unidirectional</td><td>91.78±0.72</td><td>70.88±3.53</td><td>62.0±3.97</td></tr><tr><td>Bidirectional</td><td>92.44±0.23</td><td>73.66±1.04</td><td>63.24±3.36</td></tr></table>
+
+ribution of number of samples per combination, making learning difficult. For 3-hops, however, there is a balance, which is reflected in the results. See Figure 4 in Appendix A for an illustration of the relative percentage of each unique combination to the total for each hop.
+
+These results show that the models struggle to generalize to the long tail of the training distribution, which is a known attribute of neural networks. However, single relation types are reused extensively throughout our training data, as there are only 10 unique relations of length 1. This means that the distribution only has a long tail if one considers each 4-hop combination to be a single unique type, as opposed to being composed of four individual relations that are individually high-frequent. We argue that these results indicate that these models do not create internal representations of each 1-hop path together with a function for composing them into compounded expressions, but rather learn individual representations for each compound. This also explains why the performance drops as the complexity increases and the number of samples per relation decreases, making such a strategy less viable. This explanation is further explored in the systematicity tests. We also note that there is little difference between the models, indicating that an increase in model complexity does not add any benefits to this task.
+
+# 5.2 Productivity
+
+In our next test, we evaluate to what extent models can answer  $k$ -hop questions when trained on  $j$ -hops, with  $k \neq j$ . We define experiments requiring extrapolation and interpolation for different values of  $k$  and  $j$ . Success at this task requires generalization to sequences with a different length than those seen during training.
+
+Test design In our first experiment, we use an even amount of 2 and 3-hop questions for training while using 4-hop questions for testing, targeting extrapolation. In our second experiment, we tar
+
+Table 2: Substitutivity results.  
+
+<table><tr><td>Experiment</td><td>Acc.</td></tr><tr><td colspan="2">TRAIN: 2 AND 3-HOP. TEST: 4-HOP</td></tr><tr><td>Baseline</td><td>49.92±0.82</td></tr><tr><td>Disjoint</td><td>59.42±2.07</td></tr><tr><td>Grounded</td><td>61.79±0.52</td></tr><tr><td>Unidirectional</td><td>62.40±1.02</td></tr><tr><td>Bidirectional</td><td>62.05±0.91</td></tr><tr><td colspan="2">TRAIN: 2 AND 4-HOP. TEST: 3-HOP</td></tr><tr><td>Baseline</td><td>51.19±0.31</td></tr><tr><td>Disjoint</td><td>63.87±2.24</td></tr><tr><td>Grounded</td><td>66.10±2.02</td></tr><tr><td>Unidirectional</td><td>66.65±2.24</td></tr><tr><td>Bidirectional</td><td>66.29±1.25</td></tr><tr><td colspan="2">TRAIN: 3 AND 4-HOP. TEST: 2-HOP</td></tr><tr><td>Baseline</td><td>50.98±0.25</td></tr><tr><td>Disjoint</td><td>60.34±3.25</td></tr><tr><td>Grounded</td><td>62.32±1.98</td></tr><tr><td>Unidirectional</td><td>64.04±4.47</td></tr><tr><td>Bidirectional</td><td>63.03±3.76</td></tr></table>
+
+Table 3: Productivity results.
+
+get interpolation by training on an even amount of 2 and 4-hop questions while testing on 3-hops. For our last experiment, we target extrapolation to lower values, using a training split with an even amount of 3 and 4-hop questions while testing on 2-hops. For all three experiments, we generate 10 000 samples for training and 2 000 for testing.
+
+Results The results of the productivity tests can be seen in Table 3. In general, we observe that all models struggle to extrapolate to both shorter and longer hops. We observe some generalization for the interpolation test, where the model has seen sequences both shorter and longer during training, but the overall absolute performance is still poor. This aligns with previous work, such as Lake and Baroni (2018) and Hupkes et al. (2020). We observe a tiny increase in performance with the more complex models compared to the simpler, disjoint model, but given the overall low scores and the variance, we do not think these results are significant. This indicates that adding a more complex interaction between the encoders does not provide any added benefit for extrapolation or interpolation.
+
+# 5.3 Systematicity
+
+In our last test, we evaluate to what extent our models can generalize systematically. This means that all unique 1-hop relations are seen during training in some  $k$ -hop combination, but in the test data, we only include unseen combinations. For example, during training the models might see samples using the relations TAKES COURSE and
+
+![](images/10738a4e76ea540b1acc4de1b4e5248ec075dcaa6fd4343d2f1fa343585b795e.jpg)  
+Figure 3: Relationship between frequency of a  $k$ -hop relation and the performance of the Disjoint model on these during testing. Each blue point corresponds to a tuple of  $k$  relations for  $k = 1,2,3$ . The orange lines are the linear regressions for each setting showing positive correlations between frequencies of  $k$ -hop relations and performances of the Disjoint model.
+
+![](images/4fbdf814a10ededda6e908da8f49d0346c3c26da0b9aa37c372be46a513722dc.jpg)
+
+![](images/a75cd526d4e524697f521864c00404708a8917440e5ebf1da827813bcdf89ef7.jpg)
+
+HASTEACHINGASSISTANT, and the 2-hop combination [TAKESCOURSE, HASTEACHINGASSISTANT], but in the test we target [HASTEACHINGASSISTANT, TAKESCOURSE]. Success at this task requires the model to learn that a 3-hop question, for example, consists of three individual parts that are combined, as opposed to encoding the entire sequence as one entity.
+
+Test design With  $k$  being 2, 3, or 4, we generate question-graph pairs with length  $k$ . Then, for each  $k$ , we randomly select a fraction of the available  $k$ -length combinations of relations as our test combinations. We then separate the generated pairs into two parts: those who use the test combinations and those who do not. The former is saved as the test set. We note that the use of test combinations is not limited to the relations on the path between the head and tail entities targeted by the question, but any  $k$ -hop path that exists between these entities. For the training set, we split the remaining possible combinations into five chunks and collect all samples that use these combinations. This leaves us with five different folds of the training set. Models are then trained on each fold independently, but evaluated on the same test set. We do this to control for the fact that some combinations of relations might have a similar distribution of samples as the relations picked out for the test set, making them better fits for that particular split.
+
+As this tests out-of-distribution generalization, we argue that folding is better suited for finding the true performance and variance of the models than the more straightforward evaluation method used for our substitutivity and productivity experiments. The results are reported as the mean accuracy over all five folds.
+
+Results The results of the systematicity tests can be seen in Table 4. As with the productivity tests, we see that there is no consistent display of generalization for any of the models across hops. We see, however, that for the 3-hops setting the two simpler models achieve some success on the task. As these models had the highest performance on the substitutivity test, we take this to indicate that additional architectural complexity does not provide any performance benefit for this type of generalization. We also note that it is possible that these experiments are sensible to the hyperparameters, and that the two simpler models happened to have a better fit for the 3-hop setting. We did not do a specific hyperparameter search per model for the systematicity experiments but relied on those from the initial hyperparameter search.
+
+Overall, these results might come from undersampling, or it might be the case, as is reported in Hupkes et al. (2020), that the models are not able to construct useful representations of smaller syntactic units. We argue that our results further support the intuition from the substitutivity experiments: the models do not learn to create representations that correspond to each 1-hop relation, together with a function for combining them, but rather rely on memorization of whole combinations of relation types. For short-tailed distributions and some settings of hyperparameters this works, but it is not a robust solution to the general problem of matching the text questions to certain patterns in the graphs, illustrated by the significant drop in performance in these results.
+
+We also see adjacent work on assessing compositional generalizations in LLMs to provide possible explanations for our results. Dziri et al. (2024) hypothesize that transformer-based models try to solve a highly compositional problem, like ours, by
+
+<table><tr><td>Model</td><td>2-hop</td><td>3-hop</td><td>4-hop</td></tr><tr><td>Baseline</td><td>49.50±0.24</td><td>49.40±0.33</td><td>49.92±1.01</td></tr><tr><td>Disjoint</td><td>53.62±8.39</td><td>74.05±3.42</td><td>62.18±1.20</td></tr><tr><td>Grounded</td><td>60.02±3.22</td><td>75.68±3.27</td><td>64.96±1.39</td></tr><tr><td>Unidir.</td><td>64.24±0.75</td><td>57.12±1.81</td><td>64.10±3.62</td></tr><tr><td>Bidir.</td><td>64.15±1.10</td><td>60.37±2.31</td><td>63.72±3.63</td></tr></table>
+
+Table 4: Systematicity results.
+
+reducing it into linearized path matching. If this is the case, models do not learn the compositional rule needed to solve the task. If the samples from the test distribution only resemble the training distribution superficially, this pattern matching approach is not a viable solution for out-of-distribution generalization in both our productivity and systematicity experiments. In these experiments, the mapping from the input samples to output labels cannot be based on surface-form frequency, due to our balanced sampling, which could then explain the collapse in performance we are observing for these experiments.
+
+# 6 Previous work
+
+There have been numerous works on compositional generalization in neural networks (Andreas, 2019; Lake and Baroni, 2018; Kim and Linzen, 2020; Hupkes et al., 2020; Dankers et al., 2022b; Lake and Baroni, 2023; Dziri et al., 2024). Most similar to our work is Gu et al. (2021), which develops a large-scale dataset targeting aspects of compositional generalization using question answering over Wikidata. Both this work and similar efforts reformulate the problem of integrating the KG to a seq2seq task where the questions are first translated into an intermediate logical form, such as SPARQL, which can be executed over the KG (Shu et al., 2022). Under the same framework, Ravishankar et al. (2022) explicitly tests generalization to unseen combinations of relations in a similar fashion to our systematicity test. They too find that the performance tends to drop significantly for this setting.
+
+The mapping from natural language to logical form can also use techniques from semantic parsing, a topic where compositionality is of special interest (Lindemann et al., 2023). Our work, however, is the first to target compositionality in a setup where the models learn representations of both text and graphs directly, without any logical form as an intermediate step. In contrast to previous work on grounded language models (Lin et al., 2019; Zhang
+
+et al., 2020; Yasunaga et al., 2021; Zhang et al., 2022; Kaur et al., 2022; Sun et al., 2022), our methods can also more precisely quantify the effect of combining LMs with GNNs, as our sampling procedure ensures that the encoders can not achieve above random performance on their own, a property which we believe is unique to our approach.
+
+# 7 Conclusion
+
+Research on compositional generalization in neural networks has a long history. To the best of our knowledge, we provide the first experimental evaluation of compositional generalization in grounded LMs, using question answering over KGs as a task. Our results indicate that these models  $i$  ) require large sample sizes and quickly lose generalization power as the complexity of the compositional structure increases,  $ii$  ) struggle with extrapolation and interpolation to sequences of lengths not seen during training, and  $iii$  ) cannot systematically generalize from seen base components to novel compositions given the sample sizes used in our experiments. We show this across a set of model architectures inspired by the literature. Our results are in line with previous work on compositional generalization in other domains and for other types of neural architectures. Overall, we believe our results show that grounded LMs do not display signs of structured reasoning over KGs and that there is still much to be done on the improvement of models that try to exploit external information stored as symbolic objects. This is the case not only for knowledge graphs but also for other types of data representations, such as tabular data. We hope our generation procedure and released datasets can help motivate future efforts at overcoming these challenges.
+
+# Limitations
+
+Models Our models are inspired by previous work. However, since our experimental setup differs from the original settings these models were implemented to work in, we had to make multiple simplifications. Consequently, we are not able to conclude anything about the abilities of the specific models from the literature, but rather about the general interaction approach they propose.
+
+Question variety The questions in our dataset are formulated in English, and although they have more linguistic variety than similar studies from semantic parsing, such as Lake and Baroni (2018)
+
+and Hupkes et al. (2020), we still use a rather limited version of the language, which is by design devoid of any metaphors, idioms, analogies and other constructs that would make compositionality more difficult to measure. It is not given that our results transfer to real language data.
+
+# Acknowledgments
+
+We acknowledge Sigma2, Norway, for awarding this project access to the LUMI supercomputer, owned by the EuroHPC Joint Undertaking, hosted by CSC (Finland) and the LUMI consortium.
+
+# References
+
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+Paul M. Churchland. 1990. Cognitive activity in artificial neural netowrks. An invitation to cognitive science: Thinking, 3:199-229.  
+Verna Dankers, Elia Bruni, and Dieuwke Hupkes. 2022a. The paradox of the compositionality of natural language: A neural machine translation case study. In Proceedings of the 60th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers), pages 4154-4175, Dublin, Ireland. Association for Computational Linguistics.  
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+Brenden M. Lake and Marco Baroni. 2018. Generalization without systematicity: On the compositional skills of sequence-to-sequence recurrent networks.  
+Brenden M. Lake and Marco Baroni. 2023. Human-like systematic generalization through a meta-learning neural network. Nature, 623(7985):115-121.  
+Bill Yuchen Lin, Xinyue Chen, Jamin Chen, and Xiang Ren. 2019. KagNet: Knowledge-aware graph networks for commonsense reasoning. In Proceedings of the 2019 Conference on Empirical Methods in Natural Language Processing and the 9th International Joint Conference on Natural Language Processing (EMNLP-IJCNLP), pages 2829-2839, Hong Kong, China. Association for Computational Linguistics.
+
+Matthias Lindemann, Alexander Koller, and Ivan Titov. 2023. Compositional generalisation with structured reordering and fertility layers. In Proceedings of the 17th Conference of the European Chapter of the Association for Computational Linguistics, pages 2172-2186, Dubrovnik, Croatia. Association for Computational Linguistics.  
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+Parikshit Ram, Tim Klinger, and Alexander G. Gray. 2023. How compositional is a model? In International Joint Conference on Artificial Intelligence 2023 Workshop on Knowledge-Based Compositional Generalization.  
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+Sondre Wold, Lilja Øvrelid, and Erik Velldal. 2023. Text-to-KG alignment: Comparing current methods on classification tasks. In Proceedings of the First Workshop on Matching From Unstructured and Structured Data (MATCHING 2023), pages 1-13, Toronto, ON, Canada. Association for Computational Linguistics.  
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+
+# A Dataset generation
+
+# A.1 LUBM
+
+We use the LUBM UBA to generate knowledge graphs on the fly. We limit our graphs to the following entity types: Professor, AssociateProfessor, UndergraduateStudent, GraduateStudent, TeachingAssistant, Publication, Course; and the following relations: PUBLICATIONAUTHOR, TEACHEROF, ADVISOR, TAKESCOURSE, TEACHINGASSISTANTOF. We also add reverse edges with reverse relations for all of these to create more diverse question types in our final dataset, making  $|\mathcal{R}_{LUBM}^{\prime}| = 10$ . We remove all literals. Using a sample size of approximately 14000, we create graphs that have  $\mu = 685$ ,  $\sigma = 77.16$  nodes and  $\mu = 4949$ ,  $\sigma = 532$  edges after processing.
+
+# A.2 Statistics
+
+![](images/81adfba236d19aa9a51be36fad045a472638f20f1d072b1b532033d949364823.jpg)  
+Figure 4: The relative percentage of each unique relation path to the total for 2, 3, and 4-hops.
+
+The number of possible combinations of relations on the edges in a  $k$ -hop path increases with the number of hops. As our sampling procedure uses 10 distinct relations we have  $10^{k}$  theoretical combinations of relations for any  $k$ -hop path. As our graphs are committed to the LUBM ontology the number of relations that hold between two entity types is much lower.
+
+# A.3 Sampling procedure
+
+Given a directed multigraph  $G = (\mathcal{V}, \mathcal{E})$  with labeled entities  $v_i \in \mathcal{V}$  and labeled edges  $(v_i, r, v_j) \in \mathcal{E}$  where  $r \in \mathcal{R}$  is a relation, we sample a positive and negative example for a  $k$ -hop path using the following procedure:
+
+1. Sample two pairs of nodes  $(s_{+}$  and  $e_+$ ) and  $(s_{-}$  and  $e_{-})$  from  $\mathcal{V}$  with uniform probability, making sure that  $s_{+} \neq s_{-}$  or  $e_{+} \neq e_{-}$ , that  $s_{+}$  and  $s_{-}$  are of the same entity type, and that  $e_{+}$  and  $e_{-}$  are of the same entity type.  
+2. Let  $R_{+}$  be the set of all relation paths of length  $k$  from  $s_{+}$  to  $e_{+}$ .  
+3. Let  $R_{-}$  be the set of all relation paths of length  $k$  from  $s_{-}$  to  $e_{-}$ .  
+4. Let  $P_{+}$  be the set  $R_{+} \setminus R_{-}$  
+5. Let  $P_{-}$  be the set  $R_{-} \setminus R_{+}$  
+6. If  $P_{+} \neq \emptyset$  and  $P_{-} \neq \emptyset$ :
+
+(a) Sample a relation path  $q\colon q\sim \mathcal{U}(P_{+})$  
+(b) Return the triple  $(q, s_{+}, e_{+})$  as a positive example and  $(q, s_{-}, e_{-})$  as a negative example.
+
+This procedure returns a  $k$ -hop relation path,  $q$ , that holds between  $s_{+}$  and  $e_{+}$  but not between  $s_{-}$  and  $e_{-}$ . However, we also make sure that there are paths that hold between  $s_{-}$  and  $e_{-}$  but not  $s_{+}$  and  $e_{+}$ , ensuring symmetry.
+
+In addition, we shuffle entities labels while preserving entity types before running this procedure since the LUBM generator introduces problematic patterns with its entity numbering. For example, in the original graph, Professor1 is more likely to author Paper1 than Paper5. By randomly exchanging the labels of Paper1 and Paper5, we ensure the models cannot exploit this regularity.
+
+# B Models
+
+# B.1 Parameters
+
+All our combined models have a total of  $\approx 141000000$  parameters, with the majority of them coming from the language model. Our baseline has  $\approx 30000000$ .
+
+# B.2 Computation infrastructure
+
+All the experiments ran on the LUMI supercomputer, using a single AMD MI250X GPU. Running all the experiments reported in the paper has a total computing budget of approximately 150 hours.
+
+# B.3 Hyperparameters
+
+We tune the learning rate for the text encoder from  $\{1 \times 10^{-6}, 1 \times 10^{-5}, 2 \times 10^{-5}, 3 \times 10^{-5}, 5 \times 10^{-5}\}$ , the graph encoder module from  $\{2 \times 10^{-4}, 5 \times 10^{-4}, 1 \times 10^{-3}, 2 \times 10^{-3}, 1 \times 10^{-5}\}$ , and the MLP module from  $\{1 \times 10^{-4}, 1 \times 10^{-5}\}$ ; the dropout value from  $\{0.1, 0.2, 0.3\}$  and the epochs from  $\{5, 8, 10\}$ , with no early stopping. The hyperparameters are tuned on a development set targeting the substitutivity task with an equal mix of 2, 3, and 4-hop questions. We run 60 trials for each of the five model configurations and sample a random combination of these parameters for each trial, selecting the best combination for our experiments. We find that all models perform the best with no decay on the learning rate.
+
+<table><tr><td>Hyperparameter</td><td>BASELINE</td><td>DISJOINT</td><td>GROUNDED</td><td>UNIDIRECTIONAL</td><td>BIDIRECTIONAL</td></tr><tr><td>LM lr</td><td>-</td><td>0.00001</td><td>0.00001</td><td>0.00001</td><td>0.00001</td></tr><tr><td>GNN lr</td><td>0.00001</td><td>0.0005</td><td>0.0005</td><td>0.00005</td><td>0.0005</td></tr><tr><td>MLP lr</td><td>0.00001</td><td>0.0001</td><td>0.0001</td><td>0.0001</td><td>0.0001</td></tr><tr><td>Dropout</td><td>0.3</td><td>0.3</td><td>0.3</td><td>0.3</td><td>0.3</td></tr><tr><td>Epochs</td><td>5</td><td>8</td><td>8</td><td>8</td><td>8</td></tr></table>
+
+Table 5: Variable training hyperparameters for all five model configurations  
+
+<table><tr><td>Hyperparameter</td><td>Value</td></tr><tr><td>Pre-trained LM</td><td>bert-base-uncased (Devlin et al., 2019)</td></tr><tr><td>LM hidden size</td><td>768</td></tr><tr><td>GNN hidden size</td><td>768</td></tr><tr><td>GNN layers</td><td>4</td></tr><tr><td>Batch size</td><td>16</td></tr><tr><td>Sequence length</td><td>64</td></tr><tr><td>Learning rate decay</td><td>constant</td></tr><tr><td>Optimizer</td><td>AdamW</td></tr></table>
+
+Table 6: Constant training hyperparameters for all five model configurations

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+# Comprehensive Abstractive Comment Summarization with Dynamic Clustering and Chain of Thought
+
+Longyin Zhang $^{1}$ , Bowei Zou $^{1}$ , Jacintha Wee Yun  $\mathbf{Yi}^{1,2*}$ , Ai Ti  $\mathbf{A}\mathbf{w}^{1}$
+
+1. Institute for Infocomm Research, A*STAR, Singapore
+
+2. Nanyang Technological University, Singapore
+
+{zhang_longyin,zou_bowei,aaiti}@i2r.a-star.edu.sg
+
+jaci0003@e.ntu.edu.sg
+
+# Abstract
+
+Real-world news comments pose a significant challenge due to their noisy and ambiguous nature, which complicates their modeling for clustering and summarization tasks. Most previous research has predominantly focused on extractive summarization methods within specific constraints. This paper concentrates on Clustering and Abstractive Summarization of online news Comments (CASC). First, we introduce an enhanced fast clustering algorithm that maintains a dynamic similarity threshold to ensure the high density of each comment cluster being built. Moreover, we pioneer the exploration of tuning Large Language Models (LLMs) through a chain-of-thought strategy to generate summaries for each comment cluster. On the other hand, a notable challenge in CASC research is the scarcity of evaluation data. To address this problem, we design an annotation scheme and contribute a manual test suite tailored for CASC. Experimental results on the test suite demonstrate the effectiveness of our improvements to the baseline methods. In addition, the quantitative and qualitative analyses illustrate the adaptability of our approach to real-world news comment scenarios.
+
+# 1 Introduction
+
+With the continued development of handheld devices and the boom of social media, the proliferation of online news is swift and relentless. This has fueled heightened interest among researchers on the topic of public opinion analysis, including tasks like opinion mining (Barker et al., 2016a; Pecar, 2018; Gao et al., 2019; Yang et al., 2019; Huang et al., 2023), sensitive comments detection (Pavlopoulos et al., 2017; Chowdhury et al., 2020; Moldovan et al., 2022; Sousa and Pardo, 2022), and news comments summarization (Khabiri et al., 2011; Dalal and Zaveri,
+
+2013; Aker et al., 2016; Žagar and Robnik-Sikonja, 2021). This study concentrates on the Clustering and Abstractive Summarization of online news Comments (CASC). While the past decade has witnessed substantial progress in text summarization across diverse frameworks (Rush et al., 2015; Liu et al., 2015; Yasunaga et al., 2017; See et al., 2017; Lewis et al., 2020; Wang et al., 2021, 2022; Ouyang et al., 2022; OpenAI, 2023), research specifically targeting CASC remains scarce.
+
+Comment summarization involves extracting a collection of comments either by selecting sentences directly from the comments, referred to as extractive comment summarization, or by compressing the original comments through generative techniques for abstractive summarization. While previous studies have explored a methodology of initially clustering comments into distinct groups followed by summarization (Khabiri et al., 2011; Ma et al., 2012; Llewellyn et al., 2016; Barker et al., 2016b; Pecar, 2018; Žagar and Robnik-Sikonja, 2021), these endeavors have focused on extractive summarization. Our investigation of Reddit comments reveals a spectrum of characteristics influenced by context, platform, and user demographics. In particular, these comments exhibit diversity in style, length, level of detail, and relevance to the contextual discussion, posing significant challenges for summarization using extractive approaches.
+
+In this status quo, this work focuses on abstractive comment summarization with the goal of providing well-organized and extensive coverage of user comments across diverse topics. We confront two main challenges: Firstly, the CASC task, in its nascent phase, suffers from a lack of a formal task definition, an open-source evaluation scheme, and accessible data. This absence largely hinders the expeditious and streamlined evaluation of diverse methods, models, or algorithms. Secondly, although recent Large Language Models (LLMs) have achieved impressive performance in text sum
+
+marization (Zhang et al., 2022; Chung et al., 2022; Touvron et al., 2023a; Ouyang et al., 2022; OpenAI, 2023), there are still limitations when applying such LLMs to CASC. On the one hand, online comments on trending topics can be lengthy, surpassing the strict input sequence length constraints of existing foundational models. On the other hand, while existing LLMs excel as text generators, their efficacy in clustering remains underdeveloped.
+
+In this paper, we propose a novel task on abstractive news comment summarization to address the aforementioned challenges. Our contributions encompass three points:
+
+- This paper introduces a straightforward yet effective comment clustering algorithm, coupled with a task-specific ranking mechanism, to dynamically adjust the similarity threshold for comment clustering and rank candidate clusters based on both their density and topical relevance. This method ensures that each comment cluster yields high compactness and discernibleness.  
+- Based on the clustering algorithm, we propose harnessing moderate-scale LLMs for comment cluster summarization. Particularly, we fine-tune the model through a chain-of-thought manner to first predict aspect terms (ATs) for each comment cluster and then perform AT-based summarization.  
+- In particular, this work contributes the first annotation scheme and manual test suite tailored for CASC. Notably, different from previous works on topic-based clustering (Khabiri et al., 2011; Ma et al., 2012), we introduce the concept of aspect-based comment clusters to restrict the granularity of each cluster quantitatively.
+
+Quantitative experiments and qualitative analysis of the proposed CASC system demonstrate the effectiveness of our improvements over the baseline systems. Moreover, a real-scenario case study further indicates the practicability of our approach.
+
+# 2 Related Work
+
+Comment cluster summarization. Previous research on comment cluster summarization can be categorized into three main groups: some solely study comment clustering (Aker et al., 2016; Llewellyn et al., 2016), others focus on summarizing comment clusters in different forms (Dalal and Zaveri, 2013; Barker et al., 2016a; Gao et al.,
+
+2019; Huang et al., 2023), while a third group explores both clustering and summarization of news comments (Khabiri et al., 2011; Hsu et al., 2011; Llewellyn et al., 2014; Barker et al., 2016b; Žagar and Robnik-Sikonja, 2021). Our study falls within the latter category that emphasizes both clustering and summarization of comments.
+
+Previous studies of (Khabiri et al., 2011; Ma et al., 2012) are the first to explore extractive summarization of comment clusters, which first group comments into clusters under different topics and then extract comments from each cluster to form the summary. Hsu et al. (2011) alternatively proposed a hierarchical clustering method to summarize YouTube comments based on comment term normalization and key term extraction. Subsequently, Llewellyn et al. (2014) conducted a comprehensive comparison of various clustering methods, including topic-driven clustering, keyword-based clustering, k-means, and cosine distance, demonstrating the superior performance of topic-driven clustering in producing comment clusters suitable for extractive summarization.
+
+However, the above topic-oriented approaches often assume that the resulting summary, derived from topically clustered and extracted comments, aligns with user preferences and presents the crux of the discussed matters. Such assumptions may not always hold. Recognizing this problem, Barker et al. (2016b) conducted a series of data analyses and argued that a good comment summary should not only convey the central issues discussed but also encapsulate the opinions surrounding those issues, suggesting that a good summary should cover finer-grained information beyond just topics. In order to capture more informative comment representations, Žagar and Robnik-Sikonja (2021) proposed to utilize neural sentence embedding methods for extractive summarization of comment clusters. Despite these efforts have been made in comment cluster summarization, all previous works concentrated on extractive summarization, while the abstractive CASC task is largely unexplored. In this paper, we aim to conduct an in-depth study of CASC to fill the gap in this field.
+
+LLM-based summarization. The recent popular LLMs (Zhang et al., 2022; Chung et al., 2022; Touvron et al., 2023a; Ouyang et al., 2022; OpenAI, 2023) have achieved impressive performance in many NLP tasks including text summarization. Notably, the recent paper (Pu et al., 2023) argues
+
+that "summarization is almost dead". In this LLM era, our stance is that summarizing large-scale online user comments remains a challenge even for state-of-the-art (SoTA) foundation models for two reasons: (1) The strict input sequence length limitation of current foundation models makes it infeasible to take all comments as inputs for CASC; (2) Current LLMs are usually pre-trained on text generation tasks, their clustering abilities are far from perfect. Moreover, the quality of text clustering is intricately related to user preference, which is hard to describe using a textual prompt. Our work contributes to building a CASC test suite with user-preferred summaries, which aligns with the new horizons discussed in (Pu et al., 2023).
+
+# 3 CASC Test Suite
+
+This section introduces the proposed annotation scheme coupled with the manually built test suite for CASC evaluation. Diverging from conventional comment clustering works where the comments are clustered based on the coarse-grained topics, this study focuses more on the finer aspect terms within each news comment. In this paper, we introduce a concept of Comment Aspect Term (CAT), which refers to primary objects of the entire discourse, either extracted or abstracted to represent the central focus. The aspect terms serve as the focal points of explicit or implicit opinion expression within the comment. For example, in the following comment, The current Russian government doesn't represent us, and we definitely don't want a war with our closest people., the CATs are determined as the current Russian government and the war, and the comment is expressing disapproval towards the CATs.
+
+With the above background, we formulate the CASC annotation process in three stages: comment aspect term annotation, comment cluster construction, and comment cluster summarization, as detailed below.
+
+CAT annotation. The process of annotating CAT presents two challenges: (1) Since aspect terms can be either extracted or abstracted from the original comment, it is difficult to control the granularity of each annotated CAT; (2) User comments usually suffer from unclear reference caused by ellipsis or co-reference, which is hard to avoid when reading each comment independently. The two issues may essentially reduce the annotation consistency.
+
+In this work, we allow the case that each comment has multiple  $CATs$ , but we impose a quan
+
+titative limit of fewer than 10 words to control granularity. Moreover, to better cover the meaning of each comment, the annotators are instructed to read comments chronologically and refer to the pre-context when labeling aspect terms. The scope of permissible context for reference is limited to a single comment tree (the comment-reply structure). To ensure the quality of annotations and discern optimal candidates, we establish the following rules: (1) Preference is given to CATs directly extracted from the original comment rather than artificially induced ones; (2) When CATs convey the same meaning, we prefer using the same textual expression; (3) Aspect terms are not labeled for comments without opinion expression or those devoid of practical meaning.
+
+As aspect term annotation inherently involves subjective judgment from annotators, we estimate the consistency of  $CAT$  annotation by comparing the annotations of 200 news comments between two annotators. We approximate consistency by calculating the word-level coverage between each pair of summaries, resulting in a score of  $43.67\%$ .
+
+Comment cluster annotation. Manually clustering a large volume of comments from scratch, depending on the limited memory of human annotators, is time-consuming and challenging, fraught with difficulties in ensuring annotation quality. As stated before, we study clustering comments based on aspect terms. Specifically, we consider semantic affinity inferred from the frequency of word co-occurrence between  $CATs$  as a reliable indicator of similarity. First, we represent each comment by averaging the GloVe vectors within the manually annotated aspect terms. Then, the comments are clustered based on the cosine distance between aspect term representations through fast clustering with a high similarity threshold of 0.85. Comments lacking manual aspect terms are assigned to a single unique cluster, labeled as Trivial. Lastly, annotators manually check the correctness of these clusters according to the following guidelines: (1) Given a cluster  $G = \{c_1,\dots ,c_N\}$  with  $N$  comments, if the aspect terms and content of  $c_{k}$  significantly differ from others in the cluster, exclude  $c_{k}$  from  $G$  and assign it to a suitable comment cluster or the Trivial group. (2) If cluster  $G_{i}$  shares a
+
+closely related topic with cluster  $G_{j}$ , combine them into a unified cluster. (3) Check comments annotated with aspect terms in the Trivial group to determine if they can be reallocated to an existing non-Trivial cluster.
+
+Comment summary annotation. Text summarization annotation has long been contentious, primarily due to the inherent subjectivity of annotators, which can easily influence the standard of summary annotation. Recent studies (Goyal et al., 2022; Zhang et al., 2023; Yang et al., 2023; Pu et al., 2023) have demonstrated that LLM summarizers can perform on par with or better than human summarizers. Among them, the research in (Pu et al., 2023) shows that when quantitatively and qualitatively assessed against human annotators, LLM summaries with increased factuality are notably favored by human evaluators. Inspired by this, we transition from manual summary annotation to LLM-assisted summary annotation. Specifically, based on the manually adjusted comment clusters, we first use GPT3.5 to generate an LLM summary for each comment cluster. Then, we manually post-edit the summaries and refine those suffering from hallucinations to produce the final test suite.
+
+Annotated data overview. Based on comments of news articles sourced from Reddit and New York Times 2017, our annotated dataset contains 11 article clusters (ACs) covering various topics, which involve a total of 20 news articles and 7,958 comments. Guided by our annotation guidelines and with the assistance of four annotators, we constructed 848 comment clusters (CCs) along with their corresponding summaries. Further details are shown in Table 1.
+
+<table><tr><td>Dataset</td><td>Comments (#)</td><td>CCs (#)</td><td>ACs (#)</td></tr><tr><td>DEV</td><td>2,532</td><td>350</td><td>3</td></tr><tr><td>TEST</td><td>5,426</td><td>498</td><td>8</td></tr></table>
+
+Table 1: Statistics for the constructed test suite.
+
+# 4 Approach
+
+Task definition. Given a group of  $m$  news articles under the same topic,  $A = \{a_{1},\ldots ,a_{m}\}$ , the articles contain a group of  $n$  comments in total,  $C = \{c_1,\dots ,c_n\}$ , which comment on the articles from various aspects. Each comment yields a flexible length distribution ranging from a short sentence to a paragraph. The CASC task first groups
+
+the  $n$  news comments into a set of  $k$  comment clusters,  $G_{1},\ldots ,G_{k}$ , and each cluster represents a hot topic discussed by the netizens. Subsequently, a summary is abstracted for each comment cluster represented by  $S_{1},\ldots ,S_{k}$ .
+
+# 4.1 Comment Clustering
+
+Baseline method. We employ the fast clustering algorithm (Reimers and Gurevych, 2019) $^3$  as our baseline approach for comment clustering, which offers advantages over classical clustering techniques such as K-Means and Affinity Propagation and provides faster processing times while delivering superior performance. Operating on a cosine-similarity threshold coupled with SBERT sentence representation, it retrieves and ranks local communities with highly similar sentences greedily. Tailored for CASC, this paper seeks improvements to the baseline method from the following two aspects for more robust comment clustering.
+
+Dynamic comment clustering. Our investigation reveals that comment clusters with hot topics tend to attract more user comments, yielding high comment densities, while those tackling less popular topics exhibit relatively sparse clusters. However, the baseline algorithm maintains a static similarity threshold throughout clustering, which struggles to adapt to fluctuating distributions of comment cluster densities. This paper argues that an adaptive dynamic threshold according to the scale of each comment cluster is more practical. Algorithm 1 shows our core clustering algorithm in pseudocode. As cluster scale increases  $(+ \Delta)$ , the similarity threshold increases accordingly, resulting in a higher cluster density. Drawing inspiration from increasing the similarity threshold in the early stage of dynamic clustering to ensure denser comment clusters, this paper proposes a dynamic similarity threshold adjustment process based on a concave function. Formally, the algorithm automatically adjusts the threshold by fitting the following function:
+
+$$
+\varsigma_ {t} = \sqrt {\mathrm {K} _ {1} \times \left(\kappa_ {t} + \mathrm {K} _ {2}\right)} \tag {1}
+$$
+
+where  $\kappa_{t}$  denotes the cluster size,  $s_t$  denotes the similarity threshold, and  $\mathrm{K}_1$  and  $\mathbf{K}_2$  refer to the hyper-parameters to tune on the DEV set.
+
+Cluster ranking. The vanilla algorithm maintains a static similarity threshold to ensure that the distance between comments within each cluster is
+
+below the threshold. However, this algorithm may still lead to redundancy as some comments may be shared across different clusters. Then, the clusters are ranked with the redundant comments filtered out for final clustering. The baseline method ranks candidate clusters solely based on cluster size, which is not comprehensive enough. This limitation is particularly evident in CASC, where user preference is more focused on both topic relevancy and cluster compactness. Different from the baseline method, we argue that cluster density and relevance between the cluster and article background $^4$  are vital for CASC. With this motivation, we introduce a new ranking mechanism as:
+
+$$
+R _ {t} = \Sigma_ {i} ^ {n} \operatorname {c o s i n e} \left(c _ {i}, c _ {t}\right) \times \max  \left(\log \left(\xi_ {t} + 1\right), 0. 1\right)
+$$
+
+where  $c_{t}$  denotes the centroid comment of the  $t$ -th cluster,  $\xi_{t}$  denotes the stem word intersection between the centroid comment and the background, and  $R_{t}$  refers to the resulting ranking score. Notably, the first term in the formula can be regarded as the product of the cluster size and the cluster density. Therefore, our ranking scheme considers the cluster size, density, and the correlation between the cluster and background concurrently.
+
+# 4.2 Summarization of Comment Clusters
+
+With the rapid development of foundation models (Zhang et al., 2022; Chung et al., 2022; Touvron et al., 2023a; Ouyang et al., 2022; OpenAI, 2023), researchers increasingly recognize the effectiveness of LLMs across various NLP tasks. With this inspiration, we study adapting the compact yet effective Flan_T5 XL (3B) (abbr. FTX) as a benchmark summarization system to fill the gap of foundation models in CASC.
+
+Instruction-tuning. In line with our human annotation efforts, we aim to enhance the foundation model's capability to summarize each comment cluster by focusing on the aspect terms central to each cluster. With this goal, we design instruction-tuning data in a chain-of-thought style to tune LLMs to extract aspect terms from a comment cluster and then abstract the summary by considering the extracted aspect terms and comment texts. However, manual annotation of such tuning
+
+Algorithm 1 Dynamic Fast Clustering
+
+Input:  $N$  vectorized news comments  $C$
+
+Output: A list of comment clusters  $G$
+
+Initialization: initial cluster size:  $\kappa$ , initial threshold:  $\varsigma$ , ceiling threshold:  $thrM = 0.9$
+
+Begin
+
+for  $t$ -th comment  $c_t$  in  $C$  do
+
+scores  $\leftarrow$  pairwise_cos_sim(c_t,C)
+
+scores-k← scores.top-k(κ)
+
+$\varsigma^{\prime}\gets \varsigma$
+
+while scores-k[-1] >  $\varsigma'$  and  $\kappa < N$  do
+
+$\kappa \gets \operatorname{Min}(N, \kappa + \Delta)$
+
+$\varsigma^{\prime}\gets \mathrm{Min}(\sqrt{\mathrm{K}_{1}\times(\kappa + \mathrm{K}_{2})},thrM)$
+
+scores-k← scores.top-k(κ)
+
+end while
+
+$G_{t}\gets []$
+
+for  $s_i$  in scores-k do
+
+$G_{t}\gets G_{t}\cup \{c_{i}\}$  when  $s_i\geq \varsigma '$
+
+end for
+
+$G\gets G\cup \{G_t\}$
+
+Calculate the ranking score  $R_{t}$
+
+end for
+
+Rank the  $N$  clusters in  $G$  based on  $R_{1\dots N}$
+
+End
+
+data is labor-intensive and time-consuming. Besides, recent research suggests that current SoTA foundation models perform annotation on par with or better than human (Goyal et al., 2022; Zhang et al., 2023; Yang et al., 2023; Pu et al., 2023). Inspired by this, we automatically build comment clusters from Reddit comments (excluding those in the test suite) and utilize the publicly available gpt-3.5-turbo to build the instruction-tuning data. In particular, to strengthen the model's capability in chained aspect term and summary generation, we transform each tuning instance into three forms with hybrid learning goals: (1) Given clustered news comments, tune the LLM model to predict aspect terms for each comment cluster; (2) Given the comment cluster along with the aspect terms that the cluster is centered on, tune the model to generate a summary for the cluster; (3) Given the comment cluster, tune the model to predict aspect terms first and then generate a summary based on the predicted aspect terms and the comments within the comment cluster. In total, we obtain 26,438 tuning instances, consisting of 25,438 instances for tuning and 1,000 for validation.
+
+Hallucination alleviation. Upon manual examination, it was discovered that  $28\%$  of the com
+
+ment cluster summaries generated by our finetuned LLM model suffer from hallucinations. This phenomenon arises primarily due to the model's inability to grasp the context of the original articles being commented on. To solve this issue, we harness the in-context learning capability of the pretrained LLM and include background information for comment cluster ranking (see Subsection 4.1) as part of the prompt.
+
+# 5 Experiments
+
+# 5.1 Evaluation Metrics
+
+This research evaluates CASC from three aspects: comment clustering, comment cluster summarization, and pipeline evaluation.
+
+Clustering. This work considers both the homogeneity and completeness levels between the gold and predicted clusters by reporting the Normalised Mutual Information (NMI) score  $\frac{2\times I(C;L)}{H(C) + H(L)}$  as performance, where  $C$  refers to the class labels,  $L$  refers to the cluster labels,  $H(\cdot)$  is the entropy function, and  $I(C;L)$  denotes the mutual information between the two group of labels  $C$  and  $L$ .
+
+Summarization. For comment cluster summarization evaluation, we take the gold standard comment clusters as inputs to generate summaries. Afterward, we calculate the F1-based Rouge-1, -2, and -L scores (ROUGE-1.5.5) between the generated summaries and the ground truth as performance.
+
+Pipeline evaluation. In the pipeline system, the automatic clustering process could result in mismatches between predicted and standard clusters, making the pipeline evaluation hard to realize. This work introduces a scheme for CASC evaluation. Initially, we define a correct hit as when a predicted summary closely matches the ground truth with a cosine similarity exceeding 0.9 (see examples in Appendix C). On this basis, we report precision (P), recall (R), and F1 scores of the correct hits as the CASC performance.
+
+# 5.2 Clustering Results
+
+For comment clustering, we compare our approach with the following four baseline methods.
+
+<table><tr><td>Method</td><td>NMI</td></tr><tr><td>K-Means (MacQueen et al., 1967)</td><td>22.61</td></tr><tr><td>Affinity Propagation (Frey and Dueck, 2007)</td><td>32.04</td></tr><tr><td>TC (Llewellyn et al., 2014)</td><td>17.92</td></tr><tr><td>FC (Reimers and Gurevych, 2019)</td><td>32.24</td></tr><tr><td>Dynamic FC</td><td>32.84</td></tr><tr><td>+ Cluster Density</td><td>33.07</td></tr><tr><td>+ Cluster Density + BG</td><td>33.87</td></tr></table>
+
+Table 2: Performance of comment clustering. BG denotes the background information. FC and TC are abbreviations for fast clustering and topic-focused clustering.
+
+- K-Means (MacQueen et al., 1967) is a traditional approach that alternatively moves comments to the nearest comment cluster centers and updates these centers accordingly. The value of K, representing the number of clusters, needs to be manually determined.  
+- Affinity Propagation (Frey and Dueck, 2007) is a clustering algorithm that identifies exemplars or representatives within a set of data points. The algorithm can automatically determine the number of clusters based on the input data.  
+- Topic-focused clustering (Llewellyn et al., 2014) is one of the most representative works on comment clustering, which comprehensively proves that LDA topic-driven clustering produces better comment clusters for extractive summarization.  
+- Fast clustering (Reimers and Gurevych, 2019) is the benchmark system that our dynamic comment clustering algorithm sources from. It utilizes a cosine-similarity threshold in conjunction with SBERT sentence representation to avidly retrieve local communities containing sentences with high similarity.
+
+The overall results are presented in Table 2.
+
+The baseline fast clustering method yields better performance than K-Means, Affinity Propagation, and the topic-focused clustering method. Moreover, enhancing the fast clustering method with our proposed dynamic clustering algorithm further improves the performance. On top of the dynamic clustering algorithm, we further evaluate our proposed ranking mechanism in two distinct scenarios: one considering only cluster density and the other incorporating both cluster density and background information. The last two rows show our ranking mechanism improves the proposed dynamic clustering algorithm, with the final system settings achieving the best performance.
+
+<table><tr><td>Method</td><td>R-1</td><td>R-2</td><td>R-L</td></tr><tr><td>FTX (Chung et al., 2022)</td><td>19.55</td><td>6.40</td><td>14.50</td></tr><tr><td>FTX + TuneCoT</td><td>48.12</td><td>20.01</td><td>32.73</td></tr><tr><td>FTX + TuneCoT + BG</td><td>48.13</td><td>20.27</td><td>33.15</td></tr></table>
+
+# 5.3 Summarization Results
+
+Abstractive comment summarization is challenging as it requires more training data to understand and summarize noisy online comments. Due to this limitation, previous works have focused solely on extractive summarization. This work takes the compact yet robust FTX model (Chung et al., 2022) as the baseline abstractive summarizer, which uses only 3B parameters while achieving impressive performance. In particular, we contribute two main enhancements to the baseline system. As shown in Table 3, TuneCoT means employing our designed instruction-tuning instances to fine-tune the baseline model on  $CAT$  and summary generation in a chain-of-thought style. BG means harnessing the background information extracted from source articles for in-context learning to preserve the contextual integrity of the comment cluster as reflected in the summary. The first two rows show that enhancing the base model with the ability of  $CAT$  prediction and  $CAT$ -focused summarization improves performance significantly. Moreover, the last two rows indicate that normalizing the output of the LLM with background further improves performance, a point we will illustrate in Section 6.
+
+# 5.4 Overall CASC Results
+
+We build the benchmark CASC system by combining the SBERT-based fast clustering (Reimers and Gurevych, 2019) module and the FTX-based summarizer. To conduct a thorough performance evaluation, we additionally experiment with recent popular LLMs, including Llama-7B (Touvron et al., 2023a), Llama2-7B (Touvron et al., 2023b), and ChatGPT (gpt-3.5-turbo). The overall results are presented in Table 4.
+
+The first two rows show that our instruction-tuning method significantly improves the overall performance, and Line 3 indicates the proposed dynamic clustering method can further boost the performance. To emphasize the importance of clustering in the CASC task, we conducted an ablation experiment with topic-focused clustering applied. The results in Line 4 demonstrate that such an action leads to a significant drop in performance. Fur
+
+Table 3: Results of comment cluster summarization.  
+
+<table><tr><td>Method</td><td>P</td><td>R</td><td>F1</td></tr><tr><td>FC + FTX (3B)</td><td>26.25</td><td>12.00</td><td>16.47</td></tr><tr><td>FC + FTX (3B)♣</td><td>75.41</td><td>32.86</td><td>45.77</td></tr><tr><td>FC† + FTX (3B)♣</td><td>79.58</td><td>54.00</td><td>64.34</td></tr><tr><td>TC + FTX (3B)♣</td><td>12.50</td><td>2.14</td><td>3.66</td></tr><tr><td>FC† + Llama (7B)</td><td>46.66</td><td>31.86</td><td>37.86</td></tr><tr><td>FC† + Llama (7B)♣</td><td>47.59</td><td>32.43</td><td>38.57</td></tr><tr><td>FC† + Llama2 (7B)</td><td>76.32</td><td>51.57</td><td>61.55</td></tr><tr><td>FC† + Llama2 (7B)♣</td><td>76.65</td><td>53.00</td><td>62.67</td></tr><tr><td>FC† + ChatGPT (20B+)</td><td>79.18</td><td>54.86</td><td>64.81</td></tr></table>
+
+Table 4: Results of the CASC pipeline system. Sign  $\spadesuit$  denotes the model after fine-tuning, while  $\dagger$  indicates the use of the dynamic clustering strategy.
+
+![](images/c3db2ef0dee641897bac696be892ee4ca9899ea0be4acb663539c0bf274ec8c1.jpg)  
+Figure 1: Distribution of similarity threshold and cluster density concerning the comment cluster size.  $\mathbf{Y}_1$  and  $\mathbf{Y}_2$  refer to the axes with similarity and cluster size scales.
+
+thermore, the results in the lower part of Table 4 show: (1) Our instruction-tuning data and methods can be well extended to other LLMs to enhance their CASC performance. (2) Our tuned FTX-3B model performs better than the larger Llama models and is comparable to ChatGPT. This finding is meaningful for real-world CASC applications.
+
+# 6 Analysis & Discussion
+
+Comment cluster distribution. Figure 1 presents the distribution of 1,467 comment clusters constructed by our CASC system. The column bars labeled with tag  $①$  depict the distribution of comment cluster sizes, the poly-line marked with tag  $②$  denotes the similarity threshold applied to each cluster, and the poly-line labeled with  $③$  indicates the density value of each cluster. The diagram shows that as the cluster size increases, our dynamic algorithm progressively elevates the similarity threshold, to impose stringent criteria for cluster formation. Since a comment is included in the cluster only when its similarity to the centroid comment surpasses the threshold, the cluster density is distributed above the threshold line, with higher similarity thresholds leading to increased
+
+CMT-1. how do you think you came in contact with flu? CMT-2. so, if i caught it, do you think i would know or would i just think it was the regular flu? CMT-3. i am currently trying to avoid other humans. although, that sounds like a good revenge for some people. i probably picked up the flu in a public place. CMT-4. how would you explain the news describing people with "mild symptoms". do they mean mild compared to regular flu, or mild compared with dying? CMT-5. or maybe from a patient who was there for something else and was unknowingly serving as an incubator for the disease. excuse me if you've already answered this, but were you not given every possible vaccination, considering your profession? and even if none are effective, are health-care workers continuing to take every precaution against infection of this flu, or have things been a bit laxer lately? do you mind giving the region of texas in which you work?
+
+Auto aspect terms: flu, contact, symptoms, mild symptoms, vaccination, health-care workers.
+
+Summary w/o BG: The user comments revolve around various aspects related to the COVID-19 pandemic. Users express concerns about how they may have contracted the flu and how they would know if they had it if they caught it. They also discuss symptoms and severity levels of the virus as well as health-care worker precautions taken against it. Some users speculate about potential incubators of the disease such as patients who may have served as incubators for others. Overall, there is a focus on understanding how best to prevent the flu.
+
+Summary w/ BG (H1N1 virus, swine flu): The user comments revolve around various aspects related to the H1N1 virus and swine flu. Users express concerns about how they may have contracted the flu and how they would know if they had it compared to regular flu symptoms. They also discuss how mild symptoms are interpreted and whether they refer to a comparison with dying or if they indicate an unknowingly serving as an incubator for the disease. Additionally, users question whether health-care workers are taking proper precautions against infection and if things have become laxer.
+
+Figure 2: Example summaries generated by our CASC system for the comment cluster with a gray background.
+
+cluster density. Upon reviewing the real data, it becomes evident that popular topics tend to attract more comments within the cluster, while smaller clusters usually revolve around unpopular topics triggered by the leading comment. In this situation, our method raises the threshold to maintain the integrity of larger clusters and assigns lower threshold values to smaller ones to encourage diversity.
+
+Factual error analysis. LLMs enriched with dense knowledge exhibit heightened creativity but also entail risks of factual inaccuracies. Figure 2 presents an example processed by our CASC system, where all the comments are from Reddit under the topic of "swine flu". We observe that the aspect terms encompass most key points expressed in the cluster and are also embodied in the summaries. The results indicate that by establishing a coherent chain of thought for generating aspect terms and summaries, our method mitigates factual errors to some extent. Nevertheless, the first summary (w/o BG), which revolves around the COVID-19 pandemic, is inconsistent with the topic discussed within the original comments. This is due to an information gap, as the pre-trained LLM model lacks specific knowledge about the themes of the articles that the comments are focusing on. In contrast, after manually incorporating the background knowledge "H1N1 virus, swine flu" into the prompt context, the second summary correctly references the background information, thus avoiding factual errors.
+
+To quantitatively analyze the impact of the background information incorporated, we further con
+
+duct CASC on Reddit comments of ten randomly selected article clusters in real scenarios. On this basis, we perform a manual factuality evaluation based on the summaries of the first five longer comment clusters among each article cluster (fifty summaries in total). For the evaluation guideline, we adhere to the rule that a comment cluster summary is deemed factually accurate only when all the entities, events, and opinions it encompasses are entirely in line with the content of the original comments. The evaluation results in Table 5 demonstrate that utilizing background in our final system significantly enhances its factuality.
+
+<table><tr><td>Method</td><td>Factual Error</td></tr><tr><td>Final System</td><td>18%</td></tr><tr><td>w/o BG</td><td>28%</td></tr></table>
+
+Table 5: Manual evaluation of summarization factuality.
+
+# 7 Conclusion
+
+This paper presents an initial exploration into Clustering and Abstractive Summarization of online news Comments (CASC). We introduce a manual annotation scheme, create a test suite, and propose an evaluation metric tailored for the CASC task. On this basis, we introduce a dynamic clustering algorithm and a novel ranking mechanism for effective comment clustering. In particular, we perform the first practice of tuning foundation models for comment cluster summarization. To foster further studies, the data and codes will be released to the research community upon application.
+
+# 8 Limitations
+
+As an early exploration in CASC, our study faces two notable limitations: (1) Our annotation efforts have been confined to English news comments due to constraints in human resources. In future research endeavors, we will aim to broaden our resources to construct a multi-lingual CASC test suite. (2) This paper establishes a baseline CASC system using LLM. Although we utilize chain-of-thought fine-tuning along with the in-context learning of background information to alleviate the hallucination issue, the strategy is not thorough enough. We envision undertaking task-specific retraining of LLMs in future work to address this issue further. (3) Currently, the pipeline method outlined in this paper does not fully leverage LLMs. Given the rapid advancement of foundation models, further investigation is needed to explore methods that bridge the gap between clustering and summarization and the capacity to learn clustering and summarization using LLMs simultaneously. (4) When constructing the test suite, we considered the comment tree a context when performing manual annotation, but our system does not consider the comment tree. Inspired by previous work (Tan et al., 2022), exploring discourse theory within comment trees could help with more intelligent news comment analysis in future work.
+
+# 9 Acknowledgments
+
+We thank Tharini De Silva, Yang Ding, Tarun Kumar Vangani, and other team members for their useful discussions and contributions to the data construction. We express our gratitude to the anonymous reviewers who highly rated this paper and offered insightful comments that significantly contributed to the enhancement of this work.
+
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+
+# A System Settings
+
+Our system is based on the Flan_T5_XL (Chung et al., 2022) model with 3B parameters. We tuned all the model parameters for 3 epochs using our built 26,438 instruction-tuning instances. We implemented the CASC system using the PyTorch framework. We tuned our model on A40 GPU cards, and a complete model tuning took around 10 GPU hours. All tests were finished in a single run with the random seed 19. We tuned the hyper-parameters like the number of titles used as background (Table 6), the  $\Delta$  value (Table 7), the cluster number of the K-Means algorithm (Table 8), the parameters of the curve in Equation 1 (Appendix B), etc., based on the DEV set.
+
+# B Tuning Clustering Curve Steepness
+
+Our proposed dynamic clustering algorithm maintains two hyper-parameters in Equation 1 to shape
+
+<table><tr><td>Title Number</td><td>R-1</td><td>R-2</td><td>R-L</td></tr><tr><td>0</td><td>45.35</td><td>16.59</td><td>29.13</td></tr><tr><td>2</td><td>45.22</td><td>16.61</td><td>29.27</td></tr><tr><td>4</td><td>45.24</td><td>16.49</td><td>29.37</td></tr><tr><td>6</td><td>45.20</td><td>16.67</td><td>29.41</td></tr><tr><td>8</td><td>45.22</td><td>16.80</td><td>29.37</td></tr></table>
+
+Table 6: Title number determined on DEV.  
+
+<table><tr><td>Δ</td><td>NMI</td></tr><tr><td>5</td><td>67.28</td></tr><tr><td>10</td><td>67.38</td></tr><tr><td>20</td><td>67.35</td></tr><tr><td>40</td><td>67.38</td></tr><tr><td>80</td><td>67.17</td></tr></table>
+
+Table 7:  $\Delta$  value determined on DEV.
+
+the curve to control the dynamic similarity thresholds. Figure 3 illustrates an example curve. The curve steepness is determined by the two hyperparameters  $\mathrm{K}_1$  and  $\mathrm{K}_2$ , which are tuned on DEV by sampling data points with the cluster sizes  $\kappa_1 = 50$  and  $\kappa_1 = 200$  on the X-axis. The two parameters are determined by the empirical investigation that a comment cluster with 50 comments is considered a common size, so we need to establish a general similarity threshold  $\varsigma_1$  to ensure that the comments within the cluster are identifiable; a cluster with 200 comments is deemed long-winded, where we need a higher threshold  $\varsigma_2$  to strictly filter out those unrelated comments to make the cluster more readable. To achieve the above goal, we first assume the curve to be a plain horizontal line to test the effects when  $\varsigma_1$  takes different values on the Y-axis. Table 9 shows that as the value of  $\varsigma_1$  grows, the performance drops sharply. Therefore, we obtain  $\varsigma_1 = 0.52$  with the highest NMI score on DEV. Then we anchor  $(\kappa_1,\varsigma_1)$  to tune the data point  $(\kappa_2,\varsigma_2)$ , where the higher the value of  $\varsigma_2$ , the steeper the curve. It shows that it obtains the best performance when the similarity  $\varsigma_2$  is 0.8 for the cluster with 200 comments.
+
+# C Clustering Speed
+
+The section presents the speed of the fast clustering algorithm, K-Means, and Affinity Propagation for reference, as shown in Table 10. Here, the K-Means and Affinity Propagation algorithms we use are implemented by scikit-learn<sup>7</sup>. Notably, the running speed fluctuates greatly with changes in the total number of comments.
+
+<table><tr><td>K-Means</td><td>NMI</td></tr><tr><td>2</td><td>16.08</td></tr><tr><td>4</td><td>25.35</td></tr><tr><td>8</td><td>38.16</td></tr><tr><td>16</td><td>27.97</td></tr><tr><td>32</td><td>15.52</td></tr><tr><td>64</td><td>14.43</td></tr><tr><td>128</td><td>15.74</td></tr></table>
+
+![](images/5db82b5b2f78d871b5238d4bbd1a6760a8b88d6b6174d812f9bd53c8f0d47a5f.jpg)  
+Figure 3: Example curve with  $\mathrm{K}_1 = 2$  and  $\mathrm{K}_2 = 2$ .
+
+# D Successful Hit Summary Pairs in the Pipeline Evaluation
+
+As stated in the main body, this research proposes the pipeline evaluation scheme tailored for the CASC task where we set the cosine similarity threshold to 0.9 to strictly evaluate the quality of the generated summaries. This section presents some summaries that successfully hit the gold standard summaries for reference.
+
+# D.1 Example 1
+
+Ground truth. The user comments discuss the impact of high cost of living on the poorest in society and how they cannot switch to cheaper brands or travel less. They also criticize msm for claiming that high cost of living has little effect on the poor. Some users express frustration with an article that talks about the poor only focusing on wealthy individuals. There is a call for increasing GST to help the poor while others suggest taking half of mayors' salaries to subsidize them directly.
+
+Model prediction. The user comments discuss the high cost of living in Singapore and its impact on the poor. Some users criticize the choice of interviewee for the article, questioning whether it accurately represents the struggles faced by those living in poverty. Others point out that this issue
+
+Table 8: K value determined on DEV.  
+
+<table><tr><td>κ1</td><td>ζ1</td><td>NMI</td><td>κ2</td><td>ζ2</td><td>NMI</td></tr><tr><td rowspan="6">50</td><td>0.48</td><td>64.91</td><td rowspan="6">200</td><td>0.60</td><td>66.65</td></tr><tr><td>0.52</td><td>65.33</td><td>0.65</td><td>66.84</td></tr><tr><td>0.56</td><td>42.32</td><td>0.70</td><td>66.94</td></tr><tr><td>0.60</td><td>35.40</td><td>0.75</td><td>67.12</td></tr><tr><td>0.64</td><td>13.61</td><td>0.80</td><td>67.38</td></tr><tr><td>0.68</td><td>11.31</td><td>0.85</td><td>67.25</td></tr></table>
+
+Table 9: Curve steepness tuning on the DEV set.  
+
+<table><tr><td>Method</td><td>Speed</td></tr><tr><td>K-Means</td><td>228 ms / 512 comments</td></tr><tr><td>Affinity Propagation</td><td>265 ms / 512 comments</td></tr><tr><td>Fast Clustering</td><td>86 ms / 512 comments</td></tr></table>
+
+Table 10: Speed of different clustering algorithms.
+
+is not unique to Singapore and highlights the need to reduce the gap between rich and poor. There is also discussion about supermarket chains like ntuc fairprice not passing on higher prices to consumers despite being strategically placed. Overall, there is a sense that rising prices are causing hardship for those living in poverty.
+
+# D.2 Example 2
+
+Ground truth. The user comments revolve around the topic of defining and calculating the poverty line. Some users suggest using minimum income standards as a starting point while others argue that every generation's poverty line is different. There is also discussion about household division and how it can be too low below sustainable levels. The UK's definition of poverty is  $60\%$  below median household income after housing costs which some people dislike as it is a relative measure rather than an absolute measure of poverty. Some users suggest using the average wage as a metric but others argue that doing so would include irrelevant people into the calculations, making the metric useless.
+
+Model prediction. The user comments discuss different approaches to defining poverty, including the UK's  $60\%$  below median household income after housing costs and the living wage as a personal income measure. They also mention the UK's state pension system and minimum income standards for defining the poverty line. One comment suggests that Singapore should have an official poverty line defined by the bottom  $0.1\%$ , which may result in fewer poor people.
+
+# D.3 Example 3
+
+Ground truth. The user comments discuss the high number of people being helped by food banks since COVID. One user questions if this is truly
+
+# Comment Cluster
+
+1. [Aspect_Terms: poor line, poor people] Since we don&#39;t have an official poverty line, probably because that way we have less poor people. If we define the bottom  $0.1\%$  to be poor, we will have very few poor people.  
+2. [Aspect_Terms: poor line] Tbh I've been working on deriving the poverty line. the idea is that every generation poverty line is different.  
+3. [Aspect_Terms: poor line] The minimum income standards are a good start at trying to define the poverty line.  
+4. [Aspect_Terms: poor line, household division] The household division makes sense, total income divided by pax but the number here is just way too low below sustainable.  
+5. [Aspect_Terms: poor line, metric] Yes, the larger the gap is, the less accurate the metric become  
+6. [Aspect_Terms: poor line, UK] The UK definition of poverty is  $60\%$  below median <strong>household</strong> income after housing costs. So that&#39;s a household approach and is used to calculate how many live in poverty. The right don&#39;t like it because it is a relative measure rather than a measure of absolute poverty.  
+7. [Aspect_Terms: poor line, average wage] The average wage should be the poverty line tbh.  
+8. [Aspect_Terms: poor line, average wage] I don&#39;t think the average wage should be poverty line, that would mean like more than  $50\%$  of people are poor, inclusive of rich tai tais, stay at home parents etc and all children. It will become a useless metric if too many irrelevant people are included.
+
+# Extractive Summary
+
+1. Since we don\&#39;t have an official poverty line, probably because that way we have less poor people. If we define the bottom  $0.1\%$  to be poor, we will have very few poor people.  
+2. The minimum income standards are a good start at trying to define the poverty line.  
+3. The household division makes sense, total income divided by pax but the number here is just way too low below sustainable.  
+4. The average wage should be the poverty line tbh.  
+5. I don\&#39;t think the average wage should be poverty line, that would mean like more than  $50\%$  of people are poor, inclusive of rich tai tais, stay at home parents etc and all children. It will become a useless metric if too many irrelevant people are included.
+
+# Abstractive Summary
+
+The user comments revolve around the topic of defining and calculating the poverty line. Some users suggest using minimum income standards as a starting point while others argue that every generation's poverty line is different. There is also discussion about household division and how it can be too low below sustainable levels. The UK's definition of poverty is  $60\%$  below median household income after housing costs which some people dislike as it is a relative measure rather than an absolute measure of poverty. Some users suggest using the average wage as a metric but others argue that doing so would include irrelevant people into the calculations, making the metric useless.
+
+Figure 4: Example comment cluster annotated with extractive and abstractive summaries.
+
+happening while another explains that food banks are used to providing support for those in the poorest  $10\%$  of the population but are now supporting more people. It is noted that many families are close to needing their help due to unexpected events such as illness or job loss.
+
+Model prediction. The user comments discuss the claim that Singapore's food banks are helping 1 million people since COVID-19. However, one user questions if this is truly the case and suggests that it may be more accurate to say that the poorest  $10\%$  of the population is now needing help. Another user points out that many families are close to needing assistance due to unexpected events like illness or job loss. Despite this, there are still over 30,000 households reliant on foodbanks pre-pandemic and over 100k registered with foodbank.sg.
+
+# E Abstractive vs. Extractive Comment Summarization
+
+In addition to the final dataset presented in the main body of this paper, our initial exploratory research
+
+extends to the extractive summarization of news comment clusters. In extractive summarization annotation, the annotators are guided to manually extract comments from the original comment cluster following two rules: (1) Since each comment is manually annotated with aspect terms, the summary content should cover all the annotated aspect terms; (2) Each aspect term could be shared among multiple comments, the annotators should read and select the most representative comments as the summary to avoid duplication and redundancy. With this guideline, we annotated summaries for 6 article clusters. For reference, we present a comment cluster with extractive and abstraction summaries annotated in Figure 4. When compared, extractive summarization proves superior in accuracy, fluency, and conciseness. This showcases the adaptability of LLM-based summary generation to noisy real-world data.

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2024/ConTempo_ A Unified Temporally Contrastive Framework for Temporal Relation Extraction/9ded2c84-7d7d-4a7e-b160-6caf16706c14_content_list.json

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+[
+    {
+        "type": "text",
+        "text": "ConTempo: A Unified Temporally Contrastive Framework for Temporal Relation Extraction",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "Jingcheng Niu, $^{1,2,3}$  Saifei Liao, $^{2,3}$  Victoria Ng, $^{1}$  Simon De Montigny, $^{1}$  Gerald Penn $^{2,3}$",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "<sup>1</sup>Public Health Agency of Canada, <sup>2</sup>University of Toronto, <sup>3</sup>Vector Institute",
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+    {
+        "type": "text",
+        "text": "{niu,liaosaif,gpenn}@cs.toronto.edu",
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+    {
+        "type": "text",
+        "text": "{victoria.ng,simon.demontigny}@phac-aspc.gc.ca",
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+    {
+        "type": "text",
+        "text": "Abstract",
+        "text_level": 1,
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+    },
+    {
+        "type": "text",
+        "text": "The task of temporal relation extraction (TRE) involves identifying and extracting temporal relations between events from narratives. We identify two primary issues with TRE systems. First, by formulating TRE as a simple text classification task where every temporal relation is independent, it is hard to enhance the TRE model's representation of meaning of temporal relations, and its facility with the underlying temporal calculus. We solve the issue by proposing a novel Temporally Contrastive learning model (ConTempo) that increase the model's awareness of the meaning of temporal relations by leveraging their symmetric or antisymmetric properties. Second, the reusability of innovations has been limited due to incompatibilities in model architectures. Therefore, we propose a unified framework and show that ConTempo is compatible with all three main branches of TRE research. Our results demonstrate that the performance gains of ConTempo are more pronounced, with the total combination achieving state-of-the-art performance on the widely used MATRES and TBD corpora. We furthermore identified and corrected a large number of annotation errors present in the test set of MATRES, after which the performance increase brought by ConTempo becomes more apparent.",
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+    {
+        "type": "text",
+        "text": "1 Introduction",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Temporal relation extraction (TRE) is the task of classifying the temporal relations between pairs of events conveyed in narratives (Pustejovsky et al., 2006, 2010). This task is important to the natural language processing (NLP) community because the conception of time is a key component of text comprehension and reasoning. Additionally, it carries practical importance, as TRE is a crucial component of various downstream applications in question answering, information retrieval, and information extraction.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "TRE is difficult. Despite its importance and popularity, TRE systems still have relatively poor performance compared to other natural language understanding tasks. TRE is also salient because recent large language models (LLMs) and chat systems have substantially worse performance than smaller, fine-tuned TRE models (Yuan et al., 2023; Huang et al., 2023).",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "In this paper, we enhance current TRE systems by identifying and addressing two major issues that hinder their performance:",
+        "bbox": [
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+        "type": "text",
+        "text": "1. It is difficult to understand relation labels. TRE is typically formulated as a multi-label text classification task. The representation of the relation is determined by a neural classifier, which outputs logits for different label classes. These logits are then converted into label probabilities using a softmax layer. As a result, in a TRE model, all relation types are considered independent. However, temporal relations are inherently structured, governed by an underlying temporal calculus (Allen, 1981, 1983). For instance, if event A occurred before event B, it can be inferred that B happened after A. Integrating the meanings of each temporal relation and the principles of the underlying temporal calculus into the neural classifier presents a complex challenge, as there is no straightforward method to do so.",
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+    {
+        "type": "text",
+        "text": "2. The reusability of innovations has been limited. Many of the recent innovations in TRE have not built upon one another, primarily due to the lack of a unified framework (beyond annotation standards) to accommodate them. For example, despite being widely cited and used as a baseline by subsequent systems, the relative time prediction technique (Wen and Ji, 2021) has rarely been applied on top of newer models, due to incompatibilities in model architecture. The evaluation methods employed by earlier systems vary significantly, moreover, which complicates direct comparisons",
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+    },
+    {
+        "type": "page_number",
+        "text": "1521",
+        "bbox": [
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+    },
+    {
+        "type": "footer",
+        "text": "Findings of the Association for Computational Linguistics: ACL 2024, pages 1521-1533 August 11-16, 2024 ©2024 Association for Computational Linguistics",
+        "bbox": [
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+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "between models and further hinders the development of future models.",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "We propose a novel Temporally Contrastive learning method (ConTempo)<sup>1</sup> to enhance the model's representation of the meaning of temporal relations, and its facility with the underlying temporal calculus. The intuition behind ConTempo is very simple. Contrastive learning aims to pull similar (positive) samples closer and push dissimilar (negative) samples apart. We leverage the symmetric and antisymmetric properties of temporal relations to augment a base graph of positive samples for contrastive learning. For antisymmetric relations (A before B), we want to push the relation's representation away from its inverse (B after A). For a symmetric relation (A equals B), we likewise want to pull its representation closer to its inverse (B equals A). Our experimental results indicate that ConTempo is effective at creating distinctive representations for different types of temporal relation pairs and yields a substantial improvement in performance.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Then, building upon ConTempo, we create a unified framework that is compatible with various previous modes of improvement in TRE systems. In particular, we have identified two major threads of innovation in the previous literature on this topic: (1) GNN encoding of event and context information, (2) incorporation of common-sense information, and (3) the soft enforcement of logical constraints. Our experiment shows that ConTempo is compatible with techniques from all three major threads of research and can achieve state-of-the-art performance on major evaluation corpora, including MATRES (Ning et al., 2018b) and TimeBank-Dense (TBD; Cassidy et al., 2014). We nevertheless perceive the need to introduce CleanMATRES, a refined version of MATRES that we created by fixing certain annotation errors.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Among all of these innovations, an ablation study nevertheless shows that ConTempo brings the most significant performance increase. This finding underscores our initial hypothesis: the primary challenge for these models has been their difficulty with making sense of relation labels.",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "During our development of the unified ComTempo framework, we discovered a large number of annotation errors within MATRES and TBD, two commonly utilized corpora. Because of",
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+    },
+    {
+        "type": "table",
+        "img_path": "images/87d09cebd1678aba9e8d7793f5fb1e7256a93ba14101dc2837731344704a327f.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Corpus</td><td>Relations</td></tr><tr><td>MATRES</td><td>BEFORE, AFTER, EQUAL, VAGUE</td></tr><tr><td>TBD</td><td>BEFORE, AFTER, INCLUDES, IS INCLUDED, EQUAL, VAGUE</td></tr></table>",
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+    {
+        "type": "text",
+        "text": "Table 1: Temporal relations used by MATRES and TBD.",
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "TBD's dense annotation scheme, the appropriate level of underspecificity cannot be resolved without further investigation. But we are able to provide a thorough re-examination of the MATRES corpus. After correcting these errors, performance improves yet again, and the performance increase brought by ConTempo becomes more apparent.",
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+    {
+        "type": "text",
+        "text": "2 ConTempo",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "We begin our discussion by first formulating the TRE task. Then, using a comparison of relational representations, we will demonstrate the difficulty that a neural model faces in temporal reasoning and understanding the meaning of temporal labels. In particular, there is a significant correlation between the mistakes a TRE model makes and its degree of inference over the available symmetric and antisymmetric properties. Next, we will present our ConTempo method in detail, which enhances a model's awareness of the meaning of each temporal relation and each principles of temporal reasoning. Finally, we will empirically demonstrate the effectiveness of ConTempo and compare it with previous methods in increasing temporal relation awareness.",
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+    {
+        "type": "text",
+        "text": "2.1 TRE: Task Formulation",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "TRE can be formulated as a classification task. Given an input sequence  $S = [t_1, \\dots, t_n]$  and two events represented by two distinct tokens from the sequence,  $e_1, e_2 \\in S$ , where  $e_1 \\neq e_2$ , the TRE model should classify the relation between the event pair  $(e_1, e_2)$  into one of several temporal relations,  $\\mathcal{R}$ . Different corpora have different sets of temporal relations. Most TRE benchmark datasets aspire to embody Allen's (1981) 13 original temporal relations, but creating datasets with such fine-grained annotations is challenging. Attempts to utilize all 13 temporal relation types have failed due to low inter-annotator agreement. Therefore, recent TRE datasets typically simplify the relation set to a more coarse subset of the original set. As listed in Table 1, MATRES has 4 relation types, and TBD uses 6 relation types.",
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+    },
+    {
+        "type": "page_footnote",
+        "text": "<sup>1</sup>ConTempo and CleanMATRES are publicly available online: https://github.com/frankniujc/contempo.",
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+        "page_idx": 1
+    },
+    {
+        "type": "page_number",
+        "text": "1522",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "2.2 Temporal Relation Labels Awareness",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "After simplification, Allen's (1983) full temporal interval calculus can no longer be maintained. But interval symmetry and antisymmetry (as shown in Equation 1) still apply within both MATRES and TBD. $^2$  In our opinion, it is crucial for TRE models to reason with intervals in order to yield good evaluation results on benchmarks—if the models know A happened before B but do not know that B happened after A, can we really say that the model understands time in narratives?",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nA \\text {I N C l u d e s} B \\Longleftrightarrow B \\text {I S - I N C l u d e d} A\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+    {
+        "type": "equation",
+        "text": "\n$$\nA _ {\\text {B E F O R E}} B \\Longleftrightarrow B _ {\\text {A F T E R}} A \\tag {1}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+    {
+        "type": "equation",
+        "text": "\n$$\nA \\text {E Q U A L} B \\iff B \\text {E Q U A L} A\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Symmetry and antisymmetry also provide us with an opportunity to test a model's understanding of relation labels. In particular, we can measure the similarity of the model's representation of a relation  $\\mathbf{h}_r^{\\rightarrow}$  in comparison to its dual  $\\mathbf{h}_r^{\\leftarrow}$ :",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\operatorname {s i m} \\left(\\mathbf {h} _ {r} ^ {\\rightarrow}, \\mathbf {h} _ {r} ^ {\\leftarrow}\\right) = \\operatorname {s i m} \\left(\\mathbf {h} _ {\\left(e _ {1}, e _ {2}\\right)}, \\mathbf {h} _ {\\left(e _ {2}, e _ {1}\\right)}\\right), \\tag {2}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "It is relatively commonplace in the context of TRE to speak of a representation of a temporal relation, although this in fact refers to the representation of one of its instances over some event pair  $\\mathbf{h}_{(e_1,e_2)}$ . Therefore, we will speak of the two interchangeably. If the relation between  $e_1$  and  $e_2$  is symmetric, then we can interpret high similarity as a sign of awareness concerning the relation's meaning because the relation and its inverse are nearly the same. On the other hand, if the relation is antisymmetric, we should expect the relations to be distinct and, therefore, we should interpret low similarity as a good sign. Here, we measure similarity with cosine similarity  $(\\mathrm{sim}(\\mathbf{a},\\mathbf{b}) = \\frac{\\mathbf{a}\\cdot\\mathbf{b}}{\\|\\mathbf{a}\\|\\|\\mathbf{b}\\|})$ .",
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+    {
+        "type": "text",
+        "text": "2.3 Temporal Relation Awareness of Fine-tuned BERT-based Models",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "In this section, we examine the extent to which typical, fine-tuned BERT-based models can be said to understand temporal relations and the temporal calculus. All contemporary TRE systems use this paradigm. Therefore, we experimented with a baseline model (described in Equation 3) to establish a foundation for the capacity of TRE models to summarize the temporal interval calculus.",
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+        "type": "image",
+        "img_path": "images/9cc44225faa3052d8d38a98fc3c99faa7173e32b9526019e7bbf1e514ce8f632.jpg",
+        "image_caption": [
+            "Figure 1: Similarity measures of event pair representations with their inverses. Each dot represents a relation in the MATRES test set: green means the model classified the relation correctly and red means the model made a mistake. The box plots underneath show the quantile statistics. There is an obvious negative correlation between the correctness of the prediction and the similarity measure. This is evident from observing that the incorrect predictions (red points) are located in the upper region of the figure for BEFORE and AFTER."
+        ],
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+    {
+        "type": "text",
+        "text": "The baseline model has three components: a pretrained encoder (we use a RoBERTa-large model (Liu et al., 2019)), a 2-layer MLP module  $(f_{1})$  that encodes the relation of the event pair under a unified representation scheme, and another single layer MLP  $(f_{2})$  that decodes the relational representation into logits for each, different relational type:",
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+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathbf {E} = \\operatorname {e n c o d e r} (S) = [ \\mathbf {h} _ {1}, \\dots , \\mathbf {h} _ {n} ],\n$$\n",
+        "text_format": "latex",
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+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathbf {h} _ {\\left(e _ {1}, e _ {2}\\right)} = f _ {1} \\left(\\left[ \\mathbf {h} _ {e _ {1}} \\| \\mathbf {h} _ {e _ {2}} \\right]\\right), \\tag {3}\n$$\n",
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+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathbb {P} _ {\\mathcal {R}} \\left(e _ {1}, e _ {2}\\right) = \\operatorname {s o f t m a x} \\left(f _ {2} \\left(\\mathbf {h} _ {\\left(e _ {1}, e _ {2}\\right)}\\right)\\right).\n$$\n",
+        "text_format": "latex",
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+    {
+        "type": "text",
+        "text": "The implementation details and hyperparameter settings are described in Appendix A.",
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Baseline Model Temporal Awareness Figure 1 shows the similarity between the relational representations  $\\mathbf{h}_r^{\\rightarrow}$  and their symmetric duals  $\\mathbf{h}_r^{\\leftarrow}$  as generated by the baseline model. We can see an obvious negative correlation between the correctness of the prediction and the similarity measure. This is evident from observing that the incorrect predictions (red points) are located in the upper region of the figure for BEFORE and AFTER. Furthermore, the baseline model often assigns similar representations to relations and their symmetric duals, even when the two are diametrically opposite in meaning. As shown by the box plot, the first quantile of both the BEFORE and AFTER relations occupy",
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+        "page_idx": 2
+    },
+    {
+        "type": "page_footnote",
+        "text": "2We ignore the VAGUE relation in this part of the analysis because whether symmetry applies to the VAGUE relation requires more careful consideration (Appendix D.3).",
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+    {
+        "type": "page_number",
+        "text": "1523",
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+        "page_idx": 2
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+    {
+        "type": "text",
+        "text": "the upper part of the figure, which corresponds to high similarity. This shows that while fine-tuned models might have some basic perception of the significance of these temporal labels, it is by no means efficient, as all temporal labels are presented to the model as independent.",
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+    {
+        "type": "text",
+        "text": "2.4 ConTempo: The Method",
+        "text_level": 1,
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+        "text": "Contrastive learning builds on the idea of pulling similar (positive) data points  $(x, x^{+})$  closer together and pushing dissimilar (negative) data points  $(x, x^{-})$  apart by adding a contrastive loss term to the training objective (Robinson et al., 2021). We thus need to define positive and negative samples for temporal relation instances, i.e., event pairs. In this section, we will explain how positive and negative samples are constructed based on whether the relation is symmetric (EQUAL) or antisymmetric (BEFORE, AFTER, INCLUDES, and IS INCLUDED), and define how we compute the temporally contrastive loss term  $\\ell_{\\mathrm{tc}}$ .",
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+    {
+        "type": "text",
+        "text": "Our implementation of ConTempo is inspired by SimCSE's (Gao et al., 2021) use of contrastive learning on natural language inference (NLI) data. We likewise use a normalized temperature-scaled cross-entropy loss (NT-Xent; Chen et al., 2020).",
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+        "text": "Antisymmetric Relations For an antisymmetric relation  $\\mathbf{h}_r^{\\rightarrow} = \\mathbf{h}_{(e_1,e_2)}$ , we regard the dual of the relation  $\\mathbf{h}_r^{\\leftarrow} = \\mathbf{h}_{(e_2,e_1)}$  as a hard negative sample. However, we cannot construct further positive samples using temporal reasoning. Instead, we follow SimCSE's unsupervised approach to obtain positive pairs through the use of independently sampled dropout masks. Standard transformers will apply dropout (default  $p = 0.1$ ) at different locations in the model. Therefore, we simply feed the same input to our model twice to obtain two relational representations  $\\mathbf{h}_r^{\\rightarrow}$  and  $\\mathbf{h}_r^+$  that are slightly different; different dropout masks having been applied during the two encoding passes. Therefore, we can compute the ConTempo loss by:",
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+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\ell_ {\\mathrm {t c}} = - \\log \\frac {e ^ {\\operatorname {s i m} \\left(\\mathbf {h} _ {r} ^ {\\rightarrow} , \\mathbf {h} _ {r} ^ {+}\\right) / \\tau}}{e ^ {\\operatorname {s i m} \\left(\\mathbf {h} _ {r} ^ {\\rightarrow} , \\mathbf {h} _ {r} ^ {+}\\right) / \\tau} + e ^ {\\operatorname {s i m} \\left(\\mathbf {h} _ {r} ^ {\\rightarrow} , \\mathbf {h} _ {r} ^ {\\leftarrow}\\right) / \\tau}}, \\tag {4}\n$$\n",
+        "text_format": "latex",
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+    {
+        "type": "text",
+        "text": "where  $\\tau$  is a temperature hyperparameter.",
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+    },
+    {
+        "type": "text",
+        "text": "Unlike SimCSE, however, we did not treat other relational representations in the same mini-batch as negatives. While we are certain that the relation yields the exact dual when we reverse the order of the two events  $((e_1,e_2)$  vs.  $(e_2,e_1))$ , the compari",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "son is less clear when it is made between different event pairs. Consider the following examples:",
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+    {
+        "type": "list",
+        "sub_type": "text",
+        "list_items": [
+            "(1) Alan Turing studied at Cambridge for his undergraduate degree and attended Princeton for his Ph.D.",
+            "(2) I failed  $e_3$  my calculus course and then cried  $e_4$  all night in a McDonald's."
+        ],
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "While both temporal relations  $r_1 = (e_1, e_2)$  and  $r_2 = (e_3, e_4)$  share the same BEFORE label, it is difficult to say whether they can be regarded as a positive pair, because they are different in many respects. First, we know that  $e_1$  and  $e_2$  are years apart but  $e_3$  and  $e_4$  happen on the same day. Second, we infer BEFORE for different reasons. We know that  $e_1$  happened before  $e_2$  through common-sense: a person needs to complete their undergraduate study before working towards a Ph.D. But we conclude that  $e_3$  happened before  $e_4$  because of and then and a likely causal relation between failing the course and crying. We want to preserve these differences and therefore avoid pushing the representations of  $r_1$  and  $r_2$  closer together.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "We also do not need to consider relations with different labels, such as  $r_1^{\\rightarrow} = (e_1,e_2)$  and  $r_2^{\\leftarrow} = (e_4,e_3)$ , as negative samples. Intuitively, contrastive learning is more effective when the negative samples occur nearby but should be far apart (Robinson et al., 2021). Since event pairs from different sentences contain drastically different syntactic and semantic information, it is not a serious problem for the classifier to distinguish them.",
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+    {
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+        "text": "Symmetric Relations For a symmetric relation  $\\mathbf{h}_r^{\\rightarrow} = \\mathbf{h}_{(e_1,e_2)}$ , we use the dual of the relation  $\\mathbf{h}_r^{\\leftarrow} = \\mathbf{h}_{(e_1,e_2)}$  as an additional, positive sample. Unlike with antisymmetric relations, we follow SimCSE and use other relations in the same minibatch  $(B)$  as negative samples:",
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+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\ell_ {\\mathrm {t c}} = - \\log \\frac {e ^ {\\operatorname {s i m} \\left(\\mathbf {h} _ {r} ^ {\\rightarrow} , \\mathbf {h} _ {r} ^ {\\leftarrow}\\right) / \\tau}}}{\\sum_ {i \\in B} \\left(e ^ {\\operatorname {s i m} \\left(\\mathbf {h} _ {r} ^ {\\rightarrow} , \\mathbf {h} _ {i}\\right) / \\tau} + e ^ {\\operatorname {s i m} \\left(\\mathbf {h} _ {r} ^ {\\leftarrow} , \\mathbf {h} _ {i}\\right) / \\tau}\\right)}. \\tag {5}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "We choose a different design here than for antisymmetric relations because it is impossible to construct true hard negative samples for symmetric relations. Also, we do not check whether other samples in the mini-batch have the same relation label as  $\\mathbf{h}_r^{\\rightarrow}$  because EQUAL is the least common relation type. With only  $3.8\\%$  in MATRES and  $1.7\\%$  of the relations in TBD, it is very rare that there are multiple EQUAL relations in the same",
+        "bbox": [
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+    },
+    {
+        "type": "page_number",
+        "text": "1524",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "image",
+        "img_path": "images/6fb1a28fcd93d544baa0cb6b86d36e098a1a1eab2aceb764e346e1c9203aba30.jpg",
+        "image_caption": [
+            "Figure 2: The efficacy of ConTempo at increasing the model's awareness of temporal relations and their implications through temporal reasoning."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "mini-batch, so the effect of a colliding relation type is negligible.",
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+    },
+    {
+        "type": "text",
+        "text": "Final Training Objective The ConTempo loss is added to the final training objective with a scaling hyperparameter  $\\gamma$  (Equation 6). The classification loss  $\\ell_{\\mathrm{clf}}$  is the standard cross-entropy loss computed using the model's output logits:",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\ell = \\ell_ {\\mathrm {c l f}} + \\gamma \\cdot \\ell_ {\\mathrm {t c}}. \\tag {6}\n$$\n",
+        "text_format": "latex",
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+    {
+        "type": "text",
+        "text": "2.5 Experiment: ConTempo at Increasing Temporal Relation Awareness",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Here we present the effectiveness of ConTempo at increasing temporal relation awareness. In this section, we trained an enhanced ConTempo baseline that is identical to the fine-tuned baseline but with ConTempo loss added to the model. We trained the model using the same hyperparemeters for the same amount of time.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "In Figure 2, we compare ConTempo with baselines using the same similarity measures. We can observe that the similarity of the model's representation of a relation in comparison to its dual drops significantly after ConTempo is applied. Furthermore, now we can observe that the vast majority of similarity measures occupy the lower section of the figure, suggesting that ConTempo is effective at making antisymmetric relations generate representations that are distinct from their duals.",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Unfortunately, we also see a similar drop in similarity for the symmetric relation (EQUAL). We believe this is caused by a data imbalance as there are too few EQUAL instances to balance the overall effect of the antisymmetric relations.",
+        "bbox": [
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+    },
+    {
+        "type": "table",
+        "img_path": "images/ad03bb117c23e0fde3897f0b637d72c73eb3a39c3eeda07c724291c6de5955d4.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Method</td><td>MATRES</td><td>Antisym. Rel. Sim</td><td>Sym. Rel. Sim</td></tr><tr><td>RoBERTa</td><td>80.76</td><td>0.127</td><td>0.424</td></tr><tr><td>Data Expansion</td><td>80.16</td><td>-0.205</td><td>0.148</td></tr><tr><td>Relative Time</td><td>81.01</td><td>-0.237</td><td>0.144</td></tr><tr><td>Logical Constraints</td><td>81.26</td><td>-0.302</td><td>-0.102</td></tr><tr><td>ConTempo (Ours)</td><td>82.01</td><td>-0.352</td><td>-0.080</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Table 2: The effectiveness of different methods at improving temporal relation awareness. The table reports each method's performance together with the average similarity measure for all the antisymmetric and symmetric relations.",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "2.6 Previous Attempts at Increasing Temporal Calculus Awareness",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Does similarity reduction really lead to better temporal label awareness? Also, are there any other ways to increase temporal label awareness? Unfortunately, it is impossible to measure temporal label awareness directly, but we can infer it indirectly by observing the model's performance.",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "In this section we compared ConTempo with three previous methods that attempted to address similar problems. In the following paragraphs, we elucidate these methods, as they could also increase temporal relation awareness. In Table 2, we compare the effectiveness of all three with ConTempo. We use the same model setting for each method for a fair comparison. Overall, ConTempo is the most effective at reducing similarity. It also has the best performance on MATRES. This suggests ConTempo could help the model create more effective representations for TRE prediction.",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Inverse Data Expansion Huang et al. (2023) simply expand the training set by adding all the inverse relations. This straightforward approach, however, does not address the issue that temporal relation labels are presented independently.",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Relative Time Prediction Wen and Ji (2021) employed a relative timestamp prediction component to regulate the training process by predicting a real number (\"relative event time,\" RET) that indicates the relative position of events in a timeline. This component is trained to maximize the distance between events in antisymmetric relations and to minimize the distance between events that are equal. This approach shares broad similarities with contrastive learning but faces two major challenges. First, relative event-time prediction in RET is ultimately computed for each single event individually, which is impossible. By contrast, Contempo considers events in pairs and accounts only",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "page_number",
+        "text": "1525",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "for relative information. Second, this model cannot specify the absolute distance between events, meaning it does not differentiate between events that occur seconds apart and those that are days apart. It also makes predicting chains of events (e.g.,  $e_1 < e_2 < \\ldots < e_5$  where  $<$  indicates AFTER) difficult, as the model needs to balance various data points across the entire dataset and precisely position each event within the relative time range. ConTempo does not face this issue as the time distance between any two events  $(e_1, e_2)$  remains consistent regardless of the direction.",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Logical Constraints Wang et al. (2020) proposed to impose soft logical constraints by adding a loss term that is calculated based on the model's output logits. In particular:",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\ell_ {S} = \\sum \\left| \\log r \\left(e _ {1}, e _ {2}\\right) - \\log \\bar {r} \\left(e _ {2}, e _ {1}\\right) \\right|, \\tag {7}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "where  $r(e_1, e_2)$  denotes the logits the model outputs for relation type  $r$  given  $(e_1, e_2)$  as the input, and  $\\bar{r}$  denotes the dual of the relation. Other logical constraints such as transitivity are also enforced by Wang et al. (2020); we temporarily skip those as they are not relevant to the topic of the current section. We will return to a discussion of other types of constraint in Section 3.3.",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Logical constraint loss has some surface-level resemblance to ConTempo loss, but their method focuses on the output logits whereas ours focuses on regulating the quality of the models' representations. The major motivation for Wang et al. (2020) to add logical constraints was to avoid label conflicts; enhancing the model's understanding of temporal relation labels was secondary.",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "3 The Unified Framework",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Our survey of previous systems suggests that the reusability of innovations of TRE has been limited. For example, papers working on GNN-encoding of document-level information (Zhang et al., 2022; Mathur et al., 2021; Yao et al., 2022) rarely incorporate other published innovations, such as additional common-sense information, in their models. We call for more collaboration between different directions of TRE research.",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "In this section, we argue that ConTempo is compatible with various recent innovations across different research directions. In particular, ConTempo is complementary to: (1) GNN encodings of event and context information, (2) incorpora",
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "ing common-sense information, and (3) the soft enforcement of logical constraints.",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "3.1 Event and Context Encoder",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "All natural language understanding models need methods to encode their input sequence into vectorized representations, and to extract the relevant event and context representations. Currently, researchers typically use pre-trained language models such as BERT (Devlin et al., 2019) or RoBERTa to encode the input sequence because of the rich information these models gather during pre-training.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "In TRE, an event is usually described by a complete phrase or even an entire clause. But since it is hard to annotate a discontinuous sequence, TRE corpora typically label the semantic head as the sole event trigger to represent the complete event. Extracting representations from only the event triggers may not obtain all the relevant information to make a correct prediction, however.",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Therefore, TRE systems now utilize Graph Neural Networks (GNNs) to encode additional information about events and context. Zhang et al. (2022) proposed using dependency trees to help the model access different event arguments. TIMERS (Mathur et al., 2021) proposed using a GNN to encode three graphs: a sentence structure graph, a temporal structure graph, and a discourse structure graph. More recently, MulCo (Yao et al., 2022) reported better results using only the sentence  $(\\mathcal{G}_S)$  and temporal  $(\\mathcal{G}_T)$  structure graphs. They achieved better results with fewer graphs by using multiscale contrastive learning between the fine-tuning of BERT and the training of the GNN to decrease GPU memory usage. Unlike ConTempo, their contrastive learning is not used to enhance the understanding of temporal labels.",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "We add MulCo to the unified framework by concatenating the GNNs' outputs to the event representations as  $\\tilde{\\mathbf{h}}_e = [\\mathbf{h}_e^{\\mathcal{G}_S} \\parallel \\mathbf{h}_e^{\\mathcal{G}_T} \\parallel \\mathbf{h}_e]$ .",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Please refer to Yao et al. (2022) for the detailed description of their model. We provide only a quick overview in Appendix B.",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "3.2 Common-sense Information",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Similar to event and context encoding, we can also add additional features from external sources to enhance the representation. The feasibility of our unified framework is demonstrated by admitting temporal common-sense information.",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Earlier TRE methods (Ning et al., 2018a, 2019; Wang et al., 2020) used temporal information de",
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+        "page_idx": 5
+    },
+    {
+        "type": "page_number",
+        "text": "1526",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "GPT-3 Prompt:",
+        "bbox": [
+            129,
+            86,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "But the great-uncle of 6-year-old shipwreck survivor rafter Elian Gonzalez only ducked his head and walked faster.",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Q: In about 10 words describe how long does the event \"ducked\" typically last.",
+        "bbox": [
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+            141,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "A: Ducking typically lasts only a few seconds.",
+        "bbox": [
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+            165,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Figure 3: An example prompt and response for GPT-3. The context sentence is highlighted in orange, the event trigger, in red and GPT-3's response, in green.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "rived from simple heuristics, or from corpora such as TempProb, which contains typical temporal-relation information between event triggers. Unfortunately, TempProb's coverage and accuracy is limited. Alternatively, the MC-TACO corpus (Zhou et al., 2019) was developed for temporal commonsense knowledge, presenting typical duration information through answers to multiple-choice questions. This approach, however, requires the model to select a typical duration from a restricted set of pre-defined options, and is incapable of addressing typical granularity and underspecificity problems. Our system is the first to apply temporal commonsense information from LLMs for TRE purposes.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "We used GPT-3 (text-davinci-003), employing the template illustrated in Figure 3, to obtain descriptions of the typical durations of events in MATRES. We then use our system's underlying RoBERTa encoder to encode a description of the typical duration, and use the [CLS]-pooler output as the representation, denoted as  $\\mathbf{h}_e^{\\mathrm{dur}}$ .",
+        "bbox": [
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+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\hat {\\mathbf {h}} _ {e} = \\left[ \\mathbf {h} _ {e} ^ {\\text {d u r}} \\| \\tilde {\\mathbf {h}} _ {e} \\right] \\tag {8}\n$$\n",
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+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathbf {h} _ {(e _ {1}, e _ {2})} = f _ {1} \\left(\\left[ \\begin{array}{l l} \\mathbf {h} _ {e _ {1}} & \\parallel \\\\ \\hline \\end{array} \\right] \\mathbf {h} _ {e _ {2}}\\right)\n$$\n",
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+    {
+        "type": "text",
+        "text": "3.3 Training Objective",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "The third type of innovation is the modification of the training objective. ConTempo itself is an innovation to the training objective.",
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+    {
+        "type": "text",
+        "text": "In this section, we show that ConTempo is compatible with other techniques that have been applied to training objectives. We have incorporated the aforementioned soft logical constraints (Wang et al., 2020) into the unified framework.",
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+    {
+        "type": "text",
+        "text": "We add both the symmetric loss  $(\\ell_S)$  and the conjunction loss  $(\\ell_C)$  to the loss function. There is a bit of overlap between Wang et al.'s (2020)",
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+    {
+        "type": "text",
+        "text": "symmetric loss and ConTempo loss, but as previously discussed, we focus on regulating the representation whereas Wang et al.'s (2020) focus on avoiding label conflicts. ConTempo and the logical constraints complement each other, however, as ConTempo does not attempt to treat transitivity within contrastive learning. Instead, it is covered by conjunction restrictions. The loss terms are:",
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+    {
+        "type": "equation",
+        "text": "\n$$\n\\ell_ {S} = \\sum \\left| \\log r \\left(e _ {1}, e _ {2}\\right) - \\log \\bar {r} \\left(e _ {2}, e _ {1}\\right) \\right|, \\tag {9}\n$$\n",
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+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\ell_ {C} = \\sum | L _ {t _ {1}} | + \\sum | L _ {t _ {2}} |\n$$\n",
+        "text_format": "latex",
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+    {
+        "type": "text",
+        "text": "where  $L_{t_1}$  and  $L_{t_2}$  are defined as:",
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+    {
+        "type": "equation",
+        "text": "\n$$\nL _ {t _ {1}} = \\log r _ {1} (e _ {1}, e _ {2}) + \\log r _ {2} (e _ {2}, e _ {3}) - \\log r _ {3} (e _ {1}, e _ {3}),\n$$\n",
+        "text_format": "latex",
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+    {
+        "type": "equation",
+        "text": "\n$$\nL _ {t _ {2}} = \\log r _ {1} \\left(e _ {1}, e _ {2}\\right) + \\log r _ {2} \\left(e _ {2}, e _ {3}\\right) - \\log \\left(1 - r _ {4} \\left(e _ {1}, e _ {3}\\right)\\right). \\tag {10}\n$$\n",
+        "text_format": "latex",
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+        "type": "text",
+        "text": "See Wang et al. (2020) for details, including the induction table for the conjunctive constraints. The final training objective is:",
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+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\ell = \\ell_ {\\mathrm {c l f}} + \\gamma \\cdot \\ell_ {\\mathrm {t c}} + \\lambda_ {S} \\cdot \\ell_ {S} + \\lambda_ {C} \\cdot \\ell_ {C}. \\tag {11}\n$$\n",
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+    {
+        "type": "text",
+        "text": "4 Experiments",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "4.1 Experimental Setup",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "The hyperparameter settings and training details are explained in Appendix A.",
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+    {
+        "type": "text",
+        "text": "Data We experimented with both MATRES (Ning et al., 2018b) and TBD (Cassidy et al., 2014), the two popular corpora that are most often used to benchmark TRE systems. Both are derived from the TimeBank Corpus (Pustejovsky et al., 2003), which is annotated using the TimeML standard (Pustejovsky et al., 2005). The VAGUE labels are computed into the F1s for both MATRES and TBD but are regarded as negative labels.",
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+    {
+        "type": "text",
+        "text": "TBD is a dense re-annotation of the TimeBank corpus where every possible pair of events/times in a given window is forced to be annotated regardless of whether there exists a specified temporal relation. As a result, TBD has ample data samples (12715 relations from 39 articles) but a relatively low inter-annotator agreement, with Cohen's (1960)  $\\kappa$  ranging between 0.56 and 0.64.",
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+    {
+        "type": "text",
+        "text": "MATRES aimed at reducing noise in TBD's annotation. It introduced the concept of orthogonal temporal axes for hypothetical, negated, opined, and static events. In practice, these events are ignored during temporal relation annotation. They further reduced the number of temporal relations",
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+    },
+    {
+        "type": "page_footnote",
+        "text": "3The prompts and the generated responses from GPT-3 will be made publicly accessible online.",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "page_number",
+        "text": "1527",
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+    },
+    {
+        "type": "table",
+        "img_path": "images/2c1caac18c2ffad93f4bf68dd7d3c629fc1311cd0b486acf83a372735e5137e3.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Model</td><td>CleanMATRES</td><td>MATRES</td><td>TimeBank-Dense</td></tr><tr><td>ChatGPT 3.5</td><td>65.29</td><td>25.94</td><td>53.06</td></tr><tr><td>ChatGPT 3.5 (CoT)</td><td>66.97</td><td>35.54</td><td>57.14</td></tr><tr><td>ChatGPT 4</td><td>76.47</td><td>41.64</td><td>67.58</td></tr><tr><td>ChatGPT 4 (CoT)</td><td>80.76</td><td>56.70</td><td>65.14</td></tr><tr><td>Fine-tuned GPT 3.5</td><td>73.41</td><td>55.27</td><td>61.71</td></tr><tr><td>LSTM (Cheng and Miyao, 2017)</td><td>-</td><td>73.4</td><td>62.2</td></tr><tr><td>SCS-EERE* (Man et al., 2022)</td><td>91.25</td><td>80.98</td><td>65.92</td></tr><tr><td>Joint Constrained Learning (Wang et al., 2020)</td><td>-</td><td>78.8</td><td>-</td></tr><tr><td>Relative Time* (Wen and Ji, 2021)</td><td>89.61</td><td>81.63</td><td>66.81</td></tr><tr><td>MulCo* (Yao et al., 2022)</td><td>91.34</td><td>82.08</td><td>67.51</td></tr><tr><td>TIMERS (Mathur et al., 2021)</td><td>-</td><td>82.3</td><td>67.8</td></tr><tr><td>Endpoint Comparisons (Huang et al., 2023)</td><td>-</td><td>82.6</td><td>68.1</td></tr><tr><td>ConTempo Baseline</td><td>91.35</td><td>82.01</td><td>67.78</td></tr><tr><td>ConTempo + Unified Framework (Ours)</td><td>92.66</td><td>83.17</td><td>68.56</td></tr></table>",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "down to only four types. They also simplified the annotation scheme by asking the annotators to compare only the start times of events, as the end time of a durative event can often be ambiguous and cause confusion. During our survey of TRE baselines, we found that there are actually several versions of MATRES being used by different research labs (see Appendix C). We use the version that is available on the Ning et al.'s (2018b) GitHub page<sup>4</sup> and reproduced several key baseline systems' performances using our unified evaluation standards.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "During the development of ConTempo, we discovered a large number of annotation errors in both MATRES and TBD. To further reduce the noise in the annotations, we re-examined and corrected the test set annotations of MATRES, creating the CleanMATRES test set. We will detail the process and describe the data in Section D.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Baseline Systems We compared ConTempo's performance with seven prior systems: LSTM (Cheng and Miyao, 2017), SCS-EERE (Man et al., 2022), Joint Constrained Learning (Wang et al., 2020), Relative Time (Wen and Ji, 2021), MulCo (Yao et al., 2022), TIMERS (Mathur et al., 2021) and Endpoint Comparisons (Huang et al., 2023). We reproduced the results of SCS-EERE and Relative Time using their publicly available code. Additionally, we reimplemented MulCo according to the specifications provided in the paper.",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "LLM Baselines We incorporated the performance of LLMs as an additional baseline alongside the aforementioned baseline systems. Specifically,",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "table",
+        "img_path": "images/6ca3ef3d05076c7930b0bd4b2fb5ebbaefa99cc84294dfc640a9ed4b3a5eef7f.jpg",
+        "table_caption": [
+            "Table 3: F1 on CleanMATRES, MATRES and TBD. ConTempo achieved substantial improvements over strong baselines. Rows with results that we reproduced using the same evaluation settings as our model are labelled with * ."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Model</td><td>CleanMATRES</td></tr><tr><td>ConTempo + Unified Framework</td><td>92.66</td></tr><tr><td>- ConTempo</td><td>91.30 (-1.36)</td></tr><tr><td>- GNN</td><td>91.65 (-1.01)</td></tr><tr><td>- GPT-3 Typical Duration</td><td>92.06 (-0.60)</td></tr><tr><td>- Logical Constraints</td><td>92.14 (-0.52)</td></tr></table>",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Table 4: Ablation study results.",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "we reproduced the results from Yuan et al.'s (2023) using both ChatGPT-3.5 and ChatGPT-4. Chain-of-thought (CoT) was deployed in the experiments. Additionally, we fine-tuned GPT-3.5 utilizing OpenAI's API using the suggested settings to perform the task.",
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+    {
+        "type": "text",
+        "text": "4.2 Experimental Results",
+        "text_level": 1,
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+    },
+    {
+        "type": "text",
+        "text": "Table 3 reports the performance of our ConTempo model compared to other baseline models on CleanMATRES, MATRES, and TBD. The results of our models and our reproductions are the average over three different runs with different random seeds.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Overall, ConTempo brings a substantial performance increase to the TRE model. Even the simple ConTempo baseline's performance is in the same ballpark as previous state-of-the-art systems. When enhanced by other innovations under the unified framework, our model outperformed the previous state-of-the-art models by  $1.32\\%$ ,  $0.57\\%$ , and  $0.46\\%$  for the three datasets, respectively.",
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+    {
+        "type": "text",
+        "text": "4.3 Ablation Study",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "In order to evaluate the efficacy of the proposed components in the unified framework, we conducted an ablation study, wherein we removed one",
+        "bbox": [
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+    {
+        "type": "page_footnote",
+        "text": "4https://github.com/qiangning/MATRES",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "page_number",
+        "text": "1528",
+        "bbox": [
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+        "page_idx": 7
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+    {
+        "type": "text",
+        "text": "component at a time and reran the experiment using the aforementioned hyperparameters. The results of this study are presented in Table 4. Among the four components, contrastive learning demonstrated the most substantial impact on performance, with its removal leading to a  $1.36\\%$  decrease in the model's effectiveness. The GNN module also makes a substantial contribution to overall performance. Finally, both GPT-3 typical duration information and logical constraints exhibit moderate effects on the system's performance.",
+        "bbox": [
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+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "The ablation study result confirms our initial hypothesis: the primary challenge for these models has been making sense of relational labels.",
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+    {
+        "type": "text",
+        "text": "5 Conclusion",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "In this paper, we propose a novel ConTempo method that utilizes contrastive learning on the symmetric and antisymmetric properties to enhance the model's awareness of temporal relations. Using ConTempo, we observe an apparent change in the representation of relations generated by the model. Particularly, we see a significant reduction in the similarity between relation representations  $\\mathbf{h}_r^{\\rightarrow}$  in comparison to their dual  $\\mathbf{h}_r^{\\leftarrow}$ .",
+        "bbox": [
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+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "ConTempo and GNN encoding, temporal common-sense information, and soft logical constraints can work in synergy to create a unified system that has achieved state-of-the-art performance across various benchmark corpora. Our success demonstrates the flexibility of ConTempo, and we call for more collaboration between different directions of TRE research.",
+        "bbox": [
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+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "TRE is a rare and curious case where fine-tuned small LMs perform considerably better LLMs. Even with the help of groundbreaking techniques such as chain-of-thought (Wei et al., 2022), the best performance ChatGPT can achieve is  $52.4\\%$  on MATRES (Yuan et al., 2023) and  $41.0\\%$  on TBD (Huang et al., 2023) — remarkably lower than the fine-tuned small language models' performance. This anomaly presents tremendous opportunity for both TRE researchers and LLM researchers. TRE can be used as a hard task for the LLMs' to analyse their capabilities at reasoning and comprehension. In conclusion, exploring the integration of existing TRE innovations with LLMs and incorporating LLMs as a key component within TRE frameworks could significantly enhance performance and drive forward the advancement of both fields.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Acknowledgement",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "This study is funded by the Canadian Safety and Security Program (CSSP) from Defence Research and Development Canada (DRDC) awarded to the Public Health Agency of Canada (CSSP-2018-CP2334: Incorporating Advanced Data Analytics into a Health Intelligence Surveillance System). We thank the Global Public Health Intelligence Network (GPHIN) and Epidemic Intelligence from Open Sources (EIOS) teams for their support.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Limitations",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "We only evaluate ConTempo's performance using RoBERTa. Other language models, such as DeBERTa (He et al., 2021), T5 (Raffel et al., 2020) and DistilBERT (Sanh et al., 2020) may provide even better performance. We leave further exploration for future work.",
+        "bbox": [
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Due to restricted dataset resources, our unified model's evaluation was conducted only using TB-Dense and MATRES. There are other TimeML-based and even non-TimeML-based corpora related to TRE. We leave more evaluation to future work and encourage the community to reproduce our results on more datasets.",
+        "bbox": [
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+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "References",
+        "text_level": 1,
+        "bbox": [
+            510,
+            533,
+            608,
+            548
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "list",
+        "sub_type": "ref_text",
+        "list_items": [
+            "James F. Allen. 1981. An interval-based representation of temporal knowledge. In In Proceedings 7th IJCAI, pages 221-226.",
+            "James F. Allen. 1983. Maintaining knowledge about temporal intervals. Communications of the ACM, 26(11):832-843.",
+            "Taylor Cassidy, Bill McDowell, Nathanael Chambers, and Steven Bethard. 2014. An Annotation Framework for Dense Event Ordering. In Proceedings of the 52nd Annual Meeting of the Association for Computational Linguistics (Volume 2: Short Papers), pages 501-506, Baltimore, Maryland. Association for Computational Linguistics.",
+            "Ting Chen, Simon Kornblith, Mohammad Norouzi, and Geoffrey Hinton. 2020. A Simple Framework for Contrastive Learning of Visual Representations. In Proceedings of the 37th International Conference on Machine Learning, pages 1597-1607. PMLR.",
+            "Fei Cheng and Yusuke Miyao. 2017. Classifying Temporal Relations by Bidirectional LSTM over Dependency Paths. In Proceedings of the 55th Annual Meeting of the Association for Computational Linguistics (Volume 2: Short Papers), pages 1-6, Vancouver, Canada. Association for Computational Linguistics."
+        ],
+        "bbox": [
+            509,
+            556,
+            884,
+            921
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "page_number",
+        "text": "1529",
+        "bbox": [
+            482,
+            927,
+            519,
+            940
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "list",
+        "sub_type": "ref_text",
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+            "Jacob Cohen. 1960. A Coefficient of Agreement for Nominal Scales. Educational and Psychological Measurement, 20(1):37-46.",
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+        ],
+        "bbox": [
+            115,
+            85,
+            487,
+            835
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "A Training Details",
+        "text_level": 1,
+        "bbox": [
+            114,
+            847,
+            292,
+            864
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "We use roberta-large as the pre-trained encoder. The best model is selected with the highest development set performance among 20 epochs of training,",
+        "bbox": [
+            112,
+            873,
+            487,
+            921
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "optimized using AdamW (Loshchilov and Hutter, 2019) with an initial learning rate of 1e-5 and a 0.01 weight decay. We use a linear scheduler with a warm-up ratio of 0.1 and a batch size of 64. The dropout rate is 0.1 across the system. For ConTempo, we determined  $\\tau = 0.05$ ,  $\\gamma = 1.0$  using a grid search over  $\\{0.1, 0.05, 0.01\\} \\times \\{1, 0.1, 0.01\\}$ .",
+        "bbox": [
+            507,
+            84,
+            882,
+            197
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "For the components in the unified systems, we follow the hyperparameter suggested by the corresponding papers (Yao et al., 2022; Wang et al., 2020).",
+        "bbox": [
+            507,
+            198,
+            882,
+            260
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "B MulCo",
+        "text_level": 1,
+        "bbox": [
+            509,
+            273,
+            608,
+            288
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "MulCon utilized a sentence structure graph  $\\mathcal{G}_S$  and a temporal structure graph  $\\mathcal{G}_T$  to encode document-level information. The sentence structure graph has three types of nodes: the document, the sentences and the tokens. All sentences are connected to the document node and each token node is connected to the sentence it located in. For an event,  $\\mathcal{G}_S$ 's embedding of the event trigger token is used.",
+        "bbox": [
+            507,
+            299,
+            882,
+            426
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "The temporal structure graph, on the other hand, also has three types of nodes. The document creation time (DCT) node, the time expressions, and the events. Each time expression is connected to the DCT, and each event is connected to a time expression if there is an E2T link in the corpus. Finally, each event node has an edge point to itself.",
+        "bbox": [
+            507,
+            428,
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+            539
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "C MATRES Versions",
+        "text_level": 1,
+        "bbox": [
+            507,
+            552,
+            710,
+            567
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "We found two versions of MATRES that has been used by different works. Ning et al. (2018b) released a version on GitHub  $^{5}$  that contains 837 relations in the Platinum test set. Wang et al. (2020) released another version with 818 relations in the Platinum test set. The difference (19 relations) could constitute as  $2.32\\%$  of the test set data. We use Ning et al.'s (2018b).",
+        "bbox": [
+            507,
+            577,
+            882,
+            706
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "D CleanMATRES",
+        "text_level": 1,
+        "bbox": [
+            507,
+            719,
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+            734
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "As we previously mentioned, we identified a large quantity of annotation errors within both MATRES and TBD. This is not surprising, however, as both corpora reported adequate inter-annotator agreements. TBD reported  $\\kappa$  ranged from 0.56 to 0.64 and MATRES reported a good — but not perfect —  $\\kappa$  of 0.84 (Table 6). In this section, we will first provide a description of the annotation errors",
+        "bbox": [
+            505,
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+        "page_idx": 10
+    },
+    {
+        "type": "page_footnote",
+        "text": "$^{5}$ https://github.com/qiangning/MATRES  \n $^{6}$ https://github.com/CogComp/  \nJointConstrainedLearning/tree/main/MATRES",
+        "bbox": [
+            507,
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+        "page_idx": 10
+    },
+    {
+        "type": "page_number",
+        "text": "1531",
+        "bbox": [
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+        "page_idx": 10
+    },
+    {
+        "type": "table",
+        "img_path": "images/c81c8942aad5d46c5f85067d05002e9c4a6481e4c2d791c7e12e4c3959e747a7.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Relabelling</td><td colspan=\"2\">EQUAL</td><td colspan=\"2\">VAGUE</td><td colspan=\"2\">BEFORE</td><td colspan=\"2\">AFTER</td></tr><tr><td>EQUAL</td><td>10</td><td>32.26%</td><td>15</td><td>13.27%</td><td>1</td><td>0.24%</td><td>0</td><td>0%</td></tr><tr><td>VAGUE</td><td>3</td><td>9.68%</td><td>24</td><td>21.24%</td><td>5</td><td>1.17%</td><td>5</td><td>1.86%</td></tr><tr><td>BEFORE</td><td>6</td><td>19.35%</td><td>39</td><td>34.51%</td><td>405</td><td>95.52%</td><td>0</td><td>0%</td></tr><tr><td>AFTER</td><td>10</td><td>32.26%</td><td>26</td><td>23.01%</td><td>4</td><td>0.94%</td><td>256</td><td>95.17%</td></tr><tr><td>Orth. Axes</td><td>2</td><td>6.45%</td><td>9</td><td>7.96%</td><td>9</td><td>2.12%</td><td>8</td><td>2.97%</td></tr><tr><td>Total</td><td>31</td><td>100%</td><td>113</td><td>100%</td><td>424</td><td>100%</td><td>269</td><td>100%</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "table",
+        "img_path": "images/0d9089518fe1e6c1bc8ef825a1de822056241d8248b569d64539a272e032a88d.jpg",
+        "table_caption": [
+            "Table 5: Re-annotation of the MATRES test set. The statistics of the correct labels are highlighted in bold. Each column corresponds to an original MATRES label. Some relations involve events that should have been placed on one of the orthogonal axes."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Corpus</td><td>Cohen&#x27;s κ</td></tr><tr><td>TimeBank-Dense</td><td>0.56-0.64</td></tr><tr><td>MATRES</td><td>0.84</td></tr><tr><td>MATRES EQUAL</td><td>1.0</td></tr><tr><td>MATRES VAGUE</td><td>0.75</td></tr></table>",
+        "bbox": [
+            176,
+            274,
+            426,
+            379
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "Table 6: Detailed inter-annotator agreement of MA-TRES and TBD.",
+        "bbox": [
+            112,
+            388,
+            489,
+            418
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "we identified in MATRES. Then, we will describe our re-annotation process. Finally, we will present an overview of the result of the re-annotation — CleanMATRES.",
+        "bbox": [
+            112,
+            443,
+            490,
+            506
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "D.1 A Qualitative Analysis of the Annotation Errors",
+        "text_level": 1,
+        "bbox": [
+            112,
+            520,
+            484,
+            551
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "(3) He won $_{e_1}$  the Gusher Marathon, finishing $_{e_2}$  in 3:07:35.",
+        "bbox": [
+            131,
+            560,
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+            593
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "Original Annotation: VAGUE Correct Annotation: EQUAL",
+        "bbox": [
+            169,
+            606,
+            371,
+            633
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "(4) The last surviving member of the team which first  $\\mathbf{conquered}_{e_1}$  Everest in 1953 has  $\\mathbf{died}_{e_2}$  in a Derbyshire nursing home.",
+        "bbox": [
+            131,
+            653,
+            485,
+            702
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "Original Annotation: VAGUE Correct Annotation: BEFORE",
+        "bbox": [
+            169,
+            715,
+            379,
+            741
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "(5) More than 16,000 dead pigs have been found $_{e_1}$  floating $_{e_2}$  in rivers that provide drinking water to Shanghai.",
+        "bbox": [
+            131,
+            760,
+            485,
+            810
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "Original Annotation: EQUAL Correct Annotation: AFTER",
+        "bbox": [
+            169,
+            824,
+            371,
+            850
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "Examples (3-5) show three examples of incorrect annotations in MATRES. In example 3, the relation between won and finishing is labelled as VAGUE,",
+        "bbox": [
+            112,
+            873,
+            489,
+            921
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "but, nonetheless, the two mentions refer to two aspects of the same punctual event. For example 4, it is clear that the member died a long time after they conquered Everest. For example 5, since MATRES annotators were only comparing the start-time of events, the pigs floating in rivers must took place before the event that they were found.",
+        "bbox": [
+            507,
+            277,
+            884,
+            388
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "The two examples presented in this study illustrate the main sources of annotation errors commonly found in data sets. As posited by Ning et al. (2018b), the first example's error likely stems from the annotators' lack of comprehension regarding time granularity and event coreference. MATRES annotations are created by asking annotators two heuristic questions:",
+        "bbox": [
+            507,
+            392,
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+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "list",
+        "sub_type": "text",
+        "list_items": [
+            "(Q1) Is it possible that  $e_{start}^{1}$  is before  $e_{start}^{2}$ ?",
+            "(Q2) Is it possible that  $e_{start}^{2}$  is before  $e_{start}^{1}$ ?"
+        ],
+        "bbox": [
+            507,
+            519,
+            845,
+            554
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "The heuristic questions, Q1 and Q2, do not adequately address these concepts, necessitating the need to develop improved annotation guidelines. By effectively conveying the intricacies of time granularity and event coreference, the frequency of such errors may decrease, although perhaps with a lower  $\\kappa$ . The second example's mistake should perhaps be attributed to a misunderstanding of the text.",
+        "bbox": [
+            507,
+            571,
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+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "D.2 CleanMATRES Annotation",
+        "text_level": 1,
+        "bbox": [
+            507,
+            734,
+            774,
+            750
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "We undertook a re-annotation of the MATRES test set. The test set were labelled independently by two authors of this paper, who were then forced to reconcile where they disagreed. Our pass through the test set reveals a significant number of annotation inaccuracies, particularly in the cases of the EQUAL and VAGUE relations. As detailed in Table 5, we found a mere  $32.26\\%$  of the EQUAL and  $21.24\\%$  of the VAGUE edges to have been accurately annotated.",
+        "bbox": [
+            507,
+            760,
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+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "page_number",
+        "text": "1532",
+        "bbox": [
+            482,
+            927,
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+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "D.3 Discussion: Vague Relations",
+        "text_level": 1,
+        "bbox": [
+            114,
+            84,
+            386,
+            99
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "We want to take the opportunity to discuss the issues related to the VAGUE relation. The VAGUE relation, which could be better called the underspecified relation, describes relations that are uncertain due to insufficient context. However, this certainty is highly subjective to the annotator and hard to rigorously quantify. TBD adopted an \"80% rule\" that instruct annotators to label a relation as vague if they are \"80% confident that it was the writer's intent that a reader infer that relation.\" As a result, inter-annotator agreement on vague edges is the lowest among all relation types.",
+        "bbox": [
+            112,
+            105,
+            489,
+            298
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "MATRES took a different approach and treats certain combinations of the start time comparisons as vague relations. The approach attenuates the issue but by no means solve the issue. The two heuristic questions are also subject and involves a degree of uncertainty. Furthermore, similar to EQUAL relations, a simple heuristic question mistake could result in incorrect VAGUE relation annotation.",
+        "bbox": [
+            112,
+            299,
+            489,
+            441
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "With all the aforementioned issues, CleanMATRES excludes all VAGUE relations from the test set. We only consider BEFORE, AFTER, and EQUAL relations during the evaluation of CleanMATRES. We also did not include the analysis of VAGUE relations in Section 2, as it requires a more thorough examination of the application of temporal calculus when underspecificity is involved. Allen's (1983) original temporal calculus assumes all events are intervals with well-defined endpoints. Yao et al. (2020) and Niu et al. (2023) provided a more in-depth analysis to the VAGUE edges and underspecificity.",
+        "bbox": [
+            112,
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+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "page_number",
+        "text": "1533",
+        "bbox": [
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+        ],
+        "page_idx": 12
+    }
+]

2024/ConTempo_ A Unified Temporally Contrastive Framework for Temporal Relation Extraction/9ded2c84-7d7d-4a7e-b160-6caf16706c14_origin.pdf

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2024/ConTempo_ A Unified Temporally Contrastive Framework for Temporal Relation Extraction/full.md

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+# ConTempo: A Unified Temporally Contrastive Framework for Temporal Relation Extraction
+
+Jingcheng Niu, $^{1,2,3}$  Saifei Liao, $^{2,3}$  Victoria Ng, $^{1}$  Simon De Montigny, $^{1}$  Gerald Penn $^{2,3}$
+
+<sup>1</sup>Public Health Agency of Canada, <sup>2</sup>University of Toronto, <sup>3</sup>Vector Institute
+
+{niu,liaosaif,gpenn}@cs.toronto.edu
+
+{victoria.ng,simon.demontigny}@phac-aspc.gc.ca
+
+# Abstract
+
+The task of temporal relation extraction (TRE) involves identifying and extracting temporal relations between events from narratives. We identify two primary issues with TRE systems. First, by formulating TRE as a simple text classification task where every temporal relation is independent, it is hard to enhance the TRE model's representation of meaning of temporal relations, and its facility with the underlying temporal calculus. We solve the issue by proposing a novel Temporally Contrastive learning model (ConTempo) that increase the model's awareness of the meaning of temporal relations by leveraging their symmetric or antisymmetric properties. Second, the reusability of innovations has been limited due to incompatibilities in model architectures. Therefore, we propose a unified framework and show that ConTempo is compatible with all three main branches of TRE research. Our results demonstrate that the performance gains of ConTempo are more pronounced, with the total combination achieving state-of-the-art performance on the widely used MATRES and TBD corpora. We furthermore identified and corrected a large number of annotation errors present in the test set of MATRES, after which the performance increase brought by ConTempo becomes more apparent.
+
+# 1 Introduction
+
+Temporal relation extraction (TRE) is the task of classifying the temporal relations between pairs of events conveyed in narratives (Pustejovsky et al., 2006, 2010). This task is important to the natural language processing (NLP) community because the conception of time is a key component of text comprehension and reasoning. Additionally, it carries practical importance, as TRE is a crucial component of various downstream applications in question answering, information retrieval, and information extraction.
+
+TRE is difficult. Despite its importance and popularity, TRE systems still have relatively poor performance compared to other natural language understanding tasks. TRE is also salient because recent large language models (LLMs) and chat systems have substantially worse performance than smaller, fine-tuned TRE models (Yuan et al., 2023; Huang et al., 2023).
+
+In this paper, we enhance current TRE systems by identifying and addressing two major issues that hinder their performance:
+
+1. It is difficult to understand relation labels. TRE is typically formulated as a multi-label text classification task. The representation of the relation is determined by a neural classifier, which outputs logits for different label classes. These logits are then converted into label probabilities using a softmax layer. As a result, in a TRE model, all relation types are considered independent. However, temporal relations are inherently structured, governed by an underlying temporal calculus (Allen, 1981, 1983). For instance, if event A occurred before event B, it can be inferred that B happened after A. Integrating the meanings of each temporal relation and the principles of the underlying temporal calculus into the neural classifier presents a complex challenge, as there is no straightforward method to do so.
+
+2. The reusability of innovations has been limited. Many of the recent innovations in TRE have not built upon one another, primarily due to the lack of a unified framework (beyond annotation standards) to accommodate them. For example, despite being widely cited and used as a baseline by subsequent systems, the relative time prediction technique (Wen and Ji, 2021) has rarely been applied on top of newer models, due to incompatibilities in model architecture. The evaluation methods employed by earlier systems vary significantly, moreover, which complicates direct comparisons
+
+between models and further hinders the development of future models.
+
+We propose a novel Temporally Contrastive learning method (ConTempo)<sup>1</sup> to enhance the model's representation of the meaning of temporal relations, and its facility with the underlying temporal calculus. The intuition behind ConTempo is very simple. Contrastive learning aims to pull similar (positive) samples closer and push dissimilar (negative) samples apart. We leverage the symmetric and antisymmetric properties of temporal relations to augment a base graph of positive samples for contrastive learning. For antisymmetric relations (A before B), we want to push the relation's representation away from its inverse (B after A). For a symmetric relation (A equals B), we likewise want to pull its representation closer to its inverse (B equals A). Our experimental results indicate that ConTempo is effective at creating distinctive representations for different types of temporal relation pairs and yields a substantial improvement in performance.
+
+Then, building upon ConTempo, we create a unified framework that is compatible with various previous modes of improvement in TRE systems. In particular, we have identified two major threads of innovation in the previous literature on this topic: (1) GNN encoding of event and context information, (2) incorporation of common-sense information, and (3) the soft enforcement of logical constraints. Our experiment shows that ConTempo is compatible with techniques from all three major threads of research and can achieve state-of-the-art performance on major evaluation corpora, including MATRES (Ning et al., 2018b) and TimeBank-Dense (TBD; Cassidy et al., 2014). We nevertheless perceive the need to introduce CleanMATRES, a refined version of MATRES that we created by fixing certain annotation errors.
+
+Among all of these innovations, an ablation study nevertheless shows that ConTempo brings the most significant performance increase. This finding underscores our initial hypothesis: the primary challenge for these models has been their difficulty with making sense of relation labels.
+
+During our development of the unified ComTempo framework, we discovered a large number of annotation errors within MATRES and TBD, two commonly utilized corpora. Because of
+
+<table><tr><td>Corpus</td><td>Relations</td></tr><tr><td>MATRES</td><td>BEFORE, AFTER, EQUAL, VAGUE</td></tr><tr><td>TBD</td><td>BEFORE, AFTER, INCLUDES, IS INCLUDED, EQUAL, VAGUE</td></tr></table>
+
+Table 1: Temporal relations used by MATRES and TBD.
+
+TBD's dense annotation scheme, the appropriate level of underspecificity cannot be resolved without further investigation. But we are able to provide a thorough re-examination of the MATRES corpus. After correcting these errors, performance improves yet again, and the performance increase brought by ConTempo becomes more apparent.
+
+# 2 ConTempo
+
+We begin our discussion by first formulating the TRE task. Then, using a comparison of relational representations, we will demonstrate the difficulty that a neural model faces in temporal reasoning and understanding the meaning of temporal labels. In particular, there is a significant correlation between the mistakes a TRE model makes and its degree of inference over the available symmetric and antisymmetric properties. Next, we will present our ConTempo method in detail, which enhances a model's awareness of the meaning of each temporal relation and each principles of temporal reasoning. Finally, we will empirically demonstrate the effectiveness of ConTempo and compare it with previous methods in increasing temporal relation awareness.
+
+# 2.1 TRE: Task Formulation
+
+TRE can be formulated as a classification task. Given an input sequence  $S = [t_1, \dots, t_n]$  and two events represented by two distinct tokens from the sequence,  $e_1, e_2 \in S$ , where  $e_1 \neq e_2$ , the TRE model should classify the relation between the event pair  $(e_1, e_2)$  into one of several temporal relations,  $\mathcal{R}$ . Different corpora have different sets of temporal relations. Most TRE benchmark datasets aspire to embody Allen's (1981) 13 original temporal relations, but creating datasets with such fine-grained annotations is challenging. Attempts to utilize all 13 temporal relation types have failed due to low inter-annotator agreement. Therefore, recent TRE datasets typically simplify the relation set to a more coarse subset of the original set. As listed in Table 1, MATRES has 4 relation types, and TBD uses 6 relation types.
+
+# 2.2 Temporal Relation Labels Awareness
+
+After simplification, Allen's (1983) full temporal interval calculus can no longer be maintained. But interval symmetry and antisymmetry (as shown in Equation 1) still apply within both MATRES and TBD. $^2$  In our opinion, it is crucial for TRE models to reason with intervals in order to yield good evaluation results on benchmarks—if the models know A happened before B but do not know that B happened after A, can we really say that the model understands time in narratives?
+
+$$
+A \text {I N C l u d e s} B \Longleftrightarrow B \text {I S - I N C l u d e d} A
+$$
+
+$$
+A _ {\text {B E F O R E}} B \Longleftrightarrow B _ {\text {A F T E R}} A \tag {1}
+$$
+
+$$
+A \text {E Q U A L} B \iff B \text {E Q U A L} A
+$$
+
+Symmetry and antisymmetry also provide us with an opportunity to test a model's understanding of relation labels. In particular, we can measure the similarity of the model's representation of a relation  $\mathbf{h}_r^{\rightarrow}$  in comparison to its dual  $\mathbf{h}_r^{\leftarrow}$ :
+
+$$
+\operatorname {s i m} \left(\mathbf {h} _ {r} ^ {\rightarrow}, \mathbf {h} _ {r} ^ {\leftarrow}\right) = \operatorname {s i m} \left(\mathbf {h} _ {\left(e _ {1}, e _ {2}\right)}, \mathbf {h} _ {\left(e _ {2}, e _ {1}\right)}\right), \tag {2}
+$$
+
+It is relatively commonplace in the context of TRE to speak of a representation of a temporal relation, although this in fact refers to the representation of one of its instances over some event pair  $\mathbf{h}_{(e_1,e_2)}$ . Therefore, we will speak of the two interchangeably. If the relation between  $e_1$  and  $e_2$  is symmetric, then we can interpret high similarity as a sign of awareness concerning the relation's meaning because the relation and its inverse are nearly the same. On the other hand, if the relation is antisymmetric, we should expect the relations to be distinct and, therefore, we should interpret low similarity as a good sign. Here, we measure similarity with cosine similarity  $(\mathrm{sim}(\mathbf{a},\mathbf{b}) = \frac{\mathbf{a}\cdot\mathbf{b}}{\|\mathbf{a}\|\|\mathbf{b}\|})$ .
+
+# 2.3 Temporal Relation Awareness of Fine-tuned BERT-based Models
+
+In this section, we examine the extent to which typical, fine-tuned BERT-based models can be said to understand temporal relations and the temporal calculus. All contemporary TRE systems use this paradigm. Therefore, we experimented with a baseline model (described in Equation 3) to establish a foundation for the capacity of TRE models to summarize the temporal interval calculus.
+
+![](images/9cc44225faa3052d8d38a98fc3c99faa7173e32b9526019e7bbf1e514ce8f632.jpg)  
+Figure 1: Similarity measures of event pair representations with their inverses. Each dot represents a relation in the MATRES test set: green means the model classified the relation correctly and red means the model made a mistake. The box plots underneath show the quantile statistics. There is an obvious negative correlation between the correctness of the prediction and the similarity measure. This is evident from observing that the incorrect predictions (red points) are located in the upper region of the figure for BEFORE and AFTER.
+
+The baseline model has three components: a pretrained encoder (we use a RoBERTa-large model (Liu et al., 2019)), a 2-layer MLP module  $(f_{1})$  that encodes the relation of the event pair under a unified representation scheme, and another single layer MLP  $(f_{2})$  that decodes the relational representation into logits for each, different relational type:
+
+$$
+\mathbf {E} = \operatorname {e n c o d e r} (S) = [ \mathbf {h} _ {1}, \dots , \mathbf {h} _ {n} ],
+$$
+
+$$
+\mathbf {h} _ {\left(e _ {1}, e _ {2}\right)} = f _ {1} \left(\left[ \mathbf {h} _ {e _ {1}} \| \mathbf {h} _ {e _ {2}} \right]\right), \tag {3}
+$$
+
+$$
+\mathbb {P} _ {\mathcal {R}} \left(e _ {1}, e _ {2}\right) = \operatorname {s o f t m a x} \left(f _ {2} \left(\mathbf {h} _ {\left(e _ {1}, e _ {2}\right)}\right)\right).
+$$
+
+The implementation details and hyperparameter settings are described in Appendix A.
+
+Baseline Model Temporal Awareness Figure 1 shows the similarity between the relational representations  $\mathbf{h}_r^{\rightarrow}$  and their symmetric duals  $\mathbf{h}_r^{\leftarrow}$  as generated by the baseline model. We can see an obvious negative correlation between the correctness of the prediction and the similarity measure. This is evident from observing that the incorrect predictions (red points) are located in the upper region of the figure for BEFORE and AFTER. Furthermore, the baseline model often assigns similar representations to relations and their symmetric duals, even when the two are diametrically opposite in meaning. As shown by the box plot, the first quantile of both the BEFORE and AFTER relations occupy
+
+the upper part of the figure, which corresponds to high similarity. This shows that while fine-tuned models might have some basic perception of the significance of these temporal labels, it is by no means efficient, as all temporal labels are presented to the model as independent.
+
+# 2.4 ConTempo: The Method
+
+Contrastive learning builds on the idea of pulling similar (positive) data points  $(x, x^{+})$  closer together and pushing dissimilar (negative) data points  $(x, x^{-})$  apart by adding a contrastive loss term to the training objective (Robinson et al., 2021). We thus need to define positive and negative samples for temporal relation instances, i.e., event pairs. In this section, we will explain how positive and negative samples are constructed based on whether the relation is symmetric (EQUAL) or antisymmetric (BEFORE, AFTER, INCLUDES, and IS INCLUDED), and define how we compute the temporally contrastive loss term  $\ell_{\mathrm{tc}}$ .
+
+Our implementation of ConTempo is inspired by SimCSE's (Gao et al., 2021) use of contrastive learning on natural language inference (NLI) data. We likewise use a normalized temperature-scaled cross-entropy loss (NT-Xent; Chen et al., 2020).
+
+Antisymmetric Relations For an antisymmetric relation  $\mathbf{h}_r^{\rightarrow} = \mathbf{h}_{(e_1,e_2)}$ , we regard the dual of the relation  $\mathbf{h}_r^{\leftarrow} = \mathbf{h}_{(e_2,e_1)}$  as a hard negative sample. However, we cannot construct further positive samples using temporal reasoning. Instead, we follow SimCSE's unsupervised approach to obtain positive pairs through the use of independently sampled dropout masks. Standard transformers will apply dropout (default  $p = 0.1$ ) at different locations in the model. Therefore, we simply feed the same input to our model twice to obtain two relational representations  $\mathbf{h}_r^{\rightarrow}$  and  $\mathbf{h}_r^+$  that are slightly different; different dropout masks having been applied during the two encoding passes. Therefore, we can compute the ConTempo loss by:
+
+$$
+\ell_ {\mathrm {t c}} = - \log \frac {e ^ {\operatorname {s i m} \left(\mathbf {h} _ {r} ^ {\rightarrow} , \mathbf {h} _ {r} ^ {+}\right) / \tau}}{e ^ {\operatorname {s i m} \left(\mathbf {h} _ {r} ^ {\rightarrow} , \mathbf {h} _ {r} ^ {+}\right) / \tau} + e ^ {\operatorname {s i m} \left(\mathbf {h} _ {r} ^ {\rightarrow} , \mathbf {h} _ {r} ^ {\leftarrow}\right) / \tau}}, \tag {4}
+$$
+
+where  $\tau$  is a temperature hyperparameter.
+
+Unlike SimCSE, however, we did not treat other relational representations in the same mini-batch as negatives. While we are certain that the relation yields the exact dual when we reverse the order of the two events  $((e_1,e_2)$  vs.  $(e_2,e_1))$ , the compari
+
+son is less clear when it is made between different event pairs. Consider the following examples:
+
+(1) Alan Turing studied at Cambridge for his undergraduate degree and attended Princeton for his Ph.D.  
+(2) I failed  $e_3$  my calculus course and then cried  $e_4$  all night in a McDonald's.
+
+While both temporal relations  $r_1 = (e_1, e_2)$  and  $r_2 = (e_3, e_4)$  share the same BEFORE label, it is difficult to say whether they can be regarded as a positive pair, because they are different in many respects. First, we know that  $e_1$  and  $e_2$  are years apart but  $e_3$  and  $e_4$  happen on the same day. Second, we infer BEFORE for different reasons. We know that  $e_1$  happened before  $e_2$  through common-sense: a person needs to complete their undergraduate study before working towards a Ph.D. But we conclude that  $e_3$  happened before  $e_4$  because of and then and a likely causal relation between failing the course and crying. We want to preserve these differences and therefore avoid pushing the representations of  $r_1$  and  $r_2$  closer together.
+
+We also do not need to consider relations with different labels, such as  $r_1^{\rightarrow} = (e_1,e_2)$  and  $r_2^{\leftarrow} = (e_4,e_3)$ , as negative samples. Intuitively, contrastive learning is more effective when the negative samples occur nearby but should be far apart (Robinson et al., 2021). Since event pairs from different sentences contain drastically different syntactic and semantic information, it is not a serious problem for the classifier to distinguish them.
+
+Symmetric Relations For a symmetric relation  $\mathbf{h}_r^{\rightarrow} = \mathbf{h}_{(e_1,e_2)}$ , we use the dual of the relation  $\mathbf{h}_r^{\leftarrow} = \mathbf{h}_{(e_1,e_2)}$  as an additional, positive sample. Unlike with antisymmetric relations, we follow SimCSE and use other relations in the same minibatch  $(B)$  as negative samples:
+
+$$
+\ell_ {\mathrm {t c}} = - \log \frac {e ^ {\operatorname {s i m} \left(\mathbf {h} _ {r} ^ {\rightarrow} , \mathbf {h} _ {r} ^ {\leftarrow}\right) / \tau}}}{\sum_ {i \in B} \left(e ^ {\operatorname {s i m} \left(\mathbf {h} _ {r} ^ {\rightarrow} , \mathbf {h} _ {i}\right) / \tau} + e ^ {\operatorname {s i m} \left(\mathbf {h} _ {r} ^ {\leftarrow} , \mathbf {h} _ {i}\right) / \tau}\right)}. \tag {5}
+$$
+
+We choose a different design here than for antisymmetric relations because it is impossible to construct true hard negative samples for symmetric relations. Also, we do not check whether other samples in the mini-batch have the same relation label as  $\mathbf{h}_r^{\rightarrow}$  because EQUAL is the least common relation type. With only  $3.8\%$  in MATRES and  $1.7\%$  of the relations in TBD, it is very rare that there are multiple EQUAL relations in the same
+
+![](images/6fb1a28fcd93d544baa0cb6b86d36e098a1a1eab2aceb764e346e1c9203aba30.jpg)  
+Figure 2: The efficacy of ConTempo at increasing the model's awareness of temporal relations and their implications through temporal reasoning.
+
+mini-batch, so the effect of a colliding relation type is negligible.
+
+Final Training Objective The ConTempo loss is added to the final training objective with a scaling hyperparameter  $\gamma$  (Equation 6). The classification loss  $\ell_{\mathrm{clf}}$  is the standard cross-entropy loss computed using the model's output logits:
+
+$$
+\ell = \ell_ {\mathrm {c l f}} + \gamma \cdot \ell_ {\mathrm {t c}}. \tag {6}
+$$
+
+# 2.5 Experiment: ConTempo at Increasing Temporal Relation Awareness
+
+Here we present the effectiveness of ConTempo at increasing temporal relation awareness. In this section, we trained an enhanced ConTempo baseline that is identical to the fine-tuned baseline but with ConTempo loss added to the model. We trained the model using the same hyperparemeters for the same amount of time.
+
+In Figure 2, we compare ConTempo with baselines using the same similarity measures. We can observe that the similarity of the model's representation of a relation in comparison to its dual drops significantly after ConTempo is applied. Furthermore, now we can observe that the vast majority of similarity measures occupy the lower section of the figure, suggesting that ConTempo is effective at making antisymmetric relations generate representations that are distinct from their duals.
+
+Unfortunately, we also see a similar drop in similarity for the symmetric relation (EQUAL). We believe this is caused by a data imbalance as there are too few EQUAL instances to balance the overall effect of the antisymmetric relations.
+
+<table><tr><td>Method</td><td>MATRES</td><td>Antisym. Rel. Sim</td><td>Sym. Rel. Sim</td></tr><tr><td>RoBERTa</td><td>80.76</td><td>0.127</td><td>0.424</td></tr><tr><td>Data Expansion</td><td>80.16</td><td>-0.205</td><td>0.148</td></tr><tr><td>Relative Time</td><td>81.01</td><td>-0.237</td><td>0.144</td></tr><tr><td>Logical Constraints</td><td>81.26</td><td>-0.302</td><td>-0.102</td></tr><tr><td>ConTempo (Ours)</td><td>82.01</td><td>-0.352</td><td>-0.080</td></tr></table>
+
+Table 2: The effectiveness of different methods at improving temporal relation awareness. The table reports each method's performance together with the average similarity measure for all the antisymmetric and symmetric relations.
+
+# 2.6 Previous Attempts at Increasing Temporal Calculus Awareness
+
+Does similarity reduction really lead to better temporal label awareness? Also, are there any other ways to increase temporal label awareness? Unfortunately, it is impossible to measure temporal label awareness directly, but we can infer it indirectly by observing the model's performance.
+
+In this section we compared ConTempo with three previous methods that attempted to address similar problems. In the following paragraphs, we elucidate these methods, as they could also increase temporal relation awareness. In Table 2, we compare the effectiveness of all three with ConTempo. We use the same model setting for each method for a fair comparison. Overall, ConTempo is the most effective at reducing similarity. It also has the best performance on MATRES. This suggests ConTempo could help the model create more effective representations for TRE prediction.
+
+Inverse Data Expansion Huang et al. (2023) simply expand the training set by adding all the inverse relations. This straightforward approach, however, does not address the issue that temporal relation labels are presented independently.
+
+Relative Time Prediction Wen and Ji (2021) employed a relative timestamp prediction component to regulate the training process by predicting a real number ("relative event time," RET) that indicates the relative position of events in a timeline. This component is trained to maximize the distance between events in antisymmetric relations and to minimize the distance between events that are equal. This approach shares broad similarities with contrastive learning but faces two major challenges. First, relative event-time prediction in RET is ultimately computed for each single event individually, which is impossible. By contrast, Contempo considers events in pairs and accounts only
+
+for relative information. Second, this model cannot specify the absolute distance between events, meaning it does not differentiate between events that occur seconds apart and those that are days apart. It also makes predicting chains of events (e.g.,  $e_1 < e_2 < \ldots < e_5$  where  $<$  indicates AFTER) difficult, as the model needs to balance various data points across the entire dataset and precisely position each event within the relative time range. ConTempo does not face this issue as the time distance between any two events  $(e_1, e_2)$  remains consistent regardless of the direction.
+
+Logical Constraints Wang et al. (2020) proposed to impose soft logical constraints by adding a loss term that is calculated based on the model's output logits. In particular:
+
+$$
+\ell_ {S} = \sum \left| \log r \left(e _ {1}, e _ {2}\right) - \log \bar {r} \left(e _ {2}, e _ {1}\right) \right|, \tag {7}
+$$
+
+where  $r(e_1, e_2)$  denotes the logits the model outputs for relation type  $r$  given  $(e_1, e_2)$  as the input, and  $\bar{r}$  denotes the dual of the relation. Other logical constraints such as transitivity are also enforced by Wang et al. (2020); we temporarily skip those as they are not relevant to the topic of the current section. We will return to a discussion of other types of constraint in Section 3.3.
+
+Logical constraint loss has some surface-level resemblance to ConTempo loss, but their method focuses on the output logits whereas ours focuses on regulating the quality of the models' representations. The major motivation for Wang et al. (2020) to add logical constraints was to avoid label conflicts; enhancing the model's understanding of temporal relation labels was secondary.
+
+# 3 The Unified Framework
+
+Our survey of previous systems suggests that the reusability of innovations of TRE has been limited. For example, papers working on GNN-encoding of document-level information (Zhang et al., 2022; Mathur et al., 2021; Yao et al., 2022) rarely incorporate other published innovations, such as additional common-sense information, in their models. We call for more collaboration between different directions of TRE research.
+
+In this section, we argue that ConTempo is compatible with various recent innovations across different research directions. In particular, ConTempo is complementary to: (1) GNN encodings of event and context information, (2) incorpora
+
+ing common-sense information, and (3) the soft enforcement of logical constraints.
+
+# 3.1 Event and Context Encoder
+
+All natural language understanding models need methods to encode their input sequence into vectorized representations, and to extract the relevant event and context representations. Currently, researchers typically use pre-trained language models such as BERT (Devlin et al., 2019) or RoBERTa to encode the input sequence because of the rich information these models gather during pre-training.
+
+In TRE, an event is usually described by a complete phrase or even an entire clause. But since it is hard to annotate a discontinuous sequence, TRE corpora typically label the semantic head as the sole event trigger to represent the complete event. Extracting representations from only the event triggers may not obtain all the relevant information to make a correct prediction, however.
+
+Therefore, TRE systems now utilize Graph Neural Networks (GNNs) to encode additional information about events and context. Zhang et al. (2022) proposed using dependency trees to help the model access different event arguments. TIMERS (Mathur et al., 2021) proposed using a GNN to encode three graphs: a sentence structure graph, a temporal structure graph, and a discourse structure graph. More recently, MulCo (Yao et al., 2022) reported better results using only the sentence  $(\mathcal{G}_S)$  and temporal  $(\mathcal{G}_T)$  structure graphs. They achieved better results with fewer graphs by using multiscale contrastive learning between the fine-tuning of BERT and the training of the GNN to decrease GPU memory usage. Unlike ConTempo, their contrastive learning is not used to enhance the understanding of temporal labels.
+
+We add MulCo to the unified framework by concatenating the GNNs' outputs to the event representations as  $\tilde{\mathbf{h}}_e = [\mathbf{h}_e^{\mathcal{G}_S} \parallel \mathbf{h}_e^{\mathcal{G}_T} \parallel \mathbf{h}_e]$ .
+
+Please refer to Yao et al. (2022) for the detailed description of their model. We provide only a quick overview in Appendix B.
+
+# 3.2 Common-sense Information
+
+Similar to event and context encoding, we can also add additional features from external sources to enhance the representation. The feasibility of our unified framework is demonstrated by admitting temporal common-sense information.
+
+Earlier TRE methods (Ning et al., 2018a, 2019; Wang et al., 2020) used temporal information de
+
+GPT-3 Prompt:
+
+But the great-uncle of 6-year-old shipwreck survivor rafter Elian Gonzalez only ducked his head and walked faster.
+
+Q: In about 10 words describe how long does the event "ducked" typically last.
+
+A: Ducking typically lasts only a few seconds.
+
+Figure 3: An example prompt and response for GPT-3. The context sentence is highlighted in orange, the event trigger, in red and GPT-3's response, in green.
+
+rived from simple heuristics, or from corpora such as TempProb, which contains typical temporal-relation information between event triggers. Unfortunately, TempProb's coverage and accuracy is limited. Alternatively, the MC-TACO corpus (Zhou et al., 2019) was developed for temporal commonsense knowledge, presenting typical duration information through answers to multiple-choice questions. This approach, however, requires the model to select a typical duration from a restricted set of pre-defined options, and is incapable of addressing typical granularity and underspecificity problems. Our system is the first to apply temporal commonsense information from LLMs for TRE purposes.
+
+We used GPT-3 (text-davinci-003), employing the template illustrated in Figure 3, to obtain descriptions of the typical durations of events in MATRES. We then use our system's underlying RoBERTa encoder to encode a description of the typical duration, and use the [CLS]-pooler output as the representation, denoted as  $\mathbf{h}_e^{\mathrm{dur}}$ .
+
+$$
+\hat {\mathbf {h}} _ {e} = \left[ \mathbf {h} _ {e} ^ {\text {d u r}} \| \tilde {\mathbf {h}} _ {e} \right] \tag {8}
+$$
+
+$$
+\mathbf {h} _ {(e _ {1}, e _ {2})} = f _ {1} \left(\left[ \begin{array}{l l} \mathbf {h} _ {e _ {1}} & \parallel \\ \hline \end{array} \right] \mathbf {h} _ {e _ {2}}\right)
+$$
+
+# 3.3 Training Objective
+
+The third type of innovation is the modification of the training objective. ConTempo itself is an innovation to the training objective.
+
+In this section, we show that ConTempo is compatible with other techniques that have been applied to training objectives. We have incorporated the aforementioned soft logical constraints (Wang et al., 2020) into the unified framework.
+
+We add both the symmetric loss  $(\ell_S)$  and the conjunction loss  $(\ell_C)$  to the loss function. There is a bit of overlap between Wang et al.'s (2020)
+
+symmetric loss and ConTempo loss, but as previously discussed, we focus on regulating the representation whereas Wang et al.'s (2020) focus on avoiding label conflicts. ConTempo and the logical constraints complement each other, however, as ConTempo does not attempt to treat transitivity within contrastive learning. Instead, it is covered by conjunction restrictions. The loss terms are:
+
+$$
+\ell_ {S} = \sum \left| \log r \left(e _ {1}, e _ {2}\right) - \log \bar {r} \left(e _ {2}, e _ {1}\right) \right|, \tag {9}
+$$
+
+$$
+\ell_ {C} = \sum | L _ {t _ {1}} | + \sum | L _ {t _ {2}} |
+$$
+
+where  $L_{t_1}$  and  $L_{t_2}$  are defined as:
+
+$$
+L _ {t _ {1}} = \log r _ {1} (e _ {1}, e _ {2}) + \log r _ {2} (e _ {2}, e _ {3}) - \log r _ {3} (e _ {1}, e _ {3}),
+$$
+
+$$
+L _ {t _ {2}} = \log r _ {1} \left(e _ {1}, e _ {2}\right) + \log r _ {2} \left(e _ {2}, e _ {3}\right) - \log \left(1 - r _ {4} \left(e _ {1}, e _ {3}\right)\right). \tag {10}
+$$
+
+See Wang et al. (2020) for details, including the induction table for the conjunctive constraints. The final training objective is:
+
+$$
+\ell = \ell_ {\mathrm {c l f}} + \gamma \cdot \ell_ {\mathrm {t c}} + \lambda_ {S} \cdot \ell_ {S} + \lambda_ {C} \cdot \ell_ {C}. \tag {11}
+$$
+
+# 4 Experiments
+
+# 4.1 Experimental Setup
+
+The hyperparameter settings and training details are explained in Appendix A.
+
+Data We experimented with both MATRES (Ning et al., 2018b) and TBD (Cassidy et al., 2014), the two popular corpora that are most often used to benchmark TRE systems. Both are derived from the TimeBank Corpus (Pustejovsky et al., 2003), which is annotated using the TimeML standard (Pustejovsky et al., 2005). The VAGUE labels are computed into the F1s for both MATRES and TBD but are regarded as negative labels.
+
+TBD is a dense re-annotation of the TimeBank corpus where every possible pair of events/times in a given window is forced to be annotated regardless of whether there exists a specified temporal relation. As a result, TBD has ample data samples (12715 relations from 39 articles) but a relatively low inter-annotator agreement, with Cohen's (1960)  $\kappa$  ranging between 0.56 and 0.64.
+
+MATRES aimed at reducing noise in TBD's annotation. It introduced the concept of orthogonal temporal axes for hypothetical, negated, opined, and static events. In practice, these events are ignored during temporal relation annotation. They further reduced the number of temporal relations
+
+<table><tr><td>Model</td><td>CleanMATRES</td><td>MATRES</td><td>TimeBank-Dense</td></tr><tr><td>ChatGPT 3.5</td><td>65.29</td><td>25.94</td><td>53.06</td></tr><tr><td>ChatGPT 3.5 (CoT)</td><td>66.97</td><td>35.54</td><td>57.14</td></tr><tr><td>ChatGPT 4</td><td>76.47</td><td>41.64</td><td>67.58</td></tr><tr><td>ChatGPT 4 (CoT)</td><td>80.76</td><td>56.70</td><td>65.14</td></tr><tr><td>Fine-tuned GPT 3.5</td><td>73.41</td><td>55.27</td><td>61.71</td></tr><tr><td>LSTM (Cheng and Miyao, 2017)</td><td>-</td><td>73.4</td><td>62.2</td></tr><tr><td>SCS-EERE* (Man et al., 2022)</td><td>91.25</td><td>80.98</td><td>65.92</td></tr><tr><td>Joint Constrained Learning (Wang et al., 2020)</td><td>-</td><td>78.8</td><td>-</td></tr><tr><td>Relative Time* (Wen and Ji, 2021)</td><td>89.61</td><td>81.63</td><td>66.81</td></tr><tr><td>MulCo* (Yao et al., 2022)</td><td>91.34</td><td>82.08</td><td>67.51</td></tr><tr><td>TIMERS (Mathur et al., 2021)</td><td>-</td><td>82.3</td><td>67.8</td></tr><tr><td>Endpoint Comparisons (Huang et al., 2023)</td><td>-</td><td>82.6</td><td>68.1</td></tr><tr><td>ConTempo Baseline</td><td>91.35</td><td>82.01</td><td>67.78</td></tr><tr><td>ConTempo + Unified Framework (Ours)</td><td>92.66</td><td>83.17</td><td>68.56</td></tr></table>
+
+down to only four types. They also simplified the annotation scheme by asking the annotators to compare only the start times of events, as the end time of a durative event can often be ambiguous and cause confusion. During our survey of TRE baselines, we found that there are actually several versions of MATRES being used by different research labs (see Appendix C). We use the version that is available on the Ning et al.'s (2018b) GitHub page<sup>4</sup> and reproduced several key baseline systems' performances using our unified evaluation standards.
+
+During the development of ConTempo, we discovered a large number of annotation errors in both MATRES and TBD. To further reduce the noise in the annotations, we re-examined and corrected the test set annotations of MATRES, creating the CleanMATRES test set. We will detail the process and describe the data in Section D.
+
+Baseline Systems We compared ConTempo's performance with seven prior systems: LSTM (Cheng and Miyao, 2017), SCS-EERE (Man et al., 2022), Joint Constrained Learning (Wang et al., 2020), Relative Time (Wen and Ji, 2021), MulCo (Yao et al., 2022), TIMERS (Mathur et al., 2021) and Endpoint Comparisons (Huang et al., 2023). We reproduced the results of SCS-EERE and Relative Time using their publicly available code. Additionally, we reimplemented MulCo according to the specifications provided in the paper.
+
+LLM Baselines We incorporated the performance of LLMs as an additional baseline alongside the aforementioned baseline systems. Specifically,
+
+Table 3: F1 on CleanMATRES, MATRES and TBD. ConTempo achieved substantial improvements over strong baselines. Rows with results that we reproduced using the same evaluation settings as our model are labelled with * .  
+
+<table><tr><td>Model</td><td>CleanMATRES</td></tr><tr><td>ConTempo + Unified Framework</td><td>92.66</td></tr><tr><td>- ConTempo</td><td>91.30 (-1.36)</td></tr><tr><td>- GNN</td><td>91.65 (-1.01)</td></tr><tr><td>- GPT-3 Typical Duration</td><td>92.06 (-0.60)</td></tr><tr><td>- Logical Constraints</td><td>92.14 (-0.52)</td></tr></table>
+
+Table 4: Ablation study results.
+
+we reproduced the results from Yuan et al.'s (2023) using both ChatGPT-3.5 and ChatGPT-4. Chain-of-thought (CoT) was deployed in the experiments. Additionally, we fine-tuned GPT-3.5 utilizing OpenAI's API using the suggested settings to perform the task.
+
+# 4.2 Experimental Results
+
+Table 3 reports the performance of our ConTempo model compared to other baseline models on CleanMATRES, MATRES, and TBD. The results of our models and our reproductions are the average over three different runs with different random seeds.
+
+Overall, ConTempo brings a substantial performance increase to the TRE model. Even the simple ConTempo baseline's performance is in the same ballpark as previous state-of-the-art systems. When enhanced by other innovations under the unified framework, our model outperformed the previous state-of-the-art models by  $1.32\%$ ,  $0.57\%$ , and  $0.46\%$  for the three datasets, respectively.
+
+# 4.3 Ablation Study
+
+In order to evaluate the efficacy of the proposed components in the unified framework, we conducted an ablation study, wherein we removed one
+
+component at a time and reran the experiment using the aforementioned hyperparameters. The results of this study are presented in Table 4. Among the four components, contrastive learning demonstrated the most substantial impact on performance, with its removal leading to a  $1.36\%$  decrease in the model's effectiveness. The GNN module also makes a substantial contribution to overall performance. Finally, both GPT-3 typical duration information and logical constraints exhibit moderate effects on the system's performance.
+
+The ablation study result confirms our initial hypothesis: the primary challenge for these models has been making sense of relational labels.
+
+# 5 Conclusion
+
+In this paper, we propose a novel ConTempo method that utilizes contrastive learning on the symmetric and antisymmetric properties to enhance the model's awareness of temporal relations. Using ConTempo, we observe an apparent change in the representation of relations generated by the model. Particularly, we see a significant reduction in the similarity between relation representations  $\mathbf{h}_r^{\rightarrow}$  in comparison to their dual  $\mathbf{h}_r^{\leftarrow}$ .
+
+ConTempo and GNN encoding, temporal common-sense information, and soft logical constraints can work in synergy to create a unified system that has achieved state-of-the-art performance across various benchmark corpora. Our success demonstrates the flexibility of ConTempo, and we call for more collaboration between different directions of TRE research.
+
+TRE is a rare and curious case where fine-tuned small LMs perform considerably better LLMs. Even with the help of groundbreaking techniques such as chain-of-thought (Wei et al., 2022), the best performance ChatGPT can achieve is  $52.4\%$  on MATRES (Yuan et al., 2023) and  $41.0\%$  on TBD (Huang et al., 2023) — remarkably lower than the fine-tuned small language models' performance. This anomaly presents tremendous opportunity for both TRE researchers and LLM researchers. TRE can be used as a hard task for the LLMs' to analyse their capabilities at reasoning and comprehension. In conclusion, exploring the integration of existing TRE innovations with LLMs and incorporating LLMs as a key component within TRE frameworks could significantly enhance performance and drive forward the advancement of both fields.
+
+# Acknowledgement
+
+This study is funded by the Canadian Safety and Security Program (CSSP) from Defence Research and Development Canada (DRDC) awarded to the Public Health Agency of Canada (CSSP-2018-CP2334: Incorporating Advanced Data Analytics into a Health Intelligence Surveillance System). We thank the Global Public Health Intelligence Network (GPHIN) and Epidemic Intelligence from Open Sources (EIOS) teams for their support.
+
+# Limitations
+
+We only evaluate ConTempo's performance using RoBERTa. Other language models, such as DeBERTa (He et al., 2021), T5 (Raffel et al., 2020) and DistilBERT (Sanh et al., 2020) may provide even better performance. We leave further exploration for future work.
+
+Due to restricted dataset resources, our unified model's evaluation was conducted only using TB-Dense and MATRES. There are other TimeML-based and even non-TimeML-based corpora related to TRE. We leave more evaluation to future work and encourage the community to reproduce our results on more datasets.
+
+# References
+
+James F. Allen. 1981. An interval-based representation of temporal knowledge. In In Proceedings 7th IJCAI, pages 221-226.  
+James F. Allen. 1983. Maintaining knowledge about temporal intervals. Communications of the ACM, 26(11):832-843.  
+Taylor Cassidy, Bill McDowell, Nathanael Chambers, and Steven Bethard. 2014. An Annotation Framework for Dense Event Ordering. In Proceedings of the 52nd Annual Meeting of the Association for Computational Linguistics (Volume 2: Short Papers), pages 501-506, Baltimore, Maryland. Association for Computational Linguistics.  
+Ting Chen, Simon Kornblith, Mohammad Norouzi, and Geoffrey Hinton. 2020. A Simple Framework for Contrastive Learning of Visual Representations. In Proceedings of the 37th International Conference on Machine Learning, pages 1597-1607. PMLR.  
+Fei Cheng and Yusuke Miyao. 2017. Classifying Temporal Relations by Bidirectional LSTM over Dependency Paths. In Proceedings of the 55th Annual Meeting of the Association for Computational Linguistics (Volume 2: Short Papers), pages 1-6, Vancouver, Canada. Association for Computational Linguistics.
+
+Jacob Cohen. 1960. A Coefficient of Agreement for Nominal Scales. Educational and Psychological Measurement, 20(1):37-46.  
+Jacob Devlin, Ming-Wei Chang, Kenton Lee, and Kristina Toutanova. 2019. BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding. In Proceedings of the 2019 Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies, Volume 1 (Long and Short Papers), pages 4171-4186, Minneapolis, Minnesota. Association for Computational Linguistics.  
+Tianyu Gao, Xingcheng Yao, and Danqi Chen. 2021. SimCSE: Simple Contrastive Learning of Sentence Embeddings. In Proceedings of the 2021 Conference on Empirical Methods in Natural Language Processing, pages 6894-6910, Online and Punta Cana, Dominican Republic. Association for Computational Linguistics.  
+Pengcheng He, Xiaodong Liu, Jianfeng Gao, and Weizhu Chen. 2021. DeBERTa: Decoding-enhanced BERT with Disentangled Attention. In International Conference on Learning Representations.  
+Quzhe Huang, Yutong Hu, Shengqi Zhu, Yansong Feng, Chang Liu, and Dongyan Zhao. 2023. More than Classification: A Unified Framework for Event Temporal Relation Extraction. In Proceedings of the 61st Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers), pages 9631-9646, Toronto, Canada. Association for Computational Linguistics.  
+Yinhan Liu, Myle Ott, Naman Goyal, Jingfei Du, Mandar Joshi, Danqi Chen, Omer Levy, Mike Lewis, Luke Zettlemoyer, and Veselin Stoyanov. 2019. RoBERTa: A Robustly Optimized BERT Pretraining Approach.  
+Ilya Loshchilov and Frank Hutter. 2019. Decoupled Weight Decay Regularization. In ICLR 2019.  
+Hieu Man, Nghia Trung Ngo, Linh Ngo Van, and Thien Huu Nguyen. 2022. Selecting Optimal Context Sentences for Event-Event Relation Extraction. Proceedings of the AAAI Conference on Artificial Intelligence, 36(10):11058-11066.  
+Puneet Mathur, Rajiv Jain, Franck Dernoncourt, Vlad Morariu, Quan Hung Tran, and Dinesh Manocha. 2021. TIMERS: Document-level Temporal Relation Extraction. In Proceedings of the 59th Annual Meeting of the Association for Computational Linguistics and the 11th International Joint Conference on Natural Language Processing (Volume 2: Short Papers), pages 524-533, Online. Association for Computational Linguistics.  
+Qiang Ning, Sanjay Subramanian, and Dan Roth. 2019. An Improved Neural Baseline for Temporal Relation Extraction. In Proceedings of the 2019 Conference on Empirical Methods in Natural Language Processing and the 9th International Joint Conference
+
+on Natural Language Processing (EMNLP-IJCNLP), pages 6203-6209, Hong Kong, China. Association for Computational Linguistics.  
+Qiang Ning, Hao Wu, Haoruo Peng, and Dan Roth. 2018a. Improving Temporal Relation Extraction with a Globally Acquired Statistical Resource. In Proceedings of the 2018 Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies, Volume 1 (Long Papers), pages 841-851, New Orleans, Louisiana. Association for Computational Linguistics.  
+Qiang Ning, Hao Wu, and Dan Roth. 2018b. A Multi-Axis Annotation Scheme for Event Temporal Relations. In Proceedings of the 56th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers), pages 1318-1328, Melbourne, Australia. Association for Computational Linguistics.  
+Jingcheng Niu, Victoria Ng, Erin Rees, Simon De Montigny, and Gerald Penn. 2023. Discourse Information for Document-Level Temporal Dependency Parsing. In Proceedings of the 4th Workshop on Computational Approaches to Discourse (CODI 2023), pages 82-88, Toronto, Canada. Association for Computational Linguistics.  
+James Pustejovsky, Patrick Hanks, Roser Saurí, Andrew See, Rob Gaizauskas, Andrea Setzer, Dragomir Radev, Beth Sundheim, David Day, Lisa Ferro, and Marcia Lazo. 2003. The TimeBank corpus. Proceedings of Corpus Linguistics.  
+James Pustejovsky, Bob Ingria, Roser Sauri, Jose Castano, Jessica Littman, Rob Gaizauskas, Andrea Setzer, Graham Katz, and Inderjeet Mani. 2005. The specification language TimeML. The language of time: A reader, pages 545-557.  
+James Pustejovsky, Kiyong Lee, Harry Bunt, and Laurent Romary. 2010. ISO-TimeML: An International Standard for Semantic Annotation. In Proceedings of the Seventh International Conference on Language Resources and Evaluation (LREC'10), Valletta, Malta. European Language Resources Association (ELRA).  
+James Pustejovsky, Marc Verhagen, Roser Sauri, Jessica Littman, Robert Gaizauskas, Graham Katz, Inderjeet Mani, Robert Knippen, and Andrea Setzer. 2006. TimeBank 1.2.  
+Colin Raffel, Noam Shazeer, Adam Roberts, Katherine Lee, Sharan Narang, Michael Matena, Yanqi Zhou, Wei Li, and Peter J. Liu. 2020. Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer. Journal of Machine Learning Research, 21(140):1-67.  
+Joshua David Robinson, Ching-Yao Chuang, Suvrit Sra, and Stefanie Jegelka. 2021. Contrastive learning with hard negative samples. In International Conference on Learning Representations.
+
+Victor Sanh, Lysandre Debut, Julien Chaumont, and Thomas Wolf. 2020. DistilBERT, a distilled version of BERT: Smaller, faster, cheaper and lighter.  
+Haoyu Wang, Muhao Chen, Hongming Zhang, and Dan Roth. 2020. Joint Constrained Learning for Event-Event Relation Extraction. In Proceedings of the 2020 Conference on Empirical Methods in Natural Language Processing (EMNLP), pages 696–706, Online. Association for Computational Linguistics.  
+Jason Wei, Xuezhi Wang, Dale Schuurmans, Maarten Bosma, brian richter, Fei Xia, Ed Chi, Quoc V Le, and Denny Zhou. 2022. Chain-of-thought prompting elicits reasoning in large language models. In Advances in Neural Information Processing Systems, volume 35, pages 24824-24837. Curran Associates, Inc.  
+Haoyang Wen and Heng Ji. 2021. Utilizing Relative Event Time to Enhance Event-Event Temporal Relation Extraction. In Proceedings of the 2021 Conference on Empirical Methods in Natural Language Processing, pages 10431–10437, Online and Punta Cana, Dominican Republic. Association for Computational Linguistics.  
+Hao-Ren Yao, Luke Breitbartler, Aakanksha Naik, Chunxiao Zhou, and Carolyn Rose. 2022. MultiScale Contrastive Co-Training for Event Temporal Relation Extraction.  
+Jiarui Yao, Haoling Qiu, Bonan Min, and Nianwen Xue. 2020. Annotating Temporal Dependency Graphs via Crowdsourcing. In Proceedings of the 2020 Conference on Empirical Methods in Natural Language Processing (EMNLP), pages 5368-5380, Online. Association for Computational Linguistics.  
+Chenhan Yuan, Qianqian Xie, and Sophia Ananiadou. 2023. Zero-shot Temporal Relation Extraction with ChatGPT.  
+Shuaicheng Zhang, Qiang Ning, and Lifu Huang. 2022. Extracting Temporal Event Relation with Syntax-guided Graph Transformer. In *Findings of the Association for Computational Linguistics: NAACL* 2022, pages 379–390, Seattle, United States. Association for Computational Linguistics.  
+Ben Zhou, Daniel Khashabi, Qiang Ning, and Dan Roth. 2019. "Going on a vacation" takes longer than "Going for a walk": A Study of Temporal Commonsense Understanding. In Proceedings of the 2019 Conference on Empirical Methods in Natural Language Processing and the 9th International Joint Conference on Natural Language Processing (EMNLP-IJCNLP), pages 3363-3369, Hong Kong, China. Association for Computational Linguistics.
+
+# A Training Details
+
+We use roberta-large as the pre-trained encoder. The best model is selected with the highest development set performance among 20 epochs of training,
+
+optimized using AdamW (Loshchilov and Hutter, 2019) with an initial learning rate of 1e-5 and a 0.01 weight decay. We use a linear scheduler with a warm-up ratio of 0.1 and a batch size of 64. The dropout rate is 0.1 across the system. For ConTempo, we determined  $\tau = 0.05$ ,  $\gamma = 1.0$  using a grid search over  $\{0.1, 0.05, 0.01\} \times \{1, 0.1, 0.01\}$ .
+
+For the components in the unified systems, we follow the hyperparameter suggested by the corresponding papers (Yao et al., 2022; Wang et al., 2020).
+
+# B MulCo
+
+MulCon utilized a sentence structure graph  $\mathcal{G}_S$  and a temporal structure graph  $\mathcal{G}_T$  to encode document-level information. The sentence structure graph has three types of nodes: the document, the sentences and the tokens. All sentences are connected to the document node and each token node is connected to the sentence it located in. For an event,  $\mathcal{G}_S$ 's embedding of the event trigger token is used.
+
+The temporal structure graph, on the other hand, also has three types of nodes. The document creation time (DCT) node, the time expressions, and the events. Each time expression is connected to the DCT, and each event is connected to a time expression if there is an E2T link in the corpus. Finally, each event node has an edge point to itself.
+
+# C MATRES Versions
+
+We found two versions of MATRES that has been used by different works. Ning et al. (2018b) released a version on GitHub  $^{5}$  that contains 837 relations in the Platinum test set. Wang et al. (2020) released another version with 818 relations in the Platinum test set. The difference (19 relations) could constitute as  $2.32\%$  of the test set data. We use Ning et al.'s (2018b).
+
+# D CleanMATRES
+
+As we previously mentioned, we identified a large quantity of annotation errors within both MATRES and TBD. This is not surprising, however, as both corpora reported adequate inter-annotator agreements. TBD reported  $\kappa$  ranged from 0.56 to 0.64 and MATRES reported a good — but not perfect —  $\kappa$  of 0.84 (Table 6). In this section, we will first provide a description of the annotation errors
+
+<table><tr><td>Relabelling</td><td colspan="2">EQUAL</td><td colspan="2">VAGUE</td><td colspan="2">BEFORE</td><td colspan="2">AFTER</td></tr><tr><td>EQUAL</td><td>10</td><td>32.26%</td><td>15</td><td>13.27%</td><td>1</td><td>0.24%</td><td>0</td><td>0%</td></tr><tr><td>VAGUE</td><td>3</td><td>9.68%</td><td>24</td><td>21.24%</td><td>5</td><td>1.17%</td><td>5</td><td>1.86%</td></tr><tr><td>BEFORE</td><td>6</td><td>19.35%</td><td>39</td><td>34.51%</td><td>405</td><td>95.52%</td><td>0</td><td>0%</td></tr><tr><td>AFTER</td><td>10</td><td>32.26%</td><td>26</td><td>23.01%</td><td>4</td><td>0.94%</td><td>256</td><td>95.17%</td></tr><tr><td>Orth. Axes</td><td>2</td><td>6.45%</td><td>9</td><td>7.96%</td><td>9</td><td>2.12%</td><td>8</td><td>2.97%</td></tr><tr><td>Total</td><td>31</td><td>100%</td><td>113</td><td>100%</td><td>424</td><td>100%</td><td>269</td><td>100%</td></tr></table>
+
+Table 5: Re-annotation of the MATRES test set. The statistics of the correct labels are highlighted in bold. Each column corresponds to an original MATRES label. Some relations involve events that should have been placed on one of the orthogonal axes.  
+
+<table><tr><td>Corpus</td><td>Cohen&#x27;s κ</td></tr><tr><td>TimeBank-Dense</td><td>0.56-0.64</td></tr><tr><td>MATRES</td><td>0.84</td></tr><tr><td>MATRES EQUAL</td><td>1.0</td></tr><tr><td>MATRES VAGUE</td><td>0.75</td></tr></table>
+
+Table 6: Detailed inter-annotator agreement of MA-TRES and TBD.
+
+we identified in MATRES. Then, we will describe our re-annotation process. Finally, we will present an overview of the result of the re-annotation — CleanMATRES.
+
+# D.1 A Qualitative Analysis of the Annotation Errors
+
+(3) He won $_{e_1}$  the Gusher Marathon, finishing $_{e_2}$  in 3:07:35.
+
+Original Annotation: VAGUE Correct Annotation: EQUAL
+
+(4) The last surviving member of the team which first  $\mathbf{conquered}_{e_1}$  Everest in 1953 has  $\mathbf{died}_{e_2}$  in a Derbyshire nursing home.
+
+Original Annotation: VAGUE Correct Annotation: BEFORE
+
+(5) More than 16,000 dead pigs have been found $_{e_1}$  floating $_{e_2}$  in rivers that provide drinking water to Shanghai.
+
+Original Annotation: EQUAL Correct Annotation: AFTER
+
+Examples (3-5) show three examples of incorrect annotations in MATRES. In example 3, the relation between won and finishing is labelled as VAGUE,
+
+but, nonetheless, the two mentions refer to two aspects of the same punctual event. For example 4, it is clear that the member died a long time after they conquered Everest. For example 5, since MATRES annotators were only comparing the start-time of events, the pigs floating in rivers must took place before the event that they were found.
+
+The two examples presented in this study illustrate the main sources of annotation errors commonly found in data sets. As posited by Ning et al. (2018b), the first example's error likely stems from the annotators' lack of comprehension regarding time granularity and event coreference. MATRES annotations are created by asking annotators two heuristic questions:
+
+(Q1) Is it possible that  $e_{start}^{1}$  is before  $e_{start}^{2}$ ?  
+(Q2) Is it possible that  $e_{start}^{2}$  is before  $e_{start}^{1}$ ?
+
+The heuristic questions, Q1 and Q2, do not adequately address these concepts, necessitating the need to develop improved annotation guidelines. By effectively conveying the intricacies of time granularity and event coreference, the frequency of such errors may decrease, although perhaps with a lower  $\kappa$ . The second example's mistake should perhaps be attributed to a misunderstanding of the text.
+
+# D.2 CleanMATRES Annotation
+
+We undertook a re-annotation of the MATRES test set. The test set were labelled independently by two authors of this paper, who were then forced to reconcile where they disagreed. Our pass through the test set reveals a significant number of annotation inaccuracies, particularly in the cases of the EQUAL and VAGUE relations. As detailed in Table 5, we found a mere  $32.26\%$  of the EQUAL and  $21.24\%$  of the VAGUE edges to have been accurately annotated.
+
+# D.3 Discussion: Vague Relations
+
+We want to take the opportunity to discuss the issues related to the VAGUE relation. The VAGUE relation, which could be better called the underspecified relation, describes relations that are uncertain due to insufficient context. However, this certainty is highly subjective to the annotator and hard to rigorously quantify. TBD adopted an "80% rule" that instruct annotators to label a relation as vague if they are "80% confident that it was the writer's intent that a reader infer that relation." As a result, inter-annotator agreement on vague edges is the lowest among all relation types.
+
+MATRES took a different approach and treats certain combinations of the start time comparisons as vague relations. The approach attenuates the issue but by no means solve the issue. The two heuristic questions are also subject and involves a degree of uncertainty. Furthermore, similar to EQUAL relations, a simple heuristic question mistake could result in incorrect VAGUE relation annotation.
+
+With all the aforementioned issues, CleanMATRES excludes all VAGUE relations from the test set. We only consider BEFORE, AFTER, and EQUAL relations during the evaluation of CleanMATRES. We also did not include the analysis of VAGUE relations in Section 2, as it requires a more thorough examination of the application of temporal calculus when underspecificity is involved. Allen's (1983) original temporal calculus assumes all events are intervals with well-defined endpoints. Yao et al. (2020) and Niu et al. (2023) provided a more in-depth analysis to the VAGUE edges and underspecificity.

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+        "text": "Artificial agents that learn to communicate in order to accomplish a given task acquire communication protocols that are typically opaque to a human. A large body of work has attempted to evaluate the emergent communication via various evaluation measures, with compositionality featuring as a prominent desired trait. However, current evaluation procedures do not directly expose the compositionality of the emergent communication. We propose a procedure to assess the compositionality of emergent communication by finding the best-match between emerged words and natural language concepts. The best-match algorithm provides both a global score and a translation-map from emergent words to natural language concepts. To the best of our knowledge, it is the first time that such direct and interpretable mapping between emergent words and human concepts is provided.",
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+        "text": "1 Introduction",
+        "text_level": 1,
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+        "type": "text",
+        "text": "Artificial agents that learn to communicate for accomplishing a given task acquire communication protocols. In the common setting, a sender observes a set of objects and sends a message to a receiver, which then needs to identify the correct target objects out of a set of distractors. The two agents learn a communication protocol over discrete vocabulary of atoms, termed \"words\". The emergent communication (EC) is typically opaque to a human. As a result, a large body of work has attempted to characterize the emergent communication in light of natural language (NL) traits, such as compositionality (Hupkes et al., 2020; Chaabouni et al., 2020), systematic generalization (Vani et al., 2021), pragmatism (Andreas and Klein, 2016; Zaslavsky et al., 2021), and more.",
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+        "text": "Chief among these is compositionality, which enables the construction of complex meanings from the meaning of parts (Li and Bowling, 2019). However, quantifying compositionality in EC is noto",
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+            "Figure 1: The multi-target shape game played in turns (showing two turns). (a) At each turn, the sender is given a set of images, a subset of them marked as targets by an Oracle. (b) Sender generates messages  $[w_1, w_2]$  for the blue-triangle (turn 1) and  $[w_2, w_3]$  for the red-triangle (turn 2). (c) During evaluation, we construct a bipartite graph of words generated by the sender and concepts provided by the Oracle for each turn. (d) The best-match algorithm matches EC words to NL concepts and provides the CBM score. In this example, all EC words are matched with NL concepts, resulting in a CBM score of 1.0."
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+        "type": "text",
+        "text": "riously difficult (Lazaridou et al., 2018). In fact, recent studies found that common compositionality measures in EC, e.g., topographic similarity (Brighton and Kirby, 2006; Li and Bowling, 2019), do not correlate well with success in the task (Chaabouni et al., 2021; Yao et al., 2022). Moreover, while seeking to assess an opaque protocol, common evaluation measures in EC are opaque themselves—they do not provide a human-interpretable characterization of the compositionality of the communication.",
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+        "text": "This work develops a method that characterizes how compositional an EC is. Our method is founded on the key insight that, in an EC setting, a communication is compositional if agents communicate successfully via complex messages formed of simple atoms and these atoms are mapped to NL concepts. Our evaluation is based on the classical",
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+        "text": "3186",
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+    {
+        "type": "footer",
+        "text": "Findings of the Association for Computational Linguistics: ACL 2024, pages 3186-3194",
+        "bbox": [
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+    },
+    {
+        "type": "footer",
+        "text": "August 11-16, 2024 ©2024 Association for Computational Linguistics",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "best-match algorithm (Hopcroft and Karp, 1973). Given a set of EC atoms and a set of NL concepts, we construct a bi-partite graph and seek the optimal one-to-one mapping between words and concepts. A perfectly compositional EC would yield a perfect match, where every EC atom is mapped to exactly one NL concept. See Figure 1 for an illustration.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "We experiment with the proposed procedure in two EC settings and compare it to two popular evaluation measures - topographic similarity and adjusted mutual information (AMI). We demonstrate that our approach provides a fine-grained characterization of emergent protocols, exposing their strengths and weaknesses, while other measures only provide coarse, opaque scores. According to our evaluation, state-of-the-art communication methods do not achieve satisfactory results.",
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+    {
+        "type": "text",
+        "text": "2 Background",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "2.1 Emergent Communication Setup",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "We follow a recent setup suggested by Mu and Goodman (2021), where a sender needs to communicate with a receiver about a set of target objects out of a larger set of candidate objects. The sender sends a message to the receiver, which uses it to distinguish targets from distractor objects. For example, to identify all red triangles out of objects with different shapes and colors. This setup is more conducive to emergence of compositional communication than the classical referential game (Lazaridou et al., 2017). Senders in this setup need to form a generalization rather than merely transmit the identity of a single target.",
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+        "text": "Formally, assume a world  $\\mathbb{X}$ , where each object is characterised by  $n$  feature-value pairs (FVPs),  $\\langle f_1 : v_1, \\ldots, f_n : v_n \\rangle$ , with feature  $i$  having  $k_i$  possible values,  $v_i \\in \\{f_i[1], \\ldots, f_i[k_i]\\}$ . For instance, the Shape world (Kuhnle and Copestake, 2017) has objects like  $\\langle \\text{shape: triangle, color: red} \\rangle$ . Labeling rules are boolean expressions over these FVPs. Each rule  $l : \\mathbb{X} \\mapsto \\{0, 1\\}$  labels each object as 0 or 1. For instance, the rule Red Triangle labels all red triangles as positive and all other objects as negative. We identify the rule Red Triangle with the NL phrase \"red triangle\", which comprises the concepts \"red\" and \"triangle\".",
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+    {
+        "type": "text",
+        "text": "At each turn of the game, we draw a set of candidate objects  $\\tilde{\\mathbb{X}}\\subset \\mathbb{X}$  that is made of target objects,  $\\mathbb{T}$ , which obey the rule, and distractors,  $\\mathbb{D}$ , which do not:  $l(x) = 1$  if  $x\\in \\mathbb{T}$  and  $l(x) = 0$  if  $x\\in \\mathbb{D}$ .",
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+    {
+        "type": "text",
+        "text": "The sender encodes the set of target objects  $\\mathbb{T}$  into a dense representation  $\\pmb{u}^s\\in \\mathbb{R}^d$  , and generates a message  $m$  , a sequence of words from some vocabulary. The receiver encodes each candidate object  $x\\in \\mathbb{X}$  into a representation  $\\pmb {u}_x^r\\in \\mathbb{R}^d$  . It decodes the message  $m$  into a representation  $\\pmb {z}\\in \\mathbb{R}^{d}$  and computes a matching score between each encoded candidate and the message representation,  $g(z,\\pmb {u}_x^r)$  . A candidate is predicted as a target if its score is  $>0.5$  . The entire system—sender and receiver networks—is trained jointly with a binary cross entropy on correctly identifying each target.",
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+    {
+        "type": "text",
+        "text": "2.2 Compositionality in EC",
+        "text_level": 1,
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+        "text": "Various measures have been proposed to evaluate if an EC protocol is compositional. We mention a few prominent ones below. However, while trying to capture the idea that a complex meaning uses the meaning of its parts, previous measures fail to provide a concrete mapping of parts—EC words and NL concepts. We say an emergent communication is compositional if the following conditions hold:",
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+        "list_items": [
+            "1. EC words are mapped to NL concepts.",
+            "2. A complex EC message is composed of simple EC words.",
+            "3. Agents communicate successfully via complex messages.",
+            "4. An EC message composed of words has the same meaning as an NL phrase composed of the respective concepts."
+        ],
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+    {
+        "type": "text",
+        "text": "Being able to compose EC words while preserving their NL meaning allows agents to generalize to new data while using interpretable communication.",
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+    {
+        "type": "text",
+        "text": "2.3 Compositionality Evaluations in EC",
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+        "type": "text",
+        "text": "We briefly describe two notable measures of compositionality in EC. Appendix A gives more details.",
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+    {
+        "type": "text",
+        "text": "Topographic Similarity (TopSim) (Brighton and Kirby, 2006) measures how well messages align with object representations. Given a set of objects and their EC messages, calculate a matrix of distances between every two messages and a separate matrix of distances between every two object representations. TopSim is the Spearman correlation of the two distance matrices.",
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+        "type": "text",
+        "text": "TopSim is a global metric that does not require a reference language and can be applied to any EC setup. However, recent studies found that TopSim does not correlate well with success in the task being played (Chaabouni et al., 2021; Yao et al., 2022). More importantly, it does not provide a",
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+    {
+        "type": "page_footnote",
+        "text": "In this work we only use conjunctive expressions.",
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+    {
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+        "text": "3187",
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+    {
+        "type": "text",
+        "text": "mapping between EC words and NL concepts, and thus cannot directly assess compositionality.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Adjusted Mutual Information (AMI) (Vinh et al., 2009) measures the MIT between a set of EC messages and a corresponding set of NL phrases, adjusted for chance. Mu and Goodman (2021) showed AMI is a better compositionality measure than TopSim, as it directly assesses the MI between a message and its NL phrases. Still, AMI operates at the level of messages and phrases, rather than atomic words and concepts, respectively.",
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+    {
+        "type": "text",
+        "text": "3 Concept Best Matching",
+        "text_level": 1,
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+        "type": "text",
+        "text": "Our key insight is that compositionality requires a mapping between words (atomic parts of EC messages) and concepts (a set of FVPs) that compose NL phrases. Given an evaluation set of examples  $D$ , consider their corresponding EC messages  $\\mathbb{M}$  and NL phrases  $\\mathbb{L}$ . Let  $\\mathbb{W}$  denote the set of unique words in  $\\mathbb{M}$ , and  $\\mathbb{V}$  the set of unique FVPs in  $\\mathbb{L}$ . Let  $\\{w\\}_i, \\{v\\}_i$  be the sets of words and FVPs in sample  $i$ , and  $m_i = |\\{w\\}_i|, l_i = |\\{v\\}_i|$  their sizes. We construct a weighted bipartite graph  $\\mathcal{G} = ((\\mathbb{W}, \\mathbb{V}), \\mathbb{E})$  with words on one side and FVPs on the other side. Edges  $\\mathbb{E}$  are defined by the evaluation set. The weight  $q_e$  of edge  $e_{ij}$  is the number of times word  $i$  appeared in a message that the sender transmitted for a labeling rule with FVP  $j$ . This construction reflects the intuition that we do not know the correct mapping between words and FVPs (concepts). See Figure 1 for an example.",
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+    {
+        "type": "text",
+        "text": "3.1 Best Match Algorithm",
+        "text_level": 1,
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+        "type": "text",
+        "text": "Given the graph  $\\mathcal{G}$ , we seek an optimal pairing between words and concepts (FVPs), such that no two edges share the same word nor the same concept. The score of a match  $\\mathbb{B} \\subseteq \\mathbb{E}$  is the sum of its edge weights,  $\\sum_{e \\in \\mathbb{B}} q_e$ . The best match,  $\\mathrm{BM} = \\mathrm{BM}(\\mathcal{G})$ , maximizes this score:",
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+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathrm {B M} = \\underset {\\mathbb {B}} {\\operatorname {a r g m a x}} \\sum_ {e \\in \\mathbb {B}} q _ {e} \\tag {1}\n$$\n",
+        "text_format": "latex",
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+    {
+        "type": "text",
+        "text": "Such an ideal mapping is fully interpretable. A high score indicates that the agents learned to generate a unique EC word for each NL concept.",
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+    {
+        "type": "text",
+        "text": "Normalizing the BM score by the number of symbols and words,  $Q = \\sum_{i\\in D}\\max (|m_i|,|l_i|)$ , guarantees that  $\\mathrm{BM}\\in [0,1]$ . The best match for a weighted bipartite graph can be found efficiently by the Hungarian algorithm (Kuhn, 1955;",
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+    {
+        "type": "text",
+        "text": "Hopcroft and Karp, 1973). Implementation is provided here.",
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+    {
+        "type": "text",
+        "text": "4 Experimental Setup",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "We experiments with agents that learn to play multi-target referential games, introduced by Mu and Goodman (2021) and described in Section 2.1. All experiments reported in Table 1 have the number of possible words  $\\geq$  the number of concepts, allowing perfect match of words to concepts. In Appendix D we report more experiments with sub-optimal configurations.",
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+    {
+        "type": "text",
+        "text": "Datasets. We experiment with two datasets, described briefly here; Appendix B has more details.",
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+        "type": "list",
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+        "list_items": [
+            "(1) SHAPE: A visual reasoning dataset (Kuhnle and Copestake, 2017) of objects over a black background. Our version of the dataset contains four attributes: shape, color, and horizontal and vertical positions. Overall, the SHAPE dataset contains 17 concepts, and a maximal labeling rule of 4 FVPs.",
+            "(2) THING: A synthetic dataset of 100,000 objects. Each object has five attributes, each with 10 possible values. Overall, the THING datasets contains 50 concepts and a maximal labeling rule of 5 FVPs."
+        ],
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+    {
+        "type": "text",
+        "text": "Communication Channel. We train the system with two types of communication channels: the popular Gumbel-Softmax (GS) (Havylov and Titov, 2017; Jang et al., 2017) and quantized communication (QT) (Carmeli et al., 2023). In GS, each word is a  $d$ -dimensional one-hot vector. In QT, each word is a  $d$ -dimensional binary vector. QT was shown to be superior and easier to optimize compared to GS in EC games. In both cases we use a recurrent network to generate multi-word messages. Appendix C has implementation details.",
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+    {
+        "type": "text",
+        "text": "5 Results",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "Table 1 shows results on several configurations of the two games. As expected, accuracy degrades as the task becomes more difficult, with longer labeling rules. QT communication yields better task accuracy than GS, consistent with Carmeli et al. (2023). TopSim is not well correlated with accuracy, as found in prior work (Section 2.3). AMI and CBM are more correlated with accuracy. With long messages and labeling rules ( $l = 4$ ), AMI is less correlated with accuracy. This may be explained by AMI operating at the level of whole messages and labeling rules—AMI struggles with large numbers of unique messages and NL phrases. In contrast,",
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+    {
+        "type": "page_footnote",
+        "text": "<sup>3</sup>https://github.com/bcarmeli/cbm",
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+    {
+        "type": "page_footnote",
+        "text": "2In practice, the lowest bound is  $q_{\\tilde{e}} / Q$  , where  $\\tilde{e}$  is the edge with the highest weight in  $\\mathcal{G}$",
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+        "text": "3188",
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+        "type": "table",
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+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\"></td><td rowspan=\"2\">Com</td><td rowspan=\"2\">l</td><td rowspan=\"2\">d</td><td colspan=\"2\">NL</td><td colspan=\"2\">EC</td><td rowspan=\"2\">Acc</td><td rowspan=\"2\">Top Sim</td><td rowspan=\"2\">AMI</td><td colspan=\"4\">Best Match</td></tr><tr><td>Cons</td><td>Phrs</td><td>#w</td><td>#m</td><td>CBM</td><td>Amb</td><td>Para</td><td>Unm</td></tr><tr><td rowspan=\"4\">Shape</td><td>GS</td><td>1</td><td>17</td><td>17</td><td>17</td><td>11</td><td>11</td><td>0.84</td><td>0.44</td><td>0.76</td><td>0.62</td><td>0.37</td><td>0.01</td><td>0.25</td></tr><tr><td>QT</td><td>1</td><td>5</td><td>17</td><td>17</td><td>26</td><td>26</td><td>0.87</td><td>0.39</td><td>0.85</td><td>0.52</td><td>0.41</td><td>0.08</td><td>0</td></tr><tr><td>GS</td><td>4</td><td>17</td><td>17</td><td>34</td><td>16</td><td>226</td><td>0.78</td><td>0.34</td><td>0.38</td><td>0.52</td><td>0.48</td><td>0</td><td>0.01</td></tr><tr><td>QT</td><td>4</td><td>5</td><td>17</td><td>34</td><td>26</td><td>187</td><td>0.83</td><td>0.23</td><td>0.37</td><td>0.55</td><td>0.37</td><td>0.08</td><td>0</td></tr><tr><td rowspan=\"4\">Thing</td><td>GS</td><td>1</td><td>50</td><td>50</td><td>50</td><td>18</td><td>18</td><td>0.86</td><td>0.45</td><td>0.72</td><td>0.38</td><td>0.62</td><td>0</td><td>0.55</td></tr><tr><td>QT</td><td>1</td><td>6</td><td>50</td><td>50</td><td>50</td><td>50</td><td>0.92</td><td>0.07</td><td>0.74</td><td>0.73</td><td>0.25</td><td>0.02</td><td>0</td></tr><tr><td>GS</td><td>4</td><td>50</td><td>50</td><td>901</td><td>36</td><td>198</td><td>0.63</td><td>0.33</td><td>0.03</td><td>0.24</td><td>0.76</td><td>0</td><td>0.28</td></tr><tr><td>QT</td><td>4</td><td>6</td><td>50</td><td>901</td><td>64</td><td>450</td><td>0.77</td><td>0.14</td><td>0.05</td><td>0.23</td><td>0.69</td><td>0.08</td><td>0</td></tr></table>",
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+    {
+        "type": "text",
+        "text": "Table 1: Results for SHAPE and THING games with Gumbel-Softmax (GS) or Quantized (QT) communication using rules of length  $l$  and words of length  $d$ , showing number of unique NL concepts (Cons) and phrases (Phrs) and EC words (\\#w) and messages (#m). TopSim and AMI give only coarse scores. Our method gives the best match score (CBM) and rates of Ambiguities (Amb), Paraphrases (Para), and Unmatched concepts (Unm).",
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+    },
+    {
+        "type": "image",
+        "img_path": "images/d9ee58b9348d750d002cb8984b3fb9b33670a05da6509829cc76649979539b07.jpg",
+        "image_caption": [
+            "Figure 2: The word  $\\leftrightarrow$  FVP best-match graph for the SHAPE game (GS communication,  $l = 1$ ). The algorithm matched just 10 concepts to EC words out of 17 possible concepts."
+        ],
+        "image_footnote": [],
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+    {
+        "type": "text",
+        "text": "CBM assesses word-to-concept matching, so it is less affected by long messages and rules. However, AMI and CBM are well correlated (Pearson 0.7 and 0.79 on the SHAPE and THING games).",
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+    {
+        "type": "text",
+        "text": "The table also shows the rate of ambiguities and paraphrases, exposed by our method. Ambiguities happen when the same EC word is mapped to different concepts. Table 1 shows higher rates of ambiguities in GS compared to QT, and in longer rules. Paraphrases are EC words that do not have a best-matched concept node. Paraphrases occur more with QT, which enables 32 and 64 unique EC words for the SHAPE and THING games, while these games have only 17 and 50 NL concepts, respectively. GS allows setting the number of unique words equal to number of concepts, thus is less exposed to this sub-optimal phenomenon.",
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+    {
+        "type": "text",
+        "text": "Finally, Unmatched concepts have no matching EC word. They result from a too narrow or underutilized channel. As Table 1 shows, GS communication suffers from a high rate of unmatched concepts (up to 0.5). This phenomenon can be observed by the low # of unique words (18) compared to # of unique concepts (50) for the THING game with GS and  $l = 1$ . QT has a sufficient number of words and thus no unmatched concepts.",
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+    {
+        "type": "text",
+        "text": "Example Match. Beyond global scores, the CBM provides an interpretable translation graph, which maps EC words to NL concepts, facilitating insights on reasons for sub-optimal communication. Figure 2 shows an example graph for the SHAPE game with GS communication. As seen, the algorithm successfully matched 10 EC words to 10 concepts. The sender generated 11 unique words in this experiment, indicating that one word is a paraphrase of an already matched concept, even within this narrow-channel setup.",
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+    {
+        "type": "text",
+        "text": "6 Conclusion",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "We proposed a new procedure for assessing compositionality of emergent communication. In contrast to other evaluations, our procedure provides a human-interpretable translation map of emerged words to natural concepts. Moreover, our approach provides detailed insights into the reasons for suboptimal translation. We demonstrated it on two EC games with two different communication types. Our evaluation reveals even that quantized communication performs better than Gumbel-softmax, yet none exhibits compositionality in a level similar to natural language.",
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+    {
+        "type": "page_footnote",
+        "text": "4The exact configuration is given in Table 1, first row.",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "page_number",
+        "text": "3189",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Limitations",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Our analysis is limited to datasets where gold label phrases exist. The evaluated dataset should be composable and the gold language should use finite set of concepts. Preferably, these concepts can be classified into several categories. We further assume an Oracle function that can divide the objects to targets and distractors during training. Importantly, our approach does not require labels during training.",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Acknowledgements",
+        "text_level": 1,
+        "bbox": [
+            114,
+            242,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "This research was supported by grant no. 2022330 from the United States - Israel Binational Science Foundation (BSF), Jerusalem, Israel. The research of YB was also supported by the Israel Science Foundation (grant 448/20), an Azrieli Foundation Early Career Faculty Fellowship, and an AI Alignment grant from Open Philanthropy. The work of RM was partially supported by the Skillman chair in biomedical sciences and by the Ollendorf center.",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "References",
+        "text_level": 1,
+        "bbox": [
+            114,
+            432,
+            213,
+            448
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "list",
+        "sub_type": "ref_text",
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+            "Angeliki Lazaridou, Alexander Peysakhovich, and Marco Baroni. 2017. Multi-agent cooperation and the emergence of (natural) language. In ICLR.",
+            "Vladimir I Levenshtein et al. 1966. Binary codes capable of correcting deletions, insertions, and reversals. In Soviet physics doklady, volume 10, pages 707-710. Soviet Union.",
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+            "Jesse Mu and Noah Goodman. 2021. Emergent communication of generalizations. Advances in Neural Information Processing Systems, 34:17994-18007.",
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+            "Shunyu Yao, Mo Yu, Yang Zhang, Karthik R Narasimhan, Joshua B. Tenenbaum, and Chuang Gan. 2022. Linking emergent and natural languages via corpus transfer. In ICLR.",
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+        ],
+        "bbox": [
+            510,
+            85,
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+            908
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "page_number",
+        "text": "3190",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Appendices",
+        "text_level": 1,
+        "bbox": [
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+            84,
+            218,
+            99
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "A Details on Evaluation Measures",
+        "text_level": 1,
+        "bbox": [
+            114,
+            109,
+            426,
+            124
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "We provide here information on how to calculate the topographic similarity (TopSim) (Brighton and Kirby, 2006; Lazaridou et al., 2018; Yao et al., 2022) and adjusted mutual information (AMI) measures (Vinh et al., 2009; Mu and Goodman, 2021), in the context of EC. Refer to the original papers for full details.",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Topographic Similarity. The topographic similarity measures how messages align with the object representations. Concretely, let  $\\cos_{ij} = \\cos (\\pmb{x}_i,\\pmb{x}_j) = \\pmb{x}_i\\cdot \\pmb{x}_j / (||\\pmb{x}_i||_2||\\pmb{x}_j||_2)$  be the cosine similarity of object representations  $\\pmb{x}_i$  and  $\\pmb{x}_j$  and  $\\mathrm{edit}_{ij} = \\mathrm{edit}(m_i,m_j)$  be the Levenshtein distance (Levenshtein et al., 1966) between messages  $m_{i}$  and  $m_j$ . Let  $\\mathrm{ncos} = -\\{\\cos_{ij}\\}_{ij}$  be the list of negative cosine similarities,  $\\mathrm{edit} = \\{\\mathrm{edit}_{ij}\\}_{ij}$  the list of Levenshtein distances, and  $R(\\cdot)$  the ranking function. Then the topographic similarity is the Spearman rank correlation of the two matrices:",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\operatorname {T o p s i m} = \\rho (R (\\operatorname {e d i t}), R (\\operatorname {n c o s})) \\tag {2}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "where  $\\rho$  is the standard Pearson correlation.",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Topographic similarity is a global metric that does not require a reference language and can be easily applied to every EC setup. However, despite its popularity, recent studies found that topographic similarity does not correlate well with success in the task being played (Chaabouni et al., 2021; Yao et al., 2022). More important, it does not provide a mapping between EC atoms and NL concepts, and thus cannot directly assess compositionality.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Adjusted Mutual Information. Given a test set  $D$ , let  $\\mathbb{M}$  denote the set of messages generated by the sender and  $\\mathbb{L}$  denote the set of NL phrases (e.g., Red Triangle, Blue Square) exist as labels in the data. The adjusted mutual information (AMI) (Vinh et al., 2009) measures the mutual information between messages and labels, adjusted for chance:",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\operatorname {A M I} (M, L) = \\frac {I (M , L) - \\mathbb {E} (I (M , L)}{\\max  (H (M) , H (L)) - \\mathbb {E} (I (M , L))} \\tag {3}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "where  $I(M,L)$  is the mutual information between  $M$  and  $L$ ,  $H(\\cdot)$  is the entropy, and  $\\mathbb{E}(I(M,L))$  is computed with respect to a hypergeometric model of randomness.",
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+    },
+    {
+        "type": "image",
+        "img_path": "images/a0a68d82b82425ddea7e647f0d26ddc9d6a925173eb17d92cdf7027b1020832a.jpg",
+        "image_caption": [
+            "Figure 3: The SHAPE dataset, presenting one turn. Top 8 images are Yellow targets. Bottom 8 images are distractors."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "B Datasets",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "We use two datasets in our experiments. Both will be made publicly available.",
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+    {
+        "type": "text",
+        "text": "Shape. A visual reasoning dataset (Kuhnle and Copestake, 2017) of objects over a black background. Our version of the dataset contains four attributes: the shape attribute has five shapes, the color attribute has six colors. To these we added horizontal and vertical position attributes each with three values. Overall, the SHAPE dataset contains 17 concepts, and a maximal labeling rule of 4 FVPs which sum to 270 unique 4-concept labels. The dataset contains many images that obey the same label. See Figure 3 for an example.",
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+    {
+        "type": "text",
+        "text": "Thing. A synthetic dataset of 100,000 objects which we design for controlled experiments. Each object in the dataset has five attributes, each with 10 possible values. Overall, the THING datasets contains 50 concepts and a maximal labeling rule of 5 FVPs. We experiments with label lengths varied from 1, describing a single concept, to 5, which completely describes an object in the dataset.",
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+    {
+        "type": "text",
+        "text": "C Implementation Details",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "We run all experiments over a modified version of the Egg framework (Kharitonov et al., 2019). In our version the communication modules used by the sender and the receiver are totally separated from their perceptual modules, which we term 'agents'. The Quantized (QT) and Gumbel-Softmax (GS) protocols are implemented at the",
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+    },
+    {
+        "type": "page_footnote",
+        "text": "Our modification is available at https://github. com/bcarmeli/egg_qtc.",
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+    },
+    {
+        "type": "page_number",
+        "text": "3191",
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+    },
+    {
+        "type": "table",
+        "img_path": "images/760a9166ecdae8e3b8e2025ff1e9af817a4fc7eeadcf67e0b930851f72e6f241.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Batch Size</td><td>lr</td><td>Num Targets</td><td>Num Distr</td><td>Cell Type</td><td>Sender Hidden</td><td>Sender Embed</td><td>Receiver Hidden</td><td>Receiver Embed</td></tr><tr><td>10</td><td>0.0005</td><td>8/20</td><td>8/20</td><td>LSTM</td><td>60</td><td>60</td><td>40</td><td>40</td></tr></table>",
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+        "page_idx": 6
+    },
+    {
+        "type": "table",
+        "img_path": "images/033c32f16b6f2a2b4724075fb16863ecac5ce02ce9f60205b7b37bdcec9c8b3c.jpg",
+        "table_caption": [
+            "Table 2: Hyper-parameters for the agents in the SHAPE game."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Exp Num</td><td>Game</td><td>Comm Type</td><td>Label Len</td><td>word Len</td><td>Msg Len</td><td>Best Epoch</td><td>ACC</td><td>AMI</td><td>Best Match</td></tr><tr><td>1</td><td>SHAPE</td><td>gs</td><td>1</td><td>8</td><td>4</td><td>97</td><td>0.829</td><td>0.404</td><td>0.405</td></tr><tr><td>2</td><td>SHAPE</td><td>gs</td><td>1</td><td>64</td><td>4</td><td>96</td><td>0.843</td><td>0.390</td><td>0.339</td></tr><tr><td>3</td><td>SHAPE</td><td>gs</td><td>4</td><td>8</td><td>1</td><td>8</td><td>0.742</td><td>0.490</td><td>0.152</td></tr><tr><td>4</td><td>SHAPE</td><td>gs</td><td>4</td><td>64</td><td>1</td><td>10</td><td>0.748</td><td>0.413</td><td>0.130</td></tr><tr><td>5</td><td>SHAPE</td><td>qt</td><td>1</td><td>3</td><td>4</td><td>86</td><td>0.878</td><td>0.540</td><td>1.401</td></tr><tr><td>6</td><td>SHAPE</td><td>qt</td><td>1</td><td>64</td><td>4</td><td>85</td><td>0.991</td><td>0.000</td><td>0.001</td></tr><tr><td>7</td><td>SHAPE</td><td>qt</td><td>4</td><td>3</td><td>1</td><td>9</td><td>0.768</td><td>0.474</td><td>0.152</td></tr><tr><td>8</td><td>SHAPE</td><td>qt</td><td>4</td><td>64</td><td>1</td><td>12</td><td>0.897</td><td>0.021</td><td>0.009</td></tr><tr><td>9</td><td>THING</td><td>gs</td><td>1</td><td>8</td><td>4</td><td>83</td><td>0.793</td><td>0.102</td><td>0.091</td></tr><tr><td>10</td><td>THING</td><td>gs</td><td>1</td><td>64</td><td>4</td><td>94</td><td>0.798</td><td>0.074</td><td>0.151</td></tr><tr><td>11</td><td>THING</td><td>gs</td><td>4</td><td>8</td><td>1</td><td>97</td><td>0.655</td><td>0.016</td><td>0.052</td></tr><tr><td>12</td><td>THING</td><td>gs</td><td>4</td><td>64</td><td>1</td><td>99</td><td>0.626</td><td>0.014</td><td>0.058</td></tr><tr><td>13</td><td>THING</td><td>qt</td><td>1</td><td>3</td><td>4</td><td>96</td><td>0.838</td><td>0.267</td><td>0.119</td></tr><tr><td>14</td><td>THING</td><td>qt</td><td>1</td><td>64</td><td>4</td><td>100</td><td>0.973</td><td>0.000</td><td>0.014</td></tr><tr><td>15</td><td>THING</td><td>qt</td><td>4</td><td>3</td><td>1</td><td>26</td><td>0.622</td><td>0.020</td><td>0.057</td></tr><tr><td>16</td><td>THING</td><td>qt</td><td>4</td><td>64</td><td>1</td><td>96</td><td>0.844</td><td>0.000</td><td>0.013</td></tr></table>",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "table",
+        "img_path": "images/b5355e49d030ec6db8fecf751b19e8a7d57022c10e692e9f4f73cfee16166957.jpg",
+        "table_caption": [
+            "Table 3: Configurations for more SHAPE and THING game experiments. In these configuration we intentionally define sub-optimal communication parameters in order to demonstrate the usefulness of the evaluation metrics. Experiment results are provided in Table 4"
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Exp Num</td><td>Unq Msgs</td><td>Unq Wrds</td><td>Unq Prs</td><td>Ung Cons</td><td>Totl Edgs</td><td>Good Edgs</td><td>Amb Edgs</td><td>Phrs Edgs</td><td>Totl Cons</td><td>Unm Cons</td><td>Par Scor</td><td>Prc</td><td>Rcl</td></tr><tr><td>1</td><td>258</td><td>7</td><td>17</td><td>17</td><td>4k</td><td>1621</td><td>2379</td><td>0</td><td>1k</td><td>444</td><td>0</td><td>0.137</td><td>0.546</td></tr><tr><td>2</td><td>442</td><td>55</td><td>17</td><td>17</td><td>4k</td><td>1356</td><td>1724</td><td>920</td><td>1k</td><td>0</td><td>0.23</td><td>0.144</td><td>0.577</td></tr><tr><td>3</td><td>8</td><td>8</td><td>34</td><td>17</td><td>4k</td><td>610</td><td>390</td><td>0</td><td>4k</td><td>1457</td><td>0</td><td>0.61</td><td>0.152</td></tr><tr><td>4</td><td>44</td><td>44</td><td>34</td><td>17</td><td>4k</td><td>520</td><td>326</td><td>154</td><td>4k</td><td>0</td><td>0.04</td><td>0.52</td><td>0.13</td></tr><tr><td>5</td><td>238</td><td>8</td><td>17</td><td>17</td><td>4k</td><td>1605</td><td>2395</td><td>0</td><td>1k</td><td>385</td><td>0</td><td>0.144</td><td>0.577</td></tr><tr><td>6</td><td>1000</td><td>3899</td><td>17</td><td>17</td><td>4k</td><td>46</td><td>0</td><td>3954</td><td>1k</td><td>0</td><td>0.99</td><td>0.011</td><td>0.044</td></tr><tr><td>7</td><td>7</td><td>7</td><td>34</td><td>17</td><td>4k</td><td>607</td><td>393</td><td>0</td><td>4k</td><td>1727</td><td>0</td><td>0.607</td><td>0.152</td></tr><tr><td>8</td><td>974</td><td>974</td><td>34</td><td>17</td><td>4k</td><td>38</td><td>0</td><td>962</td><td>4k</td><td>0</td><td>0.24</td><td>0.038</td><td>0.009</td></tr><tr><td>9</td><td>543</td><td>7</td><td>50</td><td>50</td><td>4k</td><td>366</td><td>3634</td><td>0</td><td>1k</td><td>807</td><td>0</td><td>0.048</td><td>0.19</td></tr><tr><td>10</td><td>806</td><td>60</td><td>50</td><td>50</td><td>4k</td><td>601</td><td>3369</td><td>30</td><td>1k</td><td>0</td><td>0.01</td><td>0.1</td><td>0.399</td></tr><tr><td>11</td><td>8</td><td>8</td><td>901</td><td>50</td><td>4k</td><td>210</td><td>790</td><td>0</td><td>4k</td><td>3332</td><td>0</td><td>0.21</td><td>0.052</td></tr><tr><td>12</td><td>21</td><td>21</td><td>901</td><td>50</td><td>4k</td><td>233</td><td>767</td><td>0</td><td>4k</td><td>2267</td><td>0</td><td>0.233</td><td>0.058</td></tr><tr><td>13</td><td>412</td><td>8</td><td>50</td><td>50</td><td>4k</td><td>478</td><td>3522</td><td>0</td><td>1k</td><td>795</td><td>0</td><td>0.046</td><td>0.184</td></tr><tr><td>14</td><td>1000</td><td>3991</td><td>50</td><td>50</td><td>4k</td><td>57</td><td>0</td><td>3943</td><td>1k</td><td>0</td><td>0.99</td><td>0.013</td><td>0.052</td></tr><tr><td>15</td><td>11</td><td>6</td><td>901</td><td>50</td><td>4k</td><td>229</td><td>771</td><td>0</td><td>4k</td><td>3483</td><td>0</td><td>0.229</td><td>0.057</td></tr><tr><td>16</td><td>1000</td><td>1000</td><td>901</td><td>50</td><td>4k</td><td>50</td><td>0</td><td>950</td><td>4k</td><td>0</td><td>0.24</td><td>0.05</td><td>0.013</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Table 4: Results for more SHAPE and THING game configurations described in Table 3. In these experiments we intentionally define sub-optimal communication parameters in order to demonstrate the usefulness of the evaluation metrics.",
+        "bbox": [
+            112,
+            860,
+            882,
+            902
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "page_number",
+        "text": "3192",
+        "bbox": [
+            480,
+            928,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "communication layer. For GS we use an implementation provided by the Egg framework, where we do not allow temperature to be learned, and set the straight-through estimator to False. For QT we followed parameter recommendations from Carmeli et al. (2023) and use a binary quantization in all experiments. Both GS and QT uses a recurrent neural network (RNN) for generating multiple words in a message. See Table 2 for RNN details.",
+        "bbox": [
+            112,
+            84,
+            489,
+            227
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "The agents for the THING game use fully connected feed-forward networks with input dimension of  $d = 270$ . Objects are encoded by concatenating five one-hot vectors, one per attribute. There are 50 unique values and 4 communication words (SOS, EOS, PAD, UNK), thus the total object representation length is  $d = 270$ . The agents of the SHAPE game are implemented with a convolutional neural network similar to Mu and Goodman (2021). Network hyper-parameters are provided in Table 2. In the experiments, we report results when varying the communication elements (word length and message length). Experiments in Table 1 are done with 20 targets and 20 distractors, while experiments reported in Tables 3 and 4 are done with 8 targets and 8 distractors. Our main interest in this work is to evaluate the emerged communication and not to achieve the best possible performance, thus we did not conduct a thorough hyper-parameter search for the agents themselves.",
+        "bbox": [
+            115,
+            230,
+            489,
+            549
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "We run all experiments on a single A100 GPU with 40 GB of RAM. Model size is less than 10M. We usually trained the model for 200 epochs which took about 10 hours to complete. Our code will be made publicly available upon de-anonymization.",
+        "bbox": [
+            112,
+            551,
+            487,
+            632
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "D Evaluating Sub-optimal Configurations",
+        "text_level": 1,
+        "bbox": [
+            112,
+            638,
+            485,
+            655
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Here we provide results from experiments with several sub-optimal configurations and demonstrate how CBM identifies these deficiencies. We report configuration parameters for each experiment together with accuracy, AMI, and CBM Score in Table 3. We report all CBM metrics for these experiments in Table 4. Information from the two tables is aligned by the experiment number (first column).",
+        "bbox": [
+            112,
+            661,
+            487,
+            804
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Sub-optimal communication may stem from a channel that is either too wide or too narrow. Narrow channels are restricted by a small number of words and short messages. Wide channels allow long words and/or long messages. Past studies (Tucker et al., 2022) suggest that creating an information bottleneck by narrowing the channel en",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "image",
+        "img_path": "images/4cdf223f77a9db8d1f89800710a787e1795c10df2785c627e982062e118bd7c5.jpg",
+        "image_caption": [
+            "Figure 4: Assessing CBM sensitivity to the size of the evaluation set. We show results for two randomly selected experiments. As seen, the CBM score stabilizes when assessing datasets comprising more than 500 samples."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            536,
+            93,
+            857,
+            223
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "courages generalization. As seen, CBM scores for most reported sub-optimal configurations are low. Results from experiments 1, 2, and 5 are the only ones for which the CBM score is higher than 0.2. Experiment 6 (SHAPE) achieves almost perfect accuracy (0.991) due to its wide channel. However, the paraphrase score for this experiment is 0.989 showing that the sender uses many different words to refer to the same concept. This phenomenon can also be seen by the large number of unique words (3899) generated for just 17 unique concepts. A similar phenomenon is observed for the THING game (experiment 14).",
+        "bbox": [
+            505,
+            334,
+            884,
+            542
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Experiment 11 (THING) uses a narrow channel. The vocabulary contains only 8 words and the channel allows one-word-long messages. This configuration resulted in 3332 concepts that do not match any word. Interestingly, the number of unmatched concepts remains high even when extending the word length to 64, in experiment 12. We attribute this sub-optimal phenomenon to GS communication deficiencies. The number of unique words generated by the sender in this experiment is only 21 out of the possible 64 words allowed by the configuration. For the SHAPE game, on the other hand, the same wide-channel configuration resulted in 44 unique words generated by the sender for the 17 concepts available in this game and all concepts have matched words.",
+        "bbox": [
+            507,
+            543,
+            885,
+            799
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Precision and recall. After finding the best match, precision and recall between words and concepts can be computed. We define message precision (Prc) and recall (Rcl) to be the number of matched edges in a message, divided by the number of words or concepts, respectively. Precision and recall add insights in situation where the num",
+        "bbox": [
+            507,
+            806,
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+            917
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "page_number",
+        "text": "3193",
+        "bbox": [
+            480,
+            927,
+            519,
+            940
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "ber of words in messages differs significantly from the number of concepts used for labeling the data. Experiment 5 (SHAPE) shows the highest recall, gained partially due to the long message length (four words) allowed by the channel, compared to the label length (one concept) dictated by the data. In contrast, experiment 3 (SHAPE) shows the highest precision. Indeed, this configuration restricts message the length to one word while the data dictates four-concept long phrases.",
+        "bbox": [
+            115,
+            84,
+            485,
+            243
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "E CBM Sensitivity to Dataset Size",
+        "text_level": 1,
+        "bbox": [
+            115,
+            250,
+            423,
+            266
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "We evaluated CBM scores on increased data sizes. Figure 4 shows results for two randomly selected experiments. The solid lines indicate the CBM score, computed when accumulating data samples in 100 quintets. The dashed lines indicate CBM score calculated independently for 18 successive data segments of 100 samples each. As seen, scores stabilize for evaluation sets of size larger than 500 samples. Interestingly, the 100-sample scores (dashed) lines are higher than the accumulated scores (solid lines). This is in line with our insight that low evaluation sizes result in higher match scores. Standard deviation for the 18 accumulated measures is 0.009 and 0.016, for the two experiments, respectively. Standard deviation for the 18 segmented measures is 0.044 and 0.040, for the two experiments, respectively.",
+        "bbox": [
+            115,
+            273,
+            485,
+            546
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "page_number",
+        "text": "3194",
+        "bbox": [
+            482,
+            928,
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+            940
+        ],
+        "page_idx": 8
+    }
+]

2024/Concept-Best-Matching_ Evaluating Compositionality In Emergent Communication/4ad4723c-7bbd-4934-855a-91c77ee9c3b0_model.json

@@ -0,0 +1,1703 @@
+[
+    [
+        {
+            "type": "title",
+            "bbox": [
+                0.197,
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+            ],
+            "angle": 0,
+            "content": "Concept-Best-Matching: Evaluating Compositionality in Emergent Communication"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.272,
+                0.143,
+                0.731,
+                0.159
+            ],
+            "angle": 0,
+            "content": "Boaz Carmeli Yonatan Belinkov Ron Meir"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.334,
+                0.161,
+                0.669,
+                0.177
+            ],
+            "angle": 0,
+            "content": "Technion - Israel Institute of Technology"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.292,
+                0.179,
+                0.71,
+                0.193
+            ],
+            "angle": 0,
+            "content": "boaz.carmeli@campus.technion.ac.il,"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.361,
+                0.195,
+                0.64,
+                0.209
+            ],
+            "angle": 0,
+            "content": "belinkov@technion.ac.il"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.362,
+                0.212,
+                0.641,
+                0.225
+            ],
+            "angle": 0,
+            "content": "rmeir@ee.technion.ac.il"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.261,
+                0.253,
+                0.341,
+                0.267
+            ],
+            "angle": 0,
+            "content": "Abstract"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.142,
+                0.279,
+                0.461,
+                0.564
+            ],
+            "angle": 0,
+            "content": "Artificial agents that learn to communicate in order to accomplish a given task acquire communication protocols that are typically opaque to a human. A large body of work has attempted to evaluate the emergent communication via various evaluation measures, with compositionality featuring as a prominent desired trait. However, current evaluation procedures do not directly expose the compositionality of the emergent communication. We propose a procedure to assess the compositionality of emergent communication by finding the best-match between emerged words and natural language concepts. The best-match algorithm provides both a global score and a translation-map from emergent words to natural language concepts. To the best of our knowledge, it is the first time that such direct and interpretable mapping between emergent words and human concepts is provided."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.115,
+                0.575,
+                0.26,
+                0.59
+            ],
+            "angle": 0,
+            "content": "1 Introduction"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.113,
+                0.598,
+                0.49,
+                0.854
+            ],
+            "angle": 0,
+            "content": "Artificial agents that learn to communicate for accomplishing a given task acquire communication protocols. In the common setting, a sender observes a set of objects and sends a message to a receiver, which then needs to identify the correct target objects out of a set of distractors. The two agents learn a communication protocol over discrete vocabulary of atoms, termed \"words\". The emergent communication (EC) is typically opaque to a human. As a result, a large body of work has attempted to characterize the emergent communication in light of natural language (NL) traits, such as compositionality (Hupkes et al., 2020; Chaabouni et al., 2020), systematic generalization (Vani et al., 2021), pragmatism (Andreas and Klein, 2016; Zaslavsky et al., 2021), and more."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.113,
+                0.856,
+                0.49,
+                0.92
+            ],
+            "angle": 0,
+            "content": "Chief among these is compositionality, which enables the construction of complex meanings from the meaning of parts (Li and Bowling, 2019). However, quantifying compositionality in EC is noto"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.518,
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+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
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+            "angle": 0,
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+        },
+        {
+            "type": "image",
+            "bbox": [
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+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
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+            "angle": 0,
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+        },
+        {
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+            "angle": 0,
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+        },
+        {
+            "type": "image",
+            "bbox": [
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+                0.782,
+                0.398
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.795,
+                0.339,
+                0.888,
+                0.405
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.508,
+                0.42,
+                0.884,
+                0.591
+            ],
+            "angle": 0,
+            "content": "Figure 1: The multi-target shape game played in turns (showing two turns). (a) At each turn, the sender is given a set of images, a subset of them marked as targets by an Oracle. (b) Sender generates messages \\([w_1, w_2]\\) for the blue-triangle (turn 1) and \\([w_2, w_3]\\) for the red-triangle (turn 2). (c) During evaluation, we construct a bipartite graph of words generated by the sender and concepts provided by the Oracle for each turn. (d) The best-match algorithm matches EC words to NL concepts and provides the CBM score. In this example, all EC words are matched with NL concepts, resulting in a CBM score of 1.0."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.508,
+                0.625,
+                0.885,
+                0.801
+            ],
+            "angle": 0,
+            "content": "riously difficult (Lazaridou et al., 2018). In fact, recent studies found that common compositionality measures in EC, e.g., topographic similarity (Brighton and Kirby, 2006; Li and Bowling, 2019), do not correlate well with success in the task (Chaabouni et al., 2021; Yao et al., 2022). Moreover, while seeking to assess an opaque protocol, common evaluation measures in EC are opaque themselves—they do not provide a human-interpretable characterization of the compositionality of the communication."
+        },
+        {
+            "type": "text",
+            "bbox": [
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+            ],
+            "angle": 0,
+            "content": "This work develops a method that characterizes how compositional an EC is. Our method is founded on the key insight that, in an EC setting, a communication is compositional if agents communicate successfully via complex messages formed of simple atoms and these atoms are mapped to NL concepts. Our evaluation is based on the classical"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
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+                0.522,
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+            "angle": 0,
+            "content": "3186"
+        },
+        {
+            "type": "footer",
+            "bbox": [
+                0.229,
+                0.946,
+                0.769,
+                0.959
+            ],
+            "angle": 0,
+            "content": "Findings of the Association for Computational Linguistics: ACL 2024, pages 3186-3194"
+        },
+        {
+            "type": "footer",
+            "bbox": [
+                0.285,
+                0.96,
+                0.714,
+                0.972
+            ],
+            "angle": 0,
+            "content": "August 11-16, 2024 ©2024 Association for Computational Linguistics"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.113,
+                0.085,
+                0.488,
+                0.198
+            ],
+            "angle": 0,
+            "content": "best-match algorithm (Hopcroft and Karp, 1973). Given a set of EC atoms and a set of NL concepts, we construct a bi-partite graph and seek the optimal one-to-one mapping between words and concepts. A perfectly compositional EC would yield a perfect match, where every EC atom is mapped to exactly one NL concept. See Figure 1 for an illustration."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.117,
+                0.2,
+                0.49,
+                0.358
+            ],
+            "angle": 0,
+            "content": "We experiment with the proposed procedure in two EC settings and compare it to two popular evaluation measures - topographic similarity and adjusted mutual information (AMI). We demonstrate that our approach provides a fine-grained characterization of emergent protocols, exposing their strengths and weaknesses, while other measures only provide coarse, opaque scores. According to our evaluation, state-of-the-art communication methods do not achieve satisfactory results."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.114,
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+                0.382
+            ],
+            "angle": 0,
+            "content": "2 Background"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.114,
+                0.39,
+                0.42,
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+            ],
+            "angle": 0,
+            "content": "2.1 Emergent Communication Setup"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.113,
+                0.412,
+                0.49,
+                0.621
+            ],
+            "angle": 0,
+            "content": "We follow a recent setup suggested by Mu and Goodman (2021), where a sender needs to communicate with a receiver about a set of target objects out of a larger set of candidate objects. The sender sends a message to the receiver, which uses it to distinguish targets from distractor objects. For example, to identify all red triangles out of objects with different shapes and colors. This setup is more conducive to emergence of compositional communication than the classical referential game (Lazaridou et al., 2017). Senders in this setup need to form a generalization rather than merely transmit the identity of a single target."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.113,
+                0.622,
+                0.49,
+                0.831
+            ],
+            "angle": 0,
+            "content": "Formally, assume a world \\(\\mathbb{X}\\), where each object is characterised by \\(n\\) feature-value pairs (FVPs), \\(\\langle f_1 : v_1, \\ldots, f_n : v_n \\rangle\\), with feature \\(i\\) having \\(k_i\\) possible values, \\(v_i \\in \\{f_i[1], \\ldots, f_i[k_i]\\}\\). For instance, the Shape world (Kuhnle and Copestake, 2017) has objects like \\(\\langle \\text{shape: triangle, color: red} \\rangle\\). Labeling rules are boolean expressions over these FVPs. Each rule \\(l : \\mathbb{X} \\mapsto \\{0, 1\\}\\) labels each object as 0 or 1. For instance, the rule Red Triangle labels all red triangles as positive and all other objects as negative. We identify the rule Red Triangle with the NL phrase \"red triangle\", which comprises the concepts \"red\" and \"triangle\"."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.113,
+                0.831,
+                0.49,
+                0.896
+            ],
+            "angle": 0,
+            "content": "At each turn of the game, we draw a set of candidate objects \\(\\tilde{\\mathbb{X}}\\subset \\mathbb{X}\\) that is made of target objects, \\(\\mathbb{T}\\), which obey the rule, and distractors, \\(\\mathbb{D}\\), which do not: \\(l(x) = 1\\) if \\(x\\in \\mathbb{T}\\) and \\(l(x) = 0\\) if \\(x\\in \\mathbb{D}\\)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.508,
+                0.085,
+                0.885,
+                0.278
+            ],
+            "angle": 0,
+            "content": "The sender encodes the set of target objects \\(\\mathbb{T}\\) into a dense representation \\(\\pmb{u}^s\\in \\mathbb{R}^d\\) , and generates a message \\(m\\) , a sequence of words from some vocabulary. The receiver encodes each candidate object \\(x\\in \\mathbb{X}\\) into a representation \\(\\pmb {u}_x^r\\in \\mathbb{R}^d\\) . It decodes the message \\(m\\) into a representation \\(\\pmb {z}\\in \\mathbb{R}^{d}\\) and computes a matching score between each encoded candidate and the message representation, \\(g(z,\\pmb {u}_x^r)\\) . A candidate is predicted as a target if its score is \\(>0.5\\) . The entire system—sender and receiver networks—is trained jointly with a binary cross entropy on correctly identifying each target."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.509,
+                0.286,
+                0.742,
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+            ],
+            "angle": 0,
+            "content": "2.2 Compositionality in EC"
+        },
+        {
+            "type": "text",
+            "bbox": [
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+                0.308,
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+            ],
+            "angle": 0,
+            "content": "Various measures have been proposed to evaluate if an EC protocol is compositional. We mention a few prominent ones below. However, while trying to capture the idea that a complex meaning uses the meaning of its parts, previous measures fail to provide a concrete mapping of parts—EC words and NL concepts. We say an emergent communication is compositional if the following conditions hold:"
+        },
+        {
+            "type": "text",
+            "bbox": [
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+                0.439,
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+            ],
+            "angle": 0,
+            "content": "1. EC words are mapped to NL concepts."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.524,
+                0.457,
+                0.882,
+                0.488
+            ],
+            "angle": 0,
+            "content": "2. A complex EC message is composed of simple EC words."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.524,
+                0.492,
+                0.884,
+                0.525
+            ],
+            "angle": 0,
+            "content": "3. Agents communicate successfully via complex messages."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.524,
+                0.527,
+                0.883,
+                0.575
+            ],
+            "angle": 0,
+            "content": "4. An EC message composed of words has the same meaning as an NL phrase composed of the respective concepts."
+        },
+        {
+            "type": "list",
+            "bbox": [
+                0.524,
+                0.439,
+                0.884,
+                0.575
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.508,
+                0.577,
+                0.884,
+                0.625
+            ],
+            "angle": 0,
+            "content": "Being able to compose EC words while preserving their NL meaning allows agents to generalize to new data while using interpretable communication."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.509,
+                0.632,
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+            ],
+            "angle": 0,
+            "content": "2.3 Compositionality Evaluations in EC"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.508,
+                0.655,
+                0.885,
+                0.687
+            ],
+            "angle": 0,
+            "content": "We briefly describe two notable measures of compositionality in EC. Appendix A gives more details."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.508,
+                0.694,
+                0.884,
+                0.821
+            ],
+            "angle": 0,
+            "content": "Topographic Similarity (TopSim) (Brighton and Kirby, 2006) measures how well messages align with object representations. Given a set of objects and their EC messages, calculate a matrix of distances between every two messages and a separate matrix of distances between every two object representations. TopSim is the Spearman correlation of the two distance matrices."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.508,
+                0.823,
+                0.884,
+                0.919
+            ],
+            "angle": 0,
+            "content": "TopSim is a global metric that does not require a reference language and can be applied to any EC setup. However, recent studies found that TopSim does not correlate well with success in the task being played (Chaabouni et al., 2021; Yao et al., 2022). More importantly, it does not provide a"
+        },
+        {
+            "type": "page_footnote",
+            "bbox": [
+                0.136,
+                0.904,
+                0.446,
+                0.919
+            ],
+            "angle": 0,
+            "content": "In this work we only use conjunctive expressions."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.928,
+                0.521,
+                0.941
+            ],
+            "angle": 0,
+            "content": "3187"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.113,
+                0.085,
+                0.486,
+                0.116
+            ],
+            "angle": 0,
+            "content": "mapping between EC words and NL concepts, and thus cannot directly assess compositionality."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.113,
+                0.118,
+                0.487,
+                0.262
+            ],
+            "angle": 0,
+            "content": "Adjusted Mutual Information (AMI) (Vinh et al., 2009) measures the MIT between a set of EC messages and a corresponding set of NL phrases, adjusted for chance. Mu and Goodman (2021) showed AMI is a better compositionality measure than TopSim, as it directly assesses the MI between a message and its NL phrases. Still, AMI operates at the level of messages and phrases, rather than atomic words and concepts, respectively."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.114,
+                0.268,
+                0.351,
+                0.284
+            ],
+            "angle": 0,
+            "content": "3 Concept Best Matching"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.113,
+                0.29,
+                0.49,
+                0.581
+            ],
+            "angle": 0,
+            "content": "Our key insight is that compositionality requires a mapping between words (atomic parts of EC messages) and concepts (a set of FVPs) that compose NL phrases. Given an evaluation set of examples \\(D\\), consider their corresponding EC messages \\(\\mathbb{M}\\) and NL phrases \\(\\mathbb{L}\\). Let \\(\\mathbb{W}\\) denote the set of unique words in \\(\\mathbb{M}\\), and \\(\\mathbb{V}\\) the set of unique FVPs in \\(\\mathbb{L}\\). Let \\(\\{w\\}_i, \\{v\\}_i\\) be the sets of words and FVPs in sample \\(i\\), and \\(m_i = |\\{w\\}_i|, l_i = |\\{v\\}_i|\\) their sizes. We construct a weighted bipartite graph \\(\\mathcal{G} = ((\\mathbb{W}, \\mathbb{V}), \\mathbb{E})\\) with words on one side and FVPs on the other side. Edges \\(\\mathbb{E}\\) are defined by the evaluation set. The weight \\(q_e\\) of edge \\(e_{ij}\\) is the number of times word \\(i\\) appeared in a message that the sender transmitted for a labeling rule with FVP \\(j\\). This construction reflects the intuition that we do not know the correct mapping between words and FVPs (concepts). See Figure 1 for an example."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.114,
+                0.587,
+                0.338,
+                0.601
+            ],
+            "angle": 0,
+            "content": "3.1 Best Match Algorithm"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.113,
+                0.608,
+                0.49,
+                0.703
+            ],
+            "angle": 0,
+            "content": "Given the graph \\(\\mathcal{G}\\), we seek an optimal pairing between words and concepts (FVPs), such that no two edges share the same word nor the same concept. The score of a match \\(\\mathbb{B} \\subseteq \\mathbb{E}\\) is the sum of its edge weights, \\(\\sum_{e \\in \\mathbb{B}} q_e\\). The best match, \\(\\mathrm{BM} = \\mathrm{BM}(\\mathcal{G})\\), maximizes this score:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.205,
+                0.713,
+                0.488,
+                0.747
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathrm {B M} = \\underset {\\mathbb {B}} {\\operatorname {a r g m a x}} \\sum_ {e \\in \\mathbb {B}} q _ {e} \\tag {1}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.113,
+                0.757,
+                0.488,
+                0.804
+            ],
+            "angle": 0,
+            "content": "Such an ideal mapping is fully interpretable. A high score indicates that the agents learned to generate a unique EC word for each NL concept."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.113,
+                0.805,
+                0.489,
+                0.886
+            ],
+            "angle": 0,
+            "content": "Normalizing the BM score by the number of symbols and words, \\( Q = \\sum_{i\\in D}\\max (|m_i|,|l_i|) \\), guarantees that \\( \\mathrm{BM}\\in [0,1] \\). The best match for a weighted bipartite graph can be found efficiently by the Hungarian algorithm (Kuhn, 1955;"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.509,
+                0.085,
+                0.885,
+                0.116
+            ],
+            "angle": 0,
+            "content": "Hopcroft and Karp, 1973). Implementation is provided here."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.509,
+                0.123,
+                0.719,
+                0.14
+            ],
+            "angle": 0,
+            "content": "4 Experimental Setup"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.508,
+                0.146,
+                0.884,
+                0.274
+            ],
+            "angle": 0,
+            "content": "We experiments with agents that learn to play multi-target referential games, introduced by Mu and Goodman (2021) and described in Section 2.1. All experiments reported in Table 1 have the number of possible words \\(\\geq\\) the number of concepts, allowing perfect match of words to concepts. In Appendix D we report more experiments with sub-optimal configurations."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.508,
+                0.282,
+                0.884,
+                0.313
+            ],
+            "angle": 0,
+            "content": "Datasets. We experiment with two datasets, described briefly here; Appendix B has more details."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.509,
+                0.314,
+                0.883,
+                0.409
+            ],
+            "angle": 0,
+            "content": "(1) SHAPE: A visual reasoning dataset (Kuhnle and Copestake, 2017) of objects over a black background. Our version of the dataset contains four attributes: shape, color, and horizontal and vertical positions. Overall, the SHAPE dataset contains 17 concepts, and a maximal labeling rule of 4 FVPs."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.509,
+                0.41,
+                0.884,
+                0.474
+            ],
+            "angle": 0,
+            "content": "(2) THING: A synthetic dataset of 100,000 objects. Each object has five attributes, each with 10 possible values. Overall, the THING datasets contains 50 concepts and a maximal labeling rule of 5 FVPs."
+        },
+        {
+            "type": "list",
+            "bbox": [
+                0.509,
+                0.314,
+                0.884,
+                0.474
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.508,
+                0.481,
+                0.884,
+                0.658
+            ],
+            "angle": 0,
+            "content": "Communication Channel. We train the system with two types of communication channels: the popular Gumbel-Softmax (GS) (Havylov and Titov, 2017; Jang et al., 2017) and quantized communication (QT) (Carmeli et al., 2023). In GS, each word is a \\(d\\)-dimensional one-hot vector. In QT, each word is a \\(d\\)-dimensional binary vector. QT was shown to be superior and easier to optimize compared to GS in EC games. In both cases we use a recurrent network to generate multi-word messages. Appendix C has implementation details."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.509,
+                0.664,
+                0.608,
+                0.679
+            ],
+            "angle": 0,
+            "content": "5 Results"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.508,
+                0.687,
+                0.884,
+                0.896
+            ],
+            "angle": 0,
+            "content": "Table 1 shows results on several configurations of the two games. As expected, accuracy degrades as the task becomes more difficult, with longer labeling rules. QT communication yields better task accuracy than GS, consistent with Carmeli et al. (2023). TopSim is not well correlated with accuracy, as found in prior work (Section 2.3). AMI and CBM are more correlated with accuracy. With long messages and labeling rules (\\(l = 4\\)), AMI is less correlated with accuracy. This may be explained by AMI operating at the level of whole messages and labeling rules—AMI struggles with large numbers of unique messages and NL phrases. In contrast,"
+        },
+        {
+            "type": "page_footnote",
+            "bbox": [
+                0.53,
+                0.904,
+                0.822,
+                0.918
+            ],
+            "angle": 0,
+            "content": "<sup>3</sup>https://github.com/bcarmeli/cbm"
+        },
+        {
+            "type": "page_footnote",
+            "bbox": [
+                0.113,
+                0.892,
+                0.488,
+                0.919
+            ],
+            "angle": 0,
+            "content": "2In practice, the lowest bound is \\(q_{\\tilde{e}} / Q\\) , where \\(\\tilde{e}\\) is the edge with the highest weight in \\(\\mathcal{G}\\)"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
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+            ],
+            "angle": 0,
+            "content": "3188"
+        }
+    ],
+    [
+        {
+            "type": "table",
+            "bbox": [
+                0.118,
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+            ],
+            "angle": 0,
+            "content": "<table><tr><td rowspan=\"2\"></td><td rowspan=\"2\">Com</td><td rowspan=\"2\">l</td><td rowspan=\"2\">d</td><td colspan=\"2\">NL</td><td colspan=\"2\">EC</td><td rowspan=\"2\">Acc</td><td rowspan=\"2\">Top Sim</td><td rowspan=\"2\">AMI</td><td colspan=\"4\">Best Match</td></tr><tr><td>Cons</td><td>Phrs</td><td>#w</td><td>#m</td><td>CBM</td><td>Amb</td><td>Para</td><td>Unm</td></tr><tr><td rowspan=\"4\">Shape</td><td>GS</td><td>1</td><td>17</td><td>17</td><td>17</td><td>11</td><td>11</td><td>0.84</td><td>0.44</td><td>0.76</td><td>0.62</td><td>0.37</td><td>0.01</td><td>0.25</td></tr><tr><td>QT</td><td>1</td><td>5</td><td>17</td><td>17</td><td>26</td><td>26</td><td>0.87</td><td>0.39</td><td>0.85</td><td>0.52</td><td>0.41</td><td>0.08</td><td>0</td></tr><tr><td>GS</td><td>4</td><td>17</td><td>17</td><td>34</td><td>16</td><td>226</td><td>0.78</td><td>0.34</td><td>0.38</td><td>0.52</td><td>0.48</td><td>0</td><td>0.01</td></tr><tr><td>QT</td><td>4</td><td>5</td><td>17</td><td>34</td><td>26</td><td>187</td><td>0.83</td><td>0.23</td><td>0.37</td><td>0.55</td><td>0.37</td><td>0.08</td><td>0</td></tr><tr><td rowspan=\"4\">Thing</td><td>GS</td><td>1</td><td>50</td><td>50</td><td>50</td><td>18</td><td>18</td><td>0.86</td><td>0.45</td><td>0.72</td><td>0.38</td><td>0.62</td><td>0</td><td>0.55</td></tr><tr><td>QT</td><td>1</td><td>6</td><td>50</td><td>50</td><td>50</td><td>50</td><td>0.92</td><td>0.07</td><td>0.74</td><td>0.73</td><td>0.25</td><td>0.02</td><td>0</td></tr><tr><td>GS</td><td>4</td><td>50</td><td>50</td><td>901</td><td>36</td><td>198</td><td>0.63</td><td>0.33</td><td>0.03</td><td>0.24</td><td>0.76</td><td>0</td><td>0.28</td></tr><tr><td>QT</td><td>4</td><td>6</td><td>50</td><td>901</td><td>64</td><td>450</td><td>0.77</td><td>0.14</td><td>0.05</td><td>0.23</td><td>0.69</td><td>0.08</td><td>0</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.113,
+                0.283,
+                0.884,
+                0.342
+            ],
+            "angle": 0,
+            "content": "Table 1: Results for SHAPE and THING games with Gumbel-Softmax (GS) or Quantized (QT) communication using rules of length \\( l \\) and words of length \\( d \\), showing number of unique NL concepts (Cons) and phrases (Phrs) and EC words (\\#w) and messages (#m). TopSim and AMI give only coarse scores. Our method gives the best match score (CBM) and rates of Ambiguities (Amb), Paraphrases (Para), and Unmatched concepts (Unm)."
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.128,
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+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
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+            ],
+            "angle": 0,
+            "content": "Figure 2: The word \\(\\leftrightarrow\\) FVP best-match graph for the SHAPE game (GS communication, \\(l = 1\\)). The algorithm matched just 10 concepts to EC words out of 17 possible concepts."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.113,
+                0.5,
+                0.489,
+                0.564
+            ],
+            "angle": 0,
+            "content": "CBM assesses word-to-concept matching, so it is less affected by long messages and rules. However, AMI and CBM are well correlated (Pearson 0.7 and 0.79 on the SHAPE and THING games)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.113,
+                0.565,
+                0.489,
+                0.773
+            ],
+            "angle": 0,
+            "content": "The table also shows the rate of ambiguities and paraphrases, exposed by our method. Ambiguities happen when the same EC word is mapped to different concepts. Table 1 shows higher rates of ambiguities in GS compared to QT, and in longer rules. Paraphrases are EC words that do not have a best-matched concept node. Paraphrases occur more with QT, which enables 32 and 64 unique EC words for the SHAPE and THING games, while these games have only 17 and 50 NL concepts, respectively. GS allows setting the number of unique words equal to number of concepts, thus is less exposed to this sub-optimal phenomenon."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.113,
+                0.775,
+                0.49,
+                0.92
+            ],
+            "angle": 0,
+            "content": "Finally, Unmatched concepts have no matching EC word. They result from a too narrow or underutilized channel. As Table 1 shows, GS communication suffers from a high rate of unmatched concepts (up to 0.5). This phenomenon can be observed by the low # of unique words (18) compared to # of unique concepts (50) for the THING game with GS and \\( l = 1 \\). QT has a sufficient number of words and thus no unmatched concepts."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.508,
+                0.5,
+                0.885,
+                0.676
+            ],
+            "angle": 0,
+            "content": "Example Match. Beyond global scores, the CBM provides an interpretable translation graph, which maps EC words to NL concepts, facilitating insights on reasons for sub-optimal communication. Figure 2 shows an example graph for the SHAPE game with GS communication. As seen, the algorithm successfully matched 10 EC words to 10 concepts. The sender generated 11 unique words in this experiment, indicating that one word is a paraphrase of an already matched concept, even within this narrow-channel setup."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.509,
+                0.682,
+                0.642,
+                0.697
+            ],
+            "angle": 0,
+            "content": "6 Conclusion"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.508,
+                0.705,
+                0.885,
+                0.898
+            ],
+            "angle": 0,
+            "content": "We proposed a new procedure for assessing compositionality of emergent communication. In contrast to other evaluations, our procedure provides a human-interpretable translation map of emerged words to natural concepts. Moreover, our approach provides detailed insights into the reasons for suboptimal translation. We demonstrated it on two EC games with two different communication types. Our evaluation reveals even that quantized communication performs better than Gumbel-softmax, yet none exhibits compositionality in a level similar to natural language."
+        },
+        {
+            "type": "page_footnote",
+            "bbox": [
+                0.53,
+                0.905,
+                0.86,
+                0.919
+            ],
+            "angle": 0,
+            "content": "4The exact configuration is given in Table 1, first row."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.928,
+                0.521,
+                0.941
+            ],
+            "angle": 0,
+            "content": "3189"
+        }
+    ],
+    [
+        {
+            "type": "title",
+            "bbox": [
+                0.115,
+                0.085,
+                0.221,
+                0.1
+            ],
+            "angle": 0,
+            "content": "Limitations"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.113,
+                0.107,
+                0.49,
+                0.237
+            ],
+            "angle": 0,
+            "content": "Our analysis is limited to datasets where gold label phrases exist. The evaluated dataset should be composable and the gold language should use finite set of concepts. Preferably, these concepts can be classified into several categories. We further assume an Oracle function that can divide the objects to targets and distractors during training. Importantly, our approach does not require labels during training."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.115,
+                0.243,
+                0.287,
+                0.259
+            ],
+            "angle": 0,
+            "content": "Acknowledgements"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.113,
+                0.266,
+                0.49,
+                0.412
+            ],
+            "angle": 0,
+            "content": "This research was supported by grant no. 2022330 from the United States - Israel Binational Science Foundation (BSF), Jerusalem, Israel. The research of YB was also supported by the Israel Science Foundation (grant 448/20), an Azrieli Foundation Early Career Faculty Fellowship, and an AI Alignment grant from Open Philanthropy. The work of RM was partially supported by the Skillman chair in biomedical sciences and by the Ollendorf center."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.115,
+                0.433,
+                0.214,
+                0.449
+            ],
+            "angle": 0,
+            "content": "References"
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+            "angle": 0,
+            "content": null
+        },
+        {
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+            "bbox": [
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+                0.522,
+                0.941
+            ],
+            "angle": 0,
+            "content": "3190"
+        }
+    ],
+    [
+        {
+            "type": "title",
+            "bbox": [
+                0.115,
+                0.085,
+                0.22,
+                0.101
+            ],
+            "angle": 0,
+            "content": "Appendices"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.115,
+                0.11,
+                0.427,
+                0.126
+            ],
+            "angle": 0,
+            "content": "A Details on Evaluation Measures"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.114,
+                0.135,
+                0.49,
+                0.246
+            ],
+            "angle": 0,
+            "content": "We provide here information on how to calculate the topographic similarity (TopSim) (Brighton and Kirby, 2006; Lazaridou et al., 2018; Yao et al., 2022) and adjusted mutual information (AMI) measures (Vinh et al., 2009; Mu and Goodman, 2021), in the context of EC. Refer to the original papers for full details."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.114,
+                0.257,
+                0.49,
+                0.45
+            ],
+            "angle": 0,
+            "content": "Topographic Similarity. The topographic similarity measures how messages align with the object representations. Concretely, let \\(\\cos_{ij} = \\cos (\\pmb{x}_i,\\pmb{x}_j) = \\pmb{x}_i\\cdot \\pmb{x}_j / (||\\pmb{x}_i||_2||\\pmb{x}_j||_2)\\) be the cosine similarity of object representations \\(\\pmb{x}_i\\) and \\(\\pmb{x}_j\\) and \\(\\mathrm{edit}_{ij} = \\mathrm{edit}(m_i,m_j)\\) be the Levenshtein distance (Levenshtein et al., 1966) between messages \\(m_{i}\\) and \\(m_j\\). Let \\(\\mathrm{ncos} = -\\{\\cos_{ij}\\}_{ij}\\) be the list of negative cosine similarities, \\(\\mathrm{edit} = \\{\\mathrm{edit}_{ij}\\}_{ij}\\) the list of Levenshtein distances, and \\(R(\\cdot)\\) the ranking function. Then the topographic similarity is the Spearman rank correlation of the two matrices:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.182,
+                0.466,
+                0.488,
+                0.484
+            ],
+            "angle": 0,
+            "content": "\\[\n\\operatorname {T o p s i m} = \\rho (R (\\operatorname {e d i t}), R (\\operatorname {n c o s})) \\tag {2}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.114,
+                0.5,
+                0.44,
+                0.516
+            ],
+            "angle": 0,
+            "content": "where \\(\\rho\\) is the standard Pearson correlation."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.114,
+                0.518,
+                0.489,
+                0.662
+            ],
+            "angle": 0,
+            "content": "Topographic similarity is a global metric that does not require a reference language and can be easily applied to every EC setup. However, despite its popularity, recent studies found that topographic similarity does not correlate well with success in the task being played (Chaabouni et al., 2021; Yao et al., 2022). More important, it does not provide a mapping between EC atoms and NL concepts, and thus cannot directly assess compositionality."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.114,
+                0.672,
+                0.49,
+                0.799
+            ],
+            "angle": 0,
+            "content": "Adjusted Mutual Information. Given a test set \\(D\\), let \\(\\mathbb{M}\\) denote the set of messages generated by the sender and \\(\\mathbb{L}\\) denote the set of NL phrases (e.g., Red Triangle, Blue Square) exist as labels in the data. The adjusted mutual information (AMI) (Vinh et al., 2009) measures the mutual information between messages and labels, adjusted for chance:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.13,
+                0.811,
+                0.488,
+                0.842
+            ],
+            "angle": 0,
+            "content": "\\[\n\\operatorname {A M I} (M, L) = \\frac {I (M , L) - \\mathbb {E} (I (M , L)}{\\max  (H (M) , H (L)) - \\mathbb {E} (I (M , L))} \\tag {3}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.114,
+                0.855,
+                0.489,
+                0.919
+            ],
+            "angle": 0,
+            "content": "where \\(I(M,L)\\) is the mutual information between \\(M\\) and \\(L\\), \\(H(\\cdot)\\) is the entropy, and \\(\\mathbb{E}(I(M,L))\\) is computed with respect to a hypergeometric model of randomness."
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.588,
+                0.105,
+                0.817,
+                0.267
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.509,
+                0.296,
+                0.883,
+                0.34
+            ],
+            "angle": 0,
+            "content": "Figure 3: The SHAPE dataset, presenting one turn. Top 8 images are Yellow targets. Bottom 8 images are distractors."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.51,
+                0.365,
+                0.623,
+                0.381
+            ],
+            "angle": 0,
+            "content": "B Datasets"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.508,
+                0.389,
+                0.882,
+                0.421
+            ],
+            "angle": 0,
+            "content": "We use two datasets in our experiments. Both will be made publicly available."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.508,
+                0.428,
+                0.884,
+                0.605
+            ],
+            "angle": 0,
+            "content": "Shape. A visual reasoning dataset (Kuhnle and Copestake, 2017) of objects over a black background. Our version of the dataset contains four attributes: the shape attribute has five shapes, the color attribute has six colors. To these we added horizontal and vertical position attributes each with three values. Overall, the SHAPE dataset contains 17 concepts, and a maximal labeling rule of 4 FVPs which sum to 270 unique 4-concept labels. The dataset contains many images that obey the same label. See Figure 3 for an example."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.508,
+                0.612,
+                0.884,
+                0.741
+            ],
+            "angle": 0,
+            "content": "Thing. A synthetic dataset of 100,000 objects which we design for controlled experiments. Each object in the dataset has five attributes, each with 10 possible values. Overall, the THING datasets contains 50 concepts and a maximal labeling rule of 5 FVPs. We experiments with label lengths varied from 1, describing a single concept, to 5, which completely describes an object in the dataset."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.509,
+                0.748,
+                0.753,
+                0.764
+            ],
+            "angle": 0,
+            "content": "C Implementation Details"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.508,
+                0.771,
+                0.885,
+                0.883
+            ],
+            "angle": 0,
+            "content": "We run all experiments over a modified version of the Egg framework (Kharitonov et al., 2019). In our version the communication modules used by the sender and the receiver are totally separated from their perceptual modules, which we term 'agents'. The Quantized (QT) and Gumbel-Softmax (GS) protocols are implemented at the"
+        },
+        {
+            "type": "page_footnote",
+            "bbox": [
+                0.51,
+                0.892,
+                0.885,
+                0.919
+            ],
+            "angle": 0,
+            "content": "Our modification is available at https://github. com/bcarmeli/egg_qtc."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.928,
+                0.519,
+                0.941
+            ],
+            "angle": 0,
+            "content": "3191"
+        }
+    ],
+    [
+        {
+            "type": "table",
+            "bbox": [
+                0.174,
+                0.094,
+                0.825,
+                0.159
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Batch Size</td><td>lr</td><td>Num Targets</td><td>Num Distr</td><td>Cell Type</td><td>Sender Hidden</td><td>Sender Embed</td><td>Receiver Hidden</td><td>Receiver Embed</td></tr><tr><td>10</td><td>0.0005</td><td>8/20</td><td>8/20</td><td>LSTM</td><td>60</td><td>60</td><td>40</td><td>40</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.289,
+                0.169,
+                0.707,
+                0.184
+            ],
+            "angle": 0,
+            "content": "Table 2: Hyper-parameters for the agents in the SHAPE game."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.221,
+                0.212,
+                0.779,
+                0.491
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Exp Num</td><td>Game</td><td>Comm Type</td><td>Label Len</td><td>word Len</td><td>Msg Len</td><td>Best Epoch</td><td>ACC</td><td>AMI</td><td>Best Match</td></tr><tr><td>1</td><td>SHAPE</td><td>gs</td><td>1</td><td>8</td><td>4</td><td>97</td><td>0.829</td><td>0.404</td><td>0.405</td></tr><tr><td>2</td><td>SHAPE</td><td>gs</td><td>1</td><td>64</td><td>4</td><td>96</td><td>0.843</td><td>0.390</td><td>0.339</td></tr><tr><td>3</td><td>SHAPE</td><td>gs</td><td>4</td><td>8</td><td>1</td><td>8</td><td>0.742</td><td>0.490</td><td>0.152</td></tr><tr><td>4</td><td>SHAPE</td><td>gs</td><td>4</td><td>64</td><td>1</td><td>10</td><td>0.748</td><td>0.413</td><td>0.130</td></tr><tr><td>5</td><td>SHAPE</td><td>qt</td><td>1</td><td>3</td><td>4</td><td>86</td><td>0.878</td><td>0.540</td><td>1.401</td></tr><tr><td>6</td><td>SHAPE</td><td>qt</td><td>1</td><td>64</td><td>4</td><td>85</td><td>0.991</td><td>0.000</td><td>0.001</td></tr><tr><td>7</td><td>SHAPE</td><td>qt</td><td>4</td><td>3</td><td>1</td><td>9</td><td>0.768</td><td>0.474</td><td>0.152</td></tr><tr><td>8</td><td>SHAPE</td><td>qt</td><td>4</td><td>64</td><td>1</td><td>12</td><td>0.897</td><td>0.021</td><td>0.009</td></tr><tr><td>9</td><td>THING</td><td>gs</td><td>1</td><td>8</td><td>4</td><td>83</td><td>0.793</td><td>0.102</td><td>0.091</td></tr><tr><td>10</td><td>THING</td><td>gs</td><td>1</td><td>64</td><td>4</td><td>94</td><td>0.798</td><td>0.074</td><td>0.151</td></tr><tr><td>11</td><td>THING</td><td>gs</td><td>4</td><td>8</td><td>1</td><td>97</td><td>0.655</td><td>0.016</td><td>0.052</td></tr><tr><td>12</td><td>THING</td><td>gs</td><td>4</td><td>64</td><td>1</td><td>99</td><td>0.626</td><td>0.014</td><td>0.058</td></tr><tr><td>13</td><td>THING</td><td>qt</td><td>1</td><td>3</td><td>4</td><td>96</td><td>0.838</td><td>0.267</td><td>0.119</td></tr><tr><td>14</td><td>THING</td><td>qt</td><td>1</td><td>64</td><td>4</td><td>100</td><td>0.973</td><td>0.000</td><td>0.014</td></tr><tr><td>15</td><td>THING</td><td>qt</td><td>4</td><td>3</td><td>1</td><td>26</td><td>0.622</td><td>0.020</td><td>0.057</td></tr><tr><td>16</td><td>THING</td><td>qt</td><td>4</td><td>64</td><td>1</td><td>96</td><td>0.844</td><td>0.000</td><td>0.013</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.114,
+                0.501,
+                0.884,
+                0.543
+            ],
+            "angle": 0,
+            "content": "Table 3: Configurations for more SHAPE and THING game experiments. In these configuration we intentionally define sub-optimal communication parameters in order to demonstrate the usefulness of the evaluation metrics. Experiment results are provided in Table 4"
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.139,
+                0.572,
+                0.86,
+                0.852
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Exp Num</td><td>Unq Msgs</td><td>Unq Wrds</td><td>Unq Prs</td><td>Ung Cons</td><td>Totl Edgs</td><td>Good Edgs</td><td>Amb Edgs</td><td>Phrs Edgs</td><td>Totl Cons</td><td>Unm Cons</td><td>Par Scor</td><td>Prc</td><td>Rcl</td></tr><tr><td>1</td><td>258</td><td>7</td><td>17</td><td>17</td><td>4k</td><td>1621</td><td>2379</td><td>0</td><td>1k</td><td>444</td><td>0</td><td>0.137</td><td>0.546</td></tr><tr><td>2</td><td>442</td><td>55</td><td>17</td><td>17</td><td>4k</td><td>1356</td><td>1724</td><td>920</td><td>1k</td><td>0</td><td>0.23</td><td>0.144</td><td>0.577</td></tr><tr><td>3</td><td>8</td><td>8</td><td>34</td><td>17</td><td>4k</td><td>610</td><td>390</td><td>0</td><td>4k</td><td>1457</td><td>0</td><td>0.61</td><td>0.152</td></tr><tr><td>4</td><td>44</td><td>44</td><td>34</td><td>17</td><td>4k</td><td>520</td><td>326</td><td>154</td><td>4k</td><td>0</td><td>0.04</td><td>0.52</td><td>0.13</td></tr><tr><td>5</td><td>238</td><td>8</td><td>17</td><td>17</td><td>4k</td><td>1605</td><td>2395</td><td>0</td><td>1k</td><td>385</td><td>0</td><td>0.144</td><td>0.577</td></tr><tr><td>6</td><td>1000</td><td>3899</td><td>17</td><td>17</td><td>4k</td><td>46</td><td>0</td><td>3954</td><td>1k</td><td>0</td><td>0.99</td><td>0.011</td><td>0.044</td></tr><tr><td>7</td><td>7</td><td>7</td><td>34</td><td>17</td><td>4k</td><td>607</td><td>393</td><td>0</td><td>4k</td><td>1727</td><td>0</td><td>0.607</td><td>0.152</td></tr><tr><td>8</td><td>974</td><td>974</td><td>34</td><td>17</td><td>4k</td><td>38</td><td>0</td><td>962</td><td>4k</td><td>0</td><td>0.24</td><td>0.038</td><td>0.009</td></tr><tr><td>9</td><td>543</td><td>7</td><td>50</td><td>50</td><td>4k</td><td>366</td><td>3634</td><td>0</td><td>1k</td><td>807</td><td>0</td><td>0.048</td><td>0.19</td></tr><tr><td>10</td><td>806</td><td>60</td><td>50</td><td>50</td><td>4k</td><td>601</td><td>3369</td><td>30</td><td>1k</td><td>0</td><td>0.01</td><td>0.1</td><td>0.399</td></tr><tr><td>11</td><td>8</td><td>8</td><td>901</td><td>50</td><td>4k</td><td>210</td><td>790</td><td>0</td><td>4k</td><td>3332</td><td>0</td><td>0.21</td><td>0.052</td></tr><tr><td>12</td><td>21</td><td>21</td><td>901</td><td>50</td><td>4k</td><td>233</td><td>767</td><td>0</td><td>4k</td><td>2267</td><td>0</td><td>0.233</td><td>0.058</td></tr><tr><td>13</td><td>412</td><td>8</td><td>50</td><td>50</td><td>4k</td><td>478</td><td>3522</td><td>0</td><td>1k</td><td>795</td><td>0</td><td>0.046</td><td>0.184</td></tr><tr><td>14</td><td>1000</td><td>3991</td><td>50</td><td>50</td><td>4k</td><td>57</td><td>0</td><td>3943</td><td>1k</td><td>0</td><td>0.99</td><td>0.013</td><td>0.052</td></tr><tr><td>15</td><td>11</td><td>6</td><td>901</td><td>50</td><td>4k</td><td>229</td><td>771</td><td>0</td><td>4k</td><td>3483</td><td>0</td><td>0.229</td><td>0.057</td></tr><tr><td>16</td><td>1000</td><td>1000</td><td>901</td><td>50</td><td>4k</td><td>50</td><td>0</td><td>950</td><td>4k</td><td>0</td><td>0.24</td><td>0.05</td><td>0.013</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.113,
+                0.861,
+                0.884,
+                0.903
+            ],
+            "angle": 0,
+            "content": "Table 4: Results for more SHAPE and THING game configurations described in Table 3. In these experiments we intentionally define sub-optimal communication parameters in order to demonstrate the usefulness of the evaluation metrics."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.929,
+                0.522,
+                0.941
+            ],
+            "angle": 0,
+            "content": "3192"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.113,
+                0.085,
+                0.49,
+                0.228
+            ],
+            "angle": 0,
+            "content": "communication layer. For GS we use an implementation provided by the Egg framework, where we do not allow temperature to be learned, and set the straight-through estimator to False. For QT we followed parameter recommendations from Carmeli et al. (2023) and use a binary quantization in all experiments. Both GS and QT uses a recurrent neural network (RNN) for generating multiple words in a message. See Table 2 for RNN details."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.117,
+                0.231,
+                0.49,
+                0.55
+            ],
+            "angle": 0,
+            "content": "The agents for the THING game use fully connected feed-forward networks with input dimension of \\( d = 270 \\). Objects are encoded by concatenating five one-hot vectors, one per attribute. There are 50 unique values and 4 communication words (SOS, EOS, PAD, UNK), thus the total object representation length is \\( d = 270 \\). The agents of the SHAPE game are implemented with a convolutional neural network similar to Mu and Goodman (2021). Network hyper-parameters are provided in Table 2. In the experiments, we report results when varying the communication elements (word length and message length). Experiments in Table 1 are done with 20 targets and 20 distractors, while experiments reported in Tables 3 and 4 are done with 8 targets and 8 distractors. Our main interest in this work is to evaluate the emerged communication and not to achieve the best possible performance, thus we did not conduct a thorough hyper-parameter search for the agents themselves."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.113,
+                0.552,
+                0.489,
+                0.633
+            ],
+            "angle": 0,
+            "content": "We run all experiments on a single A100 GPU with 40 GB of RAM. Model size is less than 10M. We usually trained the model for 200 epochs which took about 10 hours to complete. Our code will be made publicly available upon de-anonymization."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.114,
+                0.639,
+                0.486,
+                0.656
+            ],
+            "angle": 0,
+            "content": "D Evaluating Sub-optimal Configurations"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.113,
+                0.662,
+                0.489,
+                0.806
+            ],
+            "angle": 0,
+            "content": "Here we provide results from experiments with several sub-optimal configurations and demonstrate how CBM identifies these deficiencies. We report configuration parameters for each experiment together with accuracy, AMI, and CBM Score in Table 3. We report all CBM metrics for these experiments in Table 4. Information from the two tables is aligned by the experiment number (first column)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.113,
+                0.807,
+                0.49,
+                0.919
+            ],
+            "angle": 0,
+            "content": "Sub-optimal communication may stem from a channel that is either too wide or too narrow. Narrow channels are restricted by a small number of words and short messages. Wide channels allow long words and/or long messages. Past studies (Tucker et al., 2022) suggest that creating an information bottleneck by narrowing the channel en"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.537,
+                0.094,
+                0.858,
+                0.224
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.508,
+                0.238,
+                0.886,
+                0.309
+            ],
+            "angle": 0,
+            "content": "Figure 4: Assessing CBM sensitivity to the size of the evaluation set. We show results for two randomly selected experiments. As seen, the CBM score stabilizes when assessing datasets comprising more than 500 samples."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.507,
+                0.335,
+                0.885,
+                0.543
+            ],
+            "angle": 0,
+            "content": "courages generalization. As seen, CBM scores for most reported sub-optimal configurations are low. Results from experiments 1, 2, and 5 are the only ones for which the CBM score is higher than 0.2. Experiment 6 (SHAPE) achieves almost perfect accuracy (0.991) due to its wide channel. However, the paraphrase score for this experiment is 0.989 showing that the sender uses many different words to refer to the same concept. This phenomenon can also be seen by the large number of unique words (3899) generated for just 17 unique concepts. A similar phenomenon is observed for the THING game (experiment 14)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.508,
+                0.544,
+                0.886,
+                0.8
+            ],
+            "angle": 0,
+            "content": "Experiment 11 (THING) uses a narrow channel. The vocabulary contains only 8 words and the channel allows one-word-long messages. This configuration resulted in 3332 concepts that do not match any word. Interestingly, the number of unmatched concepts remains high even when extending the word length to 64, in experiment 12. We attribute this sub-optimal phenomenon to GS communication deficiencies. The number of unique words generated by the sender in this experiment is only 21 out of the possible 64 words allowed by the configuration. For the SHAPE game, on the other hand, the same wide-channel configuration resulted in 44 unique words generated by the sender for the 17 concepts available in this game and all concepts have matched words."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.508,
+                0.807,
+                0.886,
+                0.919
+            ],
+            "angle": 0,
+            "content": "Precision and recall. After finding the best match, precision and recall between words and concepts can be computed. We define message precision (Prc) and recall (Rcl) to be the number of matched edges in a message, divided by the number of words or concepts, respectively. Precision and recall add insights in situation where the num"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.928,
+                0.521,
+                0.941
+            ],
+            "angle": 0,
+            "content": "3193"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.117,
+                0.085,
+                0.486,
+                0.244
+            ],
+            "angle": 0,
+            "content": "ber of words in messages differs significantly from the number of concepts used for labeling the data. Experiment 5 (SHAPE) shows the highest recall, gained partially due to the long message length (four words) allowed by the channel, compared to the label length (one concept) dictated by the data. In contrast, experiment 3 (SHAPE) shows the highest precision. Indeed, this configuration restricts message the length to one word while the data dictates four-concept long phrases."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.117,
+                0.251,
+                0.425,
+                0.267
+            ],
+            "angle": 0,
+            "content": "E CBM Sensitivity to Dataset Size"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.117,
+                0.274,
+                0.486,
+                0.547
+            ],
+            "angle": 0,
+            "content": "We evaluated CBM scores on increased data sizes. Figure 4 shows results for two randomly selected experiments. The solid lines indicate the CBM score, computed when accumulating data samples in 100 quintets. The dashed lines indicate CBM score calculated independently for 18 successive data segments of 100 samples each. As seen, scores stabilize for evaluation sets of size larger than 500 samples. Interestingly, the 100-sample scores (dashed) lines are higher than the accumulated scores (solid lines). This is in line with our insight that low evaluation sizes result in higher match scores. Standard deviation for the 18 accumulated measures is 0.009 and 0.016, for the two experiments, respectively. Standard deviation for the 18 segmented measures is 0.044 and 0.040, for the two experiments, respectively."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.483,
+                0.929,
+                0.521,
+                0.941
+            ],
+            "angle": 0,
+            "content": "3194"
+        }
+    ]
+]

2024/Concept-Best-Matching_ Evaluating Compositionality In Emergent Communication/4ad4723c-7bbd-4934-855a-91c77ee9c3b0_origin.pdf

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2024/Concept-Best-Matching_ Evaluating Compositionality In Emergent Communication/full.md

@@ -0,0 +1,243 @@
+# Concept-Best-Matching: Evaluating Compositionality in Emergent Communication
+
+Boaz Carmeli Yonatan Belinkov Ron Meir
+
+Technion - Israel Institute of Technology
+
+boaz.carmeli@campus.technion.ac.il,
+
+belinkov@technion.ac.il
+
+rmeir@ee.technion.ac.il
+
+# Abstract
+
+Artificial agents that learn to communicate in order to accomplish a given task acquire communication protocols that are typically opaque to a human. A large body of work has attempted to evaluate the emergent communication via various evaluation measures, with compositionality featuring as a prominent desired trait. However, current evaluation procedures do not directly expose the compositionality of the emergent communication. We propose a procedure to assess the compositionality of emergent communication by finding the best-match between emerged words and natural language concepts. The best-match algorithm provides both a global score and a translation-map from emergent words to natural language concepts. To the best of our knowledge, it is the first time that such direct and interpretable mapping between emergent words and human concepts is provided.
+
+# 1 Introduction
+
+Artificial agents that learn to communicate for accomplishing a given task acquire communication protocols. In the common setting, a sender observes a set of objects and sends a message to a receiver, which then needs to identify the correct target objects out of a set of distractors. The two agents learn a communication protocol over discrete vocabulary of atoms, termed "words". The emergent communication (EC) is typically opaque to a human. As a result, a large body of work has attempted to characterize the emergent communication in light of natural language (NL) traits, such as compositionality (Hupkes et al., 2020; Chaabouni et al., 2020), systematic generalization (Vani et al., 2021), pragmatism (Andreas and Klein, 2016; Zaslavsky et al., 2021), and more.
+
+Chief among these is compositionality, which enables the construction of complex meanings from the meaning of parts (Li and Bowling, 2019). However, quantifying compositionality in EC is noto
+
+![](images/7efaa4f44ab3e074fc1e43b6503b044d6ba4aabf8d4ff81697e353b25ef2af64.jpg)
+
+![](images/4248688314ed681579968ffdf95456aa4afa808659c530ff77dd1101ed2fe46b.jpg)
+
+![](images/16a18c7c7c695ccd954b3173cff82d6d2a4ebecc235529be5809eb2cdf180752.jpg)
+
+![](images/aa617a2e2f45b037d25b4e706d9638828f86706efeb5073ca5cd8486ab92b152.jpg)
+
+![](images/236bd928f13a6cc074ea83943f5cea6065d12ed3eb431002eff37d053ed888cd.jpg)  
+Figure 1: The multi-target shape game played in turns (showing two turns). (a) At each turn, the sender is given a set of images, a subset of them marked as targets by an Oracle. (b) Sender generates messages  $[w_1, w_2]$  for the blue-triangle (turn 1) and  $[w_2, w_3]$  for the red-triangle (turn 2). (c) During evaluation, we construct a bipartite graph of words generated by the sender and concepts provided by the Oracle for each turn. (d) The best-match algorithm matches EC words to NL concepts and provides the CBM score. In this example, all EC words are matched with NL concepts, resulting in a CBM score of 1.0.
+
+![](images/f02978d4c6f4562f3ae144a079d8597472e6e9040d75faefad646e48a99be6fa.jpg)
+
+![](images/33617a946fab55fb86038746e076be7f423c842a353bb8acbc50ec586bac48ed.jpg)
+
+riously difficult (Lazaridou et al., 2018). In fact, recent studies found that common compositionality measures in EC, e.g., topographic similarity (Brighton and Kirby, 2006; Li and Bowling, 2019), do not correlate well with success in the task (Chaabouni et al., 2021; Yao et al., 2022). Moreover, while seeking to assess an opaque protocol, common evaluation measures in EC are opaque themselves—they do not provide a human-interpretable characterization of the compositionality of the communication.
+
+This work develops a method that characterizes how compositional an EC is. Our method is founded on the key insight that, in an EC setting, a communication is compositional if agents communicate successfully via complex messages formed of simple atoms and these atoms are mapped to NL concepts. Our evaluation is based on the classical
+
+best-match algorithm (Hopcroft and Karp, 1973). Given a set of EC atoms and a set of NL concepts, we construct a bi-partite graph and seek the optimal one-to-one mapping between words and concepts. A perfectly compositional EC would yield a perfect match, where every EC atom is mapped to exactly one NL concept. See Figure 1 for an illustration.
+
+We experiment with the proposed procedure in two EC settings and compare it to two popular evaluation measures - topographic similarity and adjusted mutual information (AMI). We demonstrate that our approach provides a fine-grained characterization of emergent protocols, exposing their strengths and weaknesses, while other measures only provide coarse, opaque scores. According to our evaluation, state-of-the-art communication methods do not achieve satisfactory results.
+
+# 2 Background
+
+# 2.1 Emergent Communication Setup
+
+We follow a recent setup suggested by Mu and Goodman (2021), where a sender needs to communicate with a receiver about a set of target objects out of a larger set of candidate objects. The sender sends a message to the receiver, which uses it to distinguish targets from distractor objects. For example, to identify all red triangles out of objects with different shapes and colors. This setup is more conducive to emergence of compositional communication than the classical referential game (Lazaridou et al., 2017). Senders in this setup need to form a generalization rather than merely transmit the identity of a single target.
+
+Formally, assume a world  $\mathbb{X}$ , where each object is characterised by  $n$  feature-value pairs (FVPs),  $\langle f_1 : v_1, \ldots, f_n : v_n \rangle$ , with feature  $i$  having  $k_i$  possible values,  $v_i \in \{f_i[1], \ldots, f_i[k_i]\}$ . For instance, the Shape world (Kuhnle and Copestake, 2017) has objects like  $\langle \text{shape: triangle, color: red} \rangle$ . Labeling rules are boolean expressions over these FVPs. Each rule  $l : \mathbb{X} \mapsto \{0, 1\}$  labels each object as 0 or 1. For instance, the rule Red Triangle labels all red triangles as positive and all other objects as negative. We identify the rule Red Triangle with the NL phrase "red triangle", which comprises the concepts "red" and "triangle".
+
+At each turn of the game, we draw a set of candidate objects  $\tilde{\mathbb{X}}\subset \mathbb{X}$  that is made of target objects,  $\mathbb{T}$ , which obey the rule, and distractors,  $\mathbb{D}$ , which do not:  $l(x) = 1$  if  $x\in \mathbb{T}$  and  $l(x) = 0$  if  $x\in \mathbb{D}$ .
+
+The sender encodes the set of target objects  $\mathbb{T}$  into a dense representation  $\pmb{u}^s\in \mathbb{R}^d$  , and generates a message  $m$  , a sequence of words from some vocabulary. The receiver encodes each candidate object  $x\in \mathbb{X}$  into a representation  $\pmb {u}_x^r\in \mathbb{R}^d$  . It decodes the message  $m$  into a representation  $\pmb {z}\in \mathbb{R}^{d}$  and computes a matching score between each encoded candidate and the message representation,  $g(z,\pmb {u}_x^r)$  . A candidate is predicted as a target if its score is  $>0.5$  . The entire system—sender and receiver networks—is trained jointly with a binary cross entropy on correctly identifying each target.
+
+# 2.2 Compositionality in EC
+
+Various measures have been proposed to evaluate if an EC protocol is compositional. We mention a few prominent ones below. However, while trying to capture the idea that a complex meaning uses the meaning of its parts, previous measures fail to provide a concrete mapping of parts—EC words and NL concepts. We say an emergent communication is compositional if the following conditions hold:
+
+1. EC words are mapped to NL concepts.  
+2. A complex EC message is composed of simple EC words.  
+3. Agents communicate successfully via complex messages.  
+4. An EC message composed of words has the same meaning as an NL phrase composed of the respective concepts.
+
+Being able to compose EC words while preserving their NL meaning allows agents to generalize to new data while using interpretable communication.
+
+# 2.3 Compositionality Evaluations in EC
+
+We briefly describe two notable measures of compositionality in EC. Appendix A gives more details.
+
+Topographic Similarity (TopSim) (Brighton and Kirby, 2006) measures how well messages align with object representations. Given a set of objects and their EC messages, calculate a matrix of distances between every two messages and a separate matrix of distances between every two object representations. TopSim is the Spearman correlation of the two distance matrices.
+
+TopSim is a global metric that does not require a reference language and can be applied to any EC setup. However, recent studies found that TopSim does not correlate well with success in the task being played (Chaabouni et al., 2021; Yao et al., 2022). More importantly, it does not provide a
+
+mapping between EC words and NL concepts, and thus cannot directly assess compositionality.
+
+Adjusted Mutual Information (AMI) (Vinh et al., 2009) measures the MIT between a set of EC messages and a corresponding set of NL phrases, adjusted for chance. Mu and Goodman (2021) showed AMI is a better compositionality measure than TopSim, as it directly assesses the MI between a message and its NL phrases. Still, AMI operates at the level of messages and phrases, rather than atomic words and concepts, respectively.
+
+# 3 Concept Best Matching
+
+Our key insight is that compositionality requires a mapping between words (atomic parts of EC messages) and concepts (a set of FVPs) that compose NL phrases. Given an evaluation set of examples  $D$ , consider their corresponding EC messages  $\mathbb{M}$  and NL phrases  $\mathbb{L}$ . Let  $\mathbb{W}$  denote the set of unique words in  $\mathbb{M}$ , and  $\mathbb{V}$  the set of unique FVPs in  $\mathbb{L}$ . Let  $\{w\}_i, \{v\}_i$  be the sets of words and FVPs in sample  $i$ , and  $m_i = |\{w\}_i|, l_i = |\{v\}_i|$  their sizes. We construct a weighted bipartite graph  $\mathcal{G} = ((\mathbb{W}, \mathbb{V}), \mathbb{E})$  with words on one side and FVPs on the other side. Edges  $\mathbb{E}$  are defined by the evaluation set. The weight  $q_e$  of edge  $e_{ij}$  is the number of times word  $i$  appeared in a message that the sender transmitted for a labeling rule with FVP  $j$ . This construction reflects the intuition that we do not know the correct mapping between words and FVPs (concepts). See Figure 1 for an example.
+
+# 3.1 Best Match Algorithm
+
+Given the graph  $\mathcal{G}$ , we seek an optimal pairing between words and concepts (FVPs), such that no two edges share the same word nor the same concept. The score of a match  $\mathbb{B} \subseteq \mathbb{E}$  is the sum of its edge weights,  $\sum_{e \in \mathbb{B}} q_e$ . The best match,  $\mathrm{BM} = \mathrm{BM}(\mathcal{G})$ , maximizes this score:
+
+$$
+\mathrm {B M} = \underset {\mathbb {B}} {\operatorname {a r g m a x}} \sum_ {e \in \mathbb {B}} q _ {e} \tag {1}
+$$
+
+Such an ideal mapping is fully interpretable. A high score indicates that the agents learned to generate a unique EC word for each NL concept.
+
+Normalizing the BM score by the number of symbols and words,  $Q = \sum_{i\in D}\max (|m_i|,|l_i|)$ , guarantees that  $\mathrm{BM}\in [0,1]$ . The best match for a weighted bipartite graph can be found efficiently by the Hungarian algorithm (Kuhn, 1955;
+
+Hopcroft and Karp, 1973). Implementation is provided here.
+
+# 4 Experimental Setup
+
+We experiments with agents that learn to play multi-target referential games, introduced by Mu and Goodman (2021) and described in Section 2.1. All experiments reported in Table 1 have the number of possible words  $\geq$  the number of concepts, allowing perfect match of words to concepts. In Appendix D we report more experiments with sub-optimal configurations.
+
+Datasets. We experiment with two datasets, described briefly here; Appendix B has more details.
+
+(1) SHAPE: A visual reasoning dataset (Kuhnle and Copestake, 2017) of objects over a black background. Our version of the dataset contains four attributes: shape, color, and horizontal and vertical positions. Overall, the SHAPE dataset contains 17 concepts, and a maximal labeling rule of 4 FVPs.  
+(2) THING: A synthetic dataset of 100,000 objects. Each object has five attributes, each with 10 possible values. Overall, the THING datasets contains 50 concepts and a maximal labeling rule of 5 FVPs.
+
+Communication Channel. We train the system with two types of communication channels: the popular Gumbel-Softmax (GS) (Havylov and Titov, 2017; Jang et al., 2017) and quantized communication (QT) (Carmeli et al., 2023). In GS, each word is a  $d$ -dimensional one-hot vector. In QT, each word is a  $d$ -dimensional binary vector. QT was shown to be superior and easier to optimize compared to GS in EC games. In both cases we use a recurrent network to generate multi-word messages. Appendix C has implementation details.
+
+# 5 Results
+
+Table 1 shows results on several configurations of the two games. As expected, accuracy degrades as the task becomes more difficult, with longer labeling rules. QT communication yields better task accuracy than GS, consistent with Carmeli et al. (2023). TopSim is not well correlated with accuracy, as found in prior work (Section 2.3). AMI and CBM are more correlated with accuracy. With long messages and labeling rules ( $l = 4$ ), AMI is less correlated with accuracy. This may be explained by AMI operating at the level of whole messages and labeling rules—AMI struggles with large numbers of unique messages and NL phrases. In contrast,
+
+<table><tr><td rowspan="2"></td><td rowspan="2">Com</td><td rowspan="2">l</td><td rowspan="2">d</td><td colspan="2">NL</td><td colspan="2">EC</td><td rowspan="2">Acc</td><td rowspan="2">Top Sim</td><td rowspan="2">AMI</td><td colspan="4">Best Match</td></tr><tr><td>Cons</td><td>Phrs</td><td>#w</td><td>#m</td><td>CBM</td><td>Amb</td><td>Para</td><td>Unm</td></tr><tr><td rowspan="4">Shape</td><td>GS</td><td>1</td><td>17</td><td>17</td><td>17</td><td>11</td><td>11</td><td>0.84</td><td>0.44</td><td>0.76</td><td>0.62</td><td>0.37</td><td>0.01</td><td>0.25</td></tr><tr><td>QT</td><td>1</td><td>5</td><td>17</td><td>17</td><td>26</td><td>26</td><td>0.87</td><td>0.39</td><td>0.85</td><td>0.52</td><td>0.41</td><td>0.08</td><td>0</td></tr><tr><td>GS</td><td>4</td><td>17</td><td>17</td><td>34</td><td>16</td><td>226</td><td>0.78</td><td>0.34</td><td>0.38</td><td>0.52</td><td>0.48</td><td>0</td><td>0.01</td></tr><tr><td>QT</td><td>4</td><td>5</td><td>17</td><td>34</td><td>26</td><td>187</td><td>0.83</td><td>0.23</td><td>0.37</td><td>0.55</td><td>0.37</td><td>0.08</td><td>0</td></tr><tr><td rowspan="4">Thing</td><td>GS</td><td>1</td><td>50</td><td>50</td><td>50</td><td>18</td><td>18</td><td>0.86</td><td>0.45</td><td>0.72</td><td>0.38</td><td>0.62</td><td>0</td><td>0.55</td></tr><tr><td>QT</td><td>1</td><td>6</td><td>50</td><td>50</td><td>50</td><td>50</td><td>0.92</td><td>0.07</td><td>0.74</td><td>0.73</td><td>0.25</td><td>0.02</td><td>0</td></tr><tr><td>GS</td><td>4</td><td>50</td><td>50</td><td>901</td><td>36</td><td>198</td><td>0.63</td><td>0.33</td><td>0.03</td><td>0.24</td><td>0.76</td><td>0</td><td>0.28</td></tr><tr><td>QT</td><td>4</td><td>6</td><td>50</td><td>901</td><td>64</td><td>450</td><td>0.77</td><td>0.14</td><td>0.05</td><td>0.23</td><td>0.69</td><td>0.08</td><td>0</td></tr></table>
+
+Table 1: Results for SHAPE and THING games with Gumbel-Softmax (GS) or Quantized (QT) communication using rules of length  $l$  and words of length  $d$ , showing number of unique NL concepts (Cons) and phrases (Phrs) and EC words (\#w) and messages (#m). TopSim and AMI give only coarse scores. Our method gives the best match score (CBM) and rates of Ambiguities (Amb), Paraphrases (Para), and Unmatched concepts (Unm).
+
+![](images/d9ee58b9348d750d002cb8984b3fb9b33670a05da6509829cc76649979539b07.jpg)  
+Figure 2: The word  $\leftrightarrow$  FVP best-match graph for the SHAPE game (GS communication,  $l = 1$ ). The algorithm matched just 10 concepts to EC words out of 17 possible concepts.
+
+CBM assesses word-to-concept matching, so it is less affected by long messages and rules. However, AMI and CBM are well correlated (Pearson 0.7 and 0.79 on the SHAPE and THING games).
+
+The table also shows the rate of ambiguities and paraphrases, exposed by our method. Ambiguities happen when the same EC word is mapped to different concepts. Table 1 shows higher rates of ambiguities in GS compared to QT, and in longer rules. Paraphrases are EC words that do not have a best-matched concept node. Paraphrases occur more with QT, which enables 32 and 64 unique EC words for the SHAPE and THING games, while these games have only 17 and 50 NL concepts, respectively. GS allows setting the number of unique words equal to number of concepts, thus is less exposed to this sub-optimal phenomenon.
+
+Finally, Unmatched concepts have no matching EC word. They result from a too narrow or underutilized channel. As Table 1 shows, GS communication suffers from a high rate of unmatched concepts (up to 0.5). This phenomenon can be observed by the low # of unique words (18) compared to # of unique concepts (50) for the THING game with GS and  $l = 1$ . QT has a sufficient number of words and thus no unmatched concepts.
+
+Example Match. Beyond global scores, the CBM provides an interpretable translation graph, which maps EC words to NL concepts, facilitating insights on reasons for sub-optimal communication. Figure 2 shows an example graph for the SHAPE game with GS communication. As seen, the algorithm successfully matched 10 EC words to 10 concepts. The sender generated 11 unique words in this experiment, indicating that one word is a paraphrase of an already matched concept, even within this narrow-channel setup.
+
+# 6 Conclusion
+
+We proposed a new procedure for assessing compositionality of emergent communication. In contrast to other evaluations, our procedure provides a human-interpretable translation map of emerged words to natural concepts. Moreover, our approach provides detailed insights into the reasons for suboptimal translation. We demonstrated it on two EC games with two different communication types. Our evaluation reveals even that quantized communication performs better than Gumbel-softmax, yet none exhibits compositionality in a level similar to natural language.
+
+# Limitations
+
+Our analysis is limited to datasets where gold label phrases exist. The evaluated dataset should be composable and the gold language should use finite set of concepts. Preferably, these concepts can be classified into several categories. We further assume an Oracle function that can divide the objects to targets and distractors during training. Importantly, our approach does not require labels during training.
+
+# Acknowledgements
+
+This research was supported by grant no. 2022330 from the United States - Israel Binational Science Foundation (BSF), Jerusalem, Israel. The research of YB was also supported by the Israel Science Foundation (grant 448/20), an Azrieli Foundation Early Career Faculty Fellowship, and an AI Alignment grant from Open Philanthropy. The work of RM was partially supported by the Skillman chair in biomedical sciences and by the Ollendorf center.
+
+# References
+
+Jacob Andreas and Dan Klein. 2016. Reasoning about pragmatics with neural listeners and speakers. In EMNLP.  
+Henry Brighton and Simon Kirby. 2006. Understanding linguistic evolution by visualizing the emergence of topographic mappings. Artificial life, 12(2):229-242.  
+Boaz Carmeli, Ron Meir, and Yonatan Belinkov. 2023. Emergent quantized communication. In Proceedings of the AAAI Conference on Artificial Intelligence, volume 37, pages 11533-11541.  
+Rahma Chaabouni, Eugene Kharitonov, Diane Bouchacourt, Emmanuel Dupoux, and Marco Baroni. 2020. Compositionality and generalization in emergent languages. In ACL, pages 4427-4442.  
+Rahma Chaabouni, Florian Strub, Florent Altché, Eugene Tarassov, Corentin Tallec, Elnaz Davoodi, Kory Wallace Mathewson, Olivier Tieleman, Angeliki Lazaridou, and Bilal Piot. 2021. Emergent communication at scale. In ICLR.  
+Serhii Havrylov and Ivan Titov. 2017. Emergence of language with multi-agent games: Learning to communicate with sequences of symbols. NeurIPS, 30.  
+John E Hopcroft and Richard M Karp. 1973. An  $\mathfrak{n}^5 /2$  algorithm for maximum matchings in bipartite graphs. SIAM Journal on computing, 2(4):225-231.  
+Dieuwke Hupkes, Verna Dankers, Mathijs Mul, and Elia Bruni. 2020. Compositionality decomposed: How do neural networks generalise? Journal of Artificial Intelligence Research, 67:757-795.
+
+Eric Jang, Shixiang Gu, and Ben Poole. 2017. Categorical reparameterization with gumbel-softmax. In ICLR.  
+Eugene Kharitonov, Rahma Chaabouni, Diane Bouchacourt, and Marco Baroni. 2019. EGG: a toolkit for research on emergence of lanGuage in games. In EMNLP-IJCNLP: System Demonstrations, pages 55-60.  
+Harold W Kuhn. 1955. The hungarian method for the assignment problem. Naval research logistics quarterly, 2(1-2):83-97.  
+Alexander Kuhnle and Ann Copestake. 2017. Shapeworld - a new test methodology for multimodal language understanding. arXiv preprint arXiv:1704.04517.  
+Angeliki Lazaridou, Karl Moritz Hermann, Karl Tuyls, and Stephen Clark. 2018. Emergence of linguistic communication from referential games with symbolic and pixel input. In ICLR.  
+Angeliki Lazaridou, Alexander Peysakhovich, and Marco Baroni. 2017. Multi-agent cooperation and the emergence of (natural) language. In ICLR.  
+Vladimir I Levenshtein et al. 1966. Binary codes capable of correcting deletions, insertions, and reversals. In Soviet physics doklady, volume 10, pages 707-710. Soviet Union.  
+Fushan Li and Michael Bowling. 2019. Ease-of-teaching and language structure from emergent communication. NeurIPS, 32.  
+Jesse Mu and Noah Goodman. 2021. Emergent communication of generalizations. Advances in Neural Information Processing Systems, 34:17994-18007.  
+Mycal Tucker, Roger P Levy, Julie Shah, and Noga Zaslavsky. 2022. Generalization and translatability in emergent communication via informational constraints. In NeurIPS 2022 Workshop on Information-Theoretic Principles in Cognitive Systems.  
+Ankit Vani, Max Schwarzer, Yuchen Lu, Eeshan Dhekane, and Aaron Courville. 2021. Iterated learning for emergent systematicity in VQA. In ICLR.  
+Nguyen Xuan Vinh, Julien Epps, and James Bailey. 2009. Information theoretic measures for clusterings comparison: is a correction for chance necessary? In Proceedings of the 26th annual international conference on machine learning, pages 1073-1080.  
+Shunyu Yao, Mo Yu, Yang Zhang, Karthik R Narasimhan, Joshua B. Tenenbaum, and Chuang Gan. 2022. Linking emergent and natural languages via corpus transfer. In ICLR.  
+Noga Zaslavsky, Jennifer Hu, and Roger P. Levy. 2021. A Rate-Distortion view of human pragmatic reasoning? In Proceedings of the Society for Computation in Linguistics, pages 347-348.
+
+# Appendices
+
+# A Details on Evaluation Measures
+
+We provide here information on how to calculate the topographic similarity (TopSim) (Brighton and Kirby, 2006; Lazaridou et al., 2018; Yao et al., 2022) and adjusted mutual information (AMI) measures (Vinh et al., 2009; Mu and Goodman, 2021), in the context of EC. Refer to the original papers for full details.
+
+Topographic Similarity. The topographic similarity measures how messages align with the object representations. Concretely, let  $\cos_{ij} = \cos (\pmb{x}_i,\pmb{x}_j) = \pmb{x}_i\cdot \pmb{x}_j / (||\pmb{x}_i||_2||\pmb{x}_j||_2)$  be the cosine similarity of object representations  $\pmb{x}_i$  and  $\pmb{x}_j$  and  $\mathrm{edit}_{ij} = \mathrm{edit}(m_i,m_j)$  be the Levenshtein distance (Levenshtein et al., 1966) between messages  $m_{i}$  and  $m_j$ . Let  $\mathrm{ncos} = -\{\cos_{ij}\}_{ij}$  be the list of negative cosine similarities,  $\mathrm{edit} = \{\mathrm{edit}_{ij}\}_{ij}$  the list of Levenshtein distances, and  $R(\cdot)$  the ranking function. Then the topographic similarity is the Spearman rank correlation of the two matrices:
+
+$$
+\operatorname {T o p s i m} = \rho (R (\operatorname {e d i t}), R (\operatorname {n c o s})) \tag {2}
+$$
+
+where  $\rho$  is the standard Pearson correlation.
+
+Topographic similarity is a global metric that does not require a reference language and can be easily applied to every EC setup. However, despite its popularity, recent studies found that topographic similarity does not correlate well with success in the task being played (Chaabouni et al., 2021; Yao et al., 2022). More important, it does not provide a mapping between EC atoms and NL concepts, and thus cannot directly assess compositionality.
+
+Adjusted Mutual Information. Given a test set  $D$ , let  $\mathbb{M}$  denote the set of messages generated by the sender and  $\mathbb{L}$  denote the set of NL phrases (e.g., Red Triangle, Blue Square) exist as labels in the data. The adjusted mutual information (AMI) (Vinh et al., 2009) measures the mutual information between messages and labels, adjusted for chance:
+
+$$
+\operatorname {A M I} (M, L) = \frac {I (M , L) - \mathbb {E} (I (M , L)}{\max  (H (M) , H (L)) - \mathbb {E} (I (M , L))} \tag {3}
+$$
+
+where  $I(M,L)$  is the mutual information between  $M$  and  $L$ ,  $H(\cdot)$  is the entropy, and  $\mathbb{E}(I(M,L))$  is computed with respect to a hypergeometric model of randomness.
+
+![](images/a0a68d82b82425ddea7e647f0d26ddc9d6a925173eb17d92cdf7027b1020832a.jpg)  
+Figure 3: The SHAPE dataset, presenting one turn. Top 8 images are Yellow targets. Bottom 8 images are distractors.
+
+# B Datasets
+
+We use two datasets in our experiments. Both will be made publicly available.
+
+Shape. A visual reasoning dataset (Kuhnle and Copestake, 2017) of objects over a black background. Our version of the dataset contains four attributes: the shape attribute has five shapes, the color attribute has six colors. To these we added horizontal and vertical position attributes each with three values. Overall, the SHAPE dataset contains 17 concepts, and a maximal labeling rule of 4 FVPs which sum to 270 unique 4-concept labels. The dataset contains many images that obey the same label. See Figure 3 for an example.
+
+Thing. A synthetic dataset of 100,000 objects which we design for controlled experiments. Each object in the dataset has five attributes, each with 10 possible values. Overall, the THING datasets contains 50 concepts and a maximal labeling rule of 5 FVPs. We experiments with label lengths varied from 1, describing a single concept, to 5, which completely describes an object in the dataset.
+
+# C Implementation Details
+
+We run all experiments over a modified version of the Egg framework (Kharitonov et al., 2019). In our version the communication modules used by the sender and the receiver are totally separated from their perceptual modules, which we term 'agents'. The Quantized (QT) and Gumbel-Softmax (GS) protocols are implemented at the
+
+<table><tr><td>Batch Size</td><td>lr</td><td>Num Targets</td><td>Num Distr</td><td>Cell Type</td><td>Sender Hidden</td><td>Sender Embed</td><td>Receiver Hidden</td><td>Receiver Embed</td></tr><tr><td>10</td><td>0.0005</td><td>8/20</td><td>8/20</td><td>LSTM</td><td>60</td><td>60</td><td>40</td><td>40</td></tr></table>
+
+Table 2: Hyper-parameters for the agents in the SHAPE game.  
+
+<table><tr><td>Exp Num</td><td>Game</td><td>Comm Type</td><td>Label Len</td><td>word Len</td><td>Msg Len</td><td>Best Epoch</td><td>ACC</td><td>AMI</td><td>Best Match</td></tr><tr><td>1</td><td>SHAPE</td><td>gs</td><td>1</td><td>8</td><td>4</td><td>97</td><td>0.829</td><td>0.404</td><td>0.405</td></tr><tr><td>2</td><td>SHAPE</td><td>gs</td><td>1</td><td>64</td><td>4</td><td>96</td><td>0.843</td><td>0.390</td><td>0.339</td></tr><tr><td>3</td><td>SHAPE</td><td>gs</td><td>4</td><td>8</td><td>1</td><td>8</td><td>0.742</td><td>0.490</td><td>0.152</td></tr><tr><td>4</td><td>SHAPE</td><td>gs</td><td>4</td><td>64</td><td>1</td><td>10</td><td>0.748</td><td>0.413</td><td>0.130</td></tr><tr><td>5</td><td>SHAPE</td><td>qt</td><td>1</td><td>3</td><td>4</td><td>86</td><td>0.878</td><td>0.540</td><td>1.401</td></tr><tr><td>6</td><td>SHAPE</td><td>qt</td><td>1</td><td>64</td><td>4</td><td>85</td><td>0.991</td><td>0.000</td><td>0.001</td></tr><tr><td>7</td><td>SHAPE</td><td>qt</td><td>4</td><td>3</td><td>1</td><td>9</td><td>0.768</td><td>0.474</td><td>0.152</td></tr><tr><td>8</td><td>SHAPE</td><td>qt</td><td>4</td><td>64</td><td>1</td><td>12</td><td>0.897</td><td>0.021</td><td>0.009</td></tr><tr><td>9</td><td>THING</td><td>gs</td><td>1</td><td>8</td><td>4</td><td>83</td><td>0.793</td><td>0.102</td><td>0.091</td></tr><tr><td>10</td><td>THING</td><td>gs</td><td>1</td><td>64</td><td>4</td><td>94</td><td>0.798</td><td>0.074</td><td>0.151</td></tr><tr><td>11</td><td>THING</td><td>gs</td><td>4</td><td>8</td><td>1</td><td>97</td><td>0.655</td><td>0.016</td><td>0.052</td></tr><tr><td>12</td><td>THING</td><td>gs</td><td>4</td><td>64</td><td>1</td><td>99</td><td>0.626</td><td>0.014</td><td>0.058</td></tr><tr><td>13</td><td>THING</td><td>qt</td><td>1</td><td>3</td><td>4</td><td>96</td><td>0.838</td><td>0.267</td><td>0.119</td></tr><tr><td>14</td><td>THING</td><td>qt</td><td>1</td><td>64</td><td>4</td><td>100</td><td>0.973</td><td>0.000</td><td>0.014</td></tr><tr><td>15</td><td>THING</td><td>qt</td><td>4</td><td>3</td><td>1</td><td>26</td><td>0.622</td><td>0.020</td><td>0.057</td></tr><tr><td>16</td><td>THING</td><td>qt</td><td>4</td><td>64</td><td>1</td><td>96</td><td>0.844</td><td>0.000</td><td>0.013</td></tr></table>
+
+Table 3: Configurations for more SHAPE and THING game experiments. In these configuration we intentionally define sub-optimal communication parameters in order to demonstrate the usefulness of the evaluation metrics. Experiment results are provided in Table 4  
+
+<table><tr><td>Exp Num</td><td>Unq Msgs</td><td>Unq Wrds</td><td>Unq Prs</td><td>Ung Cons</td><td>Totl Edgs</td><td>Good Edgs</td><td>Amb Edgs</td><td>Phrs Edgs</td><td>Totl Cons</td><td>Unm Cons</td><td>Par Scor</td><td>Prc</td><td>Rcl</td></tr><tr><td>1</td><td>258</td><td>7</td><td>17</td><td>17</td><td>4k</td><td>1621</td><td>2379</td><td>0</td><td>1k</td><td>444</td><td>0</td><td>0.137</td><td>0.546</td></tr><tr><td>2</td><td>442</td><td>55</td><td>17</td><td>17</td><td>4k</td><td>1356</td><td>1724</td><td>920</td><td>1k</td><td>0</td><td>0.23</td><td>0.144</td><td>0.577</td></tr><tr><td>3</td><td>8</td><td>8</td><td>34</td><td>17</td><td>4k</td><td>610</td><td>390</td><td>0</td><td>4k</td><td>1457</td><td>0</td><td>0.61</td><td>0.152</td></tr><tr><td>4</td><td>44</td><td>44</td><td>34</td><td>17</td><td>4k</td><td>520</td><td>326</td><td>154</td><td>4k</td><td>0</td><td>0.04</td><td>0.52</td><td>0.13</td></tr><tr><td>5</td><td>238</td><td>8</td><td>17</td><td>17</td><td>4k</td><td>1605</td><td>2395</td><td>0</td><td>1k</td><td>385</td><td>0</td><td>0.144</td><td>0.577</td></tr><tr><td>6</td><td>1000</td><td>3899</td><td>17</td><td>17</td><td>4k</td><td>46</td><td>0</td><td>3954</td><td>1k</td><td>0</td><td>0.99</td><td>0.011</td><td>0.044</td></tr><tr><td>7</td><td>7</td><td>7</td><td>34</td><td>17</td><td>4k</td><td>607</td><td>393</td><td>0</td><td>4k</td><td>1727</td><td>0</td><td>0.607</td><td>0.152</td></tr><tr><td>8</td><td>974</td><td>974</td><td>34</td><td>17</td><td>4k</td><td>38</td><td>0</td><td>962</td><td>4k</td><td>0</td><td>0.24</td><td>0.038</td><td>0.009</td></tr><tr><td>9</td><td>543</td><td>7</td><td>50</td><td>50</td><td>4k</td><td>366</td><td>3634</td><td>0</td><td>1k</td><td>807</td><td>0</td><td>0.048</td><td>0.19</td></tr><tr><td>10</td><td>806</td><td>60</td><td>50</td><td>50</td><td>4k</td><td>601</td><td>3369</td><td>30</td><td>1k</td><td>0</td><td>0.01</td><td>0.1</td><td>0.399</td></tr><tr><td>11</td><td>8</td><td>8</td><td>901</td><td>50</td><td>4k</td><td>210</td><td>790</td><td>0</td><td>4k</td><td>3332</td><td>0</td><td>0.21</td><td>0.052</td></tr><tr><td>12</td><td>21</td><td>21</td><td>901</td><td>50</td><td>4k</td><td>233</td><td>767</td><td>0</td><td>4k</td><td>2267</td><td>0</td><td>0.233</td><td>0.058</td></tr><tr><td>13</td><td>412</td><td>8</td><td>50</td><td>50</td><td>4k</td><td>478</td><td>3522</td><td>0</td><td>1k</td><td>795</td><td>0</td><td>0.046</td><td>0.184</td></tr><tr><td>14</td><td>1000</td><td>3991</td><td>50</td><td>50</td><td>4k</td><td>57</td><td>0</td><td>3943</td><td>1k</td><td>0</td><td>0.99</td><td>0.013</td><td>0.052</td></tr><tr><td>15</td><td>11</td><td>6</td><td>901</td><td>50</td><td>4k</td><td>229</td><td>771</td><td>0</td><td>4k</td><td>3483</td><td>0</td><td>0.229</td><td>0.057</td></tr><tr><td>16</td><td>1000</td><td>1000</td><td>901</td><td>50</td><td>4k</td><td>50</td><td>0</td><td>950</td><td>4k</td><td>0</td><td>0.24</td><td>0.05</td><td>0.013</td></tr></table>
+
+Table 4: Results for more SHAPE and THING game configurations described in Table 3. In these experiments we intentionally define sub-optimal communication parameters in order to demonstrate the usefulness of the evaluation metrics.
+
+communication layer. For GS we use an implementation provided by the Egg framework, where we do not allow temperature to be learned, and set the straight-through estimator to False. For QT we followed parameter recommendations from Carmeli et al. (2023) and use a binary quantization in all experiments. Both GS and QT uses a recurrent neural network (RNN) for generating multiple words in a message. See Table 2 for RNN details.
+
+The agents for the THING game use fully connected feed-forward networks with input dimension of  $d = 270$ . Objects are encoded by concatenating five one-hot vectors, one per attribute. There are 50 unique values and 4 communication words (SOS, EOS, PAD, UNK), thus the total object representation length is  $d = 270$ . The agents of the SHAPE game are implemented with a convolutional neural network similar to Mu and Goodman (2021). Network hyper-parameters are provided in Table 2. In the experiments, we report results when varying the communication elements (word length and message length). Experiments in Table 1 are done with 20 targets and 20 distractors, while experiments reported in Tables 3 and 4 are done with 8 targets and 8 distractors. Our main interest in this work is to evaluate the emerged communication and not to achieve the best possible performance, thus we did not conduct a thorough hyper-parameter search for the agents themselves.
+
+We run all experiments on a single A100 GPU with 40 GB of RAM. Model size is less than 10M. We usually trained the model for 200 epochs which took about 10 hours to complete. Our code will be made publicly available upon de-anonymization.
+
+# D Evaluating Sub-optimal Configurations
+
+Here we provide results from experiments with several sub-optimal configurations and demonstrate how CBM identifies these deficiencies. We report configuration parameters for each experiment together with accuracy, AMI, and CBM Score in Table 3. We report all CBM metrics for these experiments in Table 4. Information from the two tables is aligned by the experiment number (first column).
+
+Sub-optimal communication may stem from a channel that is either too wide or too narrow. Narrow channels are restricted by a small number of words and short messages. Wide channels allow long words and/or long messages. Past studies (Tucker et al., 2022) suggest that creating an information bottleneck by narrowing the channel en
+
+![](images/4cdf223f77a9db8d1f89800710a787e1795c10df2785c627e982062e118bd7c5.jpg)  
+Figure 4: Assessing CBM sensitivity to the size of the evaluation set. We show results for two randomly selected experiments. As seen, the CBM score stabilizes when assessing datasets comprising more than 500 samples.
+
+courages generalization. As seen, CBM scores for most reported sub-optimal configurations are low. Results from experiments 1, 2, and 5 are the only ones for which the CBM score is higher than 0.2. Experiment 6 (SHAPE) achieves almost perfect accuracy (0.991) due to its wide channel. However, the paraphrase score for this experiment is 0.989 showing that the sender uses many different words to refer to the same concept. This phenomenon can also be seen by the large number of unique words (3899) generated for just 17 unique concepts. A similar phenomenon is observed for the THING game (experiment 14).
+
+Experiment 11 (THING) uses a narrow channel. The vocabulary contains only 8 words and the channel allows one-word-long messages. This configuration resulted in 3332 concepts that do not match any word. Interestingly, the number of unmatched concepts remains high even when extending the word length to 64, in experiment 12. We attribute this sub-optimal phenomenon to GS communication deficiencies. The number of unique words generated by the sender in this experiment is only 21 out of the possible 64 words allowed by the configuration. For the SHAPE game, on the other hand, the same wide-channel configuration resulted in 44 unique words generated by the sender for the 17 concepts available in this game and all concepts have matched words.
+
+Precision and recall. After finding the best match, precision and recall between words and concepts can be computed. We define message precision (Prc) and recall (Rcl) to be the number of matched edges in a message, divided by the number of words or concepts, respectively. Precision and recall add insights in situation where the num
+
+ber of words in messages differs significantly from the number of concepts used for labeling the data. Experiment 5 (SHAPE) shows the highest recall, gained partially due to the long message length (four words) allowed by the channel, compared to the label length (one concept) dictated by the data. In contrast, experiment 3 (SHAPE) shows the highest precision. Indeed, this configuration restricts message the length to one word while the data dictates four-concept long phrases.
+
+# E CBM Sensitivity to Dataset Size
+
+We evaluated CBM scores on increased data sizes. Figure 4 shows results for two randomly selected experiments. The solid lines indicate the CBM score, computed when accumulating data samples in 100 quintets. The dashed lines indicate CBM score calculated independently for 18 successive data segments of 100 samples each. As seen, scores stabilize for evaluation sets of size larger than 500 samples. Interestingly, the 100-sample scores (dashed) lines are higher than the accumulated scores (solid lines). This is in line with our insight that low evaluation sizes result in higher match scores. Standard deviation for the 18 accumulated measures is 0.009 and 0.016, for the two experiments, respectively. Standard deviation for the 18 segmented measures is 0.044 and 0.040, for the two experiments, respectively.

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2024/Concept-aware Data Construction Improves In-context Learning of Language Models/full.md

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+# Concept-aware Data Construction Improves In-context Learning of Language Models
+
+Michal Štefánik* and Marek Kadlcik* and Petr Sojka*
+
+*Faculty of Informatics Masaryk University, Czech Republic
+
+# Abstract
+
+Many recent language models (LMs) are capable of in-context learning (ICL), manifested in the LMs' ability to perform a new task solely from a natural-language instruction. Previous work curating in-context learners assumes that ICL emerges from a vast over-parametrization or the scale of multi-task training. However, recent theoretical work attributes the ICL ability to concept-dependent training data and creates functional in-context learners even in small-scale, synthetic settings.
+
+In this work, we practically explore this newly identified axis of ICL quality. We propose Concept-aware Training (CoAT), a framework for constructing training scenarios that make it beneficial for the LM to learn to utilize the analogical reasoning concepts from demonstrations. We find that by using CoAT, pretrained transformers can learn to better utilise new latent concepts from demonstrations and that such ability makes ICL more robust to the functional deficiencies of the previous models.
+
+Finally, we show that concept-aware in-context learners are much more effective in in-context learning a majority of unseen tasks compared to traditional instruction tuning, and fare comparably also to previous in-context learners trained in large-scale multitask learning requiring magnitudes of more training data.
+
+# 1 Introduction
+
+The in-context learning (ICL), as initially uncovered by Brown et al. (2020), is a setting requiring language models (LMs) to infer and apply correct functional relationships from the pairs of inputs and outputs (i.e. demonstrations) presented in user-provided input prompt (Li et al., 2023b). Given that a small set of demonstrations can be obtained for any machine learning task, in-context learning presents a much more versatile and practical alternative to training task-specific models.
+
+![](images/f111881172adf5df1c2ebff3d96ecf0bbcf6d4c442ee770786f2179b83809492.jpg)  
+Figure 1: Example of training instruction constructed from synthetic TeaBReaC dataset where demonstrations share analogical reasoning chain. In Concept-aware Training (CoAT), we construct such examples to train in-context learners to utilise latent reasoning concepts whenever available in demonstrations.
+
+Modern in-context learners may perform ICL with quality comparable to task-specialized models (Zhao et al., 2023; Stefánik et al., 2023). However, it remains unclear why some LMs are able of ICL in such quality while others are not; Initial work introducing GPT3 (Brown et al., 2020) followed by Thoppilan et al. (2022); Chowdhery et al. (2022); inter alia explains ICL as an emergent consequence of models' scale. But more recent LMs (Sanh et al., 2022; Wang et al., 2022; Wei et al., 2021; Ouyang et al., 2022) are based on 10 to 100 times smaller models and reach comparable ICL quality, instead attributing the ICL ability to a vast volume and diversity of pre-training tasks and instructions.
+
+On the contrary, theoretical studies uncover different determinants of ICL quality than the model or data scale, relating ICL to specific data qualities, such as the occurrence of cases that can not be explained by mere statistical co-occurrence of tokens. Notably, Xie et al. (2022) specify this as the occurrence of training exemplars that can only be resolved by identifying latent concepts, i.e. underlying functional relations that explain the correct prediction. In this and other work surveyed in Sec
+
+tion 2, authors prove that ICL can also emerge with both small data and small models.
+
+Our work explores the practical potential of concept-dependent data on the quality and robustness of in-context learning. In Section 3, we propose and implement a data construction framework that encourages the occurrence of concept dependencies in training data, and hence, requires models to learn to utilise latent concepts that explain these irregularities (Fig. 1). We call this framework Concept-aware Training (CoAT).
+
+In Sections 4, we explore the impact of CoAT in controlled settings. We find that (i) it is possible to train language models for in-context learning of unseen latent concepts and (ii) that such concept-aware in-context learning is more robust to the functional deficiencies of existing in-context learners. Finally, on a set of over 70 tasks of SuperGLUE and Natural-Instructions, we find that CoAT can also improve practical in-context learning performance over traditional instruction tuning approach; in many cases, CoAT enables ICL of otherwise not learnable tasks, and with only two training tasks reaches ICL performance comparable to in-context learners of similar or larger size trained on massive collections of over 1,600 tasks.
+
+# 2 Background
+
+Methods for training in-context learners Incontext learning ability, including few-shot ICL, was first uncovered in GPT3 (Brown et al., 2020) trained unsupervisedly for causal language modelling. With no other substantial differences to previous GPT models, the emergence of ICL was attributed to GPT3's scale, having grown to over 170-billion parameters since GPT2 ( $\approx$ 800M params).
+
+Not long after, a pivotal work of Schick and Schütze (2020) on a Pattern-exploiting training (PET) has shown that even much smaller (110M) models like BERT (Devlin et al., 2019) can be finetuned using self-training in a similarly small data regime, first disputing the assumption on the necessity of the scale in rapidly learning new tasks.
+
+A line of generation models further undermined the assumption of the size conditioning of ICL. Among the first, Min et al. (2022a) fine-tune smaller models (<1B parameters) on a large mixture of tasks in the few-shot instructional format and find that such models can perform previously unseen tasks. Following approaches (Sanh et al., 2022; Wang et al., 2022) also train smaller models
+
+for instruction following on large mixtures of tasks, assuming that the model's ability to in-context learn an unseen task emerges from a large diversity of instructions and task types. A recently popularised reinforcement learning approach of INSTRUCTGPT (Ouyang et al., 2022) also presents an adaptation of an instruction-following objective, training on mixtures of instructions with automatic feedback.
+
+Recently, the instruction following was extended by joint training on programming code generation (Chen et al., 2021) and by Chain-of-Thought (CoT) targets (Wei et al., 2022), where the model is trained to respond with a sequence of natural-language steps deducing the answer (Zhao et al., 2023; Kadlcik et al., 2023). These extensions were empirically shown to enhance ICL ability (Fu and Khot, 2022) and were adopted by FLAN models (Chung et al., 2022).
+
+Analyses of ICL Recent studies shed some light on the functioning of ICL in LMs through controlled experimentation, finding that the LMs' decision-making in ICL does not align with humans. Notably, Lu et al. (2022) report on the sensitivity of LMs to the specific formulation of the instructions in the prompt, while Liu et al. (2022) measures sensitivity to the ordering of in-context demonstrations. Further, we find that LMs perform ICL comparably well when the labels of the demonstrations are randomly shuffled (Min et al., 2022b) or when the presented CoT sequences do not make sense (Wang et al., 2023). We note that such behaviours differ from learning a functional relation from demonstrations that we expect from in-context learners (Li et al., 2023b) and can be exploited to lead models to incorrect predictions.
+
+Nevertheless, other studies report that under the right conditions, LMs are able to learn functional relationships solely from the input prompt; For instance, Akyurek et al. (2023); Li et al. (2023c) show that Transformers can be trained to accurately learn regression functions solely from the prompt.
+
+Xie et al. (2022) identify the key covariate of ICL quality in the occurrence of training examples where correct predictions are conditioned by latent concepts. Consider a pre-training example 'Albert Einstein was [MASK]'; The correct prediction for [MASK] can be resolved if the model can extract and apply a latent reasoning concept from context, such as that the context exhibits a concept of nationalities and hence, [MASK] best substitutes 'German'. Such concept dependencies occur in
+
+![](images/868fbb3d57b1db85ec73c3e5159e2d34f4bc0e1648fd0216f5f9dca10165a475.jpg)  
+Figure 2: Demonstrations selection in Concept-aware training (CoAT): From all samples of the training dataset, we first (1) filter out ones sharing a specific reasoning concept  $\bigcirc$  with predicted sample  $(x_{\mathrm{pred}},y_{\mathrm{pred}})$ . From this subset, we (2) iteratively pick the candidate demonstration(s)  $c_{i}$  such that the trained model  $\Theta$ ’s probability of generating the correct prediction  $y_{\mathrm{pred}}$  if we pick  $c_{i}$  among demonstrations is minimal.
+
+language sparsely but naturally, allowing the emergence of a certain ICL quality in LMs (Wies et al., 2023). Later work attributes ICL to similar data properties labelled under the terms of statistical burstiness (Chan et al., 2022) or compositionality (Hahn and Goyal, 2023).
+
+Our work builds upon this theory, but compared to previous studies limited to in-silico experiments, we elevate the idea of concept-aware training to real-world settings, with publicly available datasets and pre-trained language models. We are first to measure the impact of concept-aware data construction in extrinsic evaluation over 70 diverse tasks and show its potential to substantially enhance data efficiency and robustness in training in-context learners, compared to previous work using magnitudes of more data and compute.
+
+# 3 Concept-Aware Training
+
+Aiming to create language models able to learn a new latent reasoning concept in-context, we propose a Concept-Aware Training (CoAT) as an instruction-tuning framework specifying conditions for a selection of few-shot demonstrations for the training instructions (Figure 2).
+
+We assume the format of training prompts widely used in the previous work training in-context few-shot learners, constructing training instructions from  $k$  demonstrations consisting of the input texts  $x$  with labels  $y$  followed by the predicted sample's input text  $x_{\mathrm{pred}}$ :
+
+$$
+[ x _ {1}, y _ {1}, \langle s e p \rangle , \dots , x _ {k}, y _ {k}, \langle s e p \rangle , x _ {\mathrm {p r e d}} ] \rightarrow y _ {\mathrm {p r e d}}
+$$
+
+In this setting, CoAT proposes to filter in-context demonstrations sequentially by two conditions.
+
+The main condition, denoted as informativeness condition, assures to pick demonstrations exhibiting a specific reasoning concept  $C$  that is shared between a picked demonstration  $(x_{i},y_{i})$  and the predicted example  $(x_{\mathrm{pred}},y_{\mathrm{pred}})$ , thus picking only the demonstrations whose reasoning pattern is informative for the correct prediction. Such settings make it beneficial for the trained model to learn to extract and apply concepts presented in demonstrations.
+
+However, as the sole informativeness condition may easily pick demonstrations very similar or identical to the predicted sample, we propose a second, non-triviality condition. This condition chooses from the informative demonstrations the ones with which it is 'difficult' for the model to respond correctly. This condition avoids the occurrence of in-context demonstrations identical to the predicted sample and may also increase the heterogeneity of different concepts that co-occur among the demonstrations, avoiding the over-reliance on the presence of a small set of specific concepts in small-data settings.
+
+We note that a body of previous work proposes better ways for picking in-context demonstrations during the inference (without updating the model) (Li et al., 2023a; Gupta et al., 2023; Luo et al., 2024). While some of these strategies are applicable in picking informative demonstrations in CoAT, note that this line of work is complementary to ours in assuming an existing in-context learner. More importantly, our motivation is substantially different; CoAT uses demonstrations of instruction training as a vehicle for creating training cases conditioned on latent concepts. This idea is not restricted to instruction tuning, but we note that instruction
+
+tuning presents an opportunity to implement it easily.
+
+What constitutes a concept applicable in CoAT? We broadly define the term concept as an arbitrary functional relation of input and prediction (Xie et al., 2022) that holds robustly for any sample of a given task. Hypothetically, once the model learns to model a specific concept perfectly, it will never produce a prediction that violates this concept (Stefanik and Kadlcek, 2023). In practice, attempts to clearly present useful concepts to the model can be obstructed by other covariates (Mikula et al., 2024), such as frequent predictive co-occurrences of tokens. Thus, we propose to pick CoAT's concepts among features that are unlikely to be substitutable by non-robust covariates, presenting as best candidates to be features conditioned on a deep or holistic decomposition of the input.
+
+Note that the goal of CoAT is not to represent chosen training concepts in the model's weights explicitly but to improve the model's ability to extract and apply available concepts from demonstrations. Towards this goal, CoAT fundamentally assumes that the ability to extract and apply one concept transfers to other concepts beyond the training distribution. We verify this ability later in Section 4.4.
+
+# 3.1 Proposed Implementation
+
+In our experiments, we implement the proposed CoAT framework in two training stages: First, we train LM on a scalable synthetic QA dataset, which, contrary to traditional QA datasets, contains annotations of reasoning concepts. Second, we refresh the LM's ability to work with natural language prompts by further training on a QA dataset with only natural language inputs. Hence, contrary to previous work utilising massive multitask training, in total, we only use two QA datasets.
+
+Informativeness condition We find a large collection of annotated reasoning concepts in a TeaBReaC dataset of Trivedi et al. (2022), containing more than 900 unique explanations over a large set of synthetic QA contexts. Each TeaBReaC's explanation maps a natural question to the answer span through a sequence of declarative reasoning steps, such as "select  $\rightarrow$  group  $\rightarrow$  project". Within CoAT, we use these explanations as the shared concepts  $C$  (Fig. 1); In the training prompts, all demonstrations exhibit the same reasoning chain as the predicted sample.
+
+To restore the model's ability to work with a natural language, in the second step, we fit the resulting model to natural inputs by further fine-tuning on AdversarialQA dataset (Bartolo et al., 2021); As the annotations of reasoning concepts in general QA datasets are scarce, in this case, we naively use the initial word of the question ("Who", "Where", ...) as the shared concept, aware that such-grouped samples are not always mutually informative.
+
+Non-triviality condition In both training stages, we implement the non-triviality condition in the following steps. (i) We select a random subset of 20 samples that passed the informativeness condition (denoted  $X_{\mathrm{info}}$ ). (ii) From  $X_{\mathrm{info}}$ , we iteratively pick a sequence of  $i \in 1..k$  demonstrations (with  $k: 2 \leq k \leq 8$ ) as follows:
+
+1. For each sample  $(x_{j},y_{j})\in X_{\mathrm{info}}$  , we use the training model to compute a likelihood of generating the correct prediction  $y_{\mathrm{pred}}$  if a given sample  $(x_{j},y_{j})$  is included among demonstrations. Whenever  $y_{\mathrm{pred}}$  contains more than one token, we compute the likelihood as the average of the likelihoods of all  $y_{\mathrm{pred}}$  's tokens in the teacher-forced generation.  
+2. In each step  $i$ , we pick among the demonstrations a sample with which the likelihood of generating correct prediction is minimal.
+
+An overview of this process is depicted in Figure 2, with a schematic example of a training prompt in Figure 1. Full training prompts that our implementation of CoAT constructs in training on each dataset can be found in Table 2 in the Appendix.
+
+# 4 Experiments
+
+Our experiments provide empirical evidence towards answering three research questions (RQs):
+
+1. Can we improve models' ability to benefit from new reasoning concepts in-context?  
+2. Are the concept-aware in-context learners more robust to known functional artifacts?  
+3. Can concept-aware in-context learning also improve performance in real-world tasks?
+
+The first two RQs validate our assumptions on concept-aware training: that (1) the implementation of CoAT indeed improves models' utilisation of both seen and out-of-distribution concepts from demonstrations, and that (2) such an ability can
+
+make the in-context learning of a CoAT-trained language model more robust to artefacts revealed in previous in-context learners (Wei et al., 2023). Finally, in (3), we assess whether the enhanced models' ability to rely more on latent concepts can also improve the practical quality of low-resource in-context learning.
+
+# 4.1 Training and Evaluation
+
+To maximise comparability with the previous work, we fine-tune our models from mT5 pre-trained models of Xue et al. (2021). In both training stages (Sec. 3.1), we fine-tune all model parameters in a teacher-forced next-token prediction until convergence of evaluation loss.* We further detail the training parameters in Appendix A.
+
+In all experiments, we construct evaluation prompts from  $k = 3$  demonstrations chosen consistently for all models, with prompts including the options for expected labels. We complement all our evaluations with confidence intervals from the bootstrapped evaluation (population  $n = 100$ , repeats  $r = 200$ ). We specify evaluation setup separately for each experiment (§4.4-4.6) with further details and examples in Appendix B.
+
+# 4.2 Baselines
+
+We assess the impact CoAT's main design choices against two baselines, allowing us to measure the impact of both its data construction conditions.
+
+# Random demonstrations selection (TK-RANDOM)
+
+We evaluate the impact of all CoAT's components against a baseline trained in identical settings but picking the in-context demonstrations randomly with uniform probability over the whole training set. This baseline reproduces the methodology of a majority of the referenced work on instruction tuning, including Tk-INSTRUCT (Wang et al., 2022) and FLAN (Chung et al., 2022). Apart from the demonstration selection, all other settings, including training data, remain identical ( $\S 4.1$ ) to assure comparability with CoAT models.
+
+Demonstrations passing only informativeness condition (Tk-INFO) In this baseline, we perform ablation of CoAT's non-triviality condition (Sec. 3) by picking the demonstrations passing only the informativeness condition. Hence, such-picked demonstrations in the training instructions are informative for the prediction but can exhibit cases
+
+where some of the demonstrations are similar or even identical to the predicted sample, making it trivial for the model to perform correct prediction. All other training settings are unchanged (§4.1).
+
+# 4.3 Other evaluated models
+
+We also evaluate three recent in-context learners for which we can assess which datasets were used in their training mix: (1) T0 of Sanh et al. (2022) trained on a mixture of 35 datasets of different tasks in zero-shot settings, mostly of QA type, mapped into a self-containing human-understandable interaction format; (2) Tk-Instruct of Wang et al. (2022) pre-trained in a few-shot format similar to ours, on a mixture of 1,616 diverse tasks, and (3) FLAN models of Chung et al. (2022) that further extend data settings of Tk-Instruct to a total of 1,836 tasks, including chain-of-thought labels, i.e. a step-by-step reasoning chain mapping input prompt to a label.
+
+All these models are based on the same pretrained model (T5), making the results comparable to the level of fine-tuning methodology. TKINSTRUCT and FLAN use the data construction reproduced in our TK-RANDOM baseline, but applied in vastly larger data settings.
+
+# 4.4 CoAT's ability to improve models utilisation of latent concepts (RQ1)
+
+We pose that if the model can utilize a new reasoning concept  $C$  from demonstrations, it will be able to improve the prediction in cases where the demonstrations use the same  $C$  as the predicted sample. Thus, to evaluate if training with CoAT improves models' utilisation of concepts, we evaluate models' performance in a few-shot setting where we ensure that the demonstrations share a specific latent concept with the predicted sample. Then, we quantify models' ability to improve from the concept by computing the difference in accuracy between such concept-sharing evaluation and conventional evaluation using randomly chosen demonstrations.
+
+We perform the first analysis on TeaBReaC with annotated reasoning chains as concepts  $C$  shared between demonstrations and predicted sample (Fig. 1), but to evaluate generalization to unseen concepts, we filter out all samples with reasoning chains that were present in training. This results in 316 evaluation scenarios presenting models with 14 previously unseen reasoning patterns. In this setting, we compare the concept-improving ability of CoAT models with Tk-RANDOM baseline.
+
+![](images/d03af90080ece465d20182dd581520dac25fcbc249299551ec3c7610ff311223.jpg)  
+Figure 3: In-context learning of new concepts: Relative change of performance of models when presented with demonstrations exhibiting a reasoning concept informative for prediction. Evaluation with (left) synthetic TeaBReaC samples, and (right) diverse concepts of natural datasets (§4.4).
+
+The important limitation of evaluation with TeaBReaC's concepts is that it remains unclear whether evaluation with synthetic samples is representative for concept learning in a natural language. Hence, we also perform this analysis with samples and concepts of natural-language tasks.
+
+Previous work of Stefánik and Kadlécik (2023) evaluated ICL ability over four different functional concepts, all extracted from explanations of natural-language datasets. We adopt the concepts of this work and evaluate models for in-context learning of the following concepts: (i) reasoning logic of NLI samples of GLUE-Diagnostic dataset (Wang et al., 2018), (ii) entity relations annotated in human explanations (Inoue et al., 2020) in the HotpotQA dataset (Yang et al., 2018), (iii) functional operations annotated in general elementary-grade tests of OpenBookQA (Mihaylov et al., 2018), and (iv) shared facts in science exams of WorldTree dataset (Jansen et al., 2018; Xie et al., 2020). Examples of prompts with concept-sharing demonstrations for these datasets are shown in Table 3.
+
+Identically to the case of synthetic concepts, we evaluate the ability of CoAT models to benefit from these concepts when exhibited in demonstrations and compare to uncontrolled demonstrations' selection (TK-RANDOM) used in previous work.
+
+# Results
+
+Concept-aware training improves the ability to benefit from unseen concepts Figure 3 evaluates models' ability to improve from presented concepts as the relative difference in performance between
+
+random and concept-sharing demonstration selection. First, evaluation with unseen TeaBReaC concepts (left) assesses models' ability to extrapolate the utilisation of latent concepts to 14 previously unseen reasoning chains. Both CoAT and random-demonstration models ( $\S 4.2$ ) can improve from concepts presented in demonstrations. However, the improvement of CoAT-trained models is significantly larger and exceeds gains of  $\mathrm{TK}$ -RANDOM by 2-fold and 4-fold with the smaller and larger model, respectively. This comparison verifies that CoAT's data construction really improves our targeted skill of better utilizing concepts of demonstrations.
+
+CoAT applied with synthetic data also improves the use of natural concepts Evaluation of improvements on selected natural concepts (Figure 3; right) shows that concept-learning ability obtained with synthetic TeaBReaC concepts transfers to natural-language settings, as the CoAT-trained models can benefit from concepts significantly more than models trained without concept-aware data construction (TK-RANDOM).
+
+Despite that, evaluations over the individual reasoning concepts (Figure 7 in Appendix C.3) reveal that even CoAT models can not benefit robustly from all concepts. Nevertheless, we note that in the cases where CoAT models do not improve, also none of the baselines benefit from presented concepts. This might be attributed to several reasons: (i) the presented concepts are not really informative for prediction, (ii) our training data allowed the models to memorize relevant knowledge and, hence, do not need (and benefit from) the concepts' exposition, or (iii) our training concepts were simply not sufficient to generalize over these new concepts.
+
+# 4.5 Robustness of concept-aware in-context learners (RQ2)
+
+As we overviewed in Section 2, other work reports functional deficiencies of previous in-context learners, including surprising insensitivity of in-context learners to the assigned demonstrations' labels (Min et al., 2022b). Wei et al. (2023) attribute this to models' over-reliance on the semantic priors obtained in pre-training, which may override learning of the functional concepts. Such behaviour is defective, because the ability to learn functional relations is necessary for robust and interpretable in-context learning of truly unseen tasks.
+
+To evaluate the impact of concept-aware training on models' reliance on their semantic priors,
+
+![](images/6fe381acf9becec8e38c8f504784c4c23cbf19ab11edd225abcfcaf2b93a571a.jpg)  
+Figure 4: Models' reliance on semantic priors: Relative change of models' performance when we (left) replace labels with 'non-sensical' tokens with no correspondence to the semantics of the task, such as 'foo', 'bar', etc.; and (right) flip the original labels, so that e.g. 'negative' label corresponds to a positive-sentiment sample. CoAT models can in-context learn the input-output mapping similarly well with non-sensical labels and rely on the labels' semantics significantly less than previous in-context learners (in grey).
+
+we follow the setup of Wei et al. (2023) and assess reliance on labels' semantics in a standard few-shot evaluation (§4.1), with one of the two modifications; (i) We change the labels to tokens with irrelevant meaning for the prediction task, such as 'Foo', 'Bar' etc. (ii) We shuffle the labels so that semantically incorrect labels are assigned in the demonstrations, but the input-label mapping remains consistent. In both settings, the task's functional relation can still be recovered from demonstrations, but the sole reliance on semantics will either not help or will mislead the model.
+
+In this setting, we evaluate three model types: (i) CoAT-trained models, (ii) models with uncontrolled data construction (Tk-RANDOM & previous work), and (iii) models with uncontrolled data construction, but fine-tuned only on a natural QA dataset (denoted Tk-QA). We perform the evaluation over 8 SuperGLUE tasks with discrete labels.
+
+Results Figure 4 shows the results. Evaluation with non-sensical labels (left) reveals that all models pre-trained on a synthetic TeaBReaC dataset (TK-RANDOM, and TK-CoAT) are more robust to the labels' semantics than our natural-language baseline (TK-QA). However, a comparison of TK-RANDOM and TK-CoAT suggests that TK-CoAT's preference for learning functional relations is a
+
+![](images/d97f354104c1c2935243a225342f1edb0ba840ba359193311ea8699e57238d5e.jpg)  
+Figure 5: Effectiveness of Concept-aware training: Natural-Instructions: Win rate of models utilising Concept-aware training (CoAT; §3) and traditional instruction tuning (TK-RANDOM; §4.2) evaluated on (top) all and (bottom) reasoning tasks of Natural-Instructions collection. Values indicate the number of tasks where the referenced model reaches significantly higher accuracy than the other. For the similar tasks, the difference in models' performance is not statistically significant.
+
+composition of both using a synthetic dataset in pre-training and CoAT's data construction.
+
+A comparison to previous models reveals that all multitask models experience substantially larger decay in performance than our models. We suspect this feature could be a bias specific to massive multi-task learning emerging when label semantics can explain a large portion of training data. This result is consistent with Wei et al. (2023), but contrary to their conclusions, we show that ICL robust to semantic distractions does not emerge exclusively with very large  $(\geq 100\mathrm{B})$  model scale.
+
+Nevertheless, we note that the smaller CoAT model still relies on labels' semantics when recognizable (Flipped labels; Fig. 4 right), less than previous models, but comparable to our baselines.
+
+# 4.6 Practical effectiveness of concept-aware in-context learners (RQ3)
+
+Finally, we assess the practical quality of concept-aware ICL on previously unseen tasks in a simulated low-resource application with only three randomly-chosen demonstrations. We evaluate on samples from two collections of tasks: (i) SuperGLUE (Wang et al., 2019) consisting of 10 tasks requiring a variety of reasoning skills, and (ii) a test split of Natural-Instructions (Wang et al., 2022) from which we pick 60 extractive tasks. For SuperGLUE tasks, we verbalize both the demonstrations and predicted sample using all available templates within PromptSource library (Bach et al., 2022) and report results for the best-performing template
+
+<table><tr><td></td><td>AxG</td><td>Ax-b</td><td>WSC</td><td>CB</td><td>RTE</td><td>WiC</td><td>ReCoRD</td><td>BoolQ</td><td>COPA</td><td>MultiRC</td></tr><tr><td>TK-RANDOM-1B</td><td>49.4±5.2</td><td>43.6±4.8</td><td>52.7±5.1</td><td>21.8±3.9</td><td>29.3±4.6</td><td>18.0±4.0</td><td>15.3±3.8</td><td>34.0±5.0</td><td>74.7±3.4</td><td>5.1±2.4</td></tr><tr><td>TK-RANDOM-3B</td><td>50.2±5.4</td><td>57.5±4.8</td><td>52.0±5.5</td><td>47.8±5.1</td><td>48.9±4.8</td><td>50.1±4.4</td><td>16.3±7.3</td><td>62.8±4.6</td><td>75.5±2.8</td><td>2.1±1.5</td></tr><tr><td>TKINFO-1B</td><td>50.0±4.2</td><td>42.6±5.7</td><td>52.0±4.3</td><td>47.2±3.9</td><td>49.2±4.8</td><td>53.2±4.5</td><td>15.5±4.0</td><td>19.6±2.3</td><td>61.5±2.3</td><td>3.2±1.2</td></tr><tr><td>TKINFO-3B</td><td>50.8±4.6</td><td>57.2±4.9</td><td>53.5±4.8</td><td>47.3±5.4</td><td>54.7±4.9</td><td>53.6±4.7</td><td>22.6±4.5</td><td>64.4±4.8</td><td>76.3±3.0</td><td>2.7±2.1</td></tr><tr><td>TK-CoAT-1B</td><td>50.4±5.3</td><td>52.7±4.6</td><td>53.6±5.2</td><td>46.9±4.9</td><td>53.7±4.9</td><td>53.5±5.3</td><td>17.0±3.5</td><td>63.8±5.4</td><td>76.1±3.2</td><td>11.4±2.6</td></tr><tr><td>TK-CoAT-3B</td><td>57.9±4.9</td><td>57.2±4.8</td><td>53.6±4.5</td><td>60.4±4.8</td><td>52.0±5.4</td><td>56.9±5.0</td><td>23.1±3.8</td><td>63.6±4.3</td><td>81.3±3.3</td><td>56.9±3.6</td></tr></table>
+
+Table 1: Effectiveness of concept-aware training: SuperGLUE: ROUGE-L scores of ICL models evaluated in few-shot setting on SuperGLUE tasks (Wang et al., 2019), trained using (i) random demonstrations sampling used in previous work, (ii) informative demonstrations sampling ( $\S$ 4.2) and (iii) informative+non-trivial sampling (CoAT;  $\S$ 3). Underlined are the best results per each task and model size. See Table 5 for a comparison to previous models.
+
+for each model. For Natural-Instructions tasks, we prefix the demonstrations with the instruction provided with each task. To maximise evaluation reliability over all models, we analyse the error cases and choose to report the results in ROUGE-L for SuperGLUE, and in a standard accuracy for Natural-Instructions. We specify the metrics selection analysis and other evaluation details in Appendix B, with prompt examples in Table 4.
+
+As a primary reference point, we again compare the results of CoAT-trained models to  $\mathrm{TK}$ -RANDOM, where we can make sure that all other training configurations except for the data construction method are identical. Further, we compare to  $\mathrm{TK}$ -INFO (without Non-triviality condition; §4.2) to also evaluate the importance of the non-triviality condition. Finally, to provide additional context to our results, we also compare the performance of CoAT-trained models to previous in-context learners (§4.3).
+
+Results Figure 5 compares the accuracy of CoAT-trained models to our baselines: (i) without systematic demonstrations selection (TK-RANDOM) and (ii) without the non-triviality condition (TK-INFO), over 60 tasks of NaturalInstructions collection. In comparison to TK-RANDOM, CoAT models reach significantly higher accuracy on 41 and 45 of 60 tasks, with comparable performance on a majority (13 and 14) of other tasks. The difference is further magnified on reasoning tasks, which we argue might better evaluate models' ability to in-context learn a functional relation of the new task. A comparison of TK-INFO with TK-RANDOM shows that the performance on reasoning tasks is mainly fostered by the CoAT's informativeness condition, but in a full task collection, TK-CoAT still outperforms TK-INFO in 19 out of 60 tasks. Evaluations on other task segments can be found in Appendix C.2.
+
+In the evaluation over the tasks of SuperGLUE collection (Table 1), we additionally report the specific values of ROUGE-L that our baselines
+
+and CoAT models achieve. With a single exception, models utilising a concept-based selection of demonstrations (Tk-CoAT and Tk-INFO) consistently reach higher scores than Tk-RANDOM. Our analyses of models' predictions reveal that in 7 out of 20 evaluations, Tk-RANDOM models fail to follow the task's instruction, consequentially responding out of valid label space. Tk-CoAT is shown to mitigate this issue in all cases except for a smaller CoAT-trained model on MultiRC. A comparison of Tk-CoAT with Tk-INFO shows that non-triviality condition is more substantial for a smaller model, but the models of both sizes benefit similarly from the concept-sharing selection of demonstrations.
+
+Comparison to multitask learners Figure 6 contextualizes the performance of CoAT models trained on two datasets of a single (QA) task with existing instructional models trained on massive mixtures of 35-1,836 tasks. Over all the NI tasks (Fig. 6; top), CoAT models outperform multitask learners on a majority of tasks in 3 of 6 competitions. CoAT models are outperformed by FLAN models but perform at least similarly for the majority of the tasks in 5 out of 6 competitions. The evaluation on reasoning tasks (Fig. 6; middle) supports our hypothesis that CoAT particularly promotes improvements in in-context learning of new reasoning abilities, winning on reasoning tasks over FLAN and Tk-Instruct in a comparable number of cases than the opponents.
+
+Finally, we look at a few tasks with unseen labels for both TK-INSTRUCT and FLAN models (Fig. 6; bottom) where multitask learners can not rely on shortcuts based on unseen tasks' labels. Here, the results of competition between CoAT with FLAN models turns over, with CoAT models performing significantly better on 4 out of 6 tasks. While this sole segment is not big enough for robust conclusions, the results further support our claim that
+
+![](images/217fdad25ee376932b73ce0413b554553900eb67f3b3eb7ccf34e4a78a69d879.jpg)
+
+![](images/822a18d7419bb1220241b7840768bd54db250a506ea5363642c69cf175fcf12c.jpg)
+
+![](images/689576d059001cf0c6f48c14616fab8871e814388bb9416891ea325ff4ab4ec2.jpg)  
+Figure 6: Performance comparison to previous work: Natural-Instructions collection: Win rate of CoAT models trained using two (2) tasks and previous in-context learners trained on mixtures of 35 (T0), 1,616 (Tk-Instruct) and 1,836 tasks (Tk-FLAN). Values denote the number of tasks where the model reaches significantly better accuracy. Evaluations over (top) all tasks, (middle) reasoning tasks, (bottom) tasks with labels not present in the training mix of Tk-Instruct and Tk-FLAN.
+
+concept-based ICL is more robust to semantic distractions (RQ2).
+
+Table 5 in Appendix C details models' scores on SuperGLUE tasks, providing further evidence on overall comparability of CoAT models to multitask learners. For instance, a comparison with Tk-Instruct reveals that CoAT's 1B and 3B models reach higher absolute scores on 3 and 5 out of the 7 Tk-Instruct's unseen tasks.
+
+# 5 Conclusion
+
+Inspired by data-centric theories on emergence of in-context learning, we propose and implement a Concept-aware Training framework for constructing training scenarios that challenge language models to learn to utilise latent concepts from in-context prompts. We show that language models can be trained to benefit from unseen concepts (RQ1), and that such ICL is more robust in learning functional relations of a new task from demonstrations (RQ2). Finally, in extrinsic evaluation over 70 tasks, we demonstrate the practical efficiency of concept-dependent training data, with CoAT mod
+
+els bringing significant improvements on 41 and 45 out of 60 Natural-Instructions tasks, or 6 and 5 of 10 SuperGLUE tasks (RQ3), while reaching a performance comparable to multitask learning requiring magnitudes of more data.
+
+More broadly, our work pioneers an alternative direction for scaling the quality of in-context learning to the previously explored model and data scale axes. We wish towards inspire future work to a more proactive approach to refining training data properties so that fitting such data necessitates the emergence of the specific, robust abilities of the models, such as the concept-learning ability.
+
+Specifically, future work can build upon our findings in researching ways to upscale concept-dependent data in unsupervised settings, allowing for pre-training more robust language models with a fraction of data and computing budget.
+
+# Limitations
+
+Although our main objective is to assess the efficiency of concept-aware training, we acknowledge the limitations of our comparison to the previous work, where several aspects convolute the representative comparison of different in-context learners: (i) each of the multitask learners was trained on a different, yet massive set of tasks, making it difficult to find a broader collection that is new for multiple models; For this purpose, we surveyed three standard collections used for few-shot evaluation: CLUES (Mukherjee et al., 2021), RAFT (Alex et al., 2021) and FLEX (Bragg et al., 2021), but found in total only three tasks unseen by the multitask learners of previous work, all of the same type (classification). Therefore, in our evaluations, we use (a) Tk-Instruct's own evaluation set and (b) SuperGLUE, which significantly overlaps with the training tasks of previous work. (ii) many aspects make it "easier" for the model to improve, including the domain of labels or prompt format matching the training distribution (relevant to Tk-InSTRUCT and FLAN evaluated on Natural-Instructions).
+
+Another aspect that we neglect in our experiments in favour of more in-depth analyses is the impact of pretraining projected into the properties of the foundation model that we use. We pick T5 as a base model to maximise comparability with previous work. While we do not identify any concrete reason to assume that CoAT would perform worse with other base models, one should note that our results do not provide any evidence in this respect.
+
+Finally, we note that the applicability of CoAT is conditioned by the availability of the annotated concepts  $C$  in the training datasets, which might be difficult to obtain for natural-language datasets. Our implementation circumvents this issue by using a synthetically curated dataset. Hence, we simultaneously show that concept-aware abilities can also be obtained in the restrictive settings of synthetic-dataset pre-training, where we note that the volume and variability of the synthetic dataset can be scaled further much easier than the natural dataset(s) (Trivedi et al., 2022). Nevertheless, our experiments do not provide any empirical evidence for answering to what extent could further extension of synthetically-generated datasets, possibly covering even more complex concepts, scale to further performance gains.
+
+# Ethical Considerations & Broader Impact
+
+The primary motivation of our work is to minimise the computing demands for the creation of accurate in-context learners by deepening our understanding of the covariates of the resulting quality. We believe that our presented method, as well as the future data-efficient methods improving our understanding of in-context learning, will enable the democratization of the creation of robust and accurate in-context learning models for both research and industry.
+
+Finally, we note that data-efficient methods for training ICLs (as opposed to multitask training) might open possibilities for creating more accurate ICLs specialized to languages outside English, where training datasets are scarce. We look forward for the future work that will explore the potential of data-efficient instruction tuning specifically on the target-language datasets, creating in-context learners specially tailored for target languages outside English.
+
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+Yao Lu, Max Bartolo, Alastair Moore, Sebastian Riedel, and Pontus Stenetorp. 2022. Fantastically Ordered Prompts and Where to Find Them: Overcoming Few-Shot Prompt Order Sensitivity. In Proceedings of the
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+60th Annual Meeting of the ACL (Volume 1: Long Papers), pages 8086-8098, Dublin, Ireland. ACL.  
+Man Luo, Xin Xu, Yue Liu, Panupong Pasupat, and Mehran Kazemi. 2024. In-context Learning with Retrieved Demonstrations for Language Models: A Survey.  
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+Lukáš Mikula, Michal Štefánik, Marek Petrovic, and Petr Sojka. 2024. Think Twice: Measuring the Efficiency of Eliminating Prediction Shortcuts of Question Answering Models. In Proceedings of the 18th Conference of the European Chapter of the ACL (Volume 1: Long Papers), pages 2179-2193, St. Julian's, Malta. ACL.  
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+
+Victor Sanh, Albert Webson, Colin Raffel, Stephen Bach, Lintang Sutawika, Zaid Alyafeai, Antoine Chaffin, Arnaud Stiegler, Arun Raja, Manan Dey, M Saiful Bari, Canwen Xu, Urmish Thakker, Shanya Sharma Sharma, Eliza Szczechla, Taewoon Kim, Gunjan Chhablani, Nihal Nayak, Debajyoti Datta, Jonathan Chang, Mike Tian-Jian Jiang, Han Wang, Matteo Manica, Sheng Shen, Zheng Xin Yong, Harshit Pandey, Rachel Bawden, Thomas Wang, Trishala Neeraj, Jos Rozen, Abheesht Sharma, Andrea Santilli, Thibault Fevry, Jason Alan Fries, Ryan Teehan, Teven Le Scao, Stella Biderman, Leo Gao, Thomas Wolf, and Alexander M Rush. 2022. Multitask Prompted Training Enables Zero-Shot Task Generalization. In International Conference on Learning Representations.  
+Timo Schick and Hinrich Schütze. 2020. Exploiting cloze questions for few shot text classification and natural language inference.  
+Michal Štefánik and Marek Kadlčík. 2023. Can Incontext Learners Learn a Reasoning Concept from Demonstrations? In Proceedings of the 1st Workshop on Natural Language Reasoning and Structured Explanations (NLRSE), pages 107-115, Toronto, Canada. ACL.  
+Michal Štefánik, Marek Kadlčík, Piotr Gramacki, and Petr Sojka. 2023. Resources and Few-shot Learners for In-context Learning in Slavic Languages. In Proceedings of the 9th Workshop on Slavic Natural Language Processing 2023 (SlavicNLP 2023), pages 94-105, Dubrovnik, Croatia. ACL.  
+Michal Štefánik, Vít Novotné, Nikola Groverova, and Petr Sojka. 2022. Adaptor: Objective-Centric Adaptation Framework for Language Models. In Proceedings of the 60th Annual Meeting of the ACL: System Demonstrations, pages 261-269, Dublin, Ireland. ACL.  
+Romal Thoppilan, Daniel De Freitas, Jamie Hall, Noam Shazeer, Apoorv Kulshreshtha, Heng-Tze Cheng, Alicia Jin, Taylor Bos, Leslie Baker, Yu Du, YaGuang Li, Hongrae Lee, Huaixiu Steven Zheng, Amin Ghafouri, Marcelo Menegali, Yanping Huang, Maxim Krikun, Dmitry Lepikhin, James Qin, Dehao Chen, Yuanzhong Xu, Zhifeng Chen, Adam Roberts, Maarten Bosma, Vincent Zhao, Yanqi Zhou, Chung-Ching Chang, Igor Krivokon, Will Rusch, Marc Pickett, Pranesh Srinivasan, Laichee Man, Kathleen Meier-Hellstern, Meredith Ringel Morris, Tulsee Doshi, Renelito Delos Santos, Toju Duke, Johnny Soraker, Ben Zevenbergen, Vinodkumar Prabhakaran, Mark Diaz, Ben Hutchinson, Kristen Olson, Alejandra Molina, Erin Hoffman-John, Josh Lee, Lora Aroyo, Ravi Rajakumar, Alena Butryna, Matthew Lamm, Viktoriya Kuzmina, Joe Fenton, Aaron Cohen, Rachel Bernstein, Ray Kurzweil, Blaise Aguera-Arcas, Claire Cui, Marian Croak, Ed Chi, and Quoc Le. 2022. LaMDA: Language Models for Dialog Applications.
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+Harsh Trivedi, Niranjan Balasubramanian, Tushar Khot, and Ashish Sabharwal. 2022. Teaching Broad Reasoning Skills for Multi-Step QA by Generating Hard Contexts. In Proceedings of the 2022 Conference EMNLP, pages 6541–6566, Abu Dhabi, United Arab Emirates. ACL.  
+Michal Štefánik and Marek Kadlcík. 2023. Can Incontext Learners Learn a Reasoning Concept from Demonstrations? In Proceedings of the 1st Workshop on Natural Language Reasoning and Structured Explanations (NLRSE), pages 107-115, Toronto, Canada. ACL.  
+Alex Wang, Yada Pruksachatkun, Nikita Nangia, Amanpreet Singh, Julian Michael, Felix Hill, Omer Levy, and Samuel R. Bowman. 2019. SuperGLUE: A Stickier Benchmark for General-Purpose Language Understanding Systems, page 3266-3280. Curran Associates Inc., Red Hook, NY, USA.  
+Alex Wang, Amanpreet Singh, Julian Michael, Felix Hill, Omer Levy, and Samuel Bowman. 2018. GLUE: A Multi-Task Benchmark and Analysis Platform for Natural Language Understanding. In Proc. of the 2018 EMNLP Workshop BlackboxNLP: Analyzing and Interpreting Neural Networks for NLP, pages 353-355, Brussels, Belgium. ACL.  
+Boshi Wang, Sewon Min, Xiang Deng, Jiaming Shen, You Wu, Luke Zettlemoyer, and Huan Sun. 2023. Towards Understanding Chain-of-Thought Prompting: An Empirical Study of What Matters. In *ICLR* 2023 Workshop on Mathematical and Empirical Understanding of Foundation Models.  
+Yizhong Wang, Swaroop Mishra, Pegah Alipoormolabashi, Yeganeh Kordi, Amirreza Mirzaei, Atharva Naik, Arjun Ashok, Arut Selvan Dhanasekaran, Anjana Arunkumar, David Stap, Eshaan Pathak, Giannis Karamanolakis, Haizhi Lai, Ishan Purohit, Ishani Mondal, Jacob Anderson, Kirby Kuznia, Krima Doshi, Kuntal Kumar Pal, Maitreya Patel, Mehrad Moradshahi, Mihir Parmar, Mirali Purohit, Neeraj Varshney, Phani Rohitha Kaza, Pulkit Verma, Ravsehaj Singh Puri, Rushang Karia, Savan Doshi, Shailaja Keyur Sampat, Siddhartha Mishra, Sujan Reddy A, Sumanta Patro, Tanay Dixit, and Xudong Shen. 2022. Super-Natural Instructions: Generalization via Declarative Instructions on 1600+ NLP Tasks. In Proceedings of the 2022 Conference EMNLP, pages 5085-5109, Abu Dhabi, United Arab Emirates. ACL.  
+Jason Wei, Maarten Bosma, Vincent Y. Zhao, Kelvin Guu, Adams Wei Yu, Brian Lester, Nan Du, Andrew M. Dai, and Quoc V. Le. 2021. Finetuned language models are zero-shot learners.  
+Jason Wei, Xuezhi Wang, Dale Schuurmans, Maarten Bosma, brian richter, Fei Xia, Ed H. Chi, Quoc V Le, and Denny Zhou. 2022. Chain of Thought Prompting Elicits Reasoning in Large Language Models. In Advances in Neural Information Processing Systems.
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+Jerry Wei, Jason Wei, Yi Tay, Dustin Tran, Albert Webson, Yifeng Lu, Xinyun Chen, Hanxiao Liu, Da Huang, Denny Zhou, and Tengyu Ma. 2023. Larger language models do in-context learning differently.  
+Noam Wies, Yoav Levine, and Amnon Shashua. 2023. The Learnability of In-Context Learning.  
+Thomas Wolf, Lysandre Debut, Victor Sanh, Julien Chaumont, Clement Delangue, Anthony Moi, Pierric Cistac, Tim Rault, Remi Louf, Morgan Funtowicz, Joe Davison, Sam Shleifer, Patrick von Platen, Clara Ma, Yacine Jernite, Julien Plu, Canwen Xu, Teven Le Scao, Sylvain Gugger, Mariama Drame, Quentin Lhoest, and Alexander Rush. 2020. Transformers: State-of-the-Art Natural Language Processing. In Proc. of the 2020 Conf. EMNLP: System Demonstrations, pages 38-45. ACL.  
+Sang Michael Xie, Aditi Raghunathan, Percy Liang, and Tengyu Ma. 2022. An Explanation of In-context Learning as Implicit Bayesian Inference. In International Conference on Learning Representations.  
+Zhengnan Xie, Sebastian Thiem, Jaycie Martin, Elizabeth Wainwright, Steven Marmorstein, and Peter Jansen. 2020. WorldTree v2: A corpus of science-domain structured explanations and inference patterns supporting multi-hop inference. In Proceedings of the Twelfth Language Resources and Evaluation Conference, pages 5456-5473, Marseille, France. European Language Resources Association.  
+Linting Xue, Noah Constant, Adam Roberts, Mihir Kale, Rami Al-Rfou, Aditya Siddhant, Aditya Barua, and Colin Raffel. 2021. mT5: A Massively Multilingual Pre-trained Text-to-Text Transformer. In Proceedings of the 2021 Conference of the North American Chapter of the ACL: Human Language Technologies, pages 483-498, Online. ACL.  
+Zhilin Yang, Peng Qi, Saizheng Zhang, Yoshua Bengio, William Cohen, Ruslan Salakhutdinov, and Christopher D. Manning. 2018. HotpotQA: A Dataset for Diverse, Explainable Multi-hop Question Answering. In Proceedings of the 2018 Conference EMNLP, pages 2369-2380, Brussels, Belgium. ACL.  
+Sheng Zhang, Xiaodong Liu, Jingjing Liu, Jianfeng Gao, Kevin Duh, and Benjamin Van Durme. 2018. ReCoRD: Bridging the Gap between Human and Machine Commonsense Reading Comprehension. arXiv e-prints, page arXiv:1810.12885.  
+Wayne Xin Zhao, Kun Zhou, Junyi Li, Tianyi Tang, Xiaolei Wang, Yupeng Hou, Yingqian Min, Beichen Zhang, Junjie Zhang, Zican Dong, Yifan Du, Chen Yang, Yushuo Chen, Zhipeng Chen, Jinhao Jiang, Ruiyang Ren, Yifan Li, Xinyu Tang, Zikang Liu, Peiyu Liu, Jian-Yun Nie, and Ji-Rong Wen. 2023. A Survey of Large Language Models.
+
+# A Training details
+
+Table 2 shows a full training example for each stage of training: (1) TeaBReaC with synthetic contexts (top) and (2) AdversarialQA with natural-language contexts (bottom). In all our training setups, we fine-tune all model parameters for teacher-forced next-token prediction, conventionally used in training sequence-to-sequence language models. In the two training stages (TeaBReaC and AdversarialQA), we use a learning rate of  $5e^{-5}$  and  $2e^{-5}$ , respectively. Other parameters remain identical between stages: effective batch size = 30 samples and early stopping with the patience of 2,000 updates based on evaluation loss on a standardized validation set of each dataset. We do not report the absolute values of evaluation loss as these are not directly comparable. In CoAT training, we use a random subsample of 20 informative examples as a candidate set for a selection of non-trivial demonstrations.
+
+Other parameters of training configuration default to Training Arguments of Transformers library (Wolf et al., 2020) in version 4.19.1. For readability, we implement the relatively complex demonstrations' selection as a new objective of the Adaptor library (Štefánik et al., 2022). The picked demonstrations are encoded into a format consistent with the evaluation.
+
+# B Evaluation details
+
+Tables 3 shows an example of an instruction for each evaluation that we perform within the concept-learning evaluation. For readability, we only shorten the examples of HotpotQA, where we omit some sources of data available for the model. In the case of TeaBReaC not shown in this table, the evaluation prompt format is the same as in training (Table 2), whereas we make sure that the reasoning chains of evaluation samples differ from the training.
+
+SuperGLUE Evaluation format As mentioned in Section 4.1, we verbalize both the demonstrations and predicted sample using all available templates of PromptSource library (Bach et al., 2022), obtaining prompts for each demonstration prompt  $x_{i}$  and its label  $y_{i}$  in a free-text form. The prompts commonly contain the full-text match of the possible labels as options for the model.
+
+Following the example of Wang et al. (2022), we additionally prepend the demonstrations and
+
+labels with keywords "Input" and "Prediction" and separate demonstrations with new lines. Thus, the resulting input  $\rightarrow$  output pairs in evaluation take this format:
+
+"Input:  $x_{1}$  Prediction:  $y_{1} <   \text{newline} >$  Input:  $x_{2}$  Prediction:  $y_{2} <   \text{newline} >$  Input:  $x_{3}$  Prediction:  $y_{3} <   \text{newline} >$  Input:  $x_{pred}$  Prediction:  $\mathbf{\theta}^{\prime \prime}\rightarrow \mathbf{\theta}^{\prime \prime}y_{\mathrm{pred}}$
+
+where demonstrations  $(x_{i},y_{i})$  are picked randomly but consistently between all evaluated models.
+
+Natural-Instructions Evaluation format In the evaluations on Natural-Instructions, we closely follow the example of Wang et al. (2022) and additionally prepend the sequence of demonstrations with an instruction provided for each task:
+
+“<task instruction> <newline>  
+Input:  $x_{1}$  Prediction:  $y_{1}$  <newline>  
+Input:  $x_{2}$  Prediction:  $y_{2}$  <newline>  
+Input:  $x_{3}$  Prediction:  $y_{3}$  <newline>  
+Input:  $x_{pred}$  Prediction:  $\rightarrow$  "ypred"
+
+where the <task instruction> contains the instruction as would be given to the annotators of the evaluation task, usually spanning between 3-6 longer sentences. The demonstrations are again picked randomly but consistently between models.
+
+Examples of evaluation prompts for both SuperGLUE and Natural-Instructions can be found in Table 4.
+
+Evaluation metrics selection Previous work training in-context few-shot learners is not consistent in the use of evaluation metrics, and the choice usually boils down to either using the exact-match accuracy (Sanh et al., 2022; Chung et al., 2022) or ROUGE-L of Lin (2004) (Wang et al., 2022), evaluating the longest common sequence of tokens. We investigate these two options with the aim of not penalising the models for minor discrepancies in the output format (in the accuracy case) but avoiding false positive evaluations in predictions that are obviously incorrect (in the ROUGE case).
+
+Investigation of the models' predictions reveals that the selection of the metric makes a large difference only in the case of Tk-Instruct models, where the situation differs between SuperGLUE and Natural-Instructions, likely due to the character of the evaluation prompts.
+
+(1) On SuperGlue, e.g. on MultiRC task, for the evaluation prompt: "Does answer sound like a valid
+
+<table><tr><td>Dataset</td><td>Concept</td><td>Training instruction</td><td>Target</td></tr><tr><td>TeaBReaC</td><td>Exactly-matching reasoning chain 
+[“select”→ 
+“maximum”→ 
+“list”→ 
+“maximum”→ 
+“sum”]</td><td>“Input: how many points did the Monte Vesuvio&quot; score in their two highest scoring matches? Context: scores of games of Pentagon&quot;. 99 scores of games of monte vesuvio&quot;. 67 scores of games of Pentagon&quot;. 6 scores of games of monte vesuvio&quot;. 76 scores of games of Pentagon&quot;. 37 scores of games of monte vesuvio&quot;. 56 scores of games of Pentagon&quot;. 8 scores of games of Pentagon&quot;. 90 scores of games of Pentagon&quot;. 20 Answer: Prediction: 143 [2 more examples] Input: how many points did the Bell 212 score in their two highest scoring games? Context: scores of games of bell 212. 90 scores of games of S-50. 54 scores of games of bell 212. 41 scores of games of bell 212. 36 scores of games of S-50. 23 scores of games of bell 212. 6 scores of games of bell 212. 2 scores of games of S-50. Prediction: ”</td><td>“131”</td></tr><tr><td>AdversarialQA</td><td>Matching question-word 
+“Who”</td><td>“Input: Who was the Speaker in 1909? Context: Second, Democrats have always elevated their minority floor leader to the speakship upon reclaiming majority status. Republicans have not always followed this leadership succession pattern. In 1919, for instance, Republicans bypassed James R. Mann, R-IL, who had been minority leader for eight years, and elected Frederick Gillett, R-MA, to be Speaker. Mann &quot;had angered many Republicans by objecting to their private bills on the floor,&quot; also he was a protégé of autocratic Speaker Joseph Cannon, R-IL (1903–1911), and many Members &quot;suspected that he would try to re-centralize power in his hands if elected Speaker.&quot; More recently, although Robert H. Michel was the Minority Leader in 1994 when the Republicans regained control of the House in the 1994 midterm elections, he had already announced his retirement and had little or no involvement in the campaign, including the Contract with America which was unveiled six weeks before voting day. Prediction: Joseph Cannon, R-IL. [2 more examples] Input: Who created the legal system still in use in Florida? Context: As a result of these initiatives northeastern Florida prospered economically in a way it never did under Spanish rule. Furthermore, the British governors were directed to call general assemblies as soon as possible in order to make laws for the Floridas and in the meantime they were, with the advice of councils, to establish courts. This would be the first introduction of much of the English-derived legal system which Florida still has today including trial by jury, habeas corpus and county-based government. Neither East Florida nor West Florida would send any representatives to Philadelphia to draft the Declaration of Independence. Florida would remain a Loyalist stronghold for the duration of the American Revolution. Prediction: ”</td><td>“British”</td></tr></table>
+
+Table 2: Examples of training instructions with expected outputs, for both our datasets applied in training. Note that the shared reasoning concept is not a part of the model's input.
+
+answer to the question: question", TK-INSTRUCT-3B in our evaluation predicts "Yes." or "Yes it is" (instead of "Yes"), or "No not at all" (instead of "No"), likely due to the resemblance with the format of training outputs. As we do not wish to penalize these cases, we use ROUGE-L over all SuperGLUE evaluations.
+
+(2) In Natural-Instructions evaluation, we find that Tk-InStruct often predicts longer extracts from the input prompt. This is problematic with ROUGE-L in the cases where the extract contains all possible answers, such as in the Tk-InStruct1B's prediction: "yes or no" to the prompt whose instruction ends with "Please answer in the form of yes or no". As we encounter this behaviour in a large portion of Natural-Instructions tasks, we evaluate all models on Natural-Instructions for exact-match accuracy after the normalization of the casing and the removal of non-alphabetic symbols. To make sure that the model is presented with the exact-matching answer option, we exclude from evaluation the tasks where the correct answer is not presented in the task's instruction. The reference to the list of Natural-Instructions evaluation tasks can be found in Appendix C.4.
+
+For the reported evaluations of the Reasoning tasks, we pick from the list of evaluation tasks the
+
+![](images/e0e7d532479e385b1f3973af687e58615cefb4fd580f78d58078d46b6d6a6651.jpg)  
+Figure 7: In-context learning of natural concepts for each dataset: While CoAT improves the ability to benefit from reasoning concepts on average (Fig. 3), per-concept evaluation reveals that this ability is not consistently robust.
+
+ones concerned with the reasoning task by simply matching the tasks with 'reasoning' in their name, resulting in the collection of 20 evaluation tasks.
+
+# C Further evaluations
+
+# C.1 SuperGLUE evaluations of other models
+
+Table 5 compares the performance over the tasks of SuperGLUE collection (Wang et al., 2019) for CoAT models trained on two tasks of the same (QA) type with in-context learners trained on 35-1,836 tasks of the comparable size. Despite the
+
+<table><tr><td>Dataset</td><td>Concept</td><td>Model instruction</td><td>Expected output</td></tr><tr><td>GLUE NLI Diag.</td><td>Double negation</td><td>“Input: I will say that she stole my money. Question: I won’t say that she didn’t steal my money. True, False, or Neither? Prediction: Neither Input: I won’t say that she didn’t steal my money. Question: I will say that she stole my money. True, False, or Neither? Prediction: Neither Input: A rabbi is at this wedding, standing right there standing behind that tree. Question: It’s not the case that there is no rabbi at this wedding; he is right there standing behind that tree. True, False, or Neither? Prediction: True Input: Even after now finding out that it’s animal feed, I won’t ever stop being addicted to Flamin’ Hot Cheetos. Question: Even after now finding out that it’s animal feed, I will never stop being addicted to Flamin’ Hot Cheetos. True, False, or Neither? Prediction: ”</td><td>“True”</td></tr><tr><td>OpenBookQA</td><td>Shared facts: {&quot;Earth is greater in mass than Mars&quot;, &quot;gravity means gravitational pull; gravitational force; gravitational attraction&quot;, &quot;as the force of gravity increases, the weight of objects will increase.&quot;}</td><td>“Facts: a decrease is a kind of change. increase means more. as mass of a planet; of a celestial body increases, the force of gravity on that planet will increase. to change means to become different. an animal is a kind of living thing. the gravitational force of a planet; of a celestial object does not change the mass of an object on that planet or celestial body. an increase is the opposite of a decrease. an astronaut is a kind of human. massive means great in mass. the Mars Rover is a kind of vehicle. a living thing is a kind of object. Earth is greater in mass than Mars. gravity means gravitational pull; gravitational energy; gravitational force; gravitational attraction. greater means higher; more in value. stay the same means not changing. a moon is a kind of celestial object; body. an increase is a kind of change. Earth is a kind of planet. as the force of gravity increases, the weight of objects will increase. less is similar to decrease. Mars is a kind of planet. Input: An object has a weight of 10 kg on the surface of Earth. If the same object were transported to the surface of Mars, the object would have a weight of 3.8 kg. Which best explains why the weight of the object changed when transported from Earth to Mars? (A) The density of the object is greater on Earth than it is on Mars. (B) The volume of the object is greater on Earth than it is on Mars. (C) Gravitational force is greater on Earth than it is on Mars. (D) Atmospheric pressure is less on Earth than it is on Mars. Prediction: Gravitational force is greater on Earth than it is on Mars [two more examples] Input: When astronauts walked on the Moon, they used weighted boots to help them walk due to the lower gravitational pull. What difference between Earth and the Moon accounts for the difference in gravity? (A) density (B) diameter (C) mass (D) volume. Prediction: ”</td><td>&quot;mass”</td></tr><tr><td>HotpotQA</td><td>Shared relation in reasoning: “X is a genus”</td><td>“Input: Are Broughtonia and Laeliocattleya both orchids? Hint: use the information from the paragraphs below to answer the question. Otaara, abbreviated Otr. in the horticultural trade, is an intergeneric hybrid of orchids, with &quot;Brassavola&quot;, &quot;Broughtonia&quot;, &quot;Cattleya&quot;, &quot;Laelia&quot; and &quot;Sophronitis&quot; as parent genera. Paracaleana commonly known as duck orchids, is a genus of flowering plants in the orchid family, Orchidaceae that is found in Australia and New Zealand. Duck orchids have a single leaf and one or a few, dull-coloured, inconspicuous flowers. (...) Prediction: yes [two more examples] Input: Are both Parodia and Thalictrum flowering plants? Hint: use the information from the paragraphs below to answer the question. - Thalictrum () is a genus of 120-200 species of herbaceous perennial flowering plants in the Ranunculaceae (buttercup) family native mostly to temperate regions. Meadow-rue is a common name for plants in this genus. - Parodia is a genus of flowering plants in the cactus family Cactaceae, native to the uplands of Argentina, Peru, Bolivia, Brazil, Colombia and Uruguay. This genus has about 50 species, many of which have been transferred from &quot;Eriocactus&quot;, &quot;Notocactus&quot; and &quot;Wigginsia&quot;. They range from small globose plants to 1 m tall columnar cacti. All are deeply ribbed and spiny, with single flowers at or near the crown. Some species produce offsets at the base. They are popular in cultivation, but must be grown indoors where temperatures fall below 10 degrees. Prediction: ”</td><td>“yes”</td></tr><tr><td>WorldTree</td><td>Relation of objects: &quot;generate&quot;</td><td>“Input: Despite what some think, instead around themselves, our planet spins around...”</td><td>“the closest star from star from</td></tr></table>
+
+Table 3: Examples of evaluation instructions with expected outputs, for each dataset used in evaluation of incontext learning of new concepts (RQ1). Note that the demonstrations within the instructions share the annotated Concept with the following predicted sample.
+
+<table><tr><td>SuperGLUE</td><td>-</td><td>“Input: The soldiers were concealed in the brush. Select the most plausible cause: - They were armed with rifles. - They wore camouflage uniforms. Prediction: They wore camouflage uniforms. Input: The print on the brochure was tiny. Select the most plausible effect: - The man put his glasses on. - The man retrieved a pen from his pocket. Prediction: The man put his glasses on. Input: I excused myself from the group. Select the most plausible cause: - I turned off my phone. - My phone rang. Prediction: My phone rang. Input: My body cast a shadow over the grass. Select the most plausible cause: - The sun was rising. - The grass was cut. Prediction:”</td><td>“The sun was rising.”</td></tr><tr><td>Natural-Instructions</td><td>-</td><td>“Indicate with ‘Yes’ if the given question involves the provided reasoning ‘Category’. Indicate with ‘No’, “Yes” otherwise. We define five categories of temporal reasoning. First: “event duration” which is defined as the understanding of how long events last. For example, “brushing teeth”, usually takes few minutes. Second: “transient v. stationary” events. This category is based on the understanding of whether an event will change over time or not. For example, the sentence “he was born in the U.S.” contains a stationary event since it will last forever; however, “he is hungry” contains a transient event since it will remain true for a short period of time. Third: “event ordering” which is the understanding of how events are usually ordered in nature. For example, “earning money” usually comes before “spending money”. The fourth one is “absolute timepoint”. This category deals with the understanding of when events usually happen. For example, “going to school” usually happens during the day (not at 2 A.M). The last category is “frequency” which refers to how often an event is likely to be repeated. For example, “taking showers” typically occurs 5 times a week, “going to Saturday market” usually happens every few weeks/months, etc. Input: Sentence: Jack played basketball after school, after which he was very tired. Question: How long did Jack play basketball? Category: Event Duration. Prediction: Yes Input: Sentence: He was born in China, so he went to the Embassy to apply for a U.S. Visa. Question: How often does he apply a Visa? Category: Frequency. Prediction: Yes Input: Sentence: Jack played basketball after school, after which he was very tired. Question: Was Jack still tired the next day? Category: Event Duration. Prediction: No Input: Sentence: It refers to a woman who is dangerously attractive, and lures men to their downfall with her sexual attractiveness. Question: How long does it take to lure men to their downfall? Category: Event Duration. Prediction:”</td><td></td></tr></table>
+
+Table 4: Examples of evaluation instructions with expected outputs, for selected tasks of SuperGLUE and Natural-Instructions (RQ3). Displayed samples are from CoPA and MCTato Temporal Reasoning tasks, respectively. Note that in these evaluations, demonstrations are picked randomly, regardless of their concepts.
+
+significantly smaller volumes and complexity of the training dataset, CoAT-trained models show competitive results to similar-size or even larger in-context learners of previous work. For instance, the 1-billion-parameter Tk-CoAT performs better than the 3-billion T0 in 3 cases (Ax-b, RTE, COPA) and comparably in another 3 cases (WSC, CB, WiC). In comparison with Tk-INSTRUCT of the same size, Tk-CoAT-1B outperforms Tk-INSTRUCT in 3 out of 7 unseen tasks (WSC, CB, ReCoRD), and reaches similar scores in most other cases, even in 2 out of 3 tasks that were included in Tk-INSTRUCT's training mix. Similarly, larger Tk-CoAT-3B outperforms Tk-INSTRUCT on 4 of 7 new tasks (Ax-b, WSC, WiC, ReCoRD), but with larger gaps on the others.
+
+# C.2 Natural-Instructions: other task types
+
+Figure 8 evaluates the impact of CoAT's mechanism on the quality of in-context learning separately on the English and non-English tasks. The figure reveals that CoAT works particularly well for non-English tasks. Our analyses found this is mainly due to the low performance of the baseline on the non-English tasks. We speculate that this can be a consequence of the higher reliance of the
+
+baseline on token semantics (Section 4.6, RQ2); As our models are fine-tuned on an English-only QA model, such learnt reliance is not applicable in multilingual settings.
+
+Figure 9 compares the performance of CoAT models against the models of previous work, separately on the English and non-English tasks. We can see that CoAT is slightly better at the multilingual portion of Natural-Instructions, but the difference is not principal.
+
+# C.3 Per-concept evaluations
+
+Figure 7 evaluates the performance gains of the baseline models (§4.2) and CoAT-trained models individually per each of the concepts of the natural datasets. While the CoAT models are able to benefit from concepts the largest in the relative change of quality, they are also not consistent in the ability to benefit from all the concepts. However, as discussed in Section 4.4, this does not imply that CoAT is unable to utilize these concepts.
+
+# C.4 Evaluation tasks and other configurations
+
+SuperGLUE (Wang et al., 2019) consists of the following tasks (as ordered in our Results, §4.6): Winogender Schema Diagnostics (AxG) (Rudinger
+
+<table><tr><td></td><td># train tasks</td><td>AxG</td><td>Ax-b</td><td>WSC</td><td>CB</td><td>RTE</td><td>WiC</td><td>ReCoRD</td><td>BoolQ</td><td>COPA</td><td>MultiRC</td></tr><tr><td>FLAN-1B</td><td>1,836</td><td>84.8±3.9</td><td>21.9±4.0</td><td>70.7±4.8</td><td>92.5±2.8*</td><td>92.1±3.0*</td><td>69.9±5.1*</td><td>38.9±5.2*</td><td>92.3±2.7*</td><td>97.8±1.5*</td><td>88.3±3.2*</td></tr><tr><td>FLAN-3B</td><td>1,836</td><td>95.3±3.7</td><td>22.0±8.0</td><td>80.2±9.2</td><td>92.7±6.7*</td><td>96.0±4.0*</td><td>79.7±8.3*</td><td>62.2±9.7*</td><td>92.1±5.1*</td><td>99.3±1.6*</td><td>90.4±6.4*</td></tr><tr><td>TK-INSTRUCT-1B</td><td>1,616</td><td>51.9±4.9</td><td>57.2±5.8</td><td>49.8±4.9</td><td>46.0±5.5</td><td>55.5±4.8</td><td>53.5±5.3</td><td>13.1±3.7</td><td>63.4±3.4*</td><td>76.9±3.2*</td><td>62.2±5.1*</td></tr><tr><td>TK-INSTRUCT-3B</td><td>1,616</td><td>53.5±4.7</td><td>49.9±4.9</td><td>51.2±4.9</td><td>66.3±4.6</td><td>62.7±4.6</td><td>50.4±4.8</td><td>18.6±4.2</td><td>68.8±4.4*</td><td>73.8±3.5*</td><td>59.9±4.9*</td></tr><tr><td>T0-3B</td><td>35</td><td>65.0±4.5</td><td>36.1±4.6</td><td>53.5±5.2</td><td>48.0±5.4</td><td>51.3±5.2</td><td>54.0±5.0</td><td>20.5±4.0</td><td>60.1±4.9</td><td>56.8±3.6</td><td>56.2±4.4</td></tr><tr><td>TK-CoAT-1B</td><td>2</td><td>50.4±5.3</td><td>52.7±4.6</td><td>53.6±5.2</td><td>46.9±4.9</td><td>53.7±4.9</td><td>53.5±5.3</td><td>17.0±3.5</td><td>63.8±5.4</td><td>76.1±3.2</td><td>11.4±2.6</td></tr><tr><td>TK-CoAT-3B</td><td>2</td><td>57.9±4.9</td><td>57.2±4.8</td><td>53.6±4.5</td><td>60.4±4.8</td><td>52.0±5.4</td><td>56.9±5.0</td><td>23.1±3.8</td><td>63.6±4.3</td><td>81.3±3.3</td><td>56.9±3.6</td></tr></table>
+
+Table 5: ICL performance: comparison to previous ICL models ROUGE-L of CoAT-trained ICL models and models of comparable size in previous work. Evaluation setup is consistent with Table 1. In cases marked with *, the task was used in the model's training; Underlined are the best results per unseen task and model size.
+
+![](images/54c9eaec815aa3d5492b03da2569c7dceddc8a8964db29a2acbf6d06f7a75b00.jpg)  
+Figure 8: Impact of Concept-aware training per different language settings: Pairwise comparison of models trained using selected training configurations ( $\S 4.2$ ) on (top) Non-English tasks and (bottom) English-only tasks of Natural-Instructions collection. Values in green and red bars indicate a number of tasks where the referenced model reaches significantly higher accuracy than the other. For the tasks denoted as similar, the difference in performance falls within the evaluation's confidence intervals.
+
+et al., 2018), Broadcoverage Diagnostics (CB), The Winograd Schema Challenge, CommitmentBank (CB), Recognizing Textual Entailment (RTE), ContextWords in Context (WiC) (Pilehvar and Camacho-Collados, 2019), Reading Comprehension with Commonsense Reasoning (ReCoRD) (Zhang et al., 2018), BoolQ (Clark et al., 2019), Choice of Plausible Alternatives (COPA), Multi-Sentence Reading Comprehension (MultiRC).
+
+Natural-Instructions consists of a larger mixture of tasks, which we do not enumerate here to maintain readability; the full list of evaluation tasks can be found in the original work of Wang et al. (2022) in Figures 11 and 12.
+
+To maintain comparability of evaluations among models, we deterministically fix the demonstration selection procedure so that only the full prediction prompts for all the models are the same. In the analyses comparing the differences in performance
+
+![](images/0253f6049c35103e46365ae97cf8825bb3f7c3cf01d00aa202fa3168fd638ffc.jpg)
+
+![](images/5a436fd3e19d8940612c070722941a99dda9b2aa16b8b6543cd0675e975118bf.jpg)  
+Figure 9: Comparison to previous work per different language settings: Pairwise comparison of CoAT models vs. the models of previous work on (top) Non-English tasks and (bottom) English-only tasks of Natural-Instructions collection. Values denote the number of tasks where the model reaches significantly better accuracy. For the tasks denoted as similar, the difference in performance falls within the evaluation's confidence intervals.
+
+$(\S 4.4; \mathrm{RQ1} + 2)$ , we fixed the prediction samples  $(x_{\mathrm{pred}})$  between different demonstrations' sampling strategies to avoid perplexing our comparison with possible data selection biases. Further details can be found in the referenced implementation.
+
+# D Computational Requirements
+
+We run both training and evaluation experiments on a machine with dedicated single NVIDIA A100-SXM-80GB, 40 GB of RAM and a single CPU core. Hence, all our reproduction scripts can run on this or a similar configuration. Two stages of training in total take at most 6,600 updates and at most  $117\mathrm{h}$  of training for Tk-CoAT to converge.

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