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2023/ColD Fusion_ Collaborative Descent for Distributed Multitask Finetuning/2c863e47-04cf-47d9-b218-6b91c8b275c1_origin.pdf

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2023/ColD Fusion_ Collaborative Descent for Distributed Multitask Finetuning/full.md

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+# ColD Fusion: Collaborative Descent for Distributed Multitask Finetuning
+
+Shachar Don-Yehiya
+
+IBM Research
+
+Hebrew University of Jerusalem
+
+Elad Venezian
+
+IBM Research
+
+eladv@il.ibm.com
+
+Colin Raffel
+
+UNC Chapel Hill
+
+craffel@gmail.com
+
+shachar.don-yehiya@ibm.com
+
+Noam Slonim
+
+IBM Research
+
+noams@il.ibm.com
+
+Yoav Katz
+
+IBM Research
+
+katz@il.ibm.com
+
+Leshem Choshen
+
+IBM Research
+
+leshem.choshen@il.ibm.com
+
+# Abstract
+
+We propose a new paradigm to continually evolve pretrained models, denoted ColD Fusion. It provides the benefits of multitask learning but leverages distributed computation with limited communication and eliminates the need for shared data. Consequently, ColD Fusion can give rise to a synergistic loop, where finetuned models can be recycled to continually improve the pretrained model they are based upon. We show that ColD Fusion yields comparable benefits to multitask training by producing a model that (a) attains strong performance on all of the datasets it was trained on; and (b) is a better starting point for finetuning on unseen datasets. We show that ColD Fusion outperforms RoBERTa and even previous multitask models. Specifically, when training and testing on 35 diverse datasets, ColD Fusion-based model outperforms RoBERTa by 2.33 points on average without any changes to the architecture. $^{1}$
+
+# 1 Introduction
+
+Over the last few years, pretrained language models are changing the landscape of NLP, where finetuning a pretrained model typically yields state-of-the-art performance on a diverse set of NLP tasks (Chen et al., 2022). Consequently, improving a pretrained model has the potential to boost every model finetuned on it. However, pretraining is often so computationally expensive that practitioners rarely seek to pretrain new models from scratch.
+
+In contrast, finetuning is usually dramatically cheaper, allowing a given pretrained model to be finetuned many times; e.g., there are thousands of finetuned BERT variants on the Hugging Face Hub $^2$ . Motivated by this, we study if and how finetuned models can be "recycled" to create a better
+
+![](images/91a941ccfe28af6d6135db4a0d0b940535d135a8ed164e55d8cc118100d081a6.jpg)  
+Figure 1: Schematic of ColD Fusion. Each iteration starts from a base model. Then, each contributor downloads the model from a centralized "Repository" and finetunes it on their dataset. Next, each contributor uploads the finetuned model weights back to the Repository. After that, the Repository fuses all models into a single model by averaging their weights. Finally, the Repository replaces the base model with the fused model and the process repeats.
+
+pretrained model (c.f., Raffel, 2021). To avoid confusion, henceforth we refer to any starting point for finetuning a base model and only the vanilla model as the pretrained model.
+
+To recycle models, we take inspiration from multitask learning (§2). In multitask learning the pretrained model is finetuned over multiple datasets at once, which was shown to create a better base model than the original pretrained model (Aribandi et al., 2021; Aghajanyan et al., 2021a; Sanh et al., 2021; Chung et al., 2022). Given the availability of many finetuned models, our aim is to obtain the benefits of multitask learning by mixing multiple models rather than multiple datasets (c.f. §2.3).
+
+To achieve that, we suggest the following iterative approach (§3): In each iteration, contributors finetune the most up-to-date base model (which is presumably also the most performant) on their task, and share the fine-tuned model with the rest of the community. Then, those contributed models are fused together, by simply averaging their parameters (Choshen et al., 2022b), to create the base
+
+model for the next iteration. We call this method Collaborative Descent Fusion, or ColD Fusion.
+
+ColD Fusion fits the common finetuning paradigm, where each contributor finetunes for their own benefit and does not share their data. However, by merely requiring the finetuned model to be shared, the finetuning step can be recast as a training step for the collective's benefit. In doing so, our method allows reusing compute and data consumed by practitioners and researchers to the benefit of the entire community.
+
+Our experimental results indicate that our approach of combining finetuned models not only produces a better base model but also allows this base model to keep evolving. Instead of pretraining or multitasking on a predefined amount of data, we suggest accumulating finetuned models to continuously improve the model. Our method is hence limited only by the amount of finetuned models that are shared by the entire community. We discuss limitations in (§9).
+
+We show that ColD Fusion produces a model that performs well on the finetuned tasks, despite never manipulating more than one task at a time neither by constituent models nor their fusing (§5). Moreover, we show that ColD Fusion increases the performance of the base model substantially, outperforming the pretrained model by 2.33 points on average on 35 datasets. Through additional analysis, we further show that similar improvements are achieved regardless of whether the target tasks were seen or unseen during training (§5.2) and that accumulating models trained on additional data provides continuous improvement (§6).
+
+# 2 Background
+
+We start by motivating the use of further training on diverse data for enhancing the base model abilities (§2.1). Then, we continue with defining our framework's goals (§2.2) and constraints (§2.3).
+
+# 2.1 Performance Scaling Laws
+
+Extensive evidence suggests that pretraining with more compute (Raffel et al., 2020) and data (Liu et al., 2019; Hoffmann et al., 2022; Ivgi et al., 2022) improves the resulting pretrained model. Moreover, additional supervised data is beneficial even when introduced after the pretraining stage (Phang et al., 2018; Choshen et al., 2022a). Extending this supervised stage to multitask learning on diverse data sources improves results even further (Aribandi
+
+et al., 2021; Aghajanyan et al., 2021a; Sanh et al., 2021; Chung et al., 2022).
+
+We observe that the data used during finetuning is typically not seen during pretraining. Therefore, we hypothesize that using a large amount of the data currently used for finetuning may significantly improve the model quality as a base model for future tasks. As training on all the finetuning data directly is infeasible, here we propose an alternative paradigm to test this hypothesis.
+
+# 2.2 Goals of Multitask Learning
+
+Multitask learning is typically used towards one of two goals: Either to produce a single model that performs well on many seen tasks, or to produce a base model that will perform well on many unseen tasks after adaptation, e.g., via finetuning.
+
+Single model. To produce a single multitask model, one initializes with a base model with  $p$  parameters and optimizes the parameters  $\theta \in \mathcal{R}^p$  to minimize the loss over a set of datasets  $D$ . This reflects the traditional objective of multitask learning – to produce a set of weights that performs well on multiple tasks (Caruana, 1997).
+
+Base model. An alternative goal of multitask learning (and the primary goal in our work) is to produce a base model that will attain strong performance after adaptation. Multitask learning does not directly optimize towards this goal, but has been found to do so indirectly (Aghajanyan et al., 2021a; Liu et al., 2022). In this setting, the out-of-the-box performance of the produced model on seen tasks is less important than the performance after finetuning over new tasks, i.e., initializing with the found weights  $\theta \in \mathcal{R}^p$  and then finetuning on a desired dataset  $d'$ . We do not explicitly state whether  $d' \in D$  or  $d' \notin D$ , i.e., whether  $d$  was used during the multitask training or not. In §5.2, we empirically show that our method works well in both cases.
+
+We note that our formulation sets no restrictions on the datasets group  $D$ . Thus, a common scenario might be that some datasets do not have the same label space, number of examples, etc. On the other hand, it is also possible that some datasets are complementary samples from a distribution of the same task. In this case, our approach is similar to training this task distributively as in federated learning (Yang et al., 2019) but without communicating every batch. We demonstrate that our approach also works well in this setting in  $\S 6$ .
+
+# 2.3 Collaborative Constraints
+
+In this work, we target the goals of multitask learning discussed above, but focus on a specific setting with additional constraints, which we call  $ColD$  multitask. The constraints are required to support large-scale collaborative and distributed multitask learning. In our setting, multiple contributors have access to datasets that they do not share. A central Repository can only perform minimal computation (i.e., does not perform any training). Communication between the contributors and the Repository only occurs when a given contributor completes the finetuning on their data.
+
+# 3 Methodology - ColD Fusion
+
+Our proposed method (see Fig. 1), called ColD Fusion, is an iterative process that aims to perform multitask learning in the constrained setting outlined above. Specifically, ColD Fusion involves an iterative process where each individual contributor downloads the current base model from the Repository, finetunes this base model over their dataset, communicates the resulting model back to the Repository, and lastly, the Repository fuses (Choshen et al., 2022b) all of the contributors' models into one and sets the new fused model as the new base model for further finetuning.
+
+More formally, the Repository first initializes the shared model parameters  $\theta_0$  using a preexisting pretrained model. Then, at each iteration  $i\in \{0,1,2,\ldots \}$ , each contributor  $c\in C$  finetunes the  $\theta_{i}$  base model over a dataset  $d\in D$  to produce parameters  $\theta_i^c$ . For the purposes of our study, finetuning is any optimization process that aims to minimize the loss over a dataset  $d$ . Typically, finetuning involves minimizing the loss using a variant of gradient descent. After finetuning, each contributor sends their model's parameters  $\theta_i^c$  to the Repository. Next, the Repository fuses the contributor's models by averaging all of the contributor's model's parameters to produce a new shared model as  $\theta_{i + 1} = \frac{1}{|C|}\sum_{c}\theta_{i}^{c}$ . Finally, the process repeats for iteration  $i + 1$ .
+
+# 4 Experimental Setup
+
+In this section, we detail the datasets, models, baselines, general experiment setup, and specific experiments settings.
+
+# 4.1 Datasets
+
+In all of our experiments, we define the datasets group  $D$  to be a group of 36 English-language datasets, including most GLUE and Super-GLUE datasets, in addition to other NLI, sentiment and topic classification datasets as well as datasets based on Twitter data. A full list of datasets we use is provided in App. A.
+
+At each iteration we test on all the 36 datasets. There are two exceptions: 1) In the main experiment (§5.1) we use the entire dataset group except STSB. STSB, being a regression task incurred technical difficulties to provide a fair comparison to the multitask baseline (see §4.2). 2). For efficiency reasons, in the very compute demanding experiment of the number of contributors (§5.4) we randomly sampled 5 datasets to act as a consistent test set.
+
+# 4.2 Models and Baselines
+
+For experiments in the main text, we use RoBERTabase (Liu et al., 2019) as our initial model  $\theta_0$ . To demonstrate the generality of our approach, we additionally replicate some results on T5 (Raffel et al., 2020, see App. §D).
+
+For baseline pre-trained models, we consider RoBERTa-base, RoBERTa-base fused, as well as a RoBERTa-base multitask model. The fused model is trained as in Choshen et al. (2022b). The multitask variant trains a dedicated classification head for each dataset. In addition, we consider the MUPPET (Aghajanyan et al., 2021a) model, a highly optimized multitask model trained on more datasets than we consider. MUPPET is the current state-of-the-art base pretrained model that uses the RoBERTa-base architecture (Choshen et al., 2022a).
+
+# 4.3 Finetuning Process
+
+Finetuning is used in this paper for two reasons: (a) As a way to infer and evaluate the performance of a base model and (b) as a part of the ColD Fusion scheme. We follow the exact same finetuning procedure in either case. Finetuning hyperparameters and time and memory estimates are provided in App. B
+
+# 4.4 ColD Fusion Procedure
+
+The general course of the experiments is as follows: On each iteration, several datasets are sampled and the latest base model is finetuned separately on each dataset. Then the resulting finetuned models
+
+![](images/48f045b72adc95f1a9d32123976b5b7fd525a34df8aa4be1688456d63aac0b7c.jpg)  
+(a) Single Model
+
+![](images/08f6af40eca165822e73d611061a0d28265086386628669874b5bdf7c7e92134.jpg)  
+(b) Base Model  
+Figure 2: ColD Fusion is effective at multitask learning. ColD Fusion brings significant additional benefits as a base model for finetuning (b) and improves over finetuning the pretrained model, the fuse baseline, our multitask baseline, and MUPPET (Aghajanyan et al., 2021a). ColD Fusion also produces better performance on seen tasks as evaluated with linear probing (a), almost reaching finetuned accuracy. Standard deviation across runs is shown via shaded regions.
+
+are fused to create the next base model. This new model is evaluated on the test datasets at each iteration. When we mention ColD Fusion without specifying the iteration explicitly, we refer to the model that corresponds to the final iteration.
+
+The evaluation reflects both multitask goals (§2.2): (a) To evaluate the single model goal, we train only the classification head (equivalent to Linear Probing; Alain and Bengio, 2016), freezing the rest of the layers. We refer to it as ColD-Frozen. (b) For evaluating the base model goal, we take the ColD model and use it as initialization for finetuning. We finetune separately on each dataset and report the results on the corresponding test. We refer to it as ColD.
+
+# 5 ColD Multitask Results
+
+In this section, we show ColD Fusion can produce multitask models. We show in §5.1 that ColD Fusion fulfills both multitask objectives defined in §2. We verify that improvements replicate on datasets that were not seen during training (§5.2). Then we find that base model improvements are even more apparent in few shot settings (§5.3). Finally, we consider the importance of the number of contributors hyperparameter (§5.4).
+
+# 5.1 Collaborative Multitask
+
+We show that ColD Fusion achieves the two multitask objectives (see Fig. 2). We train and test ColD Fusion for 30 iterations. We simulate 8 con
+
+tributors by sampling 8 datasets at each iteration and repeat the whole experiment using 5 different random seeds. We consider the importance of the sampling hyperparameter in §5.4.
+
+We find that ColD Fusion creates a superior base model (see Fig. 2b). The average result after finetuning the ColD Fusion model is superior to the RoBERTa pretrained model by up to 2.33 points on average over the 35 datasets (see App. §C for full results). The result can be deemed significant with a difference of over 20 standard errors of the mean between the original pretrained model and the model produced by ColD Fusion.
+
+In comparison, the standard multitask model and the fused model outperform the original RoBERTa pretrained model by only 1.62 and 0.92 points respectively. We also consider the highly optimized MUPPET model, trained on more datasets and without the ColD multitask restrictions. MUPPET indeed outperforms our standard multitask baseline model, but is outperformed by our ColD Fusion model.
+
+Another important comparison is the consistency of the improvement. We find (see App. C) that the model produced by Cold Fusion is better than the pretrained model on  $75\%$  of the datasets and degrades by only 1.73 points on the worst-case dataset. In contrast, MUPPET hurts as many models as it helps and is worse by 40 points on some datasets.
+
+ColD Fusion also achieves the single model goal: When evaluated with linear probing, the ColD
+
+![](images/cb22024259d2848d65fcec19fb83c30d072f53d12723171014418fe035ae6410.jpg)  
+Figure 3: Fine-tuned and frozen results for ColD Fusion on datasets that were used for training ("Seen", in blue) vs. datasets that were not ("Unseen", in orange). The model produced by ColD Fusion is a good base model for both seen and unseen datasets. While using a frozen model is better for seen datasets, unseen datasets still benefit the ColD Fusion process.
+
+model has high performance on the datasets seen in training (see Fig. 2a), higher in fact than those of the standard multitask baseline. Moreover, it is not far from the pretrained model when finetuned on each task separately. This implies that despite learning in a distributed way and fusing by averaging the non-linear weights of the model, the process incorporates the data well.
+
+# 5.2 Unseen Datasets
+
+We have found ColD Fusion to create a strong base model (§5). Next, to meet the requirement of improving results for new datasets, we test the ColD fused model on unseen datasets not included in the training (see Fig. 3). We achieve this by performing 3-fold cross-validation. The folds are set arbitrarily such that each fold contains 24 seen datasets (24 contributors) and 12 unseen ones that we keep for evaluation only. This ensures that each dataset has the same weight in the average score of the seen datasets and unseen datasets.
+
+We find that the model performs on unseen datasets just as well as it does on seen ones. The strikingly similar performance between seen and unseen tasks (which is similar to in-domain vs. out-of-domain) should raise a red flag in most scenarios. However, in the unique scenario of ColD multitasking, it meets our expectations. Both seen and unseen datasets are exposed at some point - either during ColD Fusion iterations (seen datasets only) or during evaluation as a base model (both seen and
+
+![](images/373548adc7aa225642f4d289bce5b0b2ccaa07551c4261920393a2cdd5eb1945.jpg)  
+Figure 4: ColD Fusion yields improvements in few-shot learning on unseen datasets. Results are from training on 24 full datasets and testing on 12 unseen datasets with 100 labels each, averaged over 3 such folds. The pretrained model performance is highlighted by a dashed line. ColD Fusion outperforms by as much as  $7\%$ .
+
+unseen). Hence, in the seen case, the model trains twice on the same data, first during base model creation and again when evaluating the base model. It is less of a surprise that training twice on the same data doesn't improve results. The improvement over the original pretrained is likely due to positive transfer across datasets.
+
+Where finetuning is restricted to only the classification head (ColD-Frozen in Fig. 3), the model achieves much better performance on the seen datasets than on the unseen datasets. These results are also in line with the fact that the model (apart from the classification head) was never exposed to the unseen datasets, while the entire model's weights were trained on the seen datasets. We further test ColD Fusion's capacity to scale with more data in §6. We note that the unseen curve consistently increases, which may suggest that the model has acquired general skills. The curve reaches a plateau around the 10th iteration, and then starts to drop a bit. Possibly, due to an overfitting caused by the limited number of seen datasets.
+
+Note that the scores in Fig. 3 are a bit lower than in the main experiment in Fig. 2b. This is most likely due to scaling, as here we keep unseen datasets aside and use fewer datasets for training. We show in a controlled experiment in §6 that using more datasets improves results.
+
+# 5.3 Few-shot
+
+In order to assess the benefit of ColD Fusion on few-shot scenarios, we repeat the setting in §5.2,
+
+![](images/0ee5d06ff2e94335d35610c55a846f5c0468e43fb9e0d434c68e3d680a6bb5cb.jpg)  
+Figure 5: Effect of the number of contributors in each iteration. The graph shows the performance (y-axis) per iteration (x-axis) during ColD Fusion. Performance of the model produced by ColD Fusion without additional finetuning is shown in dotted lines, and after finetuning in solid lines. Each color depicts a different number of contributed models in each iteration. The pretrained model performance is highlighted by another dashed line.
+
+but finetune only on 100 examples from each unseen dataset during evaluation. Fig. 4 shows a great increase in performance over the RoBERTa pretrained model, reaching an improvement of 6.73 points after 20 iterations. This provides an even stronger case for ColD Fusion in the few-shot setting.
+
+# 5.4 Number of Contributors per Iteration
+
+An important factor in ColD Fusion is the number of contributors in each iteration. Having fewer contributors per iteration implies effectively training on fewer datasets in each iteration; on the other hand, fusing fewer models may give more importance to each.
+
+We observe in Fig. 5 that starting from two contributors, the performance as a base model is hardly affected by the number of contributors in each iteration. However, adding contributors makes the process more stable. A possible reason is that some of the improvement comes from the iterations themselves and the ability to correct overfitting done in previous steps by some contributors.
+
+We note that the number of contributors is only insignificant when the data is fixed. In practice, more contributors would improve performance, by adding more data or iterations. We further test the effect of the number of contributors under controlled settings in §6.
+
+# 6 Single Dataset Analysis
+
+We now analyze the interacting effects of the core characteristics of ColD Fusion: additional data across iterations, the amount of training data per iteration, and the number of contributors in each iteration.
+
+Doing so with multiple datasets would introduce noise. For example, we can not expect additional data coming from different sources (e.g., MNLI or Twitter) to equally affect the performance. To overcome this, we explore the case where a single dataset is distributed across contributors. Using a single dataset allows us to reduce variability due to differences in the datasets (e.g., distribution, task, etc.), and isolate the parameter we wish to control. ColD Fusion may converge faster with models from a single dataset, but we still expect the general tendencies found to replicate in multiple datasets settings.
+
+We chose MNLI (Williams et al., 2018) for its large size (392K examples).
+
+Effect of additional data across iterations (Federated Learning). To simulate a never-ending data flow, the experiment runs as follows: at each iteration, 5 contributors sample 5k examples each from MNLI dataset, and another such sample is used for evaluation.
+
+This setting resembles the Federated Learning scenario (Yang et al., 2019), where multiple contributors collaborate to train a model without having to exchange the actual data.
+
+As presented in Fig. 6a, performance increases throughout the iterations. Thus, we conclude that the ColD Fusion scheme aggregates and utilizes the newly added examples and not only coarse-grained dataset characteristics.
+
+We show similar trends in the multitask scenario (see App. E). Training on more datasets results in a better best model at the cost of more iterations to get to that best model.
+
+Note the superiority of ColD-Frozen over ColD in this experiment. A possible explanation is overfitting. In evaluation, finetuning all the parameters on only part of the data is worse than keeping the fused weights that are trained on several splits.
+
+Effect of dataset size per contributor. In this and the following experiments, we train on all the data in each iteration. The contributors train over disjoint and consistent sub-datasets, i.e., we do not sample examples. We aim to analyze the ability of
+
+![](images/09818296b27f736aa4e35096d74c38d9089f6e602cc05526a3240f555a061bcd.jpg)  
+(a) Effect of Additional Data
+
+![](images/fd72df3924bf972073343dcc0a883100b8f6a97a1074b2663ec1d04515c9914f.jpg)  
+(b) Effect of Dataset Size per Contributor
+
+![](images/f0bc965943d1ed412e6ab914ec404baab5ea2f66020f4e67b13f80dc786dd79d.jpg)  
+(c) Effect of #Contributors
+
+![](images/baf719eac2b1e57d878b312b2e8c92f4d6b16ea0d63f00964f3a49151afe598f.jpg)  
+(d) Effect of Distributing  
+Figure 6: ColD Fusion with a single dataset. To test the effect of additional data across iterations (a), we sample 5k new examples from the MNLI dataset for each of the 5 contributors at each iteration. We test the effect of the dataset size (b), the number of contributors (c), and the distributing of a fixed amount of data (d). The ColD Frozen (dotted lines) outperforms ColD Finetuned (solid lines), possibly due to overfitting, and both improve with the iterations. Results keep increasing with data size. More contributors or less data per contributor slow the convergence to centralized finetuning (dashed lines).
+
+the model to aggregate knowledge from the constituent models during fusion.
+
+ColD-Finetuned is evaluated through a stage of finetuning which further learns on the task. To avoid entangling the capabilities learnt during ColD Fusion with those learnt during evaluation, we analyze the ColD-Frozen instead. We also note that during evaluation, the classification head is trained on the training data of the first contributor only (which is the only one in the baseline).
+
+We fix the number of contributors to 10 and test how the number of examples each contributor is training on affects results. We experiment with  $1.25\mathrm{K}$ ,  $2.5\mathrm{K}$ ,  $5\mathrm{K}$  and  $10\mathrm{K}$  examples. We compare these to full finetuning on the union of all the contributors' training data. A priori we would have expected large amounts of data in each contribu
+
+tor's model to obstruct the fusing process, as each model changes more. In Fig. 6b, we see the opposite – the more data each contributor trains on, the closer the fused model is to the full training baseline.
+
+Effect of the number of contributors. In this experiment, each contributor trains over "their own" data, i.e., the same 5K examples in each iteration. We test how the results change with 2, 5, 10 and 20 contributors. We see in Fig. 6c that increasing the number of contributors improves performance. Moreover, the results are not only better at every step, but also keep on improving for longer. This is a positive result in terms of the expected end result, but also means that convergence is slower.
+
+Effect of data distribution between contributors. To isolate the effect of the number of contributors and the dataset size of each contributor from that of the overall data size, we fix the overall amount of data to 50K and split it among the contributors evenly. Fig 6d shows distributing mostly affects convergence – it takes approximately 2 more iterations to converge for double the contributors and half the data seen by each.
+
+We conclude that increasing the overall amount of data improves performance, as may be expected. The distribution of the data between additional contributors has minimal impact on final performance, but may delay convergence.
+
+# 7 Related Work
+
+Our work strongly relies on model fusion. Model fusion was first introduced as a way to improve pretrained models by (Choshen et al., 2022b). In parallel, several works such as (Matena and Raffel, 2021; Wortsman et al., 2022b) and lately (Jin et al., 2022; Ramé et al., 2022) suggested different ways of fusing for other purposes such as improved finetuning.
+
+Another fusion usage is the stochastic weight averaging, aiming to stabilize the SGD process by averaging multiple points along the SGD trajectory (Izmailov et al., 2018). Unlike the previous, this method utilizes only one model and dataset.
+
+Low-communication distributed training was proposed in similar settings to ours. Wortsman et al. (2022a) proposed distributed finetuning and model fusing in order to produce better finetuned models. This suggestion is equivalent to one iteration of ColD Fusion where all models share the same dataset. Li et al. (2022); Together (2022) also share the similarity of distributed training, but during pretraining on unlabeled data.
+
+Understanding why averaging different models improve quality may be related to theoretical works discussing weight and loss spaces. These works state there is a path of minimum loss between models (Garipov et al., 2018) on which the loss along the path is not increasing. Lubana et al. (2022); Benton et al. (2021); Frankle et al. (2020) claimed that under some constraints, this path is linear, which suggests that fusing the weights could produce a model that retains the capabilities of the fused models. Although different models on the same task may converge to different locations in the loss space without linear connectivity (Juneja
+
+et al., 2022), and although the case of multitask is more complex (Mirzadeh et al., 2020), we still believe that these works can partially explain why fusing preserves the capabilities gained by the constituent and when it does not that the next iteration fixes it. Gueta et al. (2023) further suggests the linear connectivity path is merely a line in a whole connected region, future work may tell whether Cold Fusion searches in this region or crosses it to find new ones.
+
+The literature also includes methods for better aligning models during training (Javaloy and Valera, 2021; Yu et al., 2020; Chen et al., 2018) or after it (Ainsworth et al., 2022; Jordan et al., 2022) to aid in fusing. We did not use those as we wanted to reduce the load on the repository and avoid restricting the contributors' finetuning. However, these methods may improve results in ColD Multitask.
+
+We mention that multitask learning does not optimize the base model objective directly (§2.3). Some works aim to do so (Bansal et al., 2019) through meta-learning, finding models that can learn a new task well or efficiently (Hospedales et al., 2021). REPTILE (Nichol et al., 2018) meta learns in a way that resembles ours by iteratively using models trained for several batches.
+
+# 8 Conclusion and Discussion
+
+We proposed a scheme for utilizing abundant finetuned models to enhance a pretrained model. Our approach does not necessitate the sharing of datasets, but rather assumes each contributor solely finetunes on their own dataset. Hence, we believe that applying this scheme as a collaborative pretraining platform is a viable option and that doing so would result in ongoing improvement of base models.
+
+To scale this approach, it would be beneficial if the repository was updated asynchronously, perhaps relying on recent fusing techniques (Ilharco et al., 2022). In the usual finetuning setting, robustness can be improved by tuning batch size and learning rate. In analogy, in ColD Fusion, one can either increase the number of contributors (batch) and/or restrict the effect of each iteration (learning rate) (Smith and Le, 2018) to improve the process. Following this line, future work may consider regularizing the distance from the pretrained model (learning rate) when a small number of contributors exist (batch) or consider assigning individual
+
+weights to each contributor.
+
+There are many hyper parameters to optimize which might improve the method substantially. E.g., fusing the contributions with a weighted average, improving fusing itself (Matena and Raffel, 2021; Ainsworth et al., 2022), controlling the datasets seen in each iterations (related to; Choshen et al., 2021; Hacohen and Weinshall, 2019) and backtracking when a harmful update was done to the model. We hope that future work will shed more light on these issues, to further improve the approach proposed in this work.
+
+# 9 Limitations
+
+Perhaps the most important limitation regarding ColD Fusion is its deployment. This paper presents a method for multitasking, not a platform. In that sense it solves both multitask learning goals under the constraints resulting from collaboration. However, using ColD Fusion in practice might require much more effort – It would require a place to host the models, a way to make sure no malicious or erroneous model was sent, and other aspects of a platform to support this training.
+
+This is the first method to tackle collaborative multitasking and we scaled it to 35 datasets. However, future methods may be found more efficient or scale better with the amount of data and computation.
+
+ColD Fusion with many iterations and models might require more computational effort for a given amount of data (§6) than regular multitask learning. As a result, while our bottom line performance is encouraging, ColD Fusion might not be the preferred way under every possible scenario. Still, some of the costs may be alleviated by future work – for example the additional iterations when fusing many models, might be reduced by aligning models' weights before fusing (Ainsworth et al., 2022).
+
+While this paper studied the impact of various ColD Fusion parameters, it is unclear how finetuning or even pretraining parameters affect results. However, we do have a reason to believe the method is relatively robust to these refactors through our initial results and the replication on another architecture (App. §D).
+
+Another limitation is the assumption that the weights of the model change. Some adaptation methods assume the model is frozen and only its inputs change. In those cases, the model would
+
+not be improved by use. Still, even in such cases, multitask learning (Wang et al., 2023) might be applied on the inputs, or the same model might be used in different ways, where some also adapt parts of it (Hu et al.; Jang et al., 2023; Qin et al., 2022; Yadav et al., 2023). In those cases, the method might still prove useful, even if it benefits only from some of the contributions.
+
+As mentioned before, another concern is a possible harmful update done by a contributor. Handling it would require monitoring the updates by regularly evaluating the model, or measuring the updates diff to identify noisy models (too large diff / random weights).
+
+# Acknowledgements
+
+This material is based upon work supported by the National Science Foundation under Grant No. 2145822.
+
+# References
+
+Armen Aghajanyan, Anchit Gupta, Akshat Shrivastava, Xilun Chen, Luke Zettlemoyer, and Sonal Gupta. 2021a. Muppet: Massive multi-task representations with pre-finetuning. In Proceedings of the 2021 Conference on Empirical Methods in Natural Language Processing, pages 5799-5811, Online and Punta Cana, Dominican Republic. Association for Computational Linguistics.  
+Armen Aghajanyan, Anchit Gupta, Akshat Shrivastava, Xilun Chen, Luke Zettlemoyer, and Sonal Gupta. 2021b. Muppet: Massive multi-task representations with pre-finetuning. ArXiv, abs/2101.11038.  
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+
+# A Datasets used
+
+Most datasets could be downloaded from huggingface datasets. We explicitly state the download link when relevant. As we used groups of datasets we report here the full list of datasets they contain.
+
+GLUE: CoLA (Warstadt et al., 2019), SST2 (Socher et al., 2013), MRPC (Dolan and Brockett, 2005), QQP (data.quora.com/First-Quora-Dataset-Release-Question-Pairs), MNLI (Williams et al., 2018), QNLI Rajpurkar et al. 2016, RTE (Dagan et al., 2005; Bar-Haim et al., 2006; Giampiccolo et al., 2007; Bentivogli et al., 2009), WNLI (Levesque et al., 2011)
+
+SuperGLUE: BoolQ (Clark et al., 2019), CB (de Marneffé et al., 2019), CoPA (Roemmele et al., 2011), MULTIRC (Khashabi et al., 2018), WIC (Pilehvar and Camacho-Collados, 2019), WSC (Levesque et al., 2012)
+
+MNLI (Williams et al., 2018), QNLI Rajpurkar et al. 2016, RTE (Dagan et al., 2005; Bar-Haim et al., 2006; Giampiccolo et al., 2007; Bentivogli et al., 2009), WNLI (Levesque et al., 2011), ESNLI (Camburu et al., 2018), adversarial NLI (Nie et al., 2020).
+
+EmoInt (Mohammad and Bravo-Marquez, 2017), Emoji (Barbieri et al., 2018), Irony (Van Hee et al., 2018), OffenseEval (Zampieri et al., 2019), HatEval (Basile et al., 2019), Sentiment Analysis (Rosenthal et al., 2017)
+
+Poem Sentiment (Sheng and Uthus, 2020), IMDB (Maas et al., 2011), Rotten Tomatoes (Pang and Lee, 2005), SST 5bins (Socher et al., 2013), SST2 (Socher et al., 2013), Amazon reviews (He and McAuley, 2016), Financial Phrasebank (Malo et al., 2014)
+
+AG news(Zhang et al., 2015), ISEAR(Scherer and Wallbott, 1994), Yahoo answers(Zhang et al., 2015), DBpedia(Zhang et al., 2015), 20 newsgroup(Zhang et al., 2015), TREC in both fine-grained and coarse-grained labels (Li and Roth, 2002)
+
+# B Finetuning details
+
+Hyperparameters. During finetuning, we use the following hyperparameters: learning rate of 5e-5 with linear decay 0.0006 and batch size 256. Early stopping is performed on the development sets if the accuracy improvement after 256K training examples is less than 0.001. All other finetuning hyperparameters are constant across all experiments and follow the original hyperparameters
+
+published by Liu et al. (2019).
+
+Time and Memory. Most finetuning steps take an hour or less on an A100 GPU. Fusing times are inconsequential. At each iteration all finetuning runs in parallel on all datasets (8 in most cases) and also test finetuning runs in parallel, (36 in most cases). To put it all together, in the main experiment, 30 iterations with 8 contributors, 36 test sets, and 5 seeds, required approximately 4,800 A100 GPU hours and 3.2 TB of memory if all models are to be saved once.
+
+# C Datasets Accuracy
+
+The full results of the main experiment (§5) can be found in Table 1. It contains accuracy score for each dataset separately.
+
+For ease of comparison we also supply two figures (Fig.7), comparing MUPPET and COLD multitask models to the pretrained. They show that ColD is much more consistent. It has fewer datasets that lose from changing from pretrained to ColD and smaller negative effects when there are such datasets. MUPPET however also has larger maximal gain when it does show gains, which shines favourably on the average. This makes ColD a better choice for an off-the-shelf model, but gives MUPPET an advantage when one tests a target dataset on several pretrained domains.
+
+# D T5
+
+We present initial results to confirm our method is not unique to RoBERTa. Specifically, we train T5 (Raffel et al., 2020) with default hyperparameters, but 256 batch size and 0.0004 learning rate. We replicate the main experiment (§5) in a smaller scale, running on seed only and 5 iterations only. For ColD-Frozen, we train only the language model head.
+
+Fig. 8 shows the main effect reminds. Both ColD and ColD-Frozen keep increasing with the iterations.
+
+# E Multitask Scale
+
+We test the effect of the amount of datasets we use for multitasking on the performance of the resulted model as a base model. We take a random permutation of all the 36 datasets. We ColD fuse on the first 4 datasets, then the first 8, 16, and finally all the datasets. In fig. 9 we see that the 8 datasets performs worse than the 4 datasets, and
+
+![](images/ec4028737ad1e2ab7c55c6a17fb194af8bc18b98f132426cebbeaf828f410a8c.jpg)  
+(a) MUPPET Gain
+
+![](images/67f9cc34d6b5a3e1ea642e3c97dbd2b9ef5f0ca7ad277d15888bdd9abce4ccb4.jpg)  
+(b) ColD Gain  
+Figure 7: Gains of MUPPET/ColD over finetuning on the pretrained model. ColD is much more consistent, with less datasets that lose from changing from pretrained to ColD and smaller negative effects on them. MUPPET however has larger maximal gain when it does show gains.
+
+![](images/a52da065d44b26d7bdce29fad0dd8fe2c067ff7a95cfff6aa905a0c0c3d07634.jpg)  
+Figure 8: ColD Fusion on T5. We replicate the main experiment (§5) on a smaller scale. Like in RoBERTa, both ColD and ColD-Frozen lines keep increasing with the iterations.
+
+that the high regime (16 and 36 datasets) performs much better than the low regime (4 and 8 datasets). These results align with (Aghajanyan et al., 2021b) observation that under 15 datasets more datasets decrease the performance, but past some critical point more datasets increase performance.
+
+# F Fix Number of Examples
+
+We depict the ColD Fusion process with multiple tasks (Fig. 10), but only 4K examples per each contributor. This simulates a case where contributors keep streaming new information of different kinds. While this can not fully predict the effect of streaming new tasks, it shows initial positive results in this regard.
+
+![](images/b89fec7955bcaa486e90f0d6b832e5f6cd9dab39384d8559af303cf0dc43d0a5.jpg)  
+Figure 9: Number of datasets effect. The graph follows the performance (y-axis) per iteration (x-axis) during ColD Fusion. Each color depicts a different number of datasets pool from where the datasets were randomly picked at each iteration. The pretrained model performance is highlighted by another dashed line.
+
+![](images/b923ddc6c419650aeaa30f40f425c960e7532812f5b2d59b3b862ae347f78f77.jpg)  
+Figure 10: Running the main experiment with a fixed number of examples. For each finetune over the 36 datasets, we use 5000 examples - regardless the size of the dataset. We can see that although the absolute results are degraded related to the regular configuration, the performance is increasing monotonically both for the CoLD and CoLD Freeze. meaning more data yields better performance.
+
+<table><tr><td>Dataset</td><td>Finetune</td><td>Multitask</td><td>MUPPET</td><td>ColD-Fusion</td></tr><tr><td>20 Newsgroup</td><td>85.31</td><td>85.25</td><td>90.00</td><td>85.97</td></tr><tr><td>AG News</td><td>89.85</td><td>89.55</td><td>89.77</td><td>89.58</td></tr><tr><td>Amazon Reviews Multi</td><td>66.51</td><td>66.22</td><td>86.50</td><td>66.65</td></tr><tr><td>ANLI</td><td>51.51</td><td>51.48</td><td>52.59</td><td>52.00</td></tr><tr><td>BoolQ</td><td>77.14</td><td>80.27</td><td>82.17</td><td>81.39</td></tr><tr><td>CB</td><td>64.29</td><td>82.86</td><td>80.36</td><td>85.00</td></tr><tr><td>CoLA</td><td>83.43</td><td>82.42</td><td>81.21</td><td>82.74</td></tr><tr><td>COPA</td><td>47.00</td><td>60.00</td><td>65.00</td><td>64.40</td></tr><tr><td>DBPEDIA</td><td>77.49</td><td>77.69</td><td>85.17</td><td>78.15</td></tr><tr><td>ESNLI</td><td>91.00</td><td>91.27</td><td>52.59</td><td>91.31</td></tr><tr><td>Financial Phrasebank</td><td>85.40</td><td>85.26</td><td>46.10</td><td>86.72</td></tr><tr><td>IMDB</td><td>93.86</td><td>93.82</td><td>91.74</td><td>94.01</td></tr><tr><td>ISEAR</td><td>72.78</td><td>71.94</td><td>73.01</td><td>72.40</td></tr><tr><td>MNLI</td><td>87.11</td><td>87.26</td><td>93.04</td><td>87.14</td></tr><tr><td>MRPC</td><td>87.45</td><td>86.96</td><td>88.97</td><td>89.26</td></tr><tr><td>MultiRC</td><td>60.56</td><td>62.34</td><td>64.15</td><td>63.01</td></tr><tr><td>Poem Sentiment</td><td>83.85</td><td>88.27</td><td>94.14</td><td>86.54</td></tr><tr><td>QNLI</td><td>92.42</td><td>92.39</td><td>84.48</td><td>92.66</td></tr><tr><td>QQP</td><td>90.72</td><td>90.89</td><td>91.25</td><td>91.22</td></tr><tr><td>Rotten Tomatoes</td><td>88.03</td><td>90.73</td><td>58.10</td><td>91.48</td></tr><tr><td>RTE</td><td>70.11</td><td>82.17</td><td>39.44</td><td>84.48</td></tr><tr><td>SST2</td><td>93.85</td><td>94.27</td><td>67.06</td><td>95.16</td></tr><tr><td>SST 5 bins</td><td>56.24</td><td>57.56</td><td>94.84</td><td>59.52</td></tr><tr><td>Trec Coarse</td><td>97.32</td><td>97.40</td><td>85.58</td><td>97.20</td></tr><tr><td>Trec Fine</td><td>87.08</td><td>88.28</td><td>96.80</td><td>91.04</td></tr><tr><td>Twitter Emoji</td><td>46.35</td><td>46.02</td><td>82.76</td><td>46.35</td></tr><tr><td>Twitter Emotion</td><td>81.52</td><td>81.25</td><td>51.11</td><td>82.76</td></tr><tr><td>Twitter Hate</td><td>53.76</td><td>53.70</td><td>76.02</td><td>53.95</td></tr><tr><td>Twitter Irony</td><td>71.05</td><td>74.54</td><td>84.77</td><td>76.25</td></tr><tr><td>Twitter Offensive</td><td>84.58</td><td>85.16</td><td>71.57</td><td>85.79</td></tr><tr><td>Twitter Sentiment</td><td>70.94</td><td>70.47</td><td>87.07</td><td>70.72</td></tr><tr><td>WIC</td><td>65.71</td><td>68.06</td><td>66.61</td><td>68.12</td></tr><tr><td>WNLI</td><td>55.21</td><td>51.55</td><td>91.10</td><td>54.93</td></tr><tr><td>WSC</td><td>63.46</td><td>63.27</td><td>63.46</td><td>62.31</td></tr><tr><td>Yahoo Answers</td><td>72.49</td><td>71.71</td><td>71.90</td><td>72.69</td></tr></table>
+
+Table 1: Detailed results of the main experiment. Accuracy score of each dataset, for ColD Fusion and for the 3 baselines: Finetune, our Multitask, and MUPPET.
+
+A For every submission:
+
+A1. Did you describe the limitations of your work? 8  
+A2. Did you discuss any potential risks of your work? Not applicable. Left blank.  
+A3. Do the abstract and introduction summarize the paper's main claims? abstract Introduction  
+A4. Have you used AI writing assistants when working on this paper? Left blank.
+
+B Did you use or create scientific artifacts?
+
+4
+
+B1. Did you cite the creators of artifacts you used? Whenever relevant 2,3 etc.  
+B2. Did you discuss the license or terms for use and / or distribution of any artifacts? We provide a model and upload it publicly with a permissive license (MIT), this is technical and is not interesting for the scientific advancement we provide.  
+B3. Did you discuss if your use of existing artifact(s) was consistent with their intended use, provided that it was specified? For the artifacts you create, do you specify intended use and whether that is compatible with the original access conditions (in particular, derivatives of data accessed for research purposes should not be used outside of research contexts)? The whole paper is about a surprising use of current models, so it is consistent legally, but also unconventional.  
+B4. Did you discuss the steps taken to check whether the data that was collected / used contains any information that names or uniquely identifies individual people or offensive content, and the steps taken to protect / anonymize it? Not applicable. Left blank.  
+B5. Did you provide documentation of the artifacts, e.g., coverage of domains, languages, and linguistic phenomena, demographic groups represented, etc.? Not applicable. Left blank.  
+□ B6. Did you report relevant statistics like the number of examples, details of train / test / dev splits, etc. for the data that you used / created? Even for commonly-used benchmark datasets, include the number of examples in train / validation / test splits, as these provide necessary context for a reader to understand experimental results. For example, small differences in accuracy on large test sets may be significant, while on small test sets they may not be. Not applicable. Left blank.
+
+C Did you run computational experiments?
+
+3,4,5
+
+C1. Did you report the number of parameters in the models used, the total computational budget (e.g., GPU hours), and computing infrastructure used? Appendix B
+
+The Responsible NLP Checklist used at ACL 2023 is adopted from NAACL 2022, with the addition of a question on AI writing assistance.
+
+C2. Did you discuss the experimental setup, including hyperparameter search and best-found hyperparameter values?  
+Appendix B + Section 3  
+C3. Did you report descriptive statistics about your results (e.g., error bars around results, summary statistics from sets of experiments), and is it transparent whether you are reporting the max, mean, etc. or just a single run?
+
+Section 4 Fig 2 mainly (the main experiment which includes several runs) Other experiments do not have repetitions but varying a trait, so the clear (not noisy) trend serves as a way to assess variance.
+
+C4. If you used existing packages (e.g., for preprocessing, for normalization, or for evaluation), did you report the implementation, model, and parameter settings used (e.g., NLTK, Spacy, ROUGE, etc.)?
+
+Sections such as 3 and Appendices such as A
+
+D Did you use human annotators (e.g., crowdworkers) or research with human participants? Left blank.
+
+D1. Did you report the full text of instructions given to participants, including e.g., screenshots, disclaimers of any risks to participants or annotators, etc.? Not applicable. Left blank.  
+D2. Did you report information about how you recruited (e.g., crowdsourcing platform, students) and paid participants, and discuss if such payment is adequate given the participants' demographic (e.g., country of residence)?
+
+Not applicable. Left blank.
+
+D3. Did you discuss whether and how consent was obtained from people whose data you're using/curating? For example, if you collected data via crowdsourcing, did your instructions to crowdworkers explain how the data would be used?
+
+Not applicable. Left blank.
+
+D4. Was the data collection protocol approved (or determined exempt) by an ethics review board? Not applicable. Left blank.  
+D5. Did you report the basic demographic and geographic characteristics of the annotator population that is the source of the data?
+
+Not applicable. Left blank.

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2023/Combo of Thinking and Observing for Outside-Knowledge VQA/full.md

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+# Combo of Thinking and Observing for Outside-Knowledge VQA
+
+Qingyi Si $^{1,2}$ , Yuchen Mo $^{3}$ , Zheng Lin $^{1,2*}$ , Huishan Ji $^{1,2}$ , Weiping Wang $^{1}$
+
+$^{1}$ Institute of Information Engineering, Chinese Academy of Sciences, Beijing, China
+
+$^{2}$ School of Cyber Security, University of Chinese Academy of Sciences, Beijing, China
+
+3ByteDance AI Lab, Beijing, China
+
+{siqingyi,linzheng,jihuishan,wangweiping}  $@$  iie.ac.cn
+
+# Abstract
+
+Outside-knowledge visual question answering is a challenging task that requires both the acquisition and the use of open-ended real-world knowledge. Some existing solutions draw external knowledge into the cross-modality space which overlooks the much vaster textual knowledge in natural-language space, while others transform the image into a text that further fuses with the textual knowledge into the natural-language space and completely abandons the use of visual features. In this paper, we are inspired to constrain the cross-modality space into the same space of natural-language space which makes the visual features preserved directly, and the model still benefits from the vast knowledge in natural-language space. To this end, we propose a novel framework consisting of a multimodal encoder, a textual encoder and an answer decoder. Such structure allows us to introduce more types of knowledge including explicit and implicit multimodal and textual knowledge. Extensive experiments validate the superiority of the proposed method which outperforms the state-of-the-art by  $6.17\%$  accuracy. We also conduct comprehensive ablations of each component, and systematically study the roles of varying types of knowledge. Codes and knowledge data can be found at https://github.com/PhoebusSi/Thinking-while-Observing.
+
+# 1 Introduction
+
+Conventional visual question answering (VQA) (Antol et al., 2015) tasks require models to answer questions based on image content. Such tasks have been thoroughly studied (Guo et al., 2021; Jiang et al., 2020; Li et al., 2020b) on conventional VQA datasets VQAv2 (Goyal et al., 2017). However, real-world questions often rely on a certain amount of knowledge beyond images. Therefore, Knowledge Base Question Answering (KB-VQA) tasks
+
+![](images/132d8413b9f074034c1b8fae91944479937fc634126960f65a3c70519f59ba3c.jpg)  
+(a) Conventional VQA Paradigm  
+(b) Language-centric Paradigm
+
+![](images/4bed42e3d07700b95007a8487142febd7d94ba82281cc9226d59603e996320e4.jpg)  
+(c) The Proposed Paradigm  
+Figure 1: Comparison with previous paradigms. Orange lines indicate processes involving cross-modality space. (a) The conventional VQA paradigm fuses image and question text into the cross-modality space, and then predicts answers in a close-set classification manner. (b) Language-centric paradigm applies captioning and tagging tools to describe the visual context, and abandons the visual features to convert the VQA task into an open-ended generative QA task. (c) The proposed paradigm intends to constrain the cross-modality space into the same space as natural-language space so that models can directly decode both text and multimodal embeddings.
+
+(Cao et al., 2021; Wang et al., 2015, 2017; Shah et al., 2019; Lu et al., 2018) always require models to answer questions by referring to the corresponding knowledge facts in a specific pre-defined knowledge base. Yet any pre-defined knowledge base is far from covering real-world knowledge. Recently, the outside-knowledge visual question answering (OK-VQA) task has been proposed (Marino et al., 2019) and provides the most open VQA setting. That is, any knowledge resource can be used to answer its challenging and diverse questions.
+
+Most previous work (Ding et al., 2022; Gardères et al., 2020; Marino et al., 2021) on OK-VQA follows conventional VQA paradigm (as shown in Figure 1 (a)) based on visual-language pre-trained (VLP) models, and injects knowledge into the same cross-modality space afterward. However, knowl
+
+edge in cross-modality space is much less than that in natural-language space Gao et al.. This paradigm excels at visual understanding, but refers to little knowledge, like a human who focuses on observing but does not think enough.
+
+To take the advantage of the vast knowledge in natural-language space, state-of-the-art methods (Gao et al., 2022; Yang et al., 2022; Gui et al., 2021) on OK-VQA follow language-centric paradigm (as shown in Figure 1 (b)) based on pre-trained language models (PLMs). However, although more knowledge can be introduced, the paradigm is counter-intuitive because many visual details are lost when converting an image into text. Therefore, it is like a human who starts thinking after brief observing.
+
+For a human, a feasible solution to OK-VQA is combo Thinking while Observing. To this end, we propose TwO, which is a framework consisting of a multimodal encoder, a textual encoder and an answer decoder. As shown in Figure 1(c), the multimodal encoder directly encodes the visual features and acts as the role of observer, while the textual encoder encodes a range of knowledge resources and acts as the role of thinker. Finally, the answer decoder decodes the latent embeddings from both encoders to generate the final answer. In addition, a pre-training stage is added to help constrain the output of both encoders to the same latent space.
+
+Previous methods (Gui et al., 2021; Gao et al., 2022; Wu et al., 2022) have thoroughly studied explicit textual knowledge such as Wikipedia, as well as implicit textual knowledge in GPT-3 (Brown et al., 2020). However, the discussion of multimodal knowledge, which further utilizes visual features, is still in its infancy in OK-VQA. In this paper, we accumulate explicit multimodal knowledge during pre-training on VQAv2 (Ding et al., 2022). Besides, inspired by prompting GPT-3 (Yang et al., 2022) for implicit textual knowledge, we use prompt to bring in implicit multimodal knowledge stored in the unifying VLP model OFA (Wang et al., 2022). Moreover, we refine a taxonomy of existing methods by knowledge (refer to Figure 2) where our method is the first to bring in all types of knowledge.
+
+To summarize, our contributions are as follows:
+
+(1) We propose a simple and effective paradigm that combines the advantages of both conventional VQA and language-centric paradigms.
+
+![](images/a9d20230701342d2f56ef433bd8025f45960a56c0c13a6875f02d6b28ebead73.jpg)  
+Figure 2: Taxonomy of OK-VQA methods by knowledge types. Green, purple, blue and red fonts represent the introduction of one, two, three and four types of knowledge. No existing work introduces four types of knowledge in a unified framework, but ours.
+
+(2) Our method can deal with more comprehensive types of knowledge, and is the first to bring in implicit multimodal knowledge through a prompt-learning fashion. In addition, we empirically analyze the roles of different types of knowledge.  
+(3) Experimental results show the effectiveness of our method, which establishes a new SoTA accuracy on OK-VQA with a  $6.17\%$  gain.
+
+# 2 Background
+
+# 2.1 Outside-Knowledge Visual Question Answering (OK-VQA)
+
+In addition to dividing existing methods according to latent space, namely multimodal-space methods (Ding et al., 2022; Gardères et al., 2020; Zhu et al., 2020; Yu et al., 2020; Zheng et al., 2021; Marino et al., 2021) and textual-space methods (Yang et al., 2022; Gui et al., 2021; Gao et al., 2022), existing methods can also be roughly categorized into two lines by whether GPT-3 is used. Most of the GPT-3 based methods (Gui et al., 2021; Lin et al., 2022) outperform non-GPT ones by large margins, since huge-parameter-capacity GPT-3 can store abundant implicit textual knowledge. The vast implicit knowledge in GPT-3 can be easily retrieved in a prompt manner. For example, Pica (Yang et al., 2022) uses text prompts of in-context examples to query GPT-3 for answers directly. However, most existing methods for OK-VQA are non-GPT-3 based, which do not directly compare with GPT-3 based methods for a fair comparison. For completeness, we explore our model performance with and without GPT-3, respectively.
+
+Previous work has generally improved model performance in OK-VQA in two ways: one is to
+
+introduce more knowledge sources (see Figure 4), and the other is to optimize the model paradigm (see Figure 1). For example, MAVEx (Wu et al., 2022) follows the former way and introduces more knowledge sources such as Wikipedia, ConceptNet (Speer et al., 2017) and Google images to boost model performance; VRR-ERader (Luo et al., 2021) follows the latter way and replaces the classifier with an extraction reader to solve the generalization problem of classification manner. Our method goes further in both directions: On the one hand, we explore more comprehensive types of knowledge. On the other hand, we refine the paradigm to make the visual features retained, and the model still benefits from natural language space. We list the relationship between our method and previous work in Appendix A.1.
+
+# 2.2 Taxonomy of OK-VQA Methods by Knowledge Types
+
+With an in-depth look at the types of knowledge involved in each existing method, we propose a complete taxonomy of OK-VQA methods shown in Figure 2. We divide all knowledge into four types: explicit textual knowledge, explicit multimodal knowledge, implicit textual knowledge, and implicit multimodal knowledge.
+
+From Figure 2, we find that (1) most GPT-3 based methods (Yang et al., 2022; Gui et al., 2021) appear in the two circles of "Textual" because they adopt the language-centric paradigm. (2) There are few methods to use explicit multimodal knowledge, which is more challenging to introduce into models than explicit textual knowledge. Among them, Marino et al.; Ding et al. propose accumulating this knowledge through pre-training while Wu et al. use Google Image to provide similar images. (3) Recent work is usually distributed in the two circles of "Implicit". This shows that VLP models or PLMs have become one of the vital components of the model for OK-VQA. Appendix A.2 and A.3 show more related work about VLPs and PLMs.
+
+# 3 Method
+
+# 3.1 Visual Description Module
+
+Given an image  $I_{i}$ , following (Gao et al., 2022), we adopt a coarse-to-fine transformation strategy to describe it as comprehensively as possible, and obtain three parts as follows.
+
+1. Image-level caption  $C_i$ , given by the SoTA VLP model OFA (Wang et al., 2022).
+
+2. Object-level attribution description  $L_{i}$  from the VinVL (Zhang et al., 2021) detector.  
+3. Token-level Optical Character Recognition (OCR) results  $O_{i}$  from easyOCR<sup>2</sup>.
+
+To simplify, we refer to the three as visual context  $V_{i} = (Ci, Li, Oi)$ . The generated visual descriptions are in the following forms:
+
+$$
+\begin{array}{l} C _ {i} = \left\{\left(w _ {0} ^ {c a p},..., w _ {j} ^ {c a p}\right) \right\} \\ L _ {i} = \left\{p h r a s e _ {0} ^ {l a b}, \dots , p h r a s e _ {m} ^ {l a b} \right\}, \tag {1} \\ \operatorname {p h r a s e} _ {m} ^ {\text {l a b}} = \left(w _ {0} ^ {\text {a t t r}}, \dots , w _ {n} ^ {\text {a t t r}}, w ^ {\text {o b j}}\right) \\ O _ {i} = \left\{w _ {0} ^ {\mathrm {o c r}}, \dots , w _ {k} ^ {\mathrm {o c r}} \right\} \\ \end{array}
+$$
+
+# 3.2 Explicit Knowledge Retrieval and Accumulation
+
+To answer challenging questions, humans tend to query them in knowledge bases or accumulate relevant knowledge in advance. Inspired by this, we introduce explicit textual and multimodal knowledge through retrieval and accumulation, respectively.
+
+Wikipedia Passage Retrieval. We view the 21-million-passage Wikipedia dump  $D$  as an explicit textual knowledge source. In particular, we combine the question  $Q_{i}$  and caption  $C_i$  as a query  $q_{i} = (Q_{i},C_{i})$  to retrieve the relevant passages from  $D$ . To this end, our method adopts an off-the-shelf pre-trained dense passage retrieval (DPR) (Karpukhin et al., 2020) model. DPR encodes the query  $q_{i}$  and all candidate passages  $D$  separately into dense vectors  $v_{q_i}$  and  $[v_{p_0},v_{p_1},\dots,v_{p_{|D|}}]$  with two independent BERT encoders as follows:
+
+$$
+\mathbf {v} _ {q _ {i}} = B E R T _ {Q} \left(q _ {i}\right), \mathbf {v} _ {p _ {k}} = B E R T _ {P} \left(p _ {k}\right) \tag {2}
+$$
+
+We compute the inner product  $sim(q_i, p_k) = \mathbf{v}_{q_i}^T \cdot \mathbf{v}_{p_k}$  as their similarity scores, and then exploit an indexing engine FAISS (Johnson et al., 2019) to speed up the above process. The knowledge passages  $P_i = [p_{i,0}, p_{i,1}, \dots, p_{i,k}]$  with top  $k$  similarity scores are the final explicit textual knowledge.
+
+VQA Knowledge Accumulation. Compared to the rigid facts of textual knowledge, the inexpressible facts of multimodal knowledge are also indispensable (e.g., object identification and scene understanding (Ding et al., 2022). We view the conventional VQAv2 dataset as an explicit multimodal knowledge source, and our model accumulates multimodal knowledge in advance through pre-training on VQAv2.
+
+![](images/d313d8ed5a9512959acf2d194ffec68de2738e4f69e4d84bfa3ac4e3326390de.jpg)  
+Figure 3: The flowchart of our method shows how we obtain four types of knowledge (red fonts) and feed them into the proposed model, which consists of a multimodal encoder, a textual encoder and an answer decoder.
+
+# 3.3 Implicit Knowledge Retrieval
+
+Recently, the GPT-3 LLM has shown its strength in generating open domain knowledge (Gui et al., 2021; Yang et al., 2022) in a prompt-learning manner, and is widely used in OK-VQA as a source of implicit textual knowledge. However, the text descriptions of given images in prompts may lack important visual information, resulting in incomplete or irrelevant knowledge output from GPT-3. To overcome such drawbacks, we propose to view the unifying VLP model OFA as a source of implicit multimodal knowledge. Different from GPT-3, OFA can be queried directly by visual features with text prompts.
+
+Implicit Textual Knowledge in GPT-3. Following the prompt tuning procedure of KAT (Gui et al., 2021), we retrieve implicit textual knowledge in GPT-3 with supporting evidence. Specifically, we use the combination of the question, caption, and object labeling as a prompt  $X_{gpt}$  for each image-question pair. Then we add carefully designed instruction text and semantically similar samples as the in-context examples at the beginning of  $X_{gpt}$ . That is,  $X_{gpt}$  is "⟨instructions⟩ ⟨in-context examples⟩ Context: ⟨caption  $C_i \rangle + \langle objectlabeling L_i \rangle$ . Q: ⟨question  $Q_i \rangle \mathsf{A} : "$ .  $X_{gpt}$  can query a tentative answer  $A_i^{gpt}$ , and we then query GPT-3 with another prompt  $Y_{gpt}$  "⟨question  $Q_i \rangle \langle answer A_i^{gpt} \rangle$ . This is because" for supporting evidence  $E_i^{gpt}$ . The final obtained implicit textual knowledge is  $T_i = \left\{A_i^{gpt}, E_i^{gpt}\right\}$ .
+
+Implicit Multimodal Knowledge in OFA. Instruction-guided pre-training enables OFA to perform zero-shot generalization for different prompts, although it does not have a huge parameter capacity like GPT-3. To generate the tentative answer  $A_{i}^{ofa}$ , we directly feed OFA the visual features and
+
+question as the prompt  $X_{gpt}$ . In addition, "This is because" in  $Y_{gpt}$  is no longer applicable to prompt OFA to generate the evidence, as OFA excels at question-form prompts rather than writing a continuation like GPT-3. We therefore design a question-form prompt  $Y_{ofa}$  ("question  $Q_i$ ) Why  $\left\langle answer A_i^{ofa} \right\rangle$ ?" to query OFA for supporting evidence  $E_i^{ofa}$ . The final obtained implicit multimodal knowledge is  $M_i = \left\{ A_i^{ofa}, E_i^{ofa} \right\}$ .
+
+# 3.4 Model Structure of TwO
+
+We have designed the modules above for different types of knowledge, and then, as shown in Figure 3, transfer the acquired knowledge to our model, which contains the following modules:
+
+Multimodal Encoder. We directly adopt an existing VLP model as our multimodal encoder. This paper mainly uses LXMERT, the most widely used one in VQA. LXMERT encodes question  $Q_{i}$  and image  $I_{i}$  to obtain the language hidden states  $\hat{H}_i^l$  and vision hidden states  $\hat{H}_i^v$  that have fully interacted with each other.
+
+$$
+\hat {H} _ {i} ^ {l}, \hat {H} _ {i} ^ {v} = e n c _ {m m} (Q _ {i}, I _ {i}) \tag {3}
+$$
+
+where  $\hat{H}_i^l\in \mathbb{R}^{L_q*\hat{h}}$ $\hat{H}_i^v\in \mathbb{R}^{L_v*\hat{h}}$ $L_{q}$  is the length of the question,  $L_{v}$  is the number of objects, and  $\hat{h}$  is the size of hidden embedding. This encoder acts like "observing" where visual features can interact well with questions.
+
+Textual Encoder. We use T5's encoder as the textual encoder, and feed in all possible textual information, i.e.,  $Q_{i}$ ,  $V_{i}$ ,  $M_{i}(,T_{i})^{3}$  and  $P_{i}$  as input. Due to the large number of relevant Wikipedia passages, we concatenate each passage  $p_{i,k}$  that iterates over  $P_{i}$  with other inputs, and then feed each
+
+concatenated sequence into the textual encoder as:
+
+$$
+Z _ {i} ^ {k} = \operatorname {e n c} _ {t x t} \left(Q _ {i}, V _ {i}, M _ {i}, p _ {i, k}\right) \tag {4}
+$$
+
+Here, we obtain the hidden embedding sequence  $Z_{i}^{k} = (z_{0},z_{1},\dots,z_{t})$ , where  $z_{t}$  represents the  $t_{th}$  token embedding,  $Z_{i}^{k}\in \mathbb{R}^{L_{t}*h}$ ,  $L_{t} = |(Q_{i},V_{i},M_{i},p_{i,k})|$  is the length of the sequence and  $h$  is the size of the hidden embedding. This encoder acts like "thinking" where vast knowledge can interact well with questions.
+
+Combo of Both Encoders. To combine the hidden embeddings of both encoders, we map the embedding of the multimodal encoder into the same dimensional space as the textual encoder:
+
+$$
+H _ {i} ^ {l}, H _ {i} ^ {v} = F C _ {2} (r e l u (F C _ {1} ([ \hat {H} _ {i} ^ {l}, \hat {H} _ {i} ^ {v} ]))) \qquad (5)
+$$
+
+where  $H_{i}^{l}\in \mathbb{R}^{L_{q}*h}$ $H_{i}^{v}\in \mathbb{R}^{L_{v}*h}$  . The final multimodal embedding sequence is  $H_{i} = (H_{i}^{l},H_{i}^{v})$  Then we combine the multimodal and textual embedding sequence together to obtain a hybrid embedding sequence  $S_{i}^{k} = (H_{i},Z_{i}^{k})$  . Subsequently, we iterate all  $k$  passages with the same encoding process to generate  $k$  hybrid embedding sequences:
+
+$$
+S _ {i} = \left(S _ {i} ^ {0}, S _ {i} ^ {1}, \dots , S _ {i} ^ {k}\right) \tag {6}
+$$
+
+where  $S_{i}\in \mathbb{R}^{((L_{q} + L_{v} + L_{t})\cdot k)\times h}$  is the concatenation of all  $k$  sequences. Taking into account both visual features and vast knowledge, we come to a combo of "thinking and observing".
+
+Answer Decoder. We apply T5's decoder as the answer decoder, and feed in the embedding sequence  $S_{i}$  to generate the final answer according to the prediction probability  $P()$  over the vocabulary space  $|V|$  for each answer token:
+
+$$
+P \left(a _ {i} ^ {1}\right), \dots , P \left(a _ {i} ^ {l}\right) = \operatorname {s o f t m a x} \left(\operatorname {d e c} \left(\mathbf {S} _ {\mathbf {i}}\right)\right) \tag {7}
+$$
+
+where  $l$  is the length of the answer. Finally, we adopt teacher-enforcing to train the model with auto-regressive cross-entropy objective:
+
+$$
+L _ {a n s} = \frac {- 1}{N \cdot l \cdot | V |} \sum_ {i = 1} ^ {N} \sum_ {j = 1} ^ {l} \sum_ {w = 1} ^ {| V |} A _ {i} ^ {j, w} \log \left(P \left(a _ {i} ^ {j, w}\right)\right) \tag {8}
+$$
+
+where  $N$  is the size of the whole training set.
+
+Pre-training and Fine-tuning. In addition to accumulating explicit multimodal knowledge in VQAv2, the pre-training stage also makes the answer decoder suitable for decoding two different encoders. Note that the implicit knowledge  $T_{i}$  and  $M_{i}$
+
+are not used during pre-training, while the forms of other inputs are consistent with fine-tuning. To employ model ensemble, a common practice in OK-VQA, we take ensembles of six models trained with different seeds, and select the most frequent predictions as the final answers.
+
+# 4 Experiments
+
+# 4.1 Experimental Setup
+
+OK-VQA Dataset. This paper conducts extensive experiments on the OK-VQA dataset (Marino et al., 2019), the most open VQA dataset, where each question requires outside knowledge beyond the image to answer correctly. Since all questions are manually annotated with no fixed template or knowledge base, this dataset allows the use of any external knowledge source that can help answer.
+
+Evaluation Metric and Implementation Details. We evaluate performance by the standard VQA evaluation metric (Goyal et al., 2017) (denoted by Acc) and Exact Match (Gao et al., 2022) (denoted by EM). Acc defines a soft score (between 0 and 1) for each annotated answer according to a voting mechanism, reflecting the consensus subjectively of multiple annotators. In contrast, EM treats all annotated answers to a question equally as the ground truth, which is a looser metric.
+
+We adopt lxmert-base-uncased or visualbert-vqa (Li et al., 2019) and T5-large models to initialize our model. We pre-train and finetune the models on 12 and 8 A100-80GB GPUs respectively for 3 epochs with a batch size of 1. More details are shown in Appendix B.
+
+# 4.2 Comparison with Existing Approaches
+
+Comparison with SoTAs. Table 1 reports the performance of our proposed method and state-of-the-art models, from which we can derive several observations: (1) Comparing the second and third lines with the first line, we find that implicit knowledge in VLP models or PLMs, used for model initialization, further improves model performance. This was rarely discussed in previous work. (2) MuKEA and TriG are the best-performing methods to implement OK-VQA in cross-modal space and natural-language space, respectively. By comparing their performance, we find that OK-VQA solutions in natural-language space perform significantly better than those in cross-modal space. This is because squeezing the rich representation
+
+<table><tr><td>Method</td><td>Venue</td><td>Implicit Knowledge</td><td>Explicit Knowledge Resources</td><td>EM</td><td>Acc</td></tr><tr><td>BAN</td><td>NeurIPS(2018)</td><td>—</td><td>—</td><td>25.17</td><td></td></tr><tr><td>+AN</td><td>CVPR(2019)</td><td>—</td><td>Wikipedia</td><td>25.61</td><td></td></tr><tr><td>+KG-AUC</td><td>MM(2020a)</td><td>—</td><td>Wikipedia + ConceptNet</td><td>26.71</td><td></td></tr><tr><td>MUTAN</td><td>ICCV(2017)</td><td>—</td><td>—</td><td>26.41</td><td></td></tr><tr><td>+AN</td><td>CVPR(2019)</td><td>—</td><td>Wikipedia</td><td>27.84</td><td></td></tr><tr><td>Mucko</td><td>IJCAI(2020)</td><td>—</td><td>ConceptNet</td><td>29.20</td><td></td></tr><tr><td>GRUC</td><td>PR(2020)</td><td>—</td><td>ConceptNet</td><td>29.87</td><td></td></tr><tr><td>KM4</td><td>Inf Fusion(2021)</td><td>—</td><td>multimodal knowledge from OK-VQA</td><td>31.32</td><td></td></tr><tr><td>ViLBERT</td><td>ICNIP(2019)</td><td>ViLBERT</td><td></td><td>31.35</td><td></td></tr><tr><td>LXMERT</td><td>EMNLP(2019)</td><td>LXMERT</td><td></td><td>32.04</td><td></td></tr><tr><td>VRR-CReader</td><td>EMNLP(2021)</td><td>LXMERT</td><td>Google Search</td><td>36.78</td><td></td></tr><tr><td>RVLESK</td><td>LANTERN(2021)</td><td>LXMERT</td><td>ConceptNet</td><td>39.04</td><td></td></tr><tr><td>MAVEx</td><td>AAAI(2022)</td><td>ViLBERT</td><td>Wikipedia + ConceptNet + Google Images</td><td>41.37</td><td></td></tr><tr><td>MuKEA</td><td>CVPR(2022)</td><td>LXMERT</td><td>multimodal knowledge from VQAv2 and OK-VQA</td><td>42.59</td><td></td></tr><tr><td>ConceptBert</td><td>EMNLP(2020)</td><td>BERT</td><td>ConceptNet</td><td>33.66</td><td></td></tr><tr><td>KRISP(w/o mm pre.)</td><td>CVPR(2021)</td><td>BERT</td><td>DBpedia + ConceptNet + VisualGenome + haspartKB</td><td>32.31</td><td></td></tr><tr><td>KRISP(w/ mm pre.)</td><td>CVPR(2021)</td><td>BERT</td><td>ditto + VQAv2</td><td>38.90</td><td></td></tr><tr><td>VRR-ERender</td><td>EMNLP(2021)</td><td>RoBERTa</td><td>Google Search</td><td>39.20</td><td></td></tr><tr><td>TRiG</td><td>CVPR2022</td><td>T5</td><td>Wikipedia</td><td>53.59</td><td>49.35</td></tr><tr><td>TRiG, E</td><td>CVPR(2022)</td><td>T5</td><td>Wikipedia</td><td>54.73</td><td>50.50</td></tr><tr><td>Ours</td><td></td><td>LXMERT+OFA+T5</td><td>VQAv2 + Wikipedia</td><td>59.85</td><td>55.33</td></tr><tr><td>Ours, E</td><td></td><td>LXMERT+OFA+T5</td><td>VQAv2 + Wikipedia</td><td>61.12</td><td>56.49</td></tr><tr><td>Ours</td><td></td><td>visualBERT+OFA+T5</td><td>VQAv2 + Wikipedia</td><td>60.17</td><td>55.52</td></tr><tr><td>Ours, E</td><td></td><td>visualBERT+OFA+T5</td><td>VQAv2 + Wikipedia</td><td>61.32</td><td>56.67</td></tr></table>
+
+Table 1: Results comparison with existing methods. The middle two columns report the implicit knowledge and explicit knowledge sources involved in each method respectively. The middle two rows show the methods based on VLP models and PLMs respectively.  $\mathbf{E}$  denotes the model ensemble.  
+
+<table><tr><td>Method</td><td>Knowledge in Input Text</td><td>Acc</td></tr><tr><td>PICa</td><td>Frozen GPT-3 (175B)</td><td>46.50</td></tr><tr><td>PICa, E</td><td>Frozen GPT-3 (175B)</td><td>48.00</td></tr><tr><td>KAT</td><td>Wikidata+Frozen GPT-3 (175B)</td><td>53.10</td></tr><tr><td>KAT, E</td><td>Wikidata+Frozen GPT-3 (175B)</td><td>54.40</td></tr><tr><td>REVIVE</td><td>Wikidata+Frozen GPT-3 (175B)</td><td>56.60</td></tr><tr><td>REVIVE, E</td><td>Wikidata+Frozen GPT-3 (175B)</td><td>58.00</td></tr><tr><td>ours</td><td>Wikipedia+Frozen OFA (0.93B)</td><td>55.33</td></tr><tr><td>ours, E</td><td>Wikipedia+Frozen OFA (0.93B)</td><td>56.49</td></tr><tr><td>ours w/ GPT-3</td><td>ditto+Frozen GPT-3 (175B)</td><td>57.57</td></tr><tr><td>ours w/ GPT-3, E</td><td>ditto+Frozen GPT-3 (175B)</td><td>58.72</td></tr></table>
+
+Table 2: Results comparison with existing GPT-3 based methods.  $\mathbf{E}$  denotes the model ensemble.
+
+of natural-language knowledge (billion-degree pretraining corpus) into a much smaller cross-modal space (million-degree pre-training corpus) leads to a severe loss of knowledge. (3) Our method is compatible with various VLP encoders, and beats the previous SoTAs TRiG by  $6.17\%$  Acc and  $6.59\%$  EM. (4) It can be seen from the middle two columns that, compared to previous work, our method is the first to utilize all four types of knowledge at the same time, which is one of the reasons why our method is effective. Moreover, as shown in Appendix C.1, our method can outperform TRiG using 100 Wikipedia passages by  $4.37\%$  Acc even using only 5 passages, which substantially reduces computing consumption.
+
+Comparison with GPT-3 Based Methods. We also compare our method with recent GPT-3 based
+
+![](images/6d03f342e4102dcf70cc8c279f85243c7b01f6b07521bc4ae3a04c8c7d3ac9d4.jpg)  
+Figure 4: Ablation study on the pre-training and finetuning stages. 'w/o finetune' denotes that after pretraining on VQAv2, the model will be evaluated directly on the OK-VQA test set without further fine-tuning.
+
+methods. As shown in Table 2, GPT-3 Based methods are significantly superior to non-GPT-3 baselines shown in Table 1. However, even without GPT-3 (175B), we can achieve competitive results with OFA (0.93B). To compare fairly, we further improve our model performance by incorporating GPT-3, and clearly surpass all GPT-3 based SoTAs.
+
+# 4.3 Ablation Study
+
+Ablation of Pretrain-finetune Strategy. In Figure 4, we evaluate the contribution of pre-training and fine-tuning in our method. The decline in performance caused by "w/o pre-train" confirms the necessity of pre-training. Although 'w/o finetune' is far worse than the final performance, it is still competitive compared with previous methods. This further verifies that multimodal knowledge in VQAv2 is helpful in solving OK-VQA.
+
+<table><tr><td>Model</td><td>Input Form</td><td>EM</td><td>Acc</td></tr><tr><td>ours w/o pre.</td><td>visual features + textual input</td><td>59.93</td><td>55.44</td></tr><tr><td>LXMERT</td><td>visual features</td><td>—</td><td>32.04</td></tr><tr><td>w/o txt enc</td><td>visual features</td><td>29.43</td><td>26.61</td></tr><tr><td>w/o mm enc</td><td>textual input</td><td>60.01</td><td>55.56</td></tr><tr><td>ours</td><td>visual features + textual input</td><td>62.33</td><td>57.57</td></tr><tr><td>w/o txt enc</td><td>visual features</td><td>34.52</td><td>31.39</td></tr><tr><td>w/o mm enc</td><td>textual input</td><td>61.55</td><td>56.83</td></tr></table>
+
+Table 3: Ablation study on each encoder in our model structure. The middle column indicates the data format that each model can be fed. The upper part represents the models without pre-training. 'w/o txt enc' and 'w/ommmenc' denote using only multimodal encoder and textual encoder respectively.  
+
+<table><tr><td>Model</td><td>Knowledge Type</td><td>EM</td><td>Acc</td></tr><tr><td>ours</td><td>all four types</td><td>62.33</td><td>57.57</td></tr><tr><td>w/o pre.</td><td>explicit mulimodal</td><td>59.93</td><td>55.44</td></tr><tr><td>w/o Wiki</td><td>explicit textual</td><td>60.80</td><td>56.18</td></tr><tr><td>w/o OFA</td><td>implicit multimodal</td><td>57.13</td><td>52.71</td></tr><tr><td>w/o GPT-3</td><td>implicit textual</td><td>59.65</td><td>55.28</td></tr></table>
+
+Ablation of Model Structure. To prove the complementary benefits of applying the two encoders, we conduct experiments and report results in Table 3. The findings can be summarized as follows: (1) As shown in the "Input Form" column, combining both textual and multimodal encoders allows our method to handle both visual features and textual input simultaneously. (2) 'w/o txt enc' consistently underperforms 'w/o mm enc', because the natural-language space of the textual encoder contains more knowledge, which is critical to OK-VQA. (3) The upper part shows that, without pretraining, 'w/o textual enc' performs worse than LXMERT, as the answer decoder, initialized with T5, cannot directly fit the encoder initialized with LXMERT. (4) Similarly, removing the multimodal encoder without pre-training will instead result in a slight performance improvement for the same reason. (5) As shown in the lower part, adopting pre-training contributes to ameliorating the above phenomenon. That is, the performance of 'ours' is superior to both 'w/o txt enc' and 'w/o mm enc' by clear margins. This proves that pre-training can help make the answer decoder suitable for decoding both encoders, thus combining the advantages of both encoders.
+
+Ablation of Four Types of Knowledge. Table 4 shows that the absence of any type of knowledge will lead to a significant drop in performance
+
+Table 4: Ablation study on four types of knowledge. The second column lists the types of the removed knowledge source.  
+
+<table><tr><td rowspan="2">Knowledge Source</td><td colspan="2">hit</td><td rowspan="2">Knowledge Source</td><td colspan="2">hit</td></tr><tr><td>Train</td><td>Test</td><td>Train</td><td>Test</td></tr><tr><td>GPT-3 ans + evi</td><td>56.59</td><td>61.51</td><td>OFA ans + evi</td><td>63.36</td><td>66.75</td></tr><tr><td>GPT-3 ans</td><td>54.02</td><td>59.27</td><td>OFA ans</td><td>57.63</td><td>61.59</td></tr><tr><td>GPT-3 evi</td><td>34.09</td><td>37.26</td><td>OFA evi</td><td>57.84</td><td>61.47</td></tr><tr><td>Visual Context</td><td>32.28</td><td>32.92</td><td>Wikipedia(75)</td><td>82.58</td><td>85.26</td></tr><tr><td>captions</td><td>22.34</td><td>22.81</td><td>Wikipedia(50)</td><td>80.34</td><td>82.62</td></tr><tr><td>labels</td><td>23.62</td><td>24.18</td><td>Wikipedia(25)</td><td>74.28</td><td>76.56</td></tr><tr><td>OCR</td><td>0.44</td><td>0.32</td><td>Wikipedia(10)</td><td>63.20</td><td>64.74</td></tr><tr><td>all</td><td>93.18</td><td>95.30</td><td>Wikipedia(5)</td><td>51.88</td><td>54.12</td></tr></table>
+
+Table 5: Hit of each component in our model's inputs. Hit is defined as the percentage of samples in the whole dataset that get a hit on any corresponding annotated answer by the retrieved knowledge. "ans" and "evi" denote tentative answers and supporting evidence, respectively.
+
+(1.39%~4.86% Acc and 1.53%~5.20% EM), which proves the complementary benefits among the four types of knowledge. Among the four types of knowledge, implicit knowledge in OFA contributes the most and explicit knowledge of Wikipedia contributes the least. We will discuss this phenomenon in Appendix D.1. In addition, in Appendix C.3, we also perform ablations from a dependence perspective to prove the indispensability of each encoder and knowledge.
+
+Performance of Knowledge Retrieval. From Table 5, it can be seen that: (1) The combination of all the knowledge retrieved in our method can cover the answers corresponding to  $95.30\%$  of the samples. The high hit guarantees a high upper bound, allowing the model to generalize better. (2) Hit of prompting OFA significantly outperforms that of prompting GPT-3, indicating that implicit multimodal knowledge may be more effective than implicit textual knowledge in OK-VQA. (3) The supporting evidence can clearly improve hit of the tentative answers, especially for OFA (from  $61.59\%$  to  $66.75\%$ ). (4) Wikipedia's high hit demonstrates the effectiveness of our adopted DPR model in retrieval. As shown in Appendix C.1, as the number of Wikipedia passages increases, Acc/EM of our model rises first and then falls because noise is introduced when the number of passages is large.
+
+In Appendix D.1, we also conduct experiments to further explore the extent to which the model makes use of each type of knowledge. We find that compared with explicit knowledge, implicit knowledge has a higher conversion rate from knowledge to correct answers. We also qualitatively analyze the impact on OK-VQA of different versions of OFA in Appendix D.2.
+
+![](images/db0c47ccf095211c5abddcca06f9bf7f529fade8fdd0bb29f3dbb8a7441a977f.jpg)
+
+![](images/0d37e202a90af6753d53190b5b40346bc68478b61bc23c98233dadc7703bb5bc.jpg)
+
+![](images/e80eac1781c2ab31125b3e293ec165531026ecfb81dc81a3cc240973ba373624.jpg)
+
+![](images/904ae50aee1fff2cef1f8c149ee9d4a69bf702c5d1b2aa7280e197b5b08ccba7.jpg)
+
+![](images/898f1cf19fe1888275e024b8a49e89579b54a075a4a919d44bbee6db9abd3f51.jpg)  
+Figure 5: Examples of our prediction together with all the supporting knowledge when (Upper) only using a single encoder or (Lower) respectively removing each type of knowledge from our method. Pred denotes our predicted answer. ours-mm and ours-text represent the model that combines only multimodal encoder or textual encoder with answer decoder, respectively.
+
+![](images/9b8cd4065ce31dba1ddbedca604dd546d75ad70450208c91cee14f496f6060dd.jpg)  
+(f)
+
+![](images/dbf8020dea47389e234bae32af85e05bc8737c0e269ee2396ed1a5c4156f9017.jpg)  
+(g)
+
+![](images/8034b161c9390cb0dec8d060aac5f1d613da95217852f239e405ab89f33aeec1.jpg)  
+(h)
+
+# 5 Qualitative Analysis
+
+Case Study on Two Encoders. To explore the respective roles of the two encoders, the upper part of Figure 5 shows the examples that can be answered correctly by one of the two single-encoder models. Plot (a) and (b) of Figure 5 show that ours-mm excels at answering questions that need comprehension about image scenes and objects. For example, the orientation and the relative position between TV and sofa in plot (b) help generate the answer "watch tv". Such scene information is easily omitted by a single textual encoder. This further validates that the multimodal encoder supplements the missing image information, and makes better use of the image when combining knowledge.
+
+Plot (c) and (d) shows that ours-text is an expert in answering questions that require focusing more on external knowledge rather than image understanding, since the textual encoder is the primary channel for receiving knowledge from multiple sources.
+
+Case Study on Varying Types of Knowledge. As shown in the lower plots in Figure 5, we further analyze the circumstances under which each type of knowledge is essential, respectively. Plot (e) shows that the model would hardly generate correct answers, even those that have been recalled by knowledge, once pre-training is removed. This demonstrates that explicit multimodal knowledge accumulated during pre-training enhances the abl
+
+ity to use the recalled knowledge according to image content. Plot (f) shows that when a question is deeply dependent on image content (e.g., bird type detection), implicit multimodal knowledge in OFA can directly provide tentative answers from the image, which strengthens the visual understanding. Plot (g) shows that implicit textual knowledge in GPT-3 is essential for questions that require commonsense knowledge. Plot (h) shows that when a question is highly open, even if both GPT-3 and OFA fail to recall the corresponding knowledge, the retrieved Wikipedia passage can still provide enough knowledge (see Figure 4), e.g., enumerating the most plane models. In Appendix D.3, we also compare our method qualitatively against the previous methods.
+
+# 6 Conclusion and Future Work
+
+This paper proposes a simple and effective method that mimics human behavior "thinking while observing", i.e., benefiting from the vast knowledge in natural-language space while making the most of the visual features for better image understanding. Our method establishes a new SoTA accuracy of  $56.67\%$  with a  $6.17\%$  improvement on OK-VQA. Moreover, we consider more comprehensive types of knowledge, and systematically analyze the role of each type of knowledge in detail. We hope our work can stimulate followers to explore OK-VQA further along the direction of how to fuse both nature-language and cross-modality spaces better.
+
+# Limitations
+
+Although the proposed method has verified the feasibility of the idea that constrains both natural-language and cross-modality spaces together, it is still necessary to explore more ways to better combine the output of two encoders. Third, our method involves multiple offline knowledge retrieval processes, such as retrieving relevant Wikipedia passages, which will make it difficult to deploy our model as an online model.
+
+# Acknowledgement
+
+This work was supported by National Natural Science Foundation of China (No. 61976207).
+
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+
+# A More Related Work
+
+# A.1 Relationship with Previous Works
+
+TRiG (Gao et al., 2022) and MuKEA (Ding et al., 2022) respectively explored how to solve OK-VQA
+
+in natural language space and cross-modality space. The difference between our work and these two work can be explained by Figure 1. KAT (Gui et al., 2021) studied two types of knowledge, i.e., implicit and explicit knowledge in natural-language space. We further introduced four specific types of knowledge, i.e., implicit textual and multimodal knowledge, and explicit textual and multimodal knowledge.
+
+Although REVIVE (Lin et al., 2022) integrates visual features into the final model as we did, their model structure and knowledge introduction strategy are different from ours. For the model structure, they connect CLIP and T5 in series (i.e., feeding T5 with visual features obtained by CLIP) while we combine a VLP encoder and T5 encoder in parallel (i.e., fusing visual features when decoding). For knowledge exploration, their main focus is how to use the regional feature to retrieve Wikipedia and GPT-3, while we aim to explore and use more comprehensive types of knowledge, such as prompting OFA to obtain implicit multimodal knowledge.
+
+# A.2 VLP Models and PLMs
+
+Transformer-based PLMs (Devlin et al., 2018; Liu et al., 2019; Raffel et al., 2020) have achieved remarkable success in NLP, with the help of large-scale textual pre-training corpus, such as Wikipedia (2,500M words) and BookCorpus (800M words). Recently, VLP models (Li et al., 2019; Tan and Bansal, 2019; Lu et al., 2019; Chen et al., 2019; Guo et al., 2021; Jiang et al., 2020; Li et al., 2020b; Yu et al., 2019; Singh et al., 2019) have also made significant progress in various multimodal downstream tasks (Krishna et al., 2017; Hudson and Manning, 2019; Johnson et al., 2017; Tapaswi et al., 2016; Si et al., 2022). Compared to PLMs, they are considered to contain less knowledge due to the smaller size of their pre-training datasets, such as Visual Genome (0.01M images and 2M image-text pairs).
+
+We believe that models initialized with PLMs (Gardères et al., 2020; Marino et al., 2021; Gao et al., 2022) (e.g., BERT (Devlin et al., 2018), T5 (Raffel et al., 2020)) and VLP models (Wu et al., 2022; Ding et al., 2022; Shevchenko et al., 2021) (e.g., LXMERT (Tan and Bansal, 2019)) introduced implicit text knowledge and implicit multimodal knowledge, respectively, which can further enhance model performance as validated by the results in the middle two rows of Table 1.
+
+# A.3 LLMs and Super Large-scale VLP Models
+
+Recently, the super large-scale language model (LLM) GPT-3 has also been adopted as a knowledge source for OK-VQA. Unlike normal PLMs, GPT-3 is mainly used in a prompt-learning manner without any further fine-tuning. Similarly, the very recent VLP model OFA has attracted researchers' attention due to its excellent zero-shot capability for different prompts. To the best of our knowledge, the proposed method is the first to prompt OFA to obtain its implicit multimodal knowledge.
+
+Inspired by the success of LLMs in NLP, super large-scale visual-language pre-trained models, such as Flamingo (Alayrac et al., 2022) and very recent PaLI (Chen et al., 2022), has also been launched in the multimodal field recently. They are pre-trained with a billion-degree multimodal corpus which contains more knowledge than normal VLP models. We also compared our method with these large-scale VLP models in Appendix C.2.
+
+# B More Implementation Details
+
+We use the OK-VQA dataset of version v1.1<sup>4</sup> with license CC-BY 4.0<sup>5</sup>, containing 9009 training samples and 5046 test samples. Each sample contains an image, a question in English that requires outside knowledge beyond the image to answer correctly, and corresponding ground truth answers annotated by five annotators.
+
+We use the lxmert-base-uncased or visualbert-vqa model to initialize the multimodal encoder, and use T5-large model to initialize the textual encoder and answer decoder. We adopt the OFA-huge-VQA version of OFA that is fine-tuned with VQAv2. For the multimodal encoder, all the questions are trimmed to the same length of 16 with the tokenizer of BERT, and we use pre-trained Faster R-CNN to extract a set of fixed 36 objects with 2048-dimensional features from each image. For the textual encoder, we use the tokenizer of T5 to segment all the input, i.e.,  $(Q_{i},V_{i},M_{i},(T_{i},)p_{i,k})$  into the token sequence with a fixed length of 250 when the number of Wikipedia passages is less than 75. Note that, to reduce GPU memory usage, when the number of Wikipedia passages is 75, we remove the stop words in Wikipedia pas
+
+![](images/e263854cc6cb92839f4aa822940d3750ed49caeb93cf68a53982d05a4c0524d9.jpg)  
+Figure 6: Comparison of EM (left) and accuracy (right) on OK-VQA with varying number of Wikipedia passages.
+
+sages and set the token sequence length as 200. The adopted DPR (Karpukhin et al., 2020) model is pre-trained on multi-question answering datasets (Kwiatkowski et al., 2019; Joshi et al., 2017; Berant et al., 2013; Baudiš and Šedivý, 2015). The AdamW (Loshchilov and Hutter, 2017) optimizer is adopted with a learning rate of 1e-5 for the multimodal encoder and 1e-4 for the textual encoder and the answer decoder, using the linear schedule with warmup. We pre-train and finetune the models for 3 epochs with batch sizes of 12 and 8 on A100-80GB, respectively. We set the number of Wikipedia passages to 75 when our method combines GPT-3, otherwise 50. Following (Gao et al., 2022; Lin et al., 2022), we apply a normalization process (Chen et al., 2017; Lee et al., 2019) (including whitespace, lowercaseing, punctuation and removing articles) for each predictions. Following previous work, all results are obtained by a single run based on same seed.
+
+# C More Experimental Results
+
+# C.1 Performance Using Varying Number of Passages
+
+Figure 6 shows the performance with a varying number of passages, and we find that: (1) Our method is consistently superior to the previous-best TRiG no matter with a varying number of Wikipedia passages. With merely 5 passages, the proposed method can perform much better than TRiG with 100 passages, which greatly improves model training and inference speed. (2) The performance fluctuation is not as large as before under a different number of Wikipedia passages, which indicates that explicit knowledge in Wikipedia is no longer the only major source of knowledge. (3) With the increase in the number of Wikipedia passages, the performance of our model increases first and then decreases. This can be explained by the low recall rate of knowledge when the number of
+
+<table><tr><td>Method</td><td>#Params</td><td>#Pre. Data</td><td>Acc</td></tr><tr><td>Flamingo</td><td>80B</td><td>2.3B</td><td>57.80</td></tr><tr><td>PaLI</td><td>3B</td><td>1.6B</td><td>52.40</td></tr><tr><td>PaLI</td><td>15B</td><td>1.6B</td><td>56.50</td></tr><tr><td>PaLI</td><td>17B</td><td>1.6B</td><td>64.50</td></tr><tr><td>ours-LXM</td><td>0.98B (+0.93B)</td><td>0.44M</td><td>56.49</td></tr><tr><td>ours-ViB</td><td>0.88B (+0.93B)</td><td>0.44M</td><td>56.67</td></tr></table>
+
+Table 6: Results comparison with super large-scale visual-language pre-trained models. "#Pre. Data" represents the size of pre-training data. (+0.93B) represents the parameter quantity of OFA used offline.
+
+![](images/52b2ecbc72ded7c8d9dd1cd4945fc2b912551261da0d1452a1845d914580ad7a.jpg)  
+Figure 7: The proportion of the correctly-answered samples that will be answered incorrectly when the certain (left) encoder, (right) knowledge source is removed.
+
+![](images/7c82d733d0a92b5925ac8f016c28e988103111d199781d801f89235ee0c5d054.jpg)
+
+passages is small, while noise is introduced when the number of passages is large.
+
+# C.2 Comparison with Super Large-scale VLP Models
+
+Table 6 shows the excellent performance of super large-scale VLP models on OK-VQA. However, they are difficult to deploy due to the huge number of parameters. Our method achieved competitive results with these models, using much fewer parameters and only  $0.03\%$  data for pre-training.
+
+# C.3 Ablations from a Dependence Perspective
+
+As shown in the left part of Figure 7, we analyze the contribution of the two encoders in our final performance from another perspective.  $53.40\%$  and  $5.76\%$  of the correctly-answered samples rely on the textual encoder and multimodal encoder, respectively, as they will be answered incorrectly when removing the textual encoder or multimodal encoder. Moreover,  $4.49\%$  of samples can only be answered correctly by relying on both encoders at the same time, which indicates that both encoders are indispensable.
+
+From the right part of Figure 7, it can be seen that  $10.85\% \sim 19.03\%$  of correctly answered samples will go wrong if any of the knowledge types are missing. This high proportion indicates that all types of knowledge<sup>7</sup> are complementary to each
+
+![](images/b8e58f803ac2e457a6b73137363957caf34e8ba4a972cac35ae66e987496bca8.jpg)  
+Figure 8: Hit of the knowledge retrieved from GPT-3, OFA, and Wikipedia. The red and blue lines respectively represent the Acc and EM of the models that only bring in one type of knowledge without pre-training. The smaller hit and the greater Acc/EM, the higher the conversion rate of this type of knowledge to the answer.
+
+other for our method. Moreover,  $2.25\%$  of samples can only be answered correctly when all four types of knowledge are available, which proves that more comprehensive knowledge is necessary.
+
+# D More Discussion and Qualitative Analysis
+
+# D.1 Conversion Rate from Knowledge to Answers
+
+To further explore the extent to which the model makes use of each type of knowledge, we conduct experiments to evaluate the conversion rate of knowledge to the correct answers. Note that the explicit multimodal knowledge in VQAv2 is introduced in the manner of pre-training, it is thus difficult to evaluate its hit, and will not be discussed here.
+
+As shown in Figure 8, OFA (0.93B) recalls correct answers for more samples than GPT (175B). This shows that a unifying VLP model is more suitable for retrieving related knowledge in OKVQA than an LLM. Moreover, although the hit of Wikipedia is much higher than that of GPT-3 or OFA, its Acc/EM is lower than the others by a wide margin. This shows that higher hit does not necessarily lead to higher Acc/EM, and how to further extract answers from the retrieved knowledge will be an impressive direction in future work. On the whole, compared with explicit knowledge, implicit knowledge has a higher conversion rate from knowledge to correct answers.
+
+<table><tr><td>Model</td><td>zero-shot Acc</td><td>ans hit</td><td>ans + evi hit</td><td>Acc</td></tr><tr><td>OFA</td><td>33.57</td><td>45.35</td><td>49.53</td><td>52.67</td></tr><tr><td>OFA-vqa</td><td>3.26</td><td>57.63</td><td>63.36</td><td>55.33</td></tr></table>
+
+![](images/b841286b5e306bef2edb7e2590c85a5b2e10132ef230b2a1495a8992d5e0b91c.jpg)  
+Figure 9: Comparison of knowledge retrieved from OFA and OFA-vqa. "ans" and "evi" represent the tentative answers and the supporting evidence, respectively.
+
+Table 7: Comparison between different versions of OFA.  
+
+<table><tr><td>Q: What is this type of mack truck used for?
+A: [cement, cement, cement, cement, road work]</td></tr><tr><td>OFA cars: hauling
+OFA vvt: for heavy loads</td></tr><tr><td>OFA-vqa cars: cement mixer truck construction jobs drilling
+OFA-vqa vvt: cement mixer concrete construction drilling</td></tr></table>
+
+# D.2 OFA vs OFA-vqa
+
+OFA releases many versions of models, including VQA-vqa which is fine-tuned on VQAv2 dataset. As shown in Table 7, we compare the performance of the two versions and find that OFA-vqa has improved the hit of knowledge at the expense of the accuracy of its direct testing in OK-VQA and the natural fluency of the language (see Figure 9). In order to introduce more knowledge, we adopted OFA-vqa version and further improved the model performance. Note that due to the dataset bias in VQAv2 (i.e., the answer to about half of the questions is "yes" or "no"), the model always inputs the adhesion of the two items, e.g., "yesno" or "yesyesyes", we thus remove these frequently misspelled words in the output of OFA-vqa.
+
+# D.3 Qualitative Comparison between Ours and Baselines.
+
+We qualitatively evaluate the effectiveness of our method in Figure 10. The baselines selected here are MuKEA (Ding et al., 2022) and PICa (Yang et al., 2022). The former follows the conventional VQA paradigm and predicts answers in a close-set classification manner, while the latter follows the language-centric paradigm and predicts answers in an open-vocabulary generative manner.
+
+As shown in plot (a), the question is about "animal parts", while MuKEA's answer is about "sport". Obviously, MuKEA does not correctly understand the meaning of the complex question. This is because the conventional VQA paradigm has poor text comprehension compared to the language-centric paradigm. As shown in plot (b), MuKEA mistakenly predicts the answer "buddhism" as "catholicism", since the classification manner is
+
+![](images/4e4376669b60147144b1b1c57c188df81fd81e91c30fc68b54c1ba3ee1e387e1.jpg)  
+(a)
+
+Q: Which part of this animal would be in use of it was playing the game that is played with the items the man is holding?
+
+A: [month, month, month, month, month]
+
+![](images/782249019beba14a188a7d5342341d4a4417bebdf6d29013bcb77b1df8f8a9cb.jpg)  
+(b)
+
+Q: What religion does the statue belong to?  
+A: [buddhist, buddhism, buda, china, buddhist]
+
+![](images/0137afa478c7e0af883c3dd34d2060fbe9e84874d132617fd9f9062601a3f990.jpg)
+
+![](images/e81a5257fa967bfd89b90a821e8f5ea979f38dd7f318599a465aa875e3d31110.jpg)  
+(c)
+
+Q: What color is the ball for the sport being shown is?  
+A: [green, green, green, green, white]
+
+![](images/6768613d2b540c0af6e0c0bd1d4d71b516a364d6acc1b960a9c102e7624a09f1.jpg)
+
+![](images/39cec4fb3a40c4495ff0a05b2e3f64aba4736a10699987d51ff516e2b1edb27b.jpg)  
+(d)
+
+Q: What time of year is it?  
+A: [fall, fall, fall, fall, winter]
+
+![](images/506e613c14c9ea68c8c8c9325a9bbc5dc1942a2f6787b76539f9fe07d5202fb6.jpg)  
+Figure 10: Qualitative comparison between our method and baselines (MuKEA and PICa). MuKEA is based on the VLP model LXMERT, which explores knowledge in cross-modality space. PICa is based on the LLM model GPT-3, which explores knowledge in natural-language space. Pred denotes the predicted answers.
+
+easier driven by the dataset bias (Agrawal et al., 2016; Manjunatha et al., 2019) that "catholicism" appears more frequently in its pre-training and training sets. While PICa generates correct answers for the two examples due to the vast textual knowledge of the natural-language space.
+
+As shown in plots (c) and (d), PICa fails to recognize the "color of the ball" and neglects the "dead leaves" in the image scene, respectively, which are vital to answering the given questions. While MuKEA correctly predicts the two examples due to the comprehensive visual information in cross-modality space.
+
+In summary, these examples demonstrate that previous paradigms either lack knowledge or fail to capture visual information. In contrast, our method takes both into account and consistently generates the correct answers for these examples. This further reflects the rationality of our motivation to combine both natural-language and cross-modality spaces to achieve a combo of "thinking and observing".
+
+# E Potential Risks
+
+A lot of work (Agrawal et al., 2016; Manjunatha et al., 2019) has proved that VQA models are prone to learn the dataset bias. Therefore, our model may be driven by the certain bias in OK-
+
+VQA and VQAv2 training sets, such as language bias (Agrawal et al., 2018), multimodal shortcut (Dancette et al., 2021; Si et al., 2022) and harmful stereotypes (Hirota et al., 2022).
+
+A For every submission:
+
+A1. Did you describe the limitations of your work?
+
+Section (7) Limitations
+
+A2. Did you discuss any potential risks of your work?
+
+Appendix Section E
+
+A3. Do the abstract and introduction summarize the paper's main claims?
+
+Section Abstract and Section 1
+
+A4. Have you used AI writing assistants when working on this paper?
+
+Left blank.
+
+B Did you use or create scientific artifacts?
+
+Section 4.1
+
+B1. Did you cite the creators of artifacts you used?
+
+Section 1, and 4.1
+
+B2. Did you discuss the license or terms for use and / or distribution of any artifacts?
+
+Appendix B
+
+B3. Did you discuss if your use of existing artifact(s) was consistent with their intended use, provided that it was specified? For the artifacts you create, do you specify intended use and whether that is compatible with the original access conditions (in particular, derivatives of data accessed for research purposes should not be used outside of research contexts)?
+
+Section 4.1
+
+B4. Did you discuss the steps taken to check whether the data that was collected / used contains any information that names or uniquely identifies individual people or offensive content, and the steps taken to protect / anonymize it?
+
+Not applicable. Left blank.
+
+B5. Did you provide documentation of the artifacts, e.g., coverage of domains, languages, and linguistic phenomena, demographic groups represented, etc.?
+
+Section 4.1
+
+B6. Did you report relevant statistics like the number of examples, details of train / test / dev splits, etc. for the data that you used / created? Even for commonly-used benchmark datasets, include the number of examples in train / validation / test splits, as these provide necessary context for a reader to understand experimental results. For example, small differences in accuracy on large test sets may be significant, while on small test sets they may not be.
+
+Appendix B
+
+C Did you run computational experiments?
+
+Section 4.2 and 4.3
+
+C1. Did you report the number of parameters in the models used, the total computational budget (e.g., GPU hours), and computing infrastructure used?
+
+Section 4.1 and 4.2
+
+The Responsible NLP Checklist used at ACL 2023 is adopted from NAACL 2022, with the addition of a question on AI writing assistance.
+
+C2. Did you discuss the experimental setup, including hyperparameter search and best-found hyperparameter values?
+
+Section 4.1 and Appendix B
+
+C3. Did you report descriptive statistics about your results (e.g., error bars around results, summary statistics from sets of experiments), and is it transparent whether you are reporting the max, mean, etc. or just a single run?
+
+Appendix B
+
+C4. If you used existing packages (e.g., for preprocessing, for normalization, or for evaluation), did you report the implementation, model, and parameter settings used (e.g., NLTK, Spacy, ROUGE, etc.)?
+
+Section 3, Appendix B
+
+D Did you use human annotators (e.g., crowdworkers) or research with human participants?
+
+Left blank.
+
+D1. Did you report the full text of instructions given to participants, including e.g., screenshots, disclaimers of any risks to participants or annotators, etc.?
+
+No response.
+
+D2. Did you report information about how you recruited (e.g., crowdsourcing platform, students) and paid participants, and discuss if such payment is adequate given the participants' demographic (e.g., country of residence)?
+
+No response.
+
+D3. Did you discuss whether and how consent was obtained from people whose data you're using/curating? For example, if you collected data via crowdsourcing, did your instructions to crowdworkers explain how the data would be used?
+
+No response.
+
+D4. Was the data collection protocol approved (or determined exempt) by an ethics review board?
+
+No response.
+
+D5. Did you report the basic demographic and geographic characteristics of the annotator population that is the source of the data?
+
+No response.

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+# Comparative evaluation of boundary-relaxed annotation for Entity Linking performance
+
+Gabriel Herman Bernardim Andrade Shuntaro Yada Eiji Aramaki
+
+Graduate School of Information Science
+
+Nara Institute of Science and Technology
+
+Ikoma, Nara, Japan
+
+{herman_bernardim_andrade.hil1, s-yada, aramaki}@is.naist.jp
+
+# Abstract
+
+Entity Linking performance has a strong reliance on having a large quantity of high-quality annotated training data available. Yet, manual annotation of named entities, especially their boundaries, is ambiguous, error-prone, and raises many inconsistencies between annotators. While imprecise boundary annotation can degrade a model's performance, there are applications where accurate extraction of entities' surface form is not necessary. For those cases, a lenient annotation guideline could relieve the annotators' workload and speed up the process. This paper presents a case study designed to verify the feasibility of such annotation process and evaluate the impact of boundary-relaxed annotation in an Entity Linking pipeline. We first generate a set of noisy versions of the widely used AIDA CoNLL-YAGO dataset by expanding the boundaries subsets of annotated entity mentions and then train three Entity Linking models on this data and evaluate the relative impact of imprecise annotation on entity recognition and disambiguation performances. We demonstrate that the magnitude of effects caused by noise in the Named Entity Recognition phase is dependent on both model complexity and noise ratio, while Entity Disambiguation components are susceptible to entity boundary imprecision due to strong vocabulary dependency.
+
+# 1 Introduction
+
+Out of many tasks under the Natural Language Processing (NLP) umbrella, Entity Linking (EL) is one of the critical steps for Information Extraction, allowing the retrieval and understanding of information from unstructured textual sources. By definition, EL is the task of associating a Named Entity (NE) mention (a concept, person, location, etc.) to a unique identifier that describes what that mention refers to in a knowledge base (KB) (Zhang et al., 2021). This is especially significant in the biomedical domain, where it can be used to asso
+
+ciate mentions with different surface forms to a single concept in an ontology, such as the Unified Medical Language System (UMLS)<sup>1</sup>, allowing for better indexing and relation extraction (Leaman et al., 2015).
+
+In this paper's definition, EL comprises two phases, as presented in Figure 1. Named Entity Recognition (NER) searches the sentence for NE mentions, and then Entity Disambiguation (ED) assigns a unique identifier for each one. (Kolitsas et al., 2018; Ozge Sevgili et al., 2022). NER is also commonly related to classifying a detected mention into a set of categories. However, for this study, we consider it as only the location of a NE in the text.
+
+Although some methodologies have presented state-of-the-art (SoTA) results for this task (De Cao et al., 2021; Yamada et al., 2020), large amounts of high-quality labeled data are still crucial to achieve good performance models.
+
+Yet, text annotation is no trivial task. Manual annotation of vast data is costly due to the excessive workforce and long hours required. Besides, it is arduous to guarantee good quality and standardized annotation. Notably, when annotating NEs, annotators can face trouble deciding on the boundaries of a mention, which can be ambiguous and raises many inconsistencies (Marrero et al., 2013).
+
+For example, in the sentence presented in Figure 1, Arthritis can be referred to as "joint inflammation". However, a longer span "joint inflammation pain" is also applicable when referring to the same manifestation, even though it packs some peripheral information. Deciding where the boundary line of entity or non-entity should be drawn is not straightforward, and rigorous annotation guidelines can add even more bureaucracy to an already slow process. (Chapman et al., 2011).
+
+Although imprecise boundary annotation can be considered a type of noise that degrades a model's
+
+![](images/4f3c30271fb28f090ecb28c038d040f23fc6376be7b4cc1a6dd377b041fa0edb.jpg)  
+Figure 1: Example of an EL pipeline applied to a sentence. NE mentions are detected and classified by the NER stage. The ED module generates a list of candidates and ranks them to select the proper concept unique identifier.
+
+performance, some applications, especially those in the biomedical field, are not dependent on the exact span of an entity (Tsai et al., 2006; Dai et al., 2014). Due to the existence of normalized vocabularies, most extracted data can be refined to helpful information by linking to such KBs. In this scenario, the burden on annotators could be relieved by loosening the strictness of entity boundary annotation and, instead, focusing on the complete annotation of the conceptual information.
+
+We hypothesize that as long as the detected mention is longer than the target mention, in other words, it contains "more information than necessary", the concept matching to a KB should not be greatly degraded. This approach can potentially minimize the effort during corpora annotation process and improve its speed.
+
+To validate the hypothesis, we present a case study to evaluate the impact of boundary-relaxed annotation on NER and ED performance. We generated multiple variants of a popular EL dataset (AIDA CoNLL-YAGO) by expanding subsets of annotated entities' boundaries. We then train two SoTA models and our baseline model on the modified dataset and compare it with the original dataset performance on each step of the EL pipeline.
+
+# 2 Related Work
+
+Entity boundary is a common theme in NER-related research. Some evaluation criteria that relax the strictness of boundary matching have been proposed and refined through the years. Tsai et al. (2006) compares a few of those strategies, such as matching only the left or right border, any tag overlap, per-token measurements, and semantically-driven matching. The authors also present potential use cases for each evaluation technique and compare their characteristics.
+
+While several studies evaluate the impact of an-
+
+notation quality in EL (Dojchinovski et al., 2016; Chen et al., 2018; Weichselbraun et al., 2019), others tackle the issue of noisy-labeled data (Liu et al., 2021; Zhu et al., 2022), which may include but it is not limited to imprecise entity boundary.
+
+Most of the works that address the NE boundary problems attempt to improve the detection precision (Li et al., 2021; Yongming et al., 2022; Tang et al., 2022), proving that better entity boundary detection dramatically improves both entity classification and linking.
+
+However, there are a handful of studies that specifically address the impact of relaxed entity boundary annotation on linking performance. Shmanina et al. (2013) compared the impact of two different annotation guidelines for disease names on model performance, noting that the set of rules that provide low lexical variability, short entity length, and high regularity usually impact performance positively.
+
+As a sideline experiment to the main study, Choi and Cardie (2008) analyzed the impact of expanded entity boundaries and the use of the additional information as context around the annotated expression.
+
+Ghiasvand and Kate (2018) developed an unsupervised method for training clinical NER systems that automatically generate NE annotations. Due to the high surface form variability of clinical concepts, a NE boundary determination component was developed. With the ablation of this component, the authors perceived around a  $5\%$  decrease in NER precision and recall performance.
+
+Zhu and Li (2022) propose a boundary regularization technique that reallocates part of the probability to be an entity from an annotated span to its neighbor words. This effectively creates a smooth transition between an entity annotation and its nonentity surroundings to mitigate annotation boundary inconsistencies.
+
+![](images/a10b4aac8b51fe6836ad75242a39a7b2f2280e91c2fae84c9ac638cc054c0c40.jpg)  
+Figure 2: Workflow of our experiment.
+
+# 3 Method
+
+We performed a case study to assess the effect of relaxed annotation on the performance of each phase of the EL pipeline. Figure 2 depicts a representation of our workflow.
+
+The designed method aims to simulate model training using a dataset compiled by employing a hypothetical lenient and inclusive entity annotation guideline, where an annotator would roughly select the correct span of the entity mentions, possibly introducing a few unnecessary extra tokens into the annotation when in uncertainty.
+
+In particular, we focused on observing the impact of expanded entity annotations on evaluation metrics commonly used in such tasks.
+
+# 3.1 Boundary Expansion
+
+For that, we create a boundary-expanded version, denoted  $Dn$ , of our original dataset  $D$ , by adding tokens to some gold standard annotations. We call this processed variant as "noisy dataset".
+
+Modeling annotator mistakes in order to generate "human-like" annotation noise is not a simple task, as the type of errors committed are dependent on multiple factors such as annotator experience or on how the annotation process is conducted. For instance, the annotation interface used (by clicking/dragging or keyboard-based) can produce considerably distinct anomalies. Therefore, we developed an approach for noise generation based on randomly selecting annotations to be expanded. Although this approach may not produce natural mistakes in some situations due to word meaning not being considered upon selection, it is a simple way to avoid bias regarding the entity type, surface form, or textual position when selecting terms to be altered.
+
+We randomly select a subset of the entity annotations from  $D_{train}$  and  $D_{val}$  and expand their boundaries by one token (word or punctuation) to the right and/or left of the original entity span, as shown in Figure 3, thus creating  $Dn_{train}$  and  $Dn_{val}$ . In order to profile the model behavior trend, we produced multiple variants of  $Dn$  with various amounts of boundary-expanded mentions. This was done by setting a percentage of mentions to be selected during the dataset processing, defined as  $l$ , where  $l \in \{10, 20, 30, \dots, 100\}$ . We refer to  $l$  as "noise level".
+
+![](images/5e976da35a53abba542d6d16c0b4b054918cebdf36a7ab15e0b2a482b525b176.jpg)  
+Figure 3: Example of boundary expansion in an NE mention, underscored in blue. A token from either side (or both) can be selected to be merged in the annotation.
+
+When an entity mention is selected for the subset, the expansion direction is also randomly decided. In this case, all three direction options (left, right, and both sides) were given the same probability of being chosen (1/3). Table 1 shows an example document before and after expansion.
+
+We do not stop expanding the boundary even if there is an overlap with the next mention. In this case, both mentions are merged in a single annotation. The amount of entities that were unified for each noise level is presented in Appendix A.1.
+
+Given that the affected mentions are randomly selected, we generate ten different instances  $Dn_{(l,i)}$  for each noise level aiming to remove any bias that could be caused by the boundary expansion. We identify each instance by a  $i$  in the notation. In total, 100 different instances of  $Dn$  were produced.
+
+Lastly, for the sake of simplicity, we limit the
+
+<table><tr><td>Original annotation</td><td>Noisy annotation</td></tr><tr><td>CRICKET - LEICESTERSHIRE TAKE OVER AT TOP AFTER INNINGS VICTORY. LONDON 1996-08-30 West Indian all-rounder Phil Simmons took four for 38 on Friday as Leicestershire beat Somerset by an innings and 39 runs in two days to take over at the head of the county championship.</td><td>CRICKET - LEICESTERSHIRE TAKE OVER AT TOP AFTER INNINGS VICTORY. LONDON 1996-08-30 West Indian all-rounder Phil Simmons took four for 38 on Friday as Leicestershire beat Somerset by an innings and 39 runs in two days to take over at the head of the county championship.</td></tr></table>
+
+Table 1: Comparison between the original annotation and boundary expanded annotation. The entity span is marked with bold and underscore.
+
+noise generation length to a maximum of one-token length for each side of the NE mention. With the noise length limited, we can exclude one variable that may affect the models' performance. Instead, we focus on how the quantity of lenient-annotated entities influences the pipeline's output.
+
+We then train NER and ED models on each  $Dn_{(l,i)}$  and use the unmodified test set to assess the boundary relaxation leverage in performance.
+
+# 3.2 Evaluation metrics
+
+We evaluate both NER and ED models using the measurements of precision (fraction of extracted NEs that are correct), recall (fraction of NEs extracted out of all the gold-standard NEs), and  $F$ -score (harmonic mean of precision and recall) (Japkowicz and Shah, 2011). We use micro-averaged metrics, meaning the scores are computed across all documents.
+
+Being aware that the NER system's capability to precisely detect entity boundaries could be affected by the noisy data training, for NER components only, two evaluation scoring schemes were used - strict and relaxed.
+
+Strict scoring scheme follows the convention defined by CoNLL (Tjong Kim Sang and De Meulder, 2003). It only considers correct matches where boundaries exactly match the ground truth. Hence, a system gets zero credit if the extracted entity has any extra or is missing tokens compared to the gold-standard mention.
+
+On the other hand, the relaxed scheme accepts mention detections with imprecise boundaries (Uzuner et al., 2011; Ghiasvand and Kate, 2018). It also considers as correct both partial matching and extra tokens in a mention, as long as the match has at least one token that overlaps with the span of the gold-standard mention.
+
+We report NER metrics by evaluating the output of this component before being fed to the ED module of the pipeline.
+
+The results for the ED component are calculated
+
+based on the results obtained at the end of the pipeline, in other words, the final link produced by the disambiguation model after receiving the mentions detected by the NER phase. In this case, we only use strict metrics, denoting that the output prediction must be the same as the gold-standard concept to be considered correct. Although a relaxed metric could also be employed by evaluating the KB's relationship tree between the concepts, such evaluation falls out of the scope of this study as it may mask the performance impact caused by the NER phase performance.
+
+All reported metrics are averaged for all runs on each instance  $i$  of  $Dn_{(l)}$  (noisy dataset on the referring noise level  $l$ ). Therefore, an average of ten runs per noise level.
+
+# 3.3 NER mention matching types
+
+While the analysis based exclusively on the performance metrics scores allows us to grasp the trend of boundary relaxation effect in model output quality, these metrics mask distinct kinds of NER mistakes behind a single value.
+
+We classify mention detection in six matching types and report their output percentage on each evaluated model. An example sentence for each matching type is shown in Appendix A.2).
+
+Exact match Both detected mention boundaries match the NE mention boundaries.
+
+Exceeding match The detected mention contains all the NE mention text and also unnecessary neighbor words.
+
+Partial match NE mention is not completely detected, but at least a fragment was found.
+
+Invalid match The NER component extracts a span of text where there is no real NE.
+
+Missing match The NER component detects no part of an existing NE mention.
+
+# 4 Experimental Setup
+
+Dataset As our dataset, we use AIDA CoNLL-YAGO (Hoffart et al., 2011). This dataset is an extension of the well-known CoNLL-2003 dataset (Tjong Kim Sang and De Meulder, 2003), and it is vastly used for EL benchmarks. It comprises newswire articles from Reuters, containing 1,393 articles with 27,820 NE mentions linkable to its corresponding YAGO2 ID and Wikipedia article webpage. Training and validation sets contain 946 and 216 articles, respectively. Test set has 231 articles.
+
+Models We executed our experimental procedure in three EL pipelines. We selected two SoTA approaches and also developed our own method:
+
+(1) Highly Parallel Autoregressive Entity Linking with Discriminative Correction (HPAELDC) (De Cao et al., 2021):
+
+An end-to-end model for autoregressive entity linking available under MIT license. It comprises a Longformer encoder, a mention detection module including feed-forward Neural Networks, and an ED component based on a Long Short-Term Memory network for candidate generation and ranking. The whole model has a total of 202M parameters. As reported by the authors, this model achieves an F-score of 0.85 for Entity Linking on the AIDA CoNLL-YAGO dataset. Even though the authors present it as an end-to-end model, the NER and ED modules are separated components. Therefore, we could compute metrics for each step individually.
+
+(2) Language Understanding with Knowledge-based Embeddings (LUKE) (Yamada et al., 2020)<sup>3</sup>:
+
+LUKE is a contextualized representation of words and entities based on a transformer. This model can perform multiple tasks, such as NER, relation classification, or question-answering. It is available under the Apache License 2.0.
+
+While available in multiple variants, in this study we use LUKE (base), which has a total of 253M parameters. In the NER task it achieves F-score of 0.94, and 0.95 for ED on the AIDA CoNLLYAGO dataset. Since this framework is composed by modules that accomplish different tasks, we can independently create an EL pipeline using the available NER and ED components.
+
+As reported in the original paper (Yamada et al., 2022), one of LUKE's ED model limitations is not being able to handle out-of-vocabulary entities, we replace expanded entities in the model's vocabulary file before training. In case of an entity being expanded differently in two or more instances, we use the shorter of all variants.
+
+(3) VanillaNER<sup>4</sup>:
+
+Our developed NER model is intended to be used as a baseline for comparison. This model aims to simulate a simple and low-effort approach. We start from a pre-trained bert-base-cased model (Devlin et al., 2019), which has around 110M parameters, and fine-tune it using our dataset instances. The base model is publicly available in the Hugging-Face<sup>5</sup> platform, under Apache License 2.0. As we only developed the NER component, we feed the output of our model to LUKE's ED model, trained on the same  $Dn_{(l,i)}$  instance, to compute disambiguation scores.
+
+Training Parameters We used a server comprised of two NVIDIA Quadro RTX 8000 GPUs for model training. We report all used parameters and computational time needed in Appendix A.3.
+
+For both SoTA models (1 and 2), we use the implementation released by the authors and also apply the default training parameters disclosed in the referring papers.
+
+# 5 Results and Discussion
+
+In this section, we present the experimental results of our case study. Appendix A.4 presents a summary of the computed evaluation metrics after the processing of the test set by the trained models in NER and ED phases, respectively. We purposefully omit some noise levels for easier visualization, presenting some checkpoints to allow comparison.
+
+# 5.1 NER performance analysis
+
+In an overall analysis of the strict metrics, we observe that all models present a similar behavior, with a massive performance drop as boundary-expanded mentions are introduced into the training set. However, by examining the curves shaped by the evaluation points, shown in items  $a$ ,  $b$  and  $c$  of Figure 4, we can highlight some aspects.
+
+We noted that the models show some robustness against the boundary relaxation noise. While
+
+![](images/bbdd88f55af9a0a8780711d359a4c13ce8dd3f8a3a8835c34dead8ad903636ce.jpg)
+
+![](images/17a9380bf45f32ff04c82f5ba8524502d7a439400b24b8432fb17b7819c2c7c3.jpg)
+
+![](images/7d548d1b72b419acd776a76bf7adff502bdae2d6548eb349913e794e88daf976.jpg)
+
+![](images/ad7962d9ed602c95afa65270fe80b2813f936c4b5e52e444879458ebc8a2940a.jpg)
+
+![](images/3973e5d7ca26870027be8758e2ceb502fee118cc5ab038e6fe84133a2865f35d.jpg)
+
+![](images/a1b2393a7b65700996a9833498f1be76b20578ebb00b8fe7f5284c93b2b4de14.jpg)
+
+![](images/37f68b5f0901e438daccb656c1392a763ed6bf5d42021678df960fc50a830d45.jpg)  
+Figure 4: Performance scores for HPAELDC (items  $a$ ,  $d$  and  $g$ ), LUKE (items  $b$ ,  $e$  and  $h$ ) and VanillaNER (items  $c$ ,  $f$  and  $i$ ) across various dataset noise levels. Dashed lines represent the F-score on the Original dataset training.
+
+![](images/7c50cfa7020f176ee602dd827da00caca5f4b980011d1bfd3b72299a867ae60a.jpg)
+
+![](images/cdc44c42bea96d413001a41d0094d0a3afb483f2a59e96a67dba72367eea2031.jpg)
+
+HPAELDC (Fig. 4.a) appears to be more susceptible to noise, LUKE (Fig. 4.b) and VanillaNER (Fig. 4.c) keep nearly unaltered performance up to the point where  $40\%$  of the total mentions in the training set were expanded (less than  $8\%$  and  $3\%$  of performant degradation, respectively).
+
+From this point, an accentuated performance decline is perceived in all cases. Yet, the point where the model's score plummets varies between the approaches. For instance, LUKE loses over  $42\%$  of its performance in the  $50 - 70\%$  range. Meanwhile, HPAELDC, despite the initial decay, has massive degradation in the  $70 - 100\%$  noise range, with over  $70\%$  relative performance drop.
+
+Considering the relaxed metrics presented in Fig-
+
+ure 4, items  $d$  to  $f$ , we can remark on the distinct behavior of all systems. We observed that both SoTA approaches show a greater performance drop than our baseline model when considering inaccurate boundary extraction. In this scenario, VanillaNER conveys only a small relative degradation, even in noisier training environments (up to  $15\%$  lost in F-score when all training mentions were expanded). The relatively elevated precision rates portrayed by the SoTA models denote the need for a higher confidence level before indicating a NE detection.
+
+# 5.2 NER matching type analysis
+
+To better interpret the performance trend, we further inspected the models' output predictions and
+
+![](images/2f912aa349934d26e3eee090f1ac55c35d075bce4ad96dd597e087d81942884f.jpg)  
+Figure 5: NER matching types for various dataset noise levels. Values are an average from the results of 10 evaluated models and presented in percentages in relation to the total number of gold mentions.
+
+![](images/2731a0c0e3bd15de5823e60182108752ce7ad08a81dea370dc338afed8cbc5a6.jpg)
+
+![](images/c866749fe132a959cc308f91165ddcba553dfeabde128d8aa7decebd825634db.jpg)
+
+investigated the matching types produced by each model. From the results shown in Figure 5 (complete table is presented in the Appendix A.5), we noticed that both SoTA models tend to miss NE mentions as noisier training dataset instances are applied, in comparison to our approach. This finding also explains the heavier drop in the relaxed scores demonstrated by them. On the other hand, as the noise level is raised, VanillaNER (Fig 5.c) increasingly outputs a higher number of exceeding matches, indicating that it successfully adapts to the new domain presented by the boundary-expanded entities and outputs mentions that are closer to what is observed in the training and validation sets.
+
+Also, it is interesting to remark that although the missed-mention rate of this approach increases, it is nowhere near the level presented by the other two models. This distinct behavior is showcased in Table 2, where we present the output processing of an example document.
+
+We attribute the high rate of missing mentions to the greater complexity of SoTA NER approaches. We believe that the complexity of these models, while improving resilience and unlocking higher performance levels in an optimal scenario, hinders their ability to fit into unseen domains. As far as our results show, the SoTA models never actually learn the peculiar boundary information encoded in the boundary-expanded annotations, attempting to minimize the noise effect in its language model.
+
+# 5.3 ED performance analysis
+
+ED performance evaluation, presented in Figure 4, items  $g$  to  $i$ , have scores bounded to how well the earlier NER phase performed, as it feeds the disambiguation component. We are aware bad NER output quality may obfuscate the isolated evaluation
+
+of ED methods, yet the results give an overview of the pipeline as a whole.
+
+The observed metrics indicate that the disambiguation step is sensitive to imprecise boundaries. In contrast to NER models, ED is not resilient against noise. The increasing ratio of boundary-expanded mentions directly correlates to lower recall scores in all tested approaches. This characteristic denotes that boundary relaxation severely affects the overall capability of recognizing the entity. It can be attributed in part due to missing mention detections but also to the ED model's incapability of generating candidate entities for linking. This can be seen in the example shown in Table 2, where many detected mentions are associated with the  $NIL$  tag, denoting that not even a potential link to the KB was found.
+
+In further analysis of the output from a few sentences, we verified a similar scenario for both ED approaches. Even though the overall noise level of the training dataset is elevated, whenever the mentions fed by the NER component have the exact boundaries as the mention span both HPAELDC and LUKE were still able to confidently predict the correct KB entity, as shown by the high precision scores.
+
+# 5.4 ED vocabulary dependency
+
+To better understand the ED component behavior under different inputs, we computed the accuracy score separately for each valid NER matching type (Exact, Exceeding, and Partial). For the sake of simplicity, we averaged the scores across all predictions from all different noise levels.
+
+We remark on the responses both evaluated ED approaches have when dealing with non-exact mention matches, depicted by the results in Table 3.
+
+<table><tr><td>Original Annotation</td><td>[Japan] (Japan National Football Team) began the defence of their [Asian Cup] (1996 Asian Cup) title with a lucky 2-1 win against [Syria] (Syria National Football Team) in a Group C championship match on Friday. [China] (People&#x27;s Republic of China) controlled most of the match [...] until the 78th minute when [Uzbek](Uzbekistan National Football Team) striker [Igor Shkvyrin] (Igor Shkvyrin) took advantage [...]</td></tr><tr><td>HPAELDC (De Cao et al., 2021)</td><td>[Japan began] (Japan National Rugby Union Team) the defence of their [Asian Cup title] (Coppa Italia) with a lucky 2-1 win against Syria in a [Group C] (Middle East) championship match on Friday. [China] (People&#x27;s Republic of China) controlled most of the match [...] until the 78th minute when [Uzbek] (Uzbekistan National Football Team) striker Igor Shkvyrin took advantage [...]</td></tr><tr><td>LUKE (Yamada et al., 2020)</td><td>Japan began the defence of their Asian Cup title with a lucky 2-1 win against [Syria] (Syria National Football Team) in a Group C championship match on Friday. [China] (People&#x27;s Republic of China) controlled most of the match [...] until the 78th minute when Uzbek striker Igor Shkvyrin took advantage [...]</td></tr><tr><td>VanillaNER + LUKE</td><td>[Japan began] (NIL) the defence of their [Asian Cup title] (NIL) with a lucky 2-1 win [against Syria in] (Syria National Football Team) a [Group C] (NIL) championship match on Friday. [China controlled] (Syria National Football Team) most of the match [...] until the 78th minute when [Uzbek] (Uzbekistan National Football Team) [striker Igor Shkvyrin took] (Igor Shkvyrin) advantage [...]</td></tr></table>
+
+Both models exhibit low effectiveness when attempting to link NER detections with imprecise boundaries, as given by the low Exceeding and Partial match accuracy values when compared to Exact matches.
+
+Upon a closer error analysis of the mistakes for non-exact matches, we noted that the evaluated ED models are strongly reliant on the provided entity vocabulary, especially for the candidate generation step. For most of the Exceeding matches predicted, HPAELDC produced a set of candidates that didn't slightly resemble the mention surface form, while LUKE failed to even list potential matches from the KB. On the other hand, Partial matches can still be matched correctly, as the lack of one or more words from the mention surface form can still produce associations within the known vocabulary. We believe these effects could be mitigated by an approximate string retrieval method, though prediction time may be affected on such large KBs.
+
+The high values for Exact match evaluation indicate that both approaches correctly identify entities even in noisy environments, given that the provided mention spans have precise boundaries. Important to note that when ranking the entity candidates not only the surface form is used, but also the NE con
+
+text is crucial for accurate prediction. Yet, training in a noisy environment seems to have an insignificant effect on the model's contextual understanding as long as the mention boundaries and, therefore, the NE surface form matches the model's vocabulary.
+
+Table 2: Comparison of an example document processed by all models trained with a dataset at  $70\%$  of noise level. Detected spans are presented in brackets with extra words matched by the NER component marked in blue, whilst undetected and incorrect mentions are highlighted in red. The KB unique identifier is shown in parenthesis and underlined. Incorrectly recognized identifiers are highlighted in orange.  
+
+<table><tr><td rowspan="2">Model</td><td colspan="3">Matching type</td></tr><tr><td>Exact</td><td>Exceeding</td><td>Partial</td></tr><tr><td>HPAELDC</td><td>0.827</td><td>0.342</td><td>0.528</td></tr><tr><td>LUKE</td><td>0.925</td><td>0.015</td><td>0.409</td></tr><tr><td>VanillaNER + LUKE</td><td>0.874</td><td>0.048</td><td>0.152</td></tr></table>
+
+Table 3: ED accuracy by NER matching type. Values are an average of the overall produced results (Original dataset + all noise levels.
+
+# 6 Conclusion
+
+In this study, we investigated the impact of relaxed entity boundary annotation on model performance by conducting a case study with three different EL approaches. We introduced noise into a popular dataset by expanding the boundaries of some annotated entity mentions, trained models on the
+
+produced noisy data, and evaluated their output.
+
+For NER components, we verified that model complexity plays a significant role in how its influenced by noise. While complex models may achieve higher performance, they had reduced flexibility to adapt to the noisy environment, thus being outperformed by our simpler approach in this scenario. We also noted that those models are resilient against the boundary-expanded environment until more than half of the training annotations are "noisy".
+
+We also observed that ED components are sensitive to imprecise entity mentions and strongly reliant on their training vocabulary. We show that both ED approaches evaluated can still correctly predict identifiers even when trained in noisy environments, given that the detected mention boundaries are precise. On the other hand, when boundary imprecision produces out-of-vocabulary mentions, it hinders performance heavily.
+
+# 6.1 Future Work
+
+Our goal with this case study was to assess the impact suffered by an EL system without the expense of a real annotation process. Considering that we now understand the impact, we intend to continue investigating the possible gains in speed and workload reduction by applying a boundary-relaxed guideline to a corpus annotation process.
+
+We also intend to evaluate the boundary relaxation effect in specific language domains, such as medical texts. Since EL in medical vocabulary is commonly supported by standardized terminologies, typically restricted to a smaller set of words, evaluating the resilience of other linking methodologies (approximate string matching, for instance) to such noise would also be interesting.
+
+# Limitations
+
+We acknowledge that the randomness of our noise generation procedure may generate a new entity span that can be considered unnatural (for example, adding prepositions to a city name). Such aspect of our method may have some impact on the performance levels measured, as distinct types of annotation mistakes can affect model performance differently. In this case, added noisy words that are improbable to be part of the entity may be more easily "ignored" by the model, while ambiguous additions can lead to a mistake. Still, this approach can be used as a baseline and a more sophisticated
+
+performance assessment using more complex modeling or even real annotation inaccuracy could be done in future work.
+
+In addition, the constraint of expanding the mention boundary by a single token should be also taken into consideration. The reason for this design choice was not only based on narrowing the analysis spectrum by reducing the amount of data we had to investigate but also on time constraints, as the training procedure of multiple models on an even larger number of noisy dataset instances would escalate quickly. However, now conscious of the behavior relaxed annotation has on model behavior, it would be interesting to evaluate how this tendency is transformed by introducing even more unnecessary adjacent context into the annotations.
+
+A last limitation that can be pointed out is that we only evaluated the noise effect in a single dataset. There are other widely adopted benchmarks for EL, such as MSNBC (Cucerzan, 2007) and ClueWeb (Cao et al., 2007), which could be used in this work. However, we feel it would be more interesting to juxtapose with other textual domains, especially those with specific jargon and NEs, such as the medical domain.
+
+# Acknowledgements
+
+This work was supported by JST CREST Grant Number JPMJCR22N1 and JSPS KAKENHI Grant Number JP19H01118, Japan.
+
+# References
+
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+Hong Chen, Zhenhua Fan, Hao Lu, Alan Yuille, and Shu Rong. 2018. PreCo: A large-scale dataset in preschool vocabulary for coreference resolution. In Proceedings of the 2018 Conference on Empirical Methods in Natural Language Processing, pages 172-181, Brussels, Belgium. Association for Computational Linguistics.  
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+In Proceedings of the 22nd Conference on Computational Natural Language Learning, pages 519-529, Brussels, Belgium. Association for Computational Linguistics.  
+Robert Leaman, Ritu Khare, and Zhiyong Lu. 2015. Challenges in clinical natural language processing for automated disorder normalization. Journal of Biomedical Informatics, 57:28-37.  
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+Kun Liu, Yao Fu, Chuanqi Tan, Mosha Chen, Ningyu Zhang, Songfang Huang, and Sheng Gao. 2021. Noisy-labeled NER with confidence estimation. In Proceedings of the 2021 Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies, pages 3437-3445, Online. Association for Computational Linguistics.  
+Mónica Marrero, Julián Urbano, Sonia Sánchez-Cuadrado, Jorge Morato, and Juan Miguel Gómez-Berbis. 2013. Named entity recognition: Fallacies, challenges and opportunities. Computer Standards & Interfaces, 35(5):482-489.  
+Tatyana Shmanina, Ingrid Zukerman, Antonio Jimeno Yepes, Lawrence Cavedon, and Karin Verspoor. 2013. Impact of corpus diversity and complexity on NER performance. In Proceedings of the Australasian Language Technology Association Workshop 2013 (ALTA 2013), pages 91-95, Brisbane, Australia.  
+Ruixue Tang, Yanping Chen, Yongbin Qin, Ruizhang Huang, Bo Dong, and Qinghua Zheng. 2022. Boundary assembling method for joint entity and relation extraction. Knowledge-Based Systems, 250:109129.  
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+Richard Tzong-Han Tsai, Shih-Hung Wu, Wen-Chi Chou, Yu-Chun Lin, Ding He, Jieh Hsiang, Ting-Yi Sung, and Wen-Lian Hsu. 2006. Various criteria in the evaluation of biomedical named entity recognition. BMC bioinformatics, 7(1):1-8.  
+Özlem Uzuner, Brett R South, Shuying Shen, and Scott L DuVall. 2011. 2010 i2b2/VA challenge on concepts, assertions, and relations in clinical text. Journal of the American Medical Informatics Association, 18(5):552-556.
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+Ikuya Yamada, Akari Asai, Hiroyuki Shindo, Hideaki Takeda, and Yuji Matsumoto. 2020. LUKE: Deep contextualized entity representations with entity-aware self-attention. In Proceedings of the 2020 Conference on Empirical Methods in Natural Language Processing (EMNLP). Association for Computational Linguistics.  
+Ikuya Yamada, Koki Washio, Hiroyuki Shindo, and Yuji Matsumoto. 2022. Global entity disambiguation with BERT. In Proceedings of the 2022 Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies, pages 3264-3271, Seattle, United States. Association for Computational Linguistics.  
+Nian Yongming, Chen Yanping, Qin Yongbin, Huang Ruizhang, Tang Ruixue, and Hu Ying. 2022. A joint model for entity boundary detection and entity span recognition. Journal of King Saud University-Computer and Information Sciences, 34(10):8362-8369.  
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+
+# A Appendix
+
+# A.1 Amount of entities unified by boundary expansion
+
+<table><tr><td>Noise Level</td><td>Merged entities</td></tr><tr><td>10%</td><td>0.40%</td></tr><tr><td>20%</td><td>0.99%</td></tr><tr><td>30%</td><td>1.81%</td></tr><tr><td>40%</td><td>2.89%</td></tr><tr><td>50%</td><td>4.19%</td></tr><tr><td>60%</td><td>5.74%</td></tr><tr><td>70%</td><td>7.43%</td></tr><tr><td>80%</td><td>9.36%</td></tr><tr><td>90%</td><td>11.67%</td></tr><tr><td>100%</td><td>14.04%</td></tr></table>
+
+# A.2 Example of matching types
+
+Table 4: Percentage of entities that were unified by the boundary expansion process for each noise level.  
+
+<table><tr><td>Match type</td><td>Example</td></tr><tr><td>Exact match</td><td>[ Yokohama F.C. ] striker [ Kazuyoshi Miura ] scored twice.</td></tr><tr><td>Exceeding match</td><td>[ Yokohama F.C. ] striker [ Kazuyoshi Miura scored ] twice.</td></tr><tr><td>Partial match</td><td>[ Yokohama F.C. ] striker [ Kazuyoshi ] Miura scored twice.</td></tr><tr><td>Invalid match</td><td>[ Yokohama F.C. ] striker Kazuyoshi Miura [ scored ] twice.</td></tr><tr><td>Missing match</td><td>[ Yokohama F.C. ] striker Kazuyoshi Miura scored twice.</td></tr></table>
+
+# A.3 Training Parameters
+
+Table 5: Example of matching types. Correct entity spans are marked in bold, blue and red bracket represent different mention detections  
+
+<table><tr><td></td><td>HPAELDC
+(De Cao et al., 2021)</td><td>LUKE
+(Yamada et al., 2020)</td><td>VanillaNER</td></tr><tr><td>Max epochs</td><td>100</td><td>5 (NER) / 2 (ED)</td><td>10</td></tr><tr><td>Training batch size</td><td>32</td><td>8 (NER) / 16 (ED)</td><td>16</td></tr><tr><td>Learning rate</td><td>1e-4 (Longformer)/1e-3 (other components)</td><td>1e-5 (NER) /2e-5 (ED)</td><td>1e-5</td></tr><tr><td>Optimizer</td><td>Adam</td><td>AdamW</td><td>AdamW</td></tr><tr><td>Model selection</td><td>Highest validation micro F-score</td><td>Highest validation accuracy</td><td>Lowest validation loss</td></tr><tr><td>Training time (h)</td><td>1.5</td><td>3</td><td>0.5</td></tr></table>
+
+Table 6: Hyper-parameters used in the training procedure of the experiment.
+
+# A.4 Detailed scoring results
+
+<table><tr><td rowspan="2">Model</td><td rowspan="2">Noise level</td><td colspan="3">Strict</td><td colspan="3">Relaxed</td></tr><tr><td>Precision</td><td>Recall</td><td>F-score</td><td>Precision</td><td>Recall</td><td>F-score</td></tr><tr><td rowspan="5">HPAELDC (De Cao et al., 2021)</td><td>Original</td><td>0.922</td><td>0.948</td><td>0.935</td><td>0.930</td><td>0.957</td><td>0.943</td></tr><tr><td>10%</td><td>0.885</td><td>0.951</td><td>0.917</td><td>0.905</td><td>0.972</td><td>0.937</td></tr><tr><td>40%</td><td>0.826</td><td>0.857</td><td>0.841</td><td>0.873</td><td>0.881</td><td>0.877</td></tr><tr><td>70%</td><td>0.749</td><td>0.615</td><td>0.675</td><td>0.836</td><td>0.568</td><td>0.676</td></tr><tr><td>100%</td><td>0.102</td><td>0.010</td><td>0.018</td><td>0.788</td><td>0.076</td><td>0.139</td></tr><tr><td rowspan="5">LUKE (Yamada et al., 2020)</td><td>Original</td><td>0.964</td><td>0.972</td><td>0.968</td><td>0.982</td><td>0.989</td><td>0.985</td></tr><tr><td>10%</td><td>0.961</td><td>0.966</td><td>0.963</td><td>0.981</td><td>0.986</td><td>0.983</td></tr><tr><td>40%</td><td>0.942</td><td>0.846</td><td>0.891</td><td>0.982</td><td>0.885</td><td>0.931</td></tr><tr><td>70%</td><td>0.721</td><td>0.161</td><td>0.263</td><td>0.772</td><td>0.333</td><td>0.466</td></tr><tr><td>100%</td><td>0.030</td><td>0.014</td><td>0.019</td><td>0.603</td><td>0.279</td><td>0.382</td></tr><tr><td rowspan="5">VanillaNER</td><td>Original</td><td>0.916</td><td>0.937</td><td>0.927</td><td>0.945</td><td>0.962</td><td>0.954</td></tr><tr><td>10%</td><td>0.915</td><td>0.934</td><td>0.924</td><td>0.946</td><td>0.961</td><td>0.954</td></tr><tr><td>40%</td><td>0.887</td><td>0.909</td><td>0.898</td><td>0.939</td><td>0.956</td><td>0.947</td></tr><tr><td>70%</td><td>0.396</td><td>0.494</td><td>0.440</td><td>0.785</td><td>0.901</td><td>0.839</td></tr><tr><td>100%</td><td>0.075</td><td>0.079</td><td>0.077</td><td>0.805</td><td>0.828</td><td>0.816</td></tr></table>
+
+Table 7: Summary of NER evaluation scores for various dataset noise levels. Values are an average of the scores from the evaluation of 10 models. The highest values for each model are marked in bold.  
+
+<table><tr><td>Model</td><td>Noise Level</td><td>Precision</td><td>Recall</td><td>F-score</td></tr><tr><td rowspan="5">HPAELDC (De Cao et al., 2021)</td><td>Original</td><td>0.843</td><td>0.867</td><td>0.855</td></tr><tr><td>10%</td><td>0.798</td><td>0.858</td><td>0.827</td></tr><tr><td>40%</td><td>0.745</td><td>0.746</td><td>0.746</td></tr><tr><td>70%</td><td>0.650</td><td>0.413</td><td>0.505</td></tr><tr><td>100%</td><td>0.376</td><td>0.007</td><td>0.014</td></tr><tr><td rowspan="5">LUKE (Yamada et al., 2020)</td><td>Original</td><td>0.921</td><td>0.889</td><td>0.905</td></tr><tr><td>10%</td><td>0.924</td><td>0.913</td><td>0.918</td></tr><tr><td>40%</td><td>0.910</td><td>0.580</td><td>0.709</td></tr><tr><td>70%</td><td>0.801</td><td>0.145</td><td>0.246</td></tr><tr><td>100%</td><td>0.608</td><td>0.078</td><td>0.138</td></tr><tr><td rowspan="5">VanillaNER + LUKE</td><td>Original</td><td>0.913</td><td>0.882</td><td>0.897</td></tr><tr><td>10%</td><td>0.910</td><td>0.834</td><td>0.870</td></tr><tr><td>40%</td><td>0.899</td><td>0.707</td><td>0.792</td></tr><tr><td>70%</td><td>0.823</td><td>0.389</td><td>0.528</td></tr><tr><td>100%</td><td>0.772</td><td>0.190</td><td>0.305</td></tr></table>
+
+Table 8: Summary of ED evaluation scores for various dataset noise levels. Values are an average of the scores from the evaluation of 10 models. The highest values for each model are marked in bold.
+
+A.5 Breakdown of NER matching types  
+
+<table><tr><td rowspan="2">Model</td><td rowspan="2">Noise level</td><td colspan="5">Matching Type (%)</td><td rowspan="2"># of mentions</td></tr><tr><td>Exact</td><td>Exceeding</td><td>Partial</td><td>Invalid</td><td>Missing</td></tr><tr><td rowspan="5">HPAELDC (De Cao et al., 2021)</td><td>Original</td><td>88.34</td><td>0.37</td><td>0.31</td><td>6.81</td><td>4.16</td><td>4813</td></tr><tr><td>10%</td><td>86.18</td><td>1.58</td><td>0.26</td><td>9.38</td><td>2.61</td><td>4949</td></tr><tr><td>40%</td><td>71.72</td><td>3.83</td><td>0.52</td><td>13.60</td><td>10.33</td><td>5191</td></tr><tr><td>70%</td><td>45.88</td><td>4.14</td><td>5.46</td><td>10.80</td><td>33.72</td><td>5028</td></tr><tr><td>100%</td><td>2.08</td><td>5.05</td><td>2.13</td><td>1.60</td><td>89.14</td><td>4558</td></tr><tr><td rowspan="5">LUKE (Yamada et al., 2020)</td><td>Original</td><td>96.28</td><td>0.97</td><td>0.67</td><td>1.51</td><td>0.58</td><td>4993</td></tr><tr><td>10%</td><td>95.56</td><td>1.13</td><td>0.86</td><td>1.63</td><td>0.81</td><td>4941</td></tr><tr><td>40%</td><td>92.95</td><td>0.99</td><td>0.77</td><td>1.58</td><td>3.70</td><td>4934</td></tr><tr><td>70%</td><td>8.68</td><td>8.86</td><td>1.27</td><td>2.13</td><td>79.07</td><td>5360</td></tr><tr><td>100%</td><td>0.31</td><td>22.66</td><td>0.79</td><td>14.90</td><td>61.34</td><td>6316</td></tr><tr><td rowspan="5">VanillaNER</td><td>Original</td><td>92.18</td><td>2.05</td><td>1.05</td><td>1.05</td><td>3.68</td><td>4937</td></tr><tr><td>10%</td><td>91.94</td><td>2.32</td><td>1.06</td><td>1.09</td><td>3.60</td><td>4939</td></tr><tr><td>40%</td><td>88.88</td><td>4.93</td><td>0.79</td><td>1.07</td><td>4.33</td><td>4938</td></tr><tr><td>70%</td><td>40.39</td><td>37.09</td><td>0.36</td><td>0.93</td><td>21.23</td><td>4932</td></tr><tr><td>100%</td><td>8.94</td><td>83.75</td><td>0.36</td><td>1.01</td><td>5.94</td><td>4935</td></tr></table>
+
+Table 9: Breakdown of the NER prediction output by matching types.
+
+# A For every submission:
+
+A1. Did you describe the limitations of your work?
+
+In the Limitations section at the end of the paper (Section 7)
+
+A2. Did you discuss any potential risks of your work?
+
+In our paper, we simply evaluate the performance of models to address the task of Entity Linking in simulated scenarios with noisy data. We cannot think of any potential risks of our work.
+
+A3. Do the abstract and introduction summarize the paper's main claims?
+
+Abstract and Section 1 (Introduction)
+
+A4. Have you used AI writing assistants when working on this paper?
+
+Left blank.
+
+# B Did you use or create scientific artifacts?
+
+Section 4 (Dataset and models subitems)
+
+B1. Did you cite the creators of artifacts you used?
+
+Section 4
+
+B2. Did you discuss the license or terms for use and / or distribution of any artifacts?
+
+Section 4
+
+B3. Did you discuss if your use of existing artifact(s) was consistent with their intended use, provided that it was specified? For the artifacts you create, do you specify intended use and whether that is compatible with the original access conditions (in particular, derivatives of data accessed for research purposes should not be used outside of research contexts)?
+
+We do not discuss it explicitly in the paper. However, the artifacts are available under Apache License
+
+2.0 and MIT License, which gives permission on Commercial use, Modification, Distribution and
+
+Private use.
+
+B4. Did you discuss the steps taken to check whether the data that was collected / used contains any information that names or uniquely identifies individual people or offensive content, and the steps taken to protect / anonymize it?
+
+The dataset we used is a widely common open-source benchmark for Entity Linking tasks, so we didn't do any checking steps
+
+B5. Did you provide documentation of the artifacts, e.g., coverage of domains, languages, and linguistic phenomena, demographic groups represented, etc.?
+
+Section 4
+
+B6. Did you report relevant statistics like the number of examples, details of train / test / dev splits, etc. for the data that you used / created? Even for commonly-used benchmark datasets, include the number of examples in train / validation / test splits, as these provide necessary context for a reader to understand experimental results. For example, small differences in accuracy on large test sets may be significant, while on small test sets they may not be.
+
+Section 4
+
+The Responsible NLP Checklist used at ACL 2023 is adopted from NAACL 2022, with the addition of a question on AI writing assistance.
+
+# C Did you run computational experiments?
+
+Section 5
+
+C1. Did you report the number of parameters in the models used, the total computational budget (e.g., GPU hours), and computing infrastructure used?
+
+We report each model's total number of parameters and computational infrastructure used in Section 4. We report the computational times in Appendix A.2.
+
+C2. Did you discuss the experimental setup, including hyperparameter search and best-found hyperparameter values?
+
+We discuss the experimental setup in Section 4. We also report the hyperparameters used for training in Appendix A.2.
+
+C3. Did you report descriptive statistics about your results (e.g., error bars around results, summary statistics from sets of experiments), and is it transparent whether you are reporting the max, mean, etc. or just a single run?
+
+Section 5, Appendix A.3, A.4, and A.5. In Section 3 we inform that we use averaged values. We do not report the standard variation as the obtained values are very small and irrelevant.
+
+C4. If you used existing packages (e.g., for preprocessing, for normalization, or for evaluation), did you report the implementation, model, and parameter settings used (e.g., NLTK, Spacy, ROUGE, etc.)?
+
+No such packages were used
+
+# D Did you use human annotators (e.g., crowdworkers) or research with human participants?
+
+Left blank.
+
+D1. Did you report the full text of instructions given to participants, including e.g., screenshots, disclaimers of any risks to participants or annotators, etc.?
+
+No response.
+
+D2. Did you report information about how you recruited (e.g., crowdsourcing platform, students) and paid participants, and discuss if such payment is adequate given the participants' demographic (e.g., country of residence)?
+
+No response.
+
+D3. Did you discuss whether and how consent was obtained from people whose data you're using/curating? For example, if you collected data via crowdsourcing, did your instructions to crowdworkers explain how the data would be used?
+
+No response.
+
+D4. Was the data collection protocol approved (or determined exempt) by an ethics review board?
+
+No response.
+
+D5. Did you report the basic demographic and geographic characteristics of the annotator population that is the source of the data?
+
+No response.

2023/Comparative evaluation of boundary-relaxed annotation for Entity Linking performance/images.zip

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2023/Composition-contrastive Learning for Sentence Embeddings/f510d1e4-d02c-4d1e-ad49-cbe38f251241_content_list.json

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+    {
+        "type": "text",
+        "text": "Composition-contrastive Learning for Sentence Embeddings",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Sachin Chanchani and Ruihong Huang",
+        "bbox": [
+            324,
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Texas A&M University",
+        "bbox": [
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "{chanchanis, huangrh}@tamu.edu",
+        "bbox": [
+            321,
+            177,
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+            192
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Abstract",
+        "text_level": 1,
+        "bbox": [
+            260,
+            252,
+            339,
+            268
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Vector representations of natural language are ubiquitous in search applications. Recently, various methods based on contrastive learning have been proposed to learn textual representations from unlabelled data; by maximizing alignment between minimally-perturbed embeddings of the same text, and encouraging a uniform distribution of embeddings across a broader corpus. Differently, we propose maximizing alignment between texts and a composition of their phrasal constituents. We consider several realizations of this objective and elaborate the impact on representations in each case. Experimental results on semantic textual similarity tasks show improvements over baselines that are comparable with state-of-the-art approaches. Moreover, this work is the first to do so without incurring costs in auxiliary training objectives or additional network parameters. $^{1}$",
+        "bbox": [
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "1 Introduction",
+        "text_level": 1,
+        "bbox": [
+            114,
+            565,
+            260,
+            581
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Significant progress has been made on the task of learning universal sentence representations that can be used for a variety of natural language processing tasks without task-specific fine-tuning (Conneau et al., 2017, Cer et al., 2018, Kiros et al., 2015, Logeswaran and Lee, 2018, Giorgi et al., 2021a, Yan et al., 2021, Gao et al., 2021, Chuang et al., 2022a). Recent works have shown the potential to learn good sentence embeddings without labeled data by fine-tuning pre-trained language models (PLMs) using the unsupervised framework introduced in SimCLR (Chen et al., 2020), adapted to the natural language processing (NLP) domain. In computer vision (CV), SimCLR exploits a series of transformations (blurs, crops, color distortions, etc.) to construct positive pairs from otherwise unique data points. A cross entropy objective (InfoNCE; Oord et al., 2018) is then applied to minimize distance",
+        "bbox": [
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "between representations originating from the same datum, while maximizing the distance to all other points in a mini-batch. The success of the framework in computer vision is due largely to the diversity of augmentations used for creating positive pairs, which leave the identity of the original example intact while reducing pairwise mutual information in the input space (Tian et al., 2020; Wu et al., 2020; Purushwalkam and Gupta, 2020).",
+        "bbox": [
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+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Constructing positive pairs via discrete augmentations have not been effective when applying the same objective to sentence embeddings. In fact, Gao et al. (2021) perform an ablation study of textual augmentations (e.g., cropping, synonym replacement) and find that training on these pairs hurts downstream performance on semantic textual similarity (STS) tasks. Instead, they observe that minimal  $(10\\%)$  dropout noise can be used to create positive pairs on-the-fly, and empirically results in stronger representations. This framework relying on nearly identical pairs is known as SimCSE. Since the dropout noise exists as a regularization component of the BERT architecture (Devlin et al., 2019a), explicit augmentations are unnecessary, making it a simple yet effective framework for unsupervised learning of sentence embeddings.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Here, we make a case for composition as augmentation, by exploiting its presence in language as a signal for learning sentence encoders. We conduct a series of experiments to illustrate the impact of training on positive examples derived by averaging representations of textual constituents in the latent space. Following previous works, we benchmark the proposed strategy on 7 STS tasks. Our results show that it is feasible to significantly improve upon SimCSE without making expensive architectural modifications or changing the overall training objective. We hope our findings can inspire new avenues of inquiry in text representation learning that draw on long-standing notions in semantics and linguistics.",
+        "bbox": [
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+    },
+    {
+        "type": "page_footnote",
+        "text": "$^{1}$ Code, pre-trained models, and datasets will be available at github.com/perceptiveshawty/CompCSE.",
+        "bbox": [
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+        "page_idx": 0
+    },
+    {
+        "type": "page_number",
+        "text": "15836",
+        "bbox": [
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+        "page_idx": 0
+    },
+    {
+        "type": "footer",
+        "text": "Proceedings of the 61st Annual Meeting of the Association for Computational Linguistics",
+        "bbox": [
+            226,
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "footer",
+        "text": "Volume 1: Long Papers, pages 15836-15848",
+        "bbox": [
+            361,
+            958,
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+            970
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "footer",
+        "text": "July 9-14, 2023 ©2023 Association for Computational Linguistics",
+        "bbox": [
+            295,
+            972,
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "image",
+        "img_path": "images/0e00e0822a71731ed2761526e9455b5c5905407be938c1a17e1d6195731f36d3.jpg",
+        "image_caption": [
+            "(a) subsampling strategies"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            144,
+            67,
+            509,
+            318
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "image",
+        "img_path": "images/1a01938431b13e1268eef078091591ec5201c40d25fdf1325d38b1e65b42d326.jpg",
+        "image_caption": [
+            "(b) training objective",
+            "Figure 1: An overview of composition-based contrastive learning. Subsampling strategies used to expand the training dataset are illustrated on the left-hand side, where the bidirectional arrows indicate positive pairs, brackets indicate spans of text, and all other pairs are the standard in-batch negatives. The  $\\otimes$  operation is a shorthand for the augmentation strategy integrated with the framework and depicted on the right: along with dropout noise, examples are decomposed in the input space and constituents are independently passed through the encoder. Resultant [CLS] tokens are then aggregated and passed through a linear projector before computing the contrastive loss."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "2 Background and Related Work",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "2.1 Unsupervised Contrastive Learning",
+        "text_level": 1,
+        "bbox": [
+            112,
+            498,
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+            514
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Contrastive learning (Hadsell et al., 2006) aims to learn vector-valued representations of data without relying on annotations. Meaning is derived from these representations based on their proximity to other points in the same space, e.g. two images of dogs will be closer in space than a dog and a chair. Several works have theoretically verified the utility of representations derived from contrastive learning (Arora et al., 2019; Lee et al., 2020; Tosh et al., 2020) under various assumptions; Chen et al. (2020) showed that SimCLR can even outperform supervised counterparts on CV transfer learning benchmarks. In SimCLR (and SimCSE), the learning objective for an example is:",
+        "bbox": [
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nl _ {i} = - \\log \\frac {e ^ {\\operatorname {s i m} \\left(z _ {i} , z _ {i} ^ {+}\\right) / \\tau}}{\\sum_ {j = 1} ^ {N} e ^ {\\operatorname {s i m} \\left(z _ {i} , z _ {j} ^ {+}\\right) / \\tau}}, \\tag {1}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            184,
+            749,
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "where  $z_{i} = f(x_{i}),z_{i}^{+} = f(x_{i}^{+})$  are vector representations of an input and its corresponding augmented positive,  $\\tau$  is a temperature hyperparameter,  $sim(.,.)$  is cosine similarity, and  $N$  is batch size.",
+        "bbox": [
+            112,
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Drawbacks of InfoNCE. In examination of eq. 1, it is evident that InfoNCE uniformly repels examples in the mini-batch besides the minimally",
+        "bbox": [
+            112,
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "augmented positive. Consequently, the resulting embeddings show poor group-wise discrimination, especially in language, since it is likely that different examples in the batch can have different relative similarities to a given anchor. Another consequence of the unsupervised InfoNCE objective is dimensional collapse, wherein embedding vectors are mostly differentiated by a small proportion of the feature axes; thus under-utilizing the full expressive capacity of the encoder. This was theoretically posited in Jing et al. (2022). They prove that minimal augmentation, coupled with an over-parameterized network, results in low rank solutions to the unsupervised contrastive objective. We hypothesize that this is closely tied to short-cut learning (Robinson et al., 2021a) — in the context of sentence embeddings, Wu et al. (2022c) observed that spurious features related to the lengths of sentences are relied on to solve the contrastive objective. Such solutions can yield nongeneralizable features that poorly represent data from new domains.",
+        "bbox": [
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Qualifying the representation space. Wang and Isola (2020) proposed two metrics to measure the quality of embeddings derived through contrastive learning. First, alignment measures on average the proximity of pairs of examples that should be close",
+        "bbox": [
+            507,
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "page_number",
+        "text": "15837",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "in space, i.e. for a set of positive pairs  $p_{pos}$  and their normalized representations  $f(x), f(x^{+})$ :",
+        "bbox": [
+            112,
+            84,
+            487,
+            116
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\ell_ {\\text {a l i g n}} \\triangleq \\underset {(x, x ^ {+}) \\sim p _ {\\text {p o s}}} {\\mathbb {E}} \\| f (x) - f (x ^ {+}) \\| ^ {2}. \\tag {2}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            163,
+            123,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Conversely, uniformity measures how scattered the embeddings are upon the unit hypersphere:",
+        "bbox": [
+            112,
+            154,
+            485,
+            186
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\ell_ {\\text {u n i f o r m}} \\triangleq \\log \\underset {x, y \\sim p _ {\\text {d a t a}}} {\\mathbb {E}} e ^ {- 2 \\| f (x) - f (y) \\| ^ {2}}, \\tag {3}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            131,
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+            223
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "where  $p_{data}$  denotes the full data distribution. We use these metrics to explore the advantages and drawbacks of various augmentations in contrastive pre-training, similarly to Gao et al. (2021).",
+        "bbox": [
+            112,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "2.2 Learning Sentence Embeddings",
+        "text_level": 1,
+        "bbox": [
+            114,
+            302,
+            410,
+            317
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Early works. First approaches to learning sentence embeddings span unsupervised (Kiros et al., 2015; Hill et al., 2016; Logeswaran and Lee, 2018), and supervised (Conneau et al., 2017; Cer et al., 2018; Reimers and Gurevych, 2019) methods which have been studied extensively in the literature. More recent work has focused on unsupervised contrastive learning with the advent of SimCSE (Gao et al., 2021), which passes the same sentence to a language model twice; the independent dropout masks sampled in the two forward passes encode the sentence at slightly different positions in vector space. A cross-entropy objective is then used to maximize the probability of top-1 proximity between positives while uniformly repelling other examples.",
+        "bbox": [
+            112,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Successors to SimCSE. Works that follow SimCSE attempt to improve the framework with auxiliary training objectives (Chuang et al., 2022a; Nishikawa et al., 2022; Zhou et al., 2023; Zhang et al., 2022; Wu et al., 2022b; Wang et al., 2022), verbalized or continuous prompts (Wang et al., 2022; Yuxin Jiang and Wang, 2022), instance generation or weighting strategies (Zhou et al., 2022), momentum encoders with negative sample queues (He et al., 2020), or entirely new parameters with secondary networks (Wu et al., 2022a). Many works combine several of these components, making it difficult to discern their impact in isolation. As the design choices have become more intricate and less parameter-efficient, performance on STS benchmarks has too become saturated.",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3 Composition-based Contrastive Learning",
+        "text_level": 1,
+        "bbox": [
+            114,
+            846,
+            420,
+            879
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Our augmentation strategy retains the simplicity and efficiency of SimCSE, as illustrated in Fig-",
+        "bbox": [
+            112,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "ure 1. Specifically, it requires just one additional forward pass that is ultimately compensated by a non-trivial reduction in convergence time (§6). Beginning with a corpus of unlabelled sentences  $\\{x_{i}\\}_{i = 1}^{m}$ , we consider  $x_{i}^{+}$  only in the latent space, as a composition of the representations of  $(x_{i}^{\\prime +},x_{i}^{\\prime +})$ . A simple (and effective) way to curate  $(x_{i}^{\\prime +},x_{i}^{\\prime +})$  is to split the tokens of  $x_{i}$  in half, and encode the left and right phrases in independent forward passes through the encoder and linear projector. After obtaining their respective [CLS] token representations  $(z_{i},z_{i}^{\\prime +},z_{i}^{\\prime +})$ ,  $(z_{i}^{\\prime +},z_{i}^{\\prime +})$  is aggregated and taken to be the corresponding positive example for  $z_{i}$ . The training objective for a single pair is then the same as in eq. 1, where  $z^{+} = \\text{aggregate}(z_{i}^{\\prime +},z_{i}^{\\prime +})$ . We experiment with aggregation methods in §5, and find that the best approach varies according to the size and type of underlying PLM. In our final model based on BERTbase, we find that this manner of augmentation is especially suitable for the scheme proposed in DirectCLR (Jing et al., 2022), which aims to directly mitigate dimensional collapse by computing the loss from eq. 1 on a subset of the embedding vector axes before backpropagating to the entire representation.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Decomposition as data augmentation. To explain the motivation for decomposing examples in the input space, we can consider an example from the development subset of STS-B labelled as having high semantic similarity:",
+        "bbox": [
+            507,
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "A man is lifting weights in a garage.  \nA man is lifting weights.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "There are two semantic atoms at play in the first text: 1) a man is lifting weights, and 2) a man is in a garage. The similarity between the two texts can only be considered high based on the first atom; lifting weights. It cannot be said that there is a general relation between being in a garage and lifting weights - a garage is equally, if not more likely to be related to cars, parking, or storage, yet this does not preclude a connection between them. It is only through the composition of both atoms that we can relate the two. Thus, there is a need for sentence encoders to learn more generalized phrase representations; to at least implicitly abide by principles of semantic compositionality. The challenge in enforcing this kind of constraint through a contrastive objective is in the choice of data — it would require a corpus where lexical collocations are encountered across a diverse set of contexts.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "page_number",
+        "text": "15838",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "image",
+        "img_path": "images/db114902f07c910275b14610c5c732f679da2a2d83050c7d6ac174d314613256.jpg",
+        "image_caption": [
+            "Figure 2:  $\\ell_{\\mathrm{align}} - \\ell_{\\mathrm{uniform}}$  tradeoff for subsampling strategies explored in this work. Measurements are taken every 10 training steps on the development subset of STS-B, for 500 steps with  $\\mathrm{BERT}_{\\mathrm{base}}$ . The ideal trajectory is the negative direction for both axes/metrics."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Subsampling from decomposed inputs. To further examine the effect of decomposition in the input space, we leverage a pre-trained discourse parser $^2$  to extract atomic semantic units from each unique example in the training set; typically simple phrases or clauses. We experiment with 3 kinds of strategies (Figure 1a) to expand the training set, besides considering our augmentation in isolation: let  $C = \\{x_{i,k}\\}_{k=1}^{c}$  represent the  $c$  non-overlapping phrases extracted from an input  $x_i$ :",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "list",
+        "sub_type": "text",
+        "list_items": [
+            "- adjacent spans are sampled by taking each unique pair in  $C$  such that there is no overlap between inputs;",
+            "- overlapping and adjacent spans are sampled by taking (potentially) overlapping pairs in  $C$ ;",
+            "- overlapping, adjacent, and subsuming spans are sampled by recursively partitioning the elements of  $C$  in half, i.e. maximizing the lexical overlap of extracted input samples."
+        ],
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+    {
+        "type": "text",
+        "text": "Impact on the representation space. A consequence of expanding the training set with subsamples is the presence of harder in-batch negatives. Prior work has demonstrated that this is generally beneficial to contrastive learning (Robinson et al., 2021b; Kalantidis et al., 2020; Zhang and Stratos, 2021). Following Gao et al. (2021), we measure the uniformity and alignment of representations obtained for the development set of STS-B to understand the effect of training with additional sub",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "samples. STS-B is comprised of pairs of sentences accompanied by a score between 1-5 indicating degree of semantic similarity. We take all pairs as  $p_{\\mathrm{data}}$ , and pairs with a score greater than 4 as  $p_{\\mathrm{pos}}$ . Both metrics are measured every 10 steps for 500 training steps, to understand the direction in which each of our strategies drives the encoder.",
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+        "type": "text",
+        "text": "As shown in Figure 2, any of the subsampling strategies can bring non-trivial improvements over unsupervised SimCSE in both alignment and uniformity. Specifically, expanding the training set with subsamples (+ adjacent, + overlapping, + subsuming) encourages a more uniform embedding distribution. On the other hand, forgoing subsampling for just the compositional augmentation (naive partition) achieves the better alignment while retaining the uniformity of SimCSE. This is because we leave the self-prediction objective intact, while increasing its difficulty: although subsamples are potentially highly related, positive pairs are only curated from the exact same text. As a consequence, the underlying PLM is forced to effectively distinguish examples with high lexical overlap — which is precisely the intuition underlying DiffCSE Chuang et al. (2022b), and other discriminative pre-training objectives.",
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+    {
+        "type": "text",
+        "text": "4 Experiment",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Setup. In our experiments, we modify the public PyTorch implementation<sup>3</sup> of SimCSE to support our proposed augmentation and subsampling methods. All of our language models are initialized from pre-trained BERT/RoBERTa checkpoints (Devlin et al., 2019b; Liu et al., 2019), except the randomly-initialized MLP over the [CLS] representation. For all models, we employ the scheme illustrated in Figure 1 and report the best results after training with or without the 3 subsampling strategies. We keep the best checkpoints after evaluating on the development set of STS-B every 125 steps during training. Batch size is fixed at 64 for all models; for base and large sized models, learning rates are fixed to 3e-5 and 1e-5 respectively. Besides those covered in 5, extensive hyperparameter searches were not conducted in this work.",
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+    {
+        "type": "text",
+        "text": "Data. We use the same 1 million randomly sampled sentences<sup>4</sup> as SimCSE for training, be-",
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+    {
+        "type": "page_footnote",
+        "text": "<sup>3</sup>https://github.com/princeton-nlp/SimCSE",
+        "bbox": [
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+    },
+    {
+        "type": "page_footnote",
+        "text": "4https://huggingface.co/datasets/princeton-nlp/datasets-for-simcse",
+        "bbox": [
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+        ],
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+    },
+    {
+        "type": "page_footnote",
+        "text": "$^{2}$ https://github.com/seq-to-mind/DMRST_Parser",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "page_number",
+        "text": "15839",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "table",
+        "img_path": "images/00de1cc986c648539d50024a461bdd98397240f854cced17713f5df98dfdc9cc.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>PLM</td><td>Method</td><td>STS12</td><td>STS13</td><td>STS14</td><td>STS15</td><td>STS16</td><td>STS-B</td><td>SICK-R</td><td>Avg.</td></tr><tr><td rowspan=\"9\">BERTbase</td><td>SimCSE♣</td><td>68.40</td><td>82.41</td><td>74.38</td><td>80.91</td><td>78.56</td><td>76.85</td><td>72.23</td><td>76.25</td></tr><tr><td>L2P-CSR♥</td><td>70.21</td><td>83.25</td><td>75.42</td><td>82.34</td><td>78.75</td><td>77.8</td><td>72.65</td><td>77.20</td></tr><tr><td>DCLR♠</td><td>70.81</td><td>83.73</td><td>75.11</td><td>82.56</td><td>78.44</td><td>78.31</td><td>71.59</td><td>77.22</td></tr><tr><td>MoCoSE◇</td><td>71.58</td><td>81.40</td><td>74.47</td><td>83.45</td><td>78.99</td><td>78.68</td><td>72.44</td><td>77.27</td></tr><tr><td>ArcCSE†</td><td>72.08</td><td>84.27</td><td>76.25</td><td>82.32</td><td>79.54</td><td>79.92</td><td>72.39</td><td>78.11</td></tr><tr><td>PCL‡</td><td>72.74</td><td>83.36</td><td>76.05</td><td>83.07</td><td>79.26</td><td>79.72</td><td>72.75</td><td>78.14</td></tr><tr><td>*SimCSE (w/ comp.)</td><td>72.14</td><td>84.06</td><td>75.38</td><td>83.82</td><td>80.43</td><td>80.29</td><td>71.12</td><td>78.18</td></tr><tr><td>ESimCSE○</td><td>73.40</td><td>83.27</td><td>77.25</td><td>82.66</td><td>78.81</td><td>80.17</td><td>72.30</td><td>78.27</td></tr><tr><td>SNCSE$</td><td>70.67</td><td>84.79</td><td>76.99</td><td>83.69</td><td>80.51</td><td>81.35</td><td>74.77</td><td>78.97</td></tr><tr><td rowspan=\"9\">BERTlarge</td><td>SimCSE♣</td><td>70.88</td><td>84.16</td><td>76.43</td><td>84.50</td><td>79.76</td><td>79.26</td><td>73.88</td><td>78.41</td></tr><tr><td>DCLR♠</td><td>71.87</td><td>84.83</td><td>77.37</td><td>84.70</td><td>79.81</td><td>79.55</td><td>74.19</td><td>78.90</td></tr><tr><td>L2P-CSR♥</td><td>71.44</td><td>85.09</td><td>76.88</td><td>84.71</td><td>80.00</td><td>79.75</td><td>74.55</td><td>78.92</td></tr><tr><td>MoCoSE◇</td><td>74.50</td><td>84.54</td><td>77.32</td><td>84.11</td><td>79.67</td><td>80.53</td><td>73.26</td><td>79.13</td></tr><tr><td>ESimCSE○</td><td>73.21</td><td>85.37</td><td>77.73</td><td>84.30</td><td>78.92</td><td>80.73</td><td>74.89</td><td>79.31</td></tr><tr><td>ArcCSE†</td><td>73.17</td><td>86.19</td><td>77.90</td><td>84.97</td><td>79.43</td><td>80.45</td><td>73.50</td><td>79.37</td></tr><tr><td>*SimCSE (+ subsum.)</td><td>75.10</td><td>86.57</td><td>77.70</td><td>84.72</td><td>80.25</td><td>80.17</td><td>73.21</td><td>79.67</td></tr><tr><td>PCL‡</td><td>74.89</td><td>85.88</td><td>78.33</td><td>85.30</td><td>80.13</td><td>81.39</td><td>73.66</td><td>79.94</td></tr><tr><td>SNCSE$</td><td>71.94</td><td>86.66</td><td>78.84</td><td>85.74</td><td>80.72</td><td>82.29</td><td>75.11</td><td>80.19</td></tr><tr><td rowspan=\"7\">RoBERTabase</td><td>SimCSE♣</td><td>70.16</td><td>81.77</td><td>73.24</td><td>81.36</td><td>80.65</td><td>80.22</td><td>68.56</td><td>76.57</td></tr><tr><td>ESimCSE○</td><td>69.90</td><td>82.50</td><td>74.68</td><td>83.19</td><td>80.30</td><td>80.99</td><td>70.54</td><td>77.44</td></tr><tr><td>L2P-CSR♥</td><td>71.69</td><td>82.43</td><td>74.55</td><td>82.15</td><td>81.81</td><td>81.36</td><td>70.22</td><td>77.74</td></tr><tr><td>DCLR♠</td><td>70.01</td><td>83.08</td><td>75.09</td><td>83.66</td><td>81.06</td><td>81.86</td><td>70.33</td><td>77.87</td></tr><tr><td>*SimCSE (w/ comp.)</td><td>72.56</td><td>83.33</td><td>73.67</td><td>83.36</td><td>81.14</td><td>80.71</td><td>70.39</td><td>77.88</td></tr><tr><td>PCL‡</td><td>71.54</td><td>82.70</td><td>75.38</td><td>83.31</td><td>81.64</td><td>81.61</td><td>69.19</td><td>77.91</td></tr><tr><td>SNCSE$</td><td>70.62</td><td>84.42</td><td>77.24</td><td>84.85</td><td>81.49</td><td>83.07</td><td>72.92</td><td>79.23</td></tr><tr><td rowspan=\"7\">RoBERTalarge</td><td>*SimCSE (w/ comp.)</td><td>72.32</td><td>84.19</td><td>75.00</td><td>84.83</td><td>81.27</td><td>82.10</td><td>70.99</td><td>78.67</td></tr><tr><td>SimCSE♣</td><td>72.86</td><td>83.99</td><td>75.62</td><td>84.77</td><td>81.80</td><td>81.98</td><td>71.26</td><td>78.90</td></tr><tr><td>DCLR♠</td><td>73.09</td><td>84.57</td><td>76.13</td><td>85.15</td><td>81.99</td><td>82.35</td><td>71.80</td><td>79.30</td></tr><tr><td>PCL‡</td><td>73.76</td><td>84.59</td><td>76.81</td><td>85.37</td><td>81.66</td><td>82.89</td><td>70.33</td><td>79.34</td></tr><tr><td>ESimCSE○</td><td>73.20</td><td>84.93</td><td>76.88</td><td>84.86</td><td>81.21</td><td>82.79</td><td>72.27</td><td>79.45</td></tr><tr><td>L2P-CSR♥</td><td>73.29</td><td>84.08</td><td>76.65</td><td>85.47</td><td>82.70</td><td>82.15</td><td>72.36</td><td>79.53</td></tr><tr><td>SNCSE$</td><td>73.71</td><td>86.73</td><td>80.35</td><td>86.80</td><td>83.06</td><td>84.31</td><td>77.43</td><td>81.77</td></tr></table>",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Table 1: The performance on STS tasks (Spearman's correlation) for different sentence embedding models. Results are imported as follows —♣: Gao et al. (2021),♥: Zhou et al. (2023),♠: Zhou et al. (2022),◇: Cao et al. (2022), †: Zhang et al. (2022),‡: Wu et al. (2022a), Ⓞ: Wu et al. (2022c), $: Wang et al. (2022), *: our results.",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "sides incorporating the subsampling strategies from §3. We evaluate on 7 semantic textual similarity tasks: STS 2012-2016, STS-Benchmark, SICK-Relatedness (Agirre et al., 2012, 2013, 2014, 2015, 2016; Cer et al., 2017; Marelli et al., 2014) and report averaged Spearman's correlation across all available test subsets. We employ the modified SentEval<sup>5</sup> (Conneau and Kiela, 2018) package accompanying the source code of SimCSE for fair comparison with other works.",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Baselines. We compare our results with many contemporaries: ESimCSE (Wu et al., 2022c), SNCSE (Wang et al., 2022), PCL (Wu et al., 2022a), DCLR (Zhou et al., 2022), ArcCSE (Zhang et al., 2022), MoCoSE (Cao et al., 2022), and L2P-CSR (Zhou et al., 2023). We consider SimCSE (Gao et al., 2021) as our baseline, since we leave its training objective and network architecture intact.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Results. We can observe in Table 1 that our methods bring non-trivial improvements to SimCSE with both BERT encoders, as well as RoBERTa $_{\\text{base}}$ . In fact, we achieve an average F1 score within 0.8 points of SNCSE-BERT $_{\\text{base}}$  (Wang et al., 2022). SNCSE exploits biases in test sets by engineering hard negatives via explicitly negated sentences — the impact of this strategy is more apparent in the results utilizing RoBERTa, where there is parity in all works besides SNCSE. In the case of  $\\text{BERT}_{\\text{large}}$ , the gap in performance between our approach and SNCSE is narrower at 0.52 points. A clear failure of the composition-augmented objective presents itself in the results with RoBERTa $_{\\text{large}}$ . This could be attributed to poor hyperparameter settings, or a fundamental incompatibility between our approach and the model size/RoBERTa pre-training objective, since other works achieve better results with this PLM.",
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+    },
+    {
+        "type": "page_footnote",
+        "text": "$^{5}$ https://github.com/facebookresearch/SENTEval",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "page_number",
+        "text": "15840",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "5 Ablation",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "We ablate several aspects of the approach to understand their impact in isolation. We first consider the subsampling strategy, or lack thereof, in which each model achieves the best STS-B development set performance. These are then tied to each model in subsequent ablations.",
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+    {
+        "type": "text",
+        "text": "Including subsamples. In the process of designing DeCLUTR, Giorgi et al. (2021b) report gains from subsampling more than one anchor per input document. In our experiments, we find that the alignment-uniformity trade-off differs between  $\\mathrm{BERT}_{\\text {large }}$  and  $\\mathrm{BERT}_{\\text {base }}$ , i.e. different strategies can be better suited to different PLMs. In Table 2, we show that including subsamples is beneficial to the  $\\mathrm{BERT}_{\\text {large }}$  PLM, but harmful to  $\\mathrm{BERT}_{\\text {base }}$ . This is likely a result of the difference in no. of parameters — the smaller PLM may not possess the expressive capacity to distinguish highly related texts without suffering a degeneration in alignment. With  $\\mathrm{RoBERTa}_{\\text {base }}$ , we observe that subsampling non-overlapping spans gives the best results, whereas none of our strategies appeared compatible with  $\\mathrm{RoBERTa}_{\\text {large }}$ .",
+        "bbox": [
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+    },
+    {
+        "type": "table",
+        "img_path": "images/98442730976b433548c03d6ca3e6e129a3cdc0f637ab3ea2f1d3c5e8e3865a55.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>PLM</td><td>Method</td><td>STS-B</td></tr><tr><td rowspan=\"6\">BERTbase</td><td>SimCSE</td><td>81.47</td></tr><tr><td>w/ composition</td><td>83.97</td></tr><tr><td>Additional subsampling:</td><td></td></tr><tr><td>+ adjacent</td><td>83.39</td></tr><tr><td>+ overlapping</td><td>83.18</td></tr><tr><td>+ subsuming</td><td>82.97</td></tr><tr><td rowspan=\"6\">BERTlarge</td><td>SimCSE</td><td>84.41</td></tr><tr><td>w/ composition</td><td>84.79</td></tr><tr><td>Additional subsampling:</td><td></td></tr><tr><td>+ adjacent</td><td>84.84</td></tr><tr><td>+ overlapping</td><td>85.01</td></tr><tr><td>+ subsuming</td><td>85.06</td></tr><tr><td rowspan=\"6\">RoBERTabase</td><td>SimCSE</td><td>83.91</td></tr><tr><td>w/ composition</td><td>84.14</td></tr><tr><td>Additional subsampling:</td><td></td></tr><tr><td>+ adjacent</td><td>84.00</td></tr><tr><td>+ overlapping</td><td>84.10</td></tr><tr><td>+ subsuming</td><td>82.92</td></tr><tr><td rowspan=\"6\">RoBERTalarge</td><td>SimCSE</td><td>85.07</td></tr><tr><td>w/ composition</td><td>84.80</td></tr><tr><td>Additional subsampling:</td><td></td></tr><tr><td>+ adjacent</td><td>83.91</td></tr><tr><td>+ overlapping</td><td>82.74</td></tr><tr><td>+ subsuming</td><td>83.33</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Aggregation method. In SBERT (Reimers and Gurevych, 2019), and in historically effective works such as InferSent (Conneau et al., 2017), PLMs are fine-tuned with a cross entropy loss to predict whether two sentences  $u$  and  $v$  entail or contradict each other. Their pooler is a concatenation of the two sentence embeddings, along with second-order features such as the element-wise difference,  $|u - v|$ . We experiment with these aggregation methods, as well as simpler choices such as element-wise sums/averages. We can see in Table 3 that simply interpolating the embeddings is preferable to other methods for BERT-based encoders. We postulate that this interpolation functions as a form of self-distillation, and amplifies the salience of desirable sparse features correlated with sentential context (Wen and Li, 2021). For RoBERTa, we find that concatenating the first and last halves of the representations is better. Since RoBERTa does not use the next-sentence prediction (NSP) objective, its embeddings will not encode sentential knowledge. Averaging RoBERTa embeddings may not correlate well with real tokens in its vocabulary, whereas concatenating the first and last halves of constituent embeddings retains localized token-level information, making it a better choice in this case.",
+        "bbox": [
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+    },
+    {
+        "type": "table",
+        "img_path": "images/3a863b20dfff521a75d96b28ce1f2f31ff027a45998dcbba4e54a7190ef9a719.jpg",
+        "table_caption": [
+            "Table 2: Development set results of STS-B after varying the subsampling strategy on different-sized PLMs."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Aggregation</td><td>STS-B</td></tr><tr><td>BERTbase</td><td></td></tr><tr><td>sum</td><td>83.92</td></tr><tr><td>avg.</td><td>83.97</td></tr><tr><td>concat first &amp; last half</td><td>83.01</td></tr><tr><td>concat + project</td><td>69.24</td></tr><tr><td>concat w/ abs. difference + project</td><td>68.79</td></tr><tr><td>RoBERTa base</td><td></td></tr><tr><td>sum</td><td>84.00</td></tr><tr><td>avg.</td><td>84.08</td></tr><tr><td>concat first &amp; last half</td><td>84.14</td></tr><tr><td>concat + project</td><td>65.02</td></tr><tr><td>concat w/ abs. difference + project</td><td>65.44</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Table 3: Results of different aggregation methods for composing  $z^{+}$  in the latent space. Results are based on BERT<sub>base</sub> on the development set of STS-B.",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Composing  $z$  vs.  $z^{+}$ . In our training objective, there are two sets of sentence representations, one derived from pure dropout noise, and the second by averaging the coordinates of constituent representations. However, for each sentence we can: 1) compose the anchor  $z$  in latent space, which means other in-batch examples are repelled from",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "page_number",
+        "text": "15841",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "a synthetic example's coordinate, 2) compose the positive  $z^{+}$ , which means synthetic coordinates are repelled from representations of real examples, or 3) compose both  $z$  and  $z^{+}$  in the latent space. In Table 4, we can see that with  $\\mathrm{BERT}_{\\mathrm{base}}$ , we found the best results by directly embedding the anchor sentence, and composing  $z^{+}$  from constituents.",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "table",
+        "img_path": "images/6d661910b3139fda4f79d5563c370024865a3d39879a14c5852e997597eda72f.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">BERTbase</td><td>Compose</td><td>z</td><td>z+</td><td>Both</td></tr><tr><td>STS-B</td><td>83.61</td><td>83.97</td><td>83.81</td></tr></table>",
+        "bbox": [
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+        ],
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+    },
+    {
+        "type": "text",
+        "text": "Table 4: Differences between having compositional anchors and positives. In the Both case, the model framework is symmetric in that both anchors and positives are composed of constituent representations. Results are based on  $\\mathrm{BERT}_{\\mathrm{base}}$  on the development set of STS-B.",
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+    {
+        "type": "text",
+        "text": "Number of partitions. Within our framework, we can aggregate the embeddings of two or more phrases. Increasing the number of phrases increases the number of forward passes, and magnifies the impact of dropout noise. We find that partitioning into more than two bins is detrimental to the objective (Table 5), though perhaps this is the case because the evaluation data consists mostly of short-length sentences.",
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+    {
+        "type": "table",
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+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">BERTbase</td><td>Partitions</td><td>2</td><td>3</td><td>4</td></tr><tr><td>STS-B</td><td>83.97</td><td>83.48</td><td>83.52</td></tr></table>",
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+    {
+        "type": "text",
+        "text": "Hyperparameter  $d_0$ . In our experiments with BERTbase, computing the contrastive loss on a subvector of  $(z_i, z_i^+)$  is complementary to composing  $z_i^+$  in the latent space. When  $d_0 \\to d$ , our training objective is the exact same as in all *CSE works, ie. computing the loss on all coordinates of  $(z_i, z_i^+)$ . For BERTbase, we search  $d_0 \\in \\{192, 256, 384\\}$  with the compositional augmentation in isolation (w/ composition); for BERTlarge,  $d_0 \\in \\{320, 384, 512\\}$  with the expanded training set of subsamples (+ subsuming). Our results in Table 6 indicate that taking a subvector to compute the loss is beneficial for BERTbase, but the entire vector is necessary for BERTlarge. With RoBERTa encoders, we aggregate embeddings by concatenating the first and last halves of the phrase embeddings, so  $d_0$  is inapplicable.",
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+    {
+        "type": "table",
+        "img_path": "images/e1c7313631a6bf4d509ad06d2b6d2150abb0358b762661d06d7a77dbf9c7da1a.jpg",
+        "table_caption": [
+            "Table 5: Impact of splitting examples into more than 2 bins. Results are based on BERTbase with the development set of STS-B."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">BERTbase</td><td>d0</td><td>192</td><td>256</td><td>384</td><td>768</td></tr><tr><td>STS-B</td><td>83.88</td><td>84.11</td><td>83.17</td><td>83.97</td></tr><tr><td rowspan=\"2\">BERTlarge</td><td>d0</td><td>320</td><td>384</td><td>512</td><td>1024</td></tr><tr><td>STS-B</td><td>84.61</td><td>84.94</td><td>84.98</td><td>85.06</td></tr></table>",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Table 6: Varying the size of the subvector used to compute InfoNCE, as proposed in Jing et al. (2022). Results are based on the development set of STS-B.",
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+    {
+        "type": "text",
+        "text": "6 Analysis",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "Stability and efficiency of training. Successors to SimCSE have incrementally improved STS performance while disproportionately driving up resource requirements. This limits accessibility to practitioners who wish to learn embeddings from their own corpora, perhaps in other languages. Differently, our approach relies on a single additional forward pass while converging much faster than SimCSE. In Figure 3, we compare our  $\\mathrm{BERT}_{\\mathrm{base}}$  model's evaluation curve to SimCSE's for 1000 training steps in the same setting. We observe that composition as augmentation greatly speeds up convergence, with evaluation metrics plateauing much faster, and more stably than SimCSE. In fact, on a single NVIDIA A100 GPU (40GB), our model can finish training in under 15 minutes.",
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+    },
+    {
+        "type": "image",
+        "img_path": "images/137007bf55197b6f465971c7e7037060fb4ba01a5e61406f6134912f19d9971d.jpg",
+        "image_caption": [
+            "Figure 3: Evaluation curve for  $\\mathrm{BERT}_{\\mathrm{base}}$ , using dropout noise as augmentation (unsup. SimCSE) and latent space composition (naive partition). The y-axis reflects performance on the development set of STS-B."
+        ],
+        "image_footnote": [],
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+    {
+        "type": "text",
+        "text": "Text length as a feature. To investigate the structure of the learned space, In Figure 5, we visualize embeddings of sentences from the development set of STS-B after down-projecting to 2D Euclidean space. We employ UMAP (McInnes et al., 2018) with cosine distance as the metric to preserve local and global topological neighborhoods. The same",
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+    {
+        "type": "page_number",
+        "text": "15842",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/8cee787264457406038a9946edb681af715c46dcbfa2d698c6215a23bbae8314.jpg",
+        "image_caption": [
+            "Figure 4: A heatmap displaying the pairwise similarities computed by SimCSE, DiffCSE, and our model, with the same underlying PLM  $\\mathrm{BERT}_{\\mathrm{base}}$  and color scale. Lighter colors indicate higher similarity."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    {
+        "type": "image",
+        "img_path": "images/a6bd2c76da5140c3b302f61aff9e71a5cacd288bb11299a4c24f2e170f85f58e.jpg",
+        "image_caption": [
+            "(a) unsup. SimCSE"
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "image",
+        "img_path": "images/7a7c8914c5279e180a0719dd2ed6338785385b35ec93bb888e66b16ed1731586.jpg",
+        "image_caption": [
+            "(b) w/ compositional augmentations",
+            "Figure 5: 2D UMAP projection of the representations of all sentences from the validation subset of STS-B. Color indicates word count."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "parameters are used to compute the embeddings in Figure 5a and 5b, which are derived from dropout noise, and composition-based augmentations (w/ composition) respectively. In Figure 5a, we can observe several clusters of dark points corresponding to shorter sentences. This corroborates our intuition that minimal augmentation to create positive pairs can lead to shortcut learning, wherein text length is relied upon to solve the training objective. In contrast, we see a more scattered distribution of points in Figure 5b, particularly with shorter sen",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "tences. Coupled with the improved performance on STS tasks, we can conclude that our framework is less prone to learning from spurious correlations.",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Learned similarity metric. Returning to the example initially posed in §3, we show in Figure 4 similarity scores for pairs of examples computed by our  $\\mathrm{BERT}_{\\mathrm{base}}$  model, as well as the corresponding DiffCSE and SimCSE variants. Notice that all three assign higher similarities between anchor: \"A man is lifting weights in a garage\", and phrases: \"A man is lifting weights\", \"A man in a garage\". However, despite their equal constitution in the anchor text, SimCSE incorrectly assesses a higher similarity between the anchor and the first phrase, whereas DiffCSE and our model better capture the equivalence in similarity. The same occurs with anchor: \"We store it outside of the house\", and texts: \"A man is in a garage\", \"She parked on the driveway\"; despite both being unrelated to the anchor, SimCSE spuriously assigns a higher affinity to the former. Overall, we observed parity in the similarity assessments given by our model and DiffCSE, which validates the ability of our approach to remedy the suboptimal alignment of SimCSE without explicit incentive.",
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+    {
+        "type": "text",
+        "text": "7 Conclusion",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "In summary, we proposed a new way to construct positive pairs for unsupervised contrastive learning frameworks relying on pre-trained language models. Our experiments on STS tasks verified the effectiveness of the approach, which achieved competitive results with more complex learning methods, with the benefit of stabilizing and reducing the overall cost of training. We provided empirical studies and qualitative examinations into our approach, verifying its ability to train sentence encoders with better alignment. We believe this work can foster new avenues of inquiry in contrastive learning, especially those that draw upon a human cognition of language.",
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+        "page_idx": 7
+    },
+    {
+        "type": "page_number",
+        "text": "15843",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "8 Limitations",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "There are several limitations in this work. First, we have not explored how to make use of composition-based augmentations in the supervised setting. A second limitation is a lack of theoretical grounding in the impact of our latent space composition. Finally, we have not explored interoperability with other training objectives.",
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+    {
+        "type": "text",
+        "text": "9 Note on Ethics",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "We do not believe there are significant ethical considerations stemming from our work, except those that accompany the use of language models and unlabelled corpora in general. Pre-trained language models, including BERT and RoBERTa, are known to learn and reiterate harmful prejudices. Although our pre-training corpus is sourced from Wikipedia and cited in several related works, it cannot be feasibly vetted for explicit or inappropriate content.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Acknowledgements",
+        "text_level": 1,
+        "bbox": [
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+        ],
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+    },
+    {
+        "type": "text",
+        "text": "We thank the anonymous reviewers for their valuable feedback and input. We also thank Haotian Xu, for his insight and suggestions that shaped the course of this work. We gratefully acknowledge support from National Science Foundation (NSF) via the awards IIS-1942918 and IIS-2127746. Portions of this research were conducted with the advanced computing resources provided by Texas A&M High Performance Research Computing.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "References",
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+    {
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+        "list_items": [
+            "Zixin Wen and Yuanzhi Li. 2021. Toward Understanding the Feature Learning Process of Self-supervised Contrastive Learning.",
+            "Mike Wu, Chengxu Zhuang, Milan Mosse, Daniel Yamins, and Noah Goodman. 2020. On Mutual Information in Contrastive Learning for Visual Representations.",
+            "Qiyu Wu, Chongyang Tao, Tao Shen, Can Xu, Xi-ubo Geng, and Daxin Jiang. 2022a. PCL: Peercontrastive learning with diverse augmentations for unsupervised sentence embeddings.",
+            "Xing Wu, Chaochen Gao, Zijia Lin, Jizhong Han, Zhongyuan Wang, and Songlin Hu. 2022b. InfoCSE: Information-aggregated contrastive learning of sentence embeddings.",
+            "Xing Wu, Chaochen Gao, Liangjun Zang, Jizhong Han, Zhongyuan Wang, and Songlin Hu. 2022c. ESimCSE: Enhanced sample building method for contrastive learning of unsupervised sentence embedding.",
+            "Yuanmeng Yan, Rumei Li, Sirui Wang, Fuzheng Zhang, Wei Wu, and Weiran Xu. 2021. ConSERT: A contrastive framework for self-supervised sentence representation transfer. In Association for Computational Linguistics and International Joint Conference on Natural Language Processing (ACL-IJCNLP), pages 5065-5075.",
+            "Linhan Zhang Yuxin Jiang and Wei Wang. 2022. Improved universal sentence embeddings with prompt-based contrastive learning and energy-based learning.",
+            "Wenzheng Zhang and Karl Stratos. 2021. Understanding hard negatives in noise contrastive estimation. In Proceedings of the 2021 Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies, pages 1090-1101, Online. Association for Computational Linguistics.",
+            "Yuhao Zhang, Hongji Zhu, Yongliang Wang, Nan Xu, Xiaobo Li, and Binqiang Zhao. 2022. A contrastive framework for learning sentence representations from pairwise and triple-wise perspective in angular space. In Proceedings of the 60th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers), pages 4892-4903, Dublin, Ireland. Association for Computational Linguistics.",
+            "Kun Zhou, Beichen Zhang, Xin Zhao, and Ji-Rong Wen. 2022. Debiased contrastive learning of unsupervised sentence representations. In Proceedings of the 60th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers), pages 6120-6130, Dublin, Ireland. Association for Computational Linguistics.",
+            "Kun Zhou, Yuanhang Zhou, Xin Zhao, and Ji-Rong Wen. 2023. Learning to perturb for contrastive learning of unsupervised sentence representations."
+        ],
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+        "text": "Sections 1-2: \"Vector representations of natural language are ubiquitous in search, retrieval and reranking applications. Various methods based on contrastive learning have been proposed to learn textual representations from unlabelled data. These approaches maximize agreement between minimally perturbed texts, while uniformly repelling examples within a broader corpus.\"",
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+        "text": "Sections 1-6: \"Moreover, this work is the first to do so without incurring costs in auxiliary training objectives or additional network parameters.\"",
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+        "type": "text",
+        "text": "B Did you use or create scientific artifacts?",
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+        "text": "Sections 4-6.",
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+    {
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+            "B1. Did you cite the creators of artifacts you used? Sections 4-6.",
+            "B2. Did you discuss the license or terms for use and / or distribution of any artifacts? Not applicable. Left blank.",
+            "B3. Did you discuss if your use of existing artifact(s) was consistent with their intended use, provided that it was specified? For the artifacts you create, do you specify intended use and whether that is compatible with the original access conditions (in particular, derivatives of data accessed for research purposes should not be used outside of research contexts)? Not applicable. Left blank.",
+            "B4. Did you discuss the steps taken to check whether the data that was collected / used contains any information that names or uniquely identifies individual people or offensive content, and the steps taken to protect / anonymize it? Not applicable. Left blank.",
+            "B5. Did you provide documentation of the artifacts, e.g., coverage of domains, languages, and linguistic phenomena, demographic groups represented, etc.? Not applicable. Left blank.",
+            "B6. Did you report relevant statistics like the number of examples, details of train / test / dev splits, etc. for the data that you used / created? Even for commonly-used benchmark datasets, include the number of examples in train / validation / test splits, as these provide necessary context for a reader"
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+        "type": "header",
+        "text": "ACL 2023 Responsible NLP Checklist",
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+        "text": "The Responsible NLP Checklist used at ACL 2023 is adopted from NAACL 2022, with the addition of a question on AI writing assistance.",
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+    {
+        "type": "text",
+        "text": "to understand experimental results. For example, small differences in accuracy on large test sets may be significant, while on small test sets they may not be.",
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+        "text": "We include a footnote which links to a GitHub page where these statistics are available in detail; see",
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+        "type": "text",
+        "text": "Section 5. Related works do not report these statistics in the body or appendix of their paper.",
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+        "type": "text",
+        "text": "C Did you run computational experiments?",
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+    {
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+    },
+    {
+        "type": "text",
+        "text": "C1. Did you report the number of parameters in the models used, the total computational budget (e.g., GPU hours), and computing infrastructure used?",
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+        "text": "We utilize BERT and RoBERTa, and cite their papers where these parameters are listed. Additionally, we report on efficiency as a benefit of our approach in Section 6.",
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+        "text": "C2. Did you discuss the experimental setup, including hyperparameter search and best-found hyperparameter values?",
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+    {
+        "type": "text",
+        "text": "C3. Did you report descriptive statistics about your results (e.g., error bars around results, summary statistics from sets of experiments), and is it transparent whether you are reporting the max, mean, etc. or just a single run?",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "C4. If you used existing packages (e.g., for preprocessing, for normalization, or for evaluation), did you report the implementation, model, and parameter settings used (e.g., NLTK, Spacy, ROUGE, etc.)?",
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+    {
+        "type": "text",
+        "text": "We provide footnotes with links to all source codes utilized in this work; Sections 3-5",
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+        "type": "text",
+        "text": "D Did you use human annotators (e.g., crowdworkers) or research with human participants?",
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+        "type": "text",
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+    },
+    {
+        "type": "text",
+        "text": "D1. Did you report the full text of instructions given to participants, including e.g., screenshots, disclaimers of any risks to participants or annotators, etc.?",
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+        "type": "text",
+        "text": "D2. Did you report information about how you recruited (e.g., crowdsourcing platform, students) and paid participants, and discuss if such payment is adequate given the participants' demographic (e.g., country of residence)?",
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2023/Composition-contrastive Learning for Sentence Embeddings/f510d1e4-d02c-4d1e-ad49-cbe38f251241_origin.pdf

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2023/Composition-contrastive Learning for Sentence Embeddings/full.md

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+# Composition-contrastive Learning for Sentence Embeddings
+
+Sachin Chanchani and Ruihong Huang
+
+Texas A&M University
+
+{chanchanis, huangrh}@tamu.edu
+
+# Abstract
+
+Vector representations of natural language are ubiquitous in search applications. Recently, various methods based on contrastive learning have been proposed to learn textual representations from unlabelled data; by maximizing alignment between minimally-perturbed embeddings of the same text, and encouraging a uniform distribution of embeddings across a broader corpus. Differently, we propose maximizing alignment between texts and a composition of their phrasal constituents. We consider several realizations of this objective and elaborate the impact on representations in each case. Experimental results on semantic textual similarity tasks show improvements over baselines that are comparable with state-of-the-art approaches. Moreover, this work is the first to do so without incurring costs in auxiliary training objectives or additional network parameters. $^{1}$
+
+# 1 Introduction
+
+Significant progress has been made on the task of learning universal sentence representations that can be used for a variety of natural language processing tasks without task-specific fine-tuning (Conneau et al., 2017, Cer et al., 2018, Kiros et al., 2015, Logeswaran and Lee, 2018, Giorgi et al., 2021a, Yan et al., 2021, Gao et al., 2021, Chuang et al., 2022a). Recent works have shown the potential to learn good sentence embeddings without labeled data by fine-tuning pre-trained language models (PLMs) using the unsupervised framework introduced in SimCLR (Chen et al., 2020), adapted to the natural language processing (NLP) domain. In computer vision (CV), SimCLR exploits a series of transformations (blurs, crops, color distortions, etc.) to construct positive pairs from otherwise unique data points. A cross entropy objective (InfoNCE; Oord et al., 2018) is then applied to minimize distance
+
+between representations originating from the same datum, while maximizing the distance to all other points in a mini-batch. The success of the framework in computer vision is due largely to the diversity of augmentations used for creating positive pairs, which leave the identity of the original example intact while reducing pairwise mutual information in the input space (Tian et al., 2020; Wu et al., 2020; Purushwalkam and Gupta, 2020).
+
+Constructing positive pairs via discrete augmentations have not been effective when applying the same objective to sentence embeddings. In fact, Gao et al. (2021) perform an ablation study of textual augmentations (e.g., cropping, synonym replacement) and find that training on these pairs hurts downstream performance on semantic textual similarity (STS) tasks. Instead, they observe that minimal  $(10\%)$  dropout noise can be used to create positive pairs on-the-fly, and empirically results in stronger representations. This framework relying on nearly identical pairs is known as SimCSE. Since the dropout noise exists as a regularization component of the BERT architecture (Devlin et al., 2019a), explicit augmentations are unnecessary, making it a simple yet effective framework for unsupervised learning of sentence embeddings.
+
+Here, we make a case for composition as augmentation, by exploiting its presence in language as a signal for learning sentence encoders. We conduct a series of experiments to illustrate the impact of training on positive examples derived by averaging representations of textual constituents in the latent space. Following previous works, we benchmark the proposed strategy on 7 STS tasks. Our results show that it is feasible to significantly improve upon SimCSE without making expensive architectural modifications or changing the overall training objective. We hope our findings can inspire new avenues of inquiry in text representation learning that draw on long-standing notions in semantics and linguistics.
+
+![](images/0e00e0822a71731ed2761526e9455b5c5905407be938c1a17e1d6195731f36d3.jpg)  
+(a) subsampling strategies
+
+![](images/1a01938431b13e1268eef078091591ec5201c40d25fdf1325d38b1e65b42d326.jpg)  
+(b) training objective  
+Figure 1: An overview of composition-based contrastive learning. Subsampling strategies used to expand the training dataset are illustrated on the left-hand side, where the bidirectional arrows indicate positive pairs, brackets indicate spans of text, and all other pairs are the standard in-batch negatives. The  $\otimes$  operation is a shorthand for the augmentation strategy integrated with the framework and depicted on the right: along with dropout noise, examples are decomposed in the input space and constituents are independently passed through the encoder. Resultant [CLS] tokens are then aggregated and passed through a linear projector before computing the contrastive loss.
+
+# 2 Background and Related Work
+
+# 2.1 Unsupervised Contrastive Learning
+
+Contrastive learning (Hadsell et al., 2006) aims to learn vector-valued representations of data without relying on annotations. Meaning is derived from these representations based on their proximity to other points in the same space, e.g. two images of dogs will be closer in space than a dog and a chair. Several works have theoretically verified the utility of representations derived from contrastive learning (Arora et al., 2019; Lee et al., 2020; Tosh et al., 2020) under various assumptions; Chen et al. (2020) showed that SimCLR can even outperform supervised counterparts on CV transfer learning benchmarks. In SimCLR (and SimCSE), the learning objective for an example is:
+
+$$
+l _ {i} = - \log \frac {e ^ {\operatorname {s i m} \left(z _ {i} , z _ {i} ^ {+}\right) / \tau}}{\sum_ {j = 1} ^ {N} e ^ {\operatorname {s i m} \left(z _ {i} , z _ {j} ^ {+}\right) / \tau}}, \tag {1}
+$$
+
+where  $z_{i} = f(x_{i}),z_{i}^{+} = f(x_{i}^{+})$  are vector representations of an input and its corresponding augmented positive,  $\tau$  is a temperature hyperparameter,  $sim(.,.)$  is cosine similarity, and  $N$  is batch size.
+
+Drawbacks of InfoNCE. In examination of eq. 1, it is evident that InfoNCE uniformly repels examples in the mini-batch besides the minimally
+
+augmented positive. Consequently, the resulting embeddings show poor group-wise discrimination, especially in language, since it is likely that different examples in the batch can have different relative similarities to a given anchor. Another consequence of the unsupervised InfoNCE objective is dimensional collapse, wherein embedding vectors are mostly differentiated by a small proportion of the feature axes; thus under-utilizing the full expressive capacity of the encoder. This was theoretically posited in Jing et al. (2022). They prove that minimal augmentation, coupled with an over-parameterized network, results in low rank solutions to the unsupervised contrastive objective. We hypothesize that this is closely tied to short-cut learning (Robinson et al., 2021a) — in the context of sentence embeddings, Wu et al. (2022c) observed that spurious features related to the lengths of sentences are relied on to solve the contrastive objective. Such solutions can yield nongeneralizable features that poorly represent data from new domains.
+
+Qualifying the representation space. Wang and Isola (2020) proposed two metrics to measure the quality of embeddings derived through contrastive learning. First, alignment measures on average the proximity of pairs of examples that should be close
+
+in space, i.e. for a set of positive pairs  $p_{pos}$  and their normalized representations  $f(x), f(x^{+})$ :
+
+$$
+\ell_ {\text {a l i g n}} \triangleq \underset {(x, x ^ {+}) \sim p _ {\text {p o s}}} {\mathbb {E}} \| f (x) - f (x ^ {+}) \| ^ {2}. \tag {2}
+$$
+
+Conversely, uniformity measures how scattered the embeddings are upon the unit hypersphere:
+
+$$
+\ell_ {\text {u n i f o r m}} \triangleq \log \underset {x, y \sim p _ {\text {d a t a}}} {\mathbb {E}} e ^ {- 2 \| f (x) - f (y) \| ^ {2}}, \tag {3}
+$$
+
+where  $p_{data}$  denotes the full data distribution. We use these metrics to explore the advantages and drawbacks of various augmentations in contrastive pre-training, similarly to Gao et al. (2021).
+
+# 2.2 Learning Sentence Embeddings
+
+Early works. First approaches to learning sentence embeddings span unsupervised (Kiros et al., 2015; Hill et al., 2016; Logeswaran and Lee, 2018), and supervised (Conneau et al., 2017; Cer et al., 2018; Reimers and Gurevych, 2019) methods which have been studied extensively in the literature. More recent work has focused on unsupervised contrastive learning with the advent of SimCSE (Gao et al., 2021), which passes the same sentence to a language model twice; the independent dropout masks sampled in the two forward passes encode the sentence at slightly different positions in vector space. A cross-entropy objective is then used to maximize the probability of top-1 proximity between positives while uniformly repelling other examples.
+
+Successors to SimCSE. Works that follow SimCSE attempt to improve the framework with auxiliary training objectives (Chuang et al., 2022a; Nishikawa et al., 2022; Zhou et al., 2023; Zhang et al., 2022; Wu et al., 2022b; Wang et al., 2022), verbalized or continuous prompts (Wang et al., 2022; Yuxin Jiang and Wang, 2022), instance generation or weighting strategies (Zhou et al., 2022), momentum encoders with negative sample queues (He et al., 2020), or entirely new parameters with secondary networks (Wu et al., 2022a). Many works combine several of these components, making it difficult to discern their impact in isolation. As the design choices have become more intricate and less parameter-efficient, performance on STS benchmarks has too become saturated.
+
+# 3 Composition-based Contrastive Learning
+
+Our augmentation strategy retains the simplicity and efficiency of SimCSE, as illustrated in Fig-
+
+ure 1. Specifically, it requires just one additional forward pass that is ultimately compensated by a non-trivial reduction in convergence time (§6). Beginning with a corpus of unlabelled sentences  $\{x_{i}\}_{i = 1}^{m}$ , we consider  $x_{i}^{+}$  only in the latent space, as a composition of the representations of  $(x_{i}^{\prime +},x_{i}^{\prime +})$ . A simple (and effective) way to curate  $(x_{i}^{\prime +},x_{i}^{\prime +})$  is to split the tokens of  $x_{i}$  in half, and encode the left and right phrases in independent forward passes through the encoder and linear projector. After obtaining their respective [CLS] token representations  $(z_{i},z_{i}^{\prime +},z_{i}^{\prime +})$ ,  $(z_{i}^{\prime +},z_{i}^{\prime +})$  is aggregated and taken to be the corresponding positive example for  $z_{i}$ . The training objective for a single pair is then the same as in eq. 1, where  $z^{+} = \text{aggregate}(z_{i}^{\prime +},z_{i}^{\prime +})$ . We experiment with aggregation methods in §5, and find that the best approach varies according to the size and type of underlying PLM. In our final model based on BERTbase, we find that this manner of augmentation is especially suitable for the scheme proposed in DirectCLR (Jing et al., 2022), which aims to directly mitigate dimensional collapse by computing the loss from eq. 1 on a subset of the embedding vector axes before backpropagating to the entire representation.
+
+Decomposition as data augmentation. To explain the motivation for decomposing examples in the input space, we can consider an example from the development subset of STS-B labelled as having high semantic similarity:
+
+A man is lifting weights in a garage.  
+A man is lifting weights.
+
+There are two semantic atoms at play in the first text: 1) a man is lifting weights, and 2) a man is in a garage. The similarity between the two texts can only be considered high based on the first atom; lifting weights. It cannot be said that there is a general relation between being in a garage and lifting weights - a garage is equally, if not more likely to be related to cars, parking, or storage, yet this does not preclude a connection between them. It is only through the composition of both atoms that we can relate the two. Thus, there is a need for sentence encoders to learn more generalized phrase representations; to at least implicitly abide by principles of semantic compositionality. The challenge in enforcing this kind of constraint through a contrastive objective is in the choice of data — it would require a corpus where lexical collocations are encountered across a diverse set of contexts.
+
+![](images/db114902f07c910275b14610c5c732f679da2a2d83050c7d6ac174d314613256.jpg)  
+Figure 2:  $\ell_{\mathrm{align}} - \ell_{\mathrm{uniform}}$  tradeoff for subsampling strategies explored in this work. Measurements are taken every 10 training steps on the development subset of STS-B, for 500 steps with  $\mathrm{BERT}_{\mathrm{base}}$ . The ideal trajectory is the negative direction for both axes/metrics.
+
+Subsampling from decomposed inputs. To further examine the effect of decomposition in the input space, we leverage a pre-trained discourse parser $^2$  to extract atomic semantic units from each unique example in the training set; typically simple phrases or clauses. We experiment with 3 kinds of strategies (Figure 1a) to expand the training set, besides considering our augmentation in isolation: let  $C = \{x_{i,k}\}_{k=1}^{c}$  represent the  $c$  non-overlapping phrases extracted from an input  $x_i$ :
+
+- adjacent spans are sampled by taking each unique pair in  $C$  such that there is no overlap between inputs;  
+- overlapping and adjacent spans are sampled by taking (potentially) overlapping pairs in  $C$ ;  
+- overlapping, adjacent, and subsuming spans are sampled by recursively partitioning the elements of  $C$  in half, i.e. maximizing the lexical overlap of extracted input samples.
+
+Impact on the representation space. A consequence of expanding the training set with subsamples is the presence of harder in-batch negatives. Prior work has demonstrated that this is generally beneficial to contrastive learning (Robinson et al., 2021b; Kalantidis et al., 2020; Zhang and Stratos, 2021). Following Gao et al. (2021), we measure the uniformity and alignment of representations obtained for the development set of STS-B to understand the effect of training with additional sub
+
+samples. STS-B is comprised of pairs of sentences accompanied by a score between 1-5 indicating degree of semantic similarity. We take all pairs as  $p_{\mathrm{data}}$ , and pairs with a score greater than 4 as  $p_{\mathrm{pos}}$ . Both metrics are measured every 10 steps for 500 training steps, to understand the direction in which each of our strategies drives the encoder.
+
+As shown in Figure 2, any of the subsampling strategies can bring non-trivial improvements over unsupervised SimCSE in both alignment and uniformity. Specifically, expanding the training set with subsamples (+ adjacent, + overlapping, + subsuming) encourages a more uniform embedding distribution. On the other hand, forgoing subsampling for just the compositional augmentation (naive partition) achieves the better alignment while retaining the uniformity of SimCSE. This is because we leave the self-prediction objective intact, while increasing its difficulty: although subsamples are potentially highly related, positive pairs are only curated from the exact same text. As a consequence, the underlying PLM is forced to effectively distinguish examples with high lexical overlap — which is precisely the intuition underlying DiffCSE Chuang et al. (2022b), and other discriminative pre-training objectives.
+
+# 4 Experiment
+
+Setup. In our experiments, we modify the public PyTorch implementation<sup>3</sup> of SimCSE to support our proposed augmentation and subsampling methods. All of our language models are initialized from pre-trained BERT/RoBERTa checkpoints (Devlin et al., 2019b; Liu et al., 2019), except the randomly-initialized MLP over the [CLS] representation. For all models, we employ the scheme illustrated in Figure 1 and report the best results after training with or without the 3 subsampling strategies. We keep the best checkpoints after evaluating on the development set of STS-B every 125 steps during training. Batch size is fixed at 64 for all models; for base and large sized models, learning rates are fixed to 3e-5 and 1e-5 respectively. Besides those covered in 5, extensive hyperparameter searches were not conducted in this work.
+
+Data. We use the same 1 million randomly sampled sentences<sup>4</sup> as SimCSE for training, be-
+
+<table><tr><td>PLM</td><td>Method</td><td>STS12</td><td>STS13</td><td>STS14</td><td>STS15</td><td>STS16</td><td>STS-B</td><td>SICK-R</td><td>Avg.</td></tr><tr><td rowspan="9">BERTbase</td><td>SimCSE♣</td><td>68.40</td><td>82.41</td><td>74.38</td><td>80.91</td><td>78.56</td><td>76.85</td><td>72.23</td><td>76.25</td></tr><tr><td>L2P-CSR♥</td><td>70.21</td><td>83.25</td><td>75.42</td><td>82.34</td><td>78.75</td><td>77.8</td><td>72.65</td><td>77.20</td></tr><tr><td>DCLR♠</td><td>70.81</td><td>83.73</td><td>75.11</td><td>82.56</td><td>78.44</td><td>78.31</td><td>71.59</td><td>77.22</td></tr><tr><td>MoCoSE◇</td><td>71.58</td><td>81.40</td><td>74.47</td><td>83.45</td><td>78.99</td><td>78.68</td><td>72.44</td><td>77.27</td></tr><tr><td>ArcCSE†</td><td>72.08</td><td>84.27</td><td>76.25</td><td>82.32</td><td>79.54</td><td>79.92</td><td>72.39</td><td>78.11</td></tr><tr><td>PCL‡</td><td>72.74</td><td>83.36</td><td>76.05</td><td>83.07</td><td>79.26</td><td>79.72</td><td>72.75</td><td>78.14</td></tr><tr><td>*SimCSE (w/ comp.)</td><td>72.14</td><td>84.06</td><td>75.38</td><td>83.82</td><td>80.43</td><td>80.29</td><td>71.12</td><td>78.18</td></tr><tr><td>ESimCSE○</td><td>73.40</td><td>83.27</td><td>77.25</td><td>82.66</td><td>78.81</td><td>80.17</td><td>72.30</td><td>78.27</td></tr><tr><td>SNCSE$</td><td>70.67</td><td>84.79</td><td>76.99</td><td>83.69</td><td>80.51</td><td>81.35</td><td>74.77</td><td>78.97</td></tr><tr><td rowspan="9">BERTlarge</td><td>SimCSE♣</td><td>70.88</td><td>84.16</td><td>76.43</td><td>84.50</td><td>79.76</td><td>79.26</td><td>73.88</td><td>78.41</td></tr><tr><td>DCLR♠</td><td>71.87</td><td>84.83</td><td>77.37</td><td>84.70</td><td>79.81</td><td>79.55</td><td>74.19</td><td>78.90</td></tr><tr><td>L2P-CSR♥</td><td>71.44</td><td>85.09</td><td>76.88</td><td>84.71</td><td>80.00</td><td>79.75</td><td>74.55</td><td>78.92</td></tr><tr><td>MoCoSE◇</td><td>74.50</td><td>84.54</td><td>77.32</td><td>84.11</td><td>79.67</td><td>80.53</td><td>73.26</td><td>79.13</td></tr><tr><td>ESimCSE○</td><td>73.21</td><td>85.37</td><td>77.73</td><td>84.30</td><td>78.92</td><td>80.73</td><td>74.89</td><td>79.31</td></tr><tr><td>ArcCSE†</td><td>73.17</td><td>86.19</td><td>77.90</td><td>84.97</td><td>79.43</td><td>80.45</td><td>73.50</td><td>79.37</td></tr><tr><td>*SimCSE (+ subsum.)</td><td>75.10</td><td>86.57</td><td>77.70</td><td>84.72</td><td>80.25</td><td>80.17</td><td>73.21</td><td>79.67</td></tr><tr><td>PCL‡</td><td>74.89</td><td>85.88</td><td>78.33</td><td>85.30</td><td>80.13</td><td>81.39</td><td>73.66</td><td>79.94</td></tr><tr><td>SNCSE$</td><td>71.94</td><td>86.66</td><td>78.84</td><td>85.74</td><td>80.72</td><td>82.29</td><td>75.11</td><td>80.19</td></tr><tr><td rowspan="7">RoBERTabase</td><td>SimCSE♣</td><td>70.16</td><td>81.77</td><td>73.24</td><td>81.36</td><td>80.65</td><td>80.22</td><td>68.56</td><td>76.57</td></tr><tr><td>ESimCSE○</td><td>69.90</td><td>82.50</td><td>74.68</td><td>83.19</td><td>80.30</td><td>80.99</td><td>70.54</td><td>77.44</td></tr><tr><td>L2P-CSR♥</td><td>71.69</td><td>82.43</td><td>74.55</td><td>82.15</td><td>81.81</td><td>81.36</td><td>70.22</td><td>77.74</td></tr><tr><td>DCLR♠</td><td>70.01</td><td>83.08</td><td>75.09</td><td>83.66</td><td>81.06</td><td>81.86</td><td>70.33</td><td>77.87</td></tr><tr><td>*SimCSE (w/ comp.)</td><td>72.56</td><td>83.33</td><td>73.67</td><td>83.36</td><td>81.14</td><td>80.71</td><td>70.39</td><td>77.88</td></tr><tr><td>PCL‡</td><td>71.54</td><td>82.70</td><td>75.38</td><td>83.31</td><td>81.64</td><td>81.61</td><td>69.19</td><td>77.91</td></tr><tr><td>SNCSE$</td><td>70.62</td><td>84.42</td><td>77.24</td><td>84.85</td><td>81.49</td><td>83.07</td><td>72.92</td><td>79.23</td></tr><tr><td rowspan="7">RoBERTalarge</td><td>*SimCSE (w/ comp.)</td><td>72.32</td><td>84.19</td><td>75.00</td><td>84.83</td><td>81.27</td><td>82.10</td><td>70.99</td><td>78.67</td></tr><tr><td>SimCSE♣</td><td>72.86</td><td>83.99</td><td>75.62</td><td>84.77</td><td>81.80</td><td>81.98</td><td>71.26</td><td>78.90</td></tr><tr><td>DCLR♠</td><td>73.09</td><td>84.57</td><td>76.13</td><td>85.15</td><td>81.99</td><td>82.35</td><td>71.80</td><td>79.30</td></tr><tr><td>PCL‡</td><td>73.76</td><td>84.59</td><td>76.81</td><td>85.37</td><td>81.66</td><td>82.89</td><td>70.33</td><td>79.34</td></tr><tr><td>ESimCSE○</td><td>73.20</td><td>84.93</td><td>76.88</td><td>84.86</td><td>81.21</td><td>82.79</td><td>72.27</td><td>79.45</td></tr><tr><td>L2P-CSR♥</td><td>73.29</td><td>84.08</td><td>76.65</td><td>85.47</td><td>82.70</td><td>82.15</td><td>72.36</td><td>79.53</td></tr><tr><td>SNCSE$</td><td>73.71</td><td>86.73</td><td>80.35</td><td>86.80</td><td>83.06</td><td>84.31</td><td>77.43</td><td>81.77</td></tr></table>
+
+Table 1: The performance on STS tasks (Spearman's correlation) for different sentence embedding models. Results are imported as follows —♣: Gao et al. (2021),♥: Zhou et al. (2023),♠: Zhou et al. (2022),◇: Cao et al. (2022), †: Zhang et al. (2022),‡: Wu et al. (2022a), Ⓞ: Wu et al. (2022c), $: Wang et al. (2022), *: our results.
+
+sides incorporating the subsampling strategies from §3. We evaluate on 7 semantic textual similarity tasks: STS 2012-2016, STS-Benchmark, SICK-Relatedness (Agirre et al., 2012, 2013, 2014, 2015, 2016; Cer et al., 2017; Marelli et al., 2014) and report averaged Spearman's correlation across all available test subsets. We employ the modified SentEval<sup>5</sup> (Conneau and Kiela, 2018) package accompanying the source code of SimCSE for fair comparison with other works.
+
+Baselines. We compare our results with many contemporaries: ESimCSE (Wu et al., 2022c), SNCSE (Wang et al., 2022), PCL (Wu et al., 2022a), DCLR (Zhou et al., 2022), ArcCSE (Zhang et al., 2022), MoCoSE (Cao et al., 2022), and L2P-CSR (Zhou et al., 2023). We consider SimCSE (Gao et al., 2021) as our baseline, since we leave its training objective and network architecture intact.
+
+Results. We can observe in Table 1 that our methods bring non-trivial improvements to SimCSE with both BERT encoders, as well as RoBERTa $_{\text{base}}$ . In fact, we achieve an average F1 score within 0.8 points of SNCSE-BERT $_{\text{base}}$  (Wang et al., 2022). SNCSE exploits biases in test sets by engineering hard negatives via explicitly negated sentences — the impact of this strategy is more apparent in the results utilizing RoBERTa, where there is parity in all works besides SNCSE. In the case of  $\text{BERT}_{\text{large}}$ , the gap in performance between our approach and SNCSE is narrower at 0.52 points. A clear failure of the composition-augmented objective presents itself in the results with RoBERTa $_{\text{large}}$ . This could be attributed to poor hyperparameter settings, or a fundamental incompatibility between our approach and the model size/RoBERTa pre-training objective, since other works achieve better results with this PLM.
+
+# 5 Ablation
+
+We ablate several aspects of the approach to understand their impact in isolation. We first consider the subsampling strategy, or lack thereof, in which each model achieves the best STS-B development set performance. These are then tied to each model in subsequent ablations.
+
+Including subsamples. In the process of designing DeCLUTR, Giorgi et al. (2021b) report gains from subsampling more than one anchor per input document. In our experiments, we find that the alignment-uniformity trade-off differs between  $\mathrm{BERT}_{\text {large }}$  and  $\mathrm{BERT}_{\text {base }}$ , i.e. different strategies can be better suited to different PLMs. In Table 2, we show that including subsamples is beneficial to the  $\mathrm{BERT}_{\text {large }}$  PLM, but harmful to  $\mathrm{BERT}_{\text {base }}$ . This is likely a result of the difference in no. of parameters — the smaller PLM may not possess the expressive capacity to distinguish highly related texts without suffering a degeneration in alignment. With  $\mathrm{RoBERTa}_{\text {base }}$ , we observe that subsampling non-overlapping spans gives the best results, whereas none of our strategies appeared compatible with  $\mathrm{RoBERTa}_{\text {large }}$ .
+
+<table><tr><td>PLM</td><td>Method</td><td>STS-B</td></tr><tr><td rowspan="6">BERTbase</td><td>SimCSE</td><td>81.47</td></tr><tr><td>w/ composition</td><td>83.97</td></tr><tr><td>Additional subsampling:</td><td></td></tr><tr><td>+ adjacent</td><td>83.39</td></tr><tr><td>+ overlapping</td><td>83.18</td></tr><tr><td>+ subsuming</td><td>82.97</td></tr><tr><td rowspan="6">BERTlarge</td><td>SimCSE</td><td>84.41</td></tr><tr><td>w/ composition</td><td>84.79</td></tr><tr><td>Additional subsampling:</td><td></td></tr><tr><td>+ adjacent</td><td>84.84</td></tr><tr><td>+ overlapping</td><td>85.01</td></tr><tr><td>+ subsuming</td><td>85.06</td></tr><tr><td rowspan="6">RoBERTabase</td><td>SimCSE</td><td>83.91</td></tr><tr><td>w/ composition</td><td>84.14</td></tr><tr><td>Additional subsampling:</td><td></td></tr><tr><td>+ adjacent</td><td>84.00</td></tr><tr><td>+ overlapping</td><td>84.10</td></tr><tr><td>+ subsuming</td><td>82.92</td></tr><tr><td rowspan="6">RoBERTalarge</td><td>SimCSE</td><td>85.07</td></tr><tr><td>w/ composition</td><td>84.80</td></tr><tr><td>Additional subsampling:</td><td></td></tr><tr><td>+ adjacent</td><td>83.91</td></tr><tr><td>+ overlapping</td><td>82.74</td></tr><tr><td>+ subsuming</td><td>83.33</td></tr></table>
+
+Aggregation method. In SBERT (Reimers and Gurevych, 2019), and in historically effective works such as InferSent (Conneau et al., 2017), PLMs are fine-tuned with a cross entropy loss to predict whether two sentences  $u$  and  $v$  entail or contradict each other. Their pooler is a concatenation of the two sentence embeddings, along with second-order features such as the element-wise difference,  $|u - v|$ . We experiment with these aggregation methods, as well as simpler choices such as element-wise sums/averages. We can see in Table 3 that simply interpolating the embeddings is preferable to other methods for BERT-based encoders. We postulate that this interpolation functions as a form of self-distillation, and amplifies the salience of desirable sparse features correlated with sentential context (Wen and Li, 2021). For RoBERTa, we find that concatenating the first and last halves of the representations is better. Since RoBERTa does not use the next-sentence prediction (NSP) objective, its embeddings will not encode sentential knowledge. Averaging RoBERTa embeddings may not correlate well with real tokens in its vocabulary, whereas concatenating the first and last halves of constituent embeddings retains localized token-level information, making it a better choice in this case.
+
+Table 2: Development set results of STS-B after varying the subsampling strategy on different-sized PLMs.  
+
+<table><tr><td>Aggregation</td><td>STS-B</td></tr><tr><td>BERTbase</td><td></td></tr><tr><td>sum</td><td>83.92</td></tr><tr><td>avg.</td><td>83.97</td></tr><tr><td>concat first &amp; last half</td><td>83.01</td></tr><tr><td>concat + project</td><td>69.24</td></tr><tr><td>concat w/ abs. difference + project</td><td>68.79</td></tr><tr><td>RoBERTa base</td><td></td></tr><tr><td>sum</td><td>84.00</td></tr><tr><td>avg.</td><td>84.08</td></tr><tr><td>concat first &amp; last half</td><td>84.14</td></tr><tr><td>concat + project</td><td>65.02</td></tr><tr><td>concat w/ abs. difference + project</td><td>65.44</td></tr></table>
+
+Table 3: Results of different aggregation methods for composing  $z^{+}$  in the latent space. Results are based on BERT<sub>base</sub> on the development set of STS-B.
+
+Composing  $z$  vs.  $z^{+}$ . In our training objective, there are two sets of sentence representations, one derived from pure dropout noise, and the second by averaging the coordinates of constituent representations. However, for each sentence we can: 1) compose the anchor  $z$  in latent space, which means other in-batch examples are repelled from
+
+a synthetic example's coordinate, 2) compose the positive  $z^{+}$ , which means synthetic coordinates are repelled from representations of real examples, or 3) compose both  $z$  and  $z^{+}$  in the latent space. In Table 4, we can see that with  $\mathrm{BERT}_{\mathrm{base}}$ , we found the best results by directly embedding the anchor sentence, and composing  $z^{+}$  from constituents.
+
+<table><tr><td rowspan="2">BERTbase</td><td>Compose</td><td>z</td><td>z+</td><td>Both</td></tr><tr><td>STS-B</td><td>83.61</td><td>83.97</td><td>83.81</td></tr></table>
+
+Table 4: Differences between having compositional anchors and positives. In the Both case, the model framework is symmetric in that both anchors and positives are composed of constituent representations. Results are based on  $\mathrm{BERT}_{\mathrm{base}}$  on the development set of STS-B.
+
+Number of partitions. Within our framework, we can aggregate the embeddings of two or more phrases. Increasing the number of phrases increases the number of forward passes, and magnifies the impact of dropout noise. We find that partitioning into more than two bins is detrimental to the objective (Table 5), though perhaps this is the case because the evaluation data consists mostly of short-length sentences.
+
+<table><tr><td rowspan="2">BERTbase</td><td>Partitions</td><td>2</td><td>3</td><td>4</td></tr><tr><td>STS-B</td><td>83.97</td><td>83.48</td><td>83.52</td></tr></table>
+
+Hyperparameter  $d_0$ . In our experiments with BERTbase, computing the contrastive loss on a subvector of  $(z_i, z_i^+)$  is complementary to composing  $z_i^+$  in the latent space. When  $d_0 \to d$ , our training objective is the exact same as in all *CSE works, ie. computing the loss on all coordinates of  $(z_i, z_i^+)$ . For BERTbase, we search  $d_0 \in \{192, 256, 384\}$  with the compositional augmentation in isolation (w/ composition); for BERTlarge,  $d_0 \in \{320, 384, 512\}$  with the expanded training set of subsamples (+ subsuming). Our results in Table 6 indicate that taking a subvector to compute the loss is beneficial for BERTbase, but the entire vector is necessary for BERTlarge. With RoBERTa encoders, we aggregate embeddings by concatenating the first and last halves of the phrase embeddings, so  $d_0$  is inapplicable.
+
+Table 5: Impact of splitting examples into more than 2 bins. Results are based on BERTbase with the development set of STS-B.  
+
+<table><tr><td rowspan="2">BERTbase</td><td>d0</td><td>192</td><td>256</td><td>384</td><td>768</td></tr><tr><td>STS-B</td><td>83.88</td><td>84.11</td><td>83.17</td><td>83.97</td></tr><tr><td rowspan="2">BERTlarge</td><td>d0</td><td>320</td><td>384</td><td>512</td><td>1024</td></tr><tr><td>STS-B</td><td>84.61</td><td>84.94</td><td>84.98</td><td>85.06</td></tr></table>
+
+Table 6: Varying the size of the subvector used to compute InfoNCE, as proposed in Jing et al. (2022). Results are based on the development set of STS-B.
+
+# 6 Analysis
+
+Stability and efficiency of training. Successors to SimCSE have incrementally improved STS performance while disproportionately driving up resource requirements. This limits accessibility to practitioners who wish to learn embeddings from their own corpora, perhaps in other languages. Differently, our approach relies on a single additional forward pass while converging much faster than SimCSE. In Figure 3, we compare our  $\mathrm{BERT}_{\mathrm{base}}$  model's evaluation curve to SimCSE's for 1000 training steps in the same setting. We observe that composition as augmentation greatly speeds up convergence, with evaluation metrics plateauing much faster, and more stably than SimCSE. In fact, on a single NVIDIA A100 GPU (40GB), our model can finish training in under 15 minutes.
+
+![](images/137007bf55197b6f465971c7e7037060fb4ba01a5e61406f6134912f19d9971d.jpg)  
+Figure 3: Evaluation curve for  $\mathrm{BERT}_{\mathrm{base}}$ , using dropout noise as augmentation (unsup. SimCSE) and latent space composition (naive partition). The y-axis reflects performance on the development set of STS-B.
+
+Text length as a feature. To investigate the structure of the learned space, In Figure 5, we visualize embeddings of sentences from the development set of STS-B after down-projecting to 2D Euclidean space. We employ UMAP (McInnes et al., 2018) with cosine distance as the metric to preserve local and global topological neighborhoods. The same
+
+![](images/8cee787264457406038a9946edb681af715c46dcbfa2d698c6215a23bbae8314.jpg)  
+Figure 4: A heatmap displaying the pairwise similarities computed by SimCSE, DiffCSE, and our model, with the same underlying PLM  $\mathrm{BERT}_{\mathrm{base}}$  and color scale. Lighter colors indicate higher similarity.
+
+![](images/a6bd2c76da5140c3b302f61aff9e71a5cacd288bb11299a4c24f2e170f85f58e.jpg)  
+(a) unsup. SimCSE
+
+![](images/7a7c8914c5279e180a0719dd2ed6338785385b35ec93bb888e66b16ed1731586.jpg)  
+(b) w/ compositional augmentations  
+Figure 5: 2D UMAP projection of the representations of all sentences from the validation subset of STS-B. Color indicates word count.
+
+parameters are used to compute the embeddings in Figure 5a and 5b, which are derived from dropout noise, and composition-based augmentations (w/ composition) respectively. In Figure 5a, we can observe several clusters of dark points corresponding to shorter sentences. This corroborates our intuition that minimal augmentation to create positive pairs can lead to shortcut learning, wherein text length is relied upon to solve the training objective. In contrast, we see a more scattered distribution of points in Figure 5b, particularly with shorter sen
+
+tences. Coupled with the improved performance on STS tasks, we can conclude that our framework is less prone to learning from spurious correlations.
+
+Learned similarity metric. Returning to the example initially posed in §3, we show in Figure 4 similarity scores for pairs of examples computed by our  $\mathrm{BERT}_{\mathrm{base}}$  model, as well as the corresponding DiffCSE and SimCSE variants. Notice that all three assign higher similarities between anchor: "A man is lifting weights in a garage", and phrases: "A man is lifting weights", "A man in a garage". However, despite their equal constitution in the anchor text, SimCSE incorrectly assesses a higher similarity between the anchor and the first phrase, whereas DiffCSE and our model better capture the equivalence in similarity. The same occurs with anchor: "We store it outside of the house", and texts: "A man is in a garage", "She parked on the driveway"; despite both being unrelated to the anchor, SimCSE spuriously assigns a higher affinity to the former. Overall, we observed parity in the similarity assessments given by our model and DiffCSE, which validates the ability of our approach to remedy the suboptimal alignment of SimCSE without explicit incentive.
+
+# 7 Conclusion
+
+In summary, we proposed a new way to construct positive pairs for unsupervised contrastive learning frameworks relying on pre-trained language models. Our experiments on STS tasks verified the effectiveness of the approach, which achieved competitive results with more complex learning methods, with the benefit of stabilizing and reducing the overall cost of training. We provided empirical studies and qualitative examinations into our approach, verifying its ability to train sentence encoders with better alignment. We believe this work can foster new avenues of inquiry in contrastive learning, especially those that draw upon a human cognition of language.
+
+# 8 Limitations
+
+There are several limitations in this work. First, we have not explored how to make use of composition-based augmentations in the supervised setting. A second limitation is a lack of theoretical grounding in the impact of our latent space composition. Finally, we have not explored interoperability with other training objectives.
+
+# 9 Note on Ethics
+
+We do not believe there are significant ethical considerations stemming from our work, except those that accompany the use of language models and unlabelled corpora in general. Pre-trained language models, including BERT and RoBERTa, are known to learn and reiterate harmful prejudices. Although our pre-training corpus is sourced from Wikipedia and cited in several related works, it cannot be feasibly vetted for explicit or inappropriate content.
+
+# Acknowledgements
+
+We thank the anonymous reviewers for their valuable feedback and input. We also thank Haotian Xu, for his insight and suggestions that shaped the course of this work. We gratefully acknowledge support from National Science Foundation (NSF) via the awards IIS-1942918 and IIS-2127746. Portions of this research were conducted with the advanced computing resources provided by Texas A&M High Performance Research Computing.
+
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+
+# A For every submission:
+
+A1. Did you describe the limitations of your work?
+
+We provided a negative result in Section 4. We also dedicated a section to this end: Section 8.
+
+A2. Did you discuss any potential risks of your work?
+
+Provided in the appendix, although it is mostly a general statement on the use of pre-trained language models and unlabelled corpora.
+
+A3. Do the abstract and introduction summarize the paper's main claims?
+
+Sections 1-2: "Vector representations of natural language are ubiquitous in search, retrieval and reranking applications. Various methods based on contrastive learning have been proposed to learn textual representations from unlabelled data. These approaches maximize agreement between minimally perturbed texts, while uniformly repelling examples within a broader corpus."
+
+Section 3: "Different from previous works, we propose to maximize agreement between sentences and a composition of their semantic constituents. We consider several interpretations of this objective and elaborate the impact on resultant embeddings in each case."
+
+Section 4: "Experimental results on semantic textual similarity tasks demonstrate improvements over baselines that are on par with contemporary approaches."
+
+Sections 1-6: "Moreover, this work is the first to do so without incurring costs in auxiliary training objectives or additional network parameters."
+
+A4. Have you used AI writing assistants when working on this paper?
+
+Left blank.
+
+# B Did you use or create scientific artifacts?
+
+Sections 4-6.
+
+B1. Did you cite the creators of artifacts you used? Sections 4-6.  
+B2. Did you discuss the license or terms for use and / or distribution of any artifacts? Not applicable. Left blank.  
+B3. Did you discuss if your use of existing artifact(s) was consistent with their intended use, provided that it was specified? For the artifacts you create, do you specify intended use and whether that is compatible with the original access conditions (in particular, derivatives of data accessed for research purposes should not be used outside of research contexts)? Not applicable. Left blank.  
+B4. Did you discuss the steps taken to check whether the data that was collected / used contains any information that names or uniquely identifies individual people or offensive content, and the steps taken to protect / anonymize it? Not applicable. Left blank.  
+B5. Did you provide documentation of the artifacts, e.g., coverage of domains, languages, and linguistic phenomena, demographic groups represented, etc.? Not applicable. Left blank.  
+B6. Did you report relevant statistics like the number of examples, details of train / test / dev splits, etc. for the data that you used / created? Even for commonly-used benchmark datasets, include the number of examples in train / validation / test splits, as these provide necessary context for a reader
+
+to understand experimental results. For example, small differences in accuracy on large test sets may be significant, while on small test sets they may not be.
+
+We include a footnote which links to a GitHub page where these statistics are available in detail; see
+
+Section 5. Related works do not report these statistics in the body or appendix of their paper.
+
+# C Did you run computational experiments?
+
+Sections 3-6.
+
+C1. Did you report the number of parameters in the models used, the total computational budget (e.g., GPU hours), and computing infrastructure used?
+
+We utilize BERT and RoBERTa, and cite their papers where these parameters are listed. Additionally, we report on efficiency as a benefit of our approach in Section 6.
+
+C2. Did you discuss the experimental setup, including hyperparameter search and best-found hyperparameter values?
+
+Section 4
+
+C3. Did you report descriptive statistics about your results (e.g., error bars around results, summary statistics from sets of experiments), and is it transparent whether you are reporting the max, mean, etc. or just a single run?
+
+We did not conduct extensive hyperparameter searches and did not repeat experiments due to time and resource constraints.
+
+C4. If you used existing packages (e.g., for preprocessing, for normalization, or for evaluation), did you report the implementation, model, and parameter settings used (e.g., NLTK, Spacy, ROUGE, etc.)?
+
+We provide footnotes with links to all source codes utilized in this work; Sections 3-5
+
+# D Did you use human annotators (e.g., crowdworkers) or research with human participants?
+
+Left blank.
+
+D1. Did you report the full text of instructions given to participants, including e.g., screenshots, disclaimers of any risks to participants or annotators, etc.?
+
+No response.
+
+D2. Did you report information about how you recruited (e.g., crowdsourcing platform, students) and paid participants, and discuss if such payment is adequate given the participants' demographic (e.g., country of residence)?
+
+No response.
+
+D3. Did you discuss whether and how consent was obtained from people whose data you're using/curating? For example, if you collected data via crowdsourcing, did your instructions to crowdworkers explain how the data would be used?
+
+No response.
+
+D4. Was the data collection protocol approved (or determined exempt) by an ethics review board? No response.
+
+D5. Did you report the basic demographic and geographic characteristics of the annotator population that is the source of the data?
+
+No response.

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+# COMpositional Data Augmentation for Abstractive Conversation Summarization
+
+Siru Ouyang $^{1}$ , Jiaao Chen $^{2}$ , Jiawei Han $^{1}$ , Diyi Yang $^{3}$
+
+<sup>1</sup> University of Illinois Urbana-Champaign <sup>2</sup> Georgia Institute of Technology
+
+3 Stanford University
+
+{siruo2,hanj}@illinois.edu，jchen896@gatech.edu，diyiy@stanford.edu
+
+# Abstract
+
+Recent abstractive conversation summarization systems generally rely on large-scale datasets with annotated summaries. However, collecting and annotating these conversations can be a time-consuming and labor-intensive task. To address this issue, in this work, we present a sub-structure level compositional data augmentation method, COMPO, for generating diverse and high-quality pairs of conversations and summaries. Specifically, COMPO first extracts conversation structures like topic splits and action triples as basic units. Then we organize these semantically meaningful conversation snippets compositionally to create new training instances. Additionally, we explore noise-tolerant settings in both self-training and joint-training paradigms to make the most of these augmented samples. Our experiments on benchmark datasets, SAMSum and DialogSum, show that COMPO substantially outperforms prior baseline methods by achieving a nearly  $10\%$  increase of ROUGE scores with limited data. We have publicly released our code at https://github.com/ozyyshr/Compo.
+
+# 1 Introduction
+
+Abstractive conversation summarization, which condenses unstructured conversations into short, concise, and structured text, has greatly benefited from neural generative models trained on largescale annotated data. Researchers have focused on various aspects in conversation summarization, such as hierarchical modeling of conversations (Zhao et al., 2019; Zhu et al., 2020), leveraging dialogue acts (Goo and Chen, 2018), using key phrases and entities (Liu et al., 2019a; Narayan et al., 2021), utilizing topic segments (Liu et al., 2019b), incorporating stage components (Chen and Yang, 2020) and examining discourse relations (Chen and Yang, 2021b; Feng et al., 2020b). However, training these generative models often requires abundant high
+
+<table><tr><td>Conversation</td><td>Actions</td></tr><tr><td>Mary: Sorry, I didn&#x27;t make it to your birthday party : (</td><td>Mary, didn&#x27;t make, party</td></tr><tr><td>Nick: It&#x27;s OK... 
+Mary: I just got so distracted! I forgot it was yesterday!</td><td>Mary, got distracted Mary, forgot</td></tr><tr><td>Nick: do tell! 
+Mary: I met this guy...</td><td>Mary, meet, guy</td></tr><tr><td>Nick: REALLY? I want details :D 
+Mary: Yeah, his name is Kirk and he&#x27;s an architect... 
+Nick: OK, just your type then #file_gif#</td><td>Nick, want details He, is, architect</td></tr><tr><td>Mary: And we ended up spending the whole week together. 
+Nick: A WEEK?</td><td>We, end up, spend Spend, weekend</td></tr><tr><td>Mary: Yeah... It&#x27;s madness, I&#x27;ll tell you more this evening. Are we still on? 
+Nick: You bet we are!</td><td>Mary, will tell, Nick</td></tr><tr><td colspan="2">Summary</td></tr></table>
+
+Mary didn't come to Nick's birthday party. She met an architect named Kirk. Mary and Nick will meet in the evening.
+
+Figure 1: An example of conversation, extracted actions and its paired summary sentences (randomly sampled from SAMSum). The corresponding summary consists of three sentences, each sentence relates to one snippet (illustrated by color).
+
+quality data, i.e., conversation and its paired summary, which is usually time-consuming and labor-intensive to obtain. As a result, it is challenging to apply them to generalized real-world situations where labeled summaries are limited.
+
+A direct solution is to employ data augmentation (DA) (Cubuk et al., 2018; Sennrich et al., 2015; Feng et al., 2021a; Chen et al., 2021a,b; Shen et al., 2020; Yu et al., 2018; Feng et al., 2020a; Miyato et al., 2016) to generate more data. Whereas, directly applying these augmentation methods into the context of conversations usually fails to consider any unique structures of conversations such as speaker information, topic split, and conversation stages (Gritta et al., 2021; Shuster et al.,
+
+2021), which distinguish conversations from general sentences. As a result, they might be limited in creating high-quality and diverse data pairs (Chen and Yang, 2021a). Even though there are a few exceptions (Chen and Yang, 2021a; Liu et al., 2022), they still suffer from diversity and struggle with out-of-distribution compositional generalization (Feng et al., 2021a). One way to alleviate these issues is to recombine different data points to produce novel training data, i.e., compositional data augmentation (Akyurek et al., 2020; Zhang et al., 2022). However, existing compositional DA mainly focus on editing short sentences locally with words/phrases/parsing trees (Akyurek et al., 2020; Zhang et al., 2022), neglecting rich structural information between different sets of utterances in conversations (Chen and Yang, 2020; Cohen et al., 2018), which prevent them from being applied to conversations to compose multiple utterances and generate novel, diverse and high-quality conversational data.
+
+We visualize one example with the topic structures (Xu et al., 2021; Galley et al., 2003; Chen and Yang, 2020) highlighted in Figure 1. The conversation consists of several topics: "opening", "explanation", "plan", etc. And we consider every topic snippet as the basic unit. In the meantime, we extracted the "action" triples (Chen and Yang, 2021b) to represent each topic snippet. With these topic snippets and action representations, we obtain the units for compositional operations. For instance, the blue topic split and summary sentence about the meeting plan could be composed into another conversation by substitution to produce a new conversation and summary that contains a meeting plan. As it shows, by extracting the topic structures from the conversations, sub-components of conversations can be re-organized and re-composed to generate augmented conversation-summary pairs that might not be seen in the original corpus, resulting in more diverse training data.
+
+To this end, we propose COMPO, a compositional data augmentation framework operating at sub-structure level. We leverage the conversation structures (i.e., topic structure(Chen and Yang, 2020) and action triples (Chen and Yang, 2021b)) to produce compositional units for generating diverse conversation-summary pairs. Specifically, we first segment conversation into topic splits with topic modeling models, and then extract "actions triples" (Chen and Yang, 2021b) to represent each
+
+split as actions express specific socially situated identities and activities. With the extracted structures, we view the topic snippets as the basic units and perform selective retrieval based on action triples for compositional substitution to generate novel and diverse conversations. We also pair topic splits with summary sentences so that new summaries would be generated as well. An example of newly augmented conversation and summary could be found in Figure 2(b). To better leverage the newly generated conversation-summary pairs from COMPO, we further explore two noisetolerant methods including a self-training framework that uses the new conversations only, and another joint-training framework that leverages paired data. Empirical studies verify COMPO's effectiveness via both quantitative and qualitative evaluations on SAMSum (Gliwa et al., 2019) and DialogSum (Chen et al., 2021c) compared to prior state-of-the-art data augmentation techniques. We also illustrate COMPO's transferability on a news summarization dataset CNN/Dailymail.
+
+# 2 Related Work
+
+# 2.1 Abstractive Conversation Summarization
+
+Abstractive conversation summarization, as opposed to extraction summarization, requires generative models to have a strong ability in language understanding as the words in the output may not appear in the input. Prior work on abstractive conversation summarization can be divided into two categories. One is to directly apply existing document summarization models to conversations (Shang et al., 2018; Gliwa et al., 2019). The other is to design conversation-tailored methods, for instance, modeling conversations in a hierarchical way (Zhao et al., 2019; Zhu et al., 2020). The rich structured information in conversations has also been leveraged. For example, Goo and Chen (2018) used dialogue acts; Liu et al. (2019a); Narayan et al. (2021) leveraged key phrases and entities. Topic segments (Liu et al., 2019b), stage components (Chen and Yang, 2020) and discourse relations (Chen and Yang, 2021b; Feng et al., 2020b) are also explored to understand conversation context for summarization. However, most approaches in the aforementioned categories focus on neural supervised methods and require abundant data to achieve state-of-the-art performance, which is time-consuming and labor-intensive. In this work, we introduce conversation-specific data augmenta
+
+![](images/f52604a8ab1f9115af620468f859b2f36cc4a2c16c4ad59a59a62248a0904489.jpg)  
+Figure 2: General pipeline of how we leverage topic splits in conversations for compositional augmentation (a), and examples of detailed steps in new data sample construction as stated in Section 3.1 (b).
+
+tion methods to help address data scarcity on paired conversations and summaries.
+
+# 2.2 Data Augmentation in NLP
+
+Data augmentation (DA) is an effective approach to boost the performance of neural supervised models, and has been widely applied in various NLP tasks such as text classification (Wei and Zou, 2019; Zheng et al., 2020), machine reading comprehension (Yu et al., 2018), and machine translation (Sennrich et al., 2015). Commonly seen practices involve designed word/synonym replacement (Kobayashi, 2018; Niu and Bansal, 2018), word deletion/swapping/insertion (Wei and Zou, 2019), back translation (Sennrich et al., 2015; Xie et al., 2019) and compositional augmentation (Jia and Liang, 2016; Andreas, 2019).
+
+However, it is not applicable to directly adopt general DA methods to conversations as they usually neglect conversation structure. By extending general DA methods, Liu et al. (2022) generates synthetic examples by replacing semantically similar text spans in both dialogue and summary. Chen and Yang (2021a) makes an initial attempt for structured conversational DA, but their approach could not guarantee compositional generalization, making it hard to create diverse augmentations. While compositional DA methods proved to be effective in solving the aforementioned issues, they often target plain text (Furrer et al., 2020) and operate locally with words, phrases, or parsing trees with carefully-curated rules (Chen et al., 2020b; Nye et al., 2020). Thus are not suitable for conversa
+
+tions. Our work COMPO fills these gaps by naturally taking conversation structures as units for compositional augmentation. In this way, we not only explore rich structures unique for conversations but also boost the compositional generalization and diversity.
+
+# 3 Methodology
+
+To generate diverse conversation-summary pairs to deal with the data scarcity issue, this section presents a simple and effective compositional data augmentation method COMPO for supervised abstractive conversation summarization. The framework is illustrated in Figure 2.
+
+# 3.1 Compositional Augmentation
+
+Our compositional augmentation method COMPO operates at the sub-structure level of conversations. By extracting different sub-components of conversations and recombining them based on certain orderings, COMPO can produce novel and diverse conversations and their summaries that might not be seen in the original corpus. To get a reasonable granularity of conversation sub-parts, we choose to leverage the topic-view of conversations, building upon prior work on conversation structures (Althoff et al., 2016; Chen and Yang, 2020). Conversations are mostly organized around topics in a coarse-grained structure (Honneth et al., 1988). For instance, a telephone chat could possess the following topics: greetings  $\Rightarrow$  invitation  $\Rightarrow$  plan  $\Rightarrow$  farewell. Thus we propose a compositional inductive approach through composing different
+
+conversation topics (Andreas, 2019). We further employ COMPO to limited data settings in both self-training and joint learning styles.
+
+Topical Split We employ the classic topic segmentation algorithm, C99 (Choi, 2000) to get the topical split of conversations based on inter-sentence similarities. First, we use Sentence-BERT (Reimers and Gurevych, 2019a) to get the representations for each utterance in the conversation  $C = \{u_1, u_2, \dots, u_m\}$ . Then the conversation  $C$  is divided into blocks  $C_{topic} = \{b_1, b_2, \dots, b_n\}$  with C99, where  $b_i$  is one split topic block consisting of several consecutive utterances. Also, people tend to summarize conversations in an almost linear way with a strong temporal dependency (Wu et al., 2021). As a result, it is intuitive to pair each topical split  $C_{topic}$  with summary sentences  $S = \{s_1, \dots, s_n\}$  following Algorithm 1 to obtain  $s_{paired}^i$  for each  $b_i$ .
+
+Action Extraction Previous studies reveal that action information can be an effective building block for models to perform text generation (Daniel et al., 2003; Glavaš and Šnajder, 2014). Actions also help avoid less informative utterances in conversations such as dialog acts (Chen and Yang, 2021b), focusing on more concise ideas of conversation snippets. Therefore, we extract verb-centering phrases (Zhang et al., 2020a) as backbones of topic splits. We use a lightweight tool (Jiao et al., 2023; Zhong et al., 2022a) to extract the actions, where frequently-occurring syntactic patterns are leveraged. Specifically, we extract such syntactic patterns containing verbs as actions. For instance, the most common patterns contain  $n_1$ -nsubj- $v_1$  (e.g., Alice called). More details and concrete examples could be found in Appendix C.
+
+Action-based Composition With previous steps, we obtain a pool  $P$  of topical splits and their corresponding actions  $P = \{(b_{i}, s_{paired}^{i}, A_{i})\}_{i=1:p}$ . With these as units, we are now able to conduct compositional operations. To preserve the conversation structure of the augmented data, the general philosophy here is to "substitute" a selected conversation with similar candidates retrieved from the pool. The problem becomes how to filter out representative and diverse candidates. Inspired by Su et al. (2022), we use the graph-based method Vote-k to ensure similar demonstrations and total coverage. We first compute a vector representa
+
+tion for each topical unit using Sentence-BERT (Reimers and Gurevych, 2019b) by averaging the resulting vectors over the input. We then use those embeddings to create a directed graph  $G = (V,E)$ . For each vertex  $v\in V$ , edges are connected to its  $k$ -nearest neighbors in terms of cosine similarity. For every remaining vertex  $u$  (contrary to chosen units) in the graph, we score them using
+
+$$
+\operatorname {s c o r e} (u) = \sum_ {v \in \{v | (v, u) \in E, v \in U \}} s (v), \tag {1}
+$$
+
+where  $s(v) = \rho^{|\{l_{i}nL|(v,l)\in E\}|}, \rho > 1$ . In every iteration, we choose nodes that have the largest score, i.e., satisfy  $\text{argmax}_{u \in U} \text{score}(u)$ . The chosen nodes are excluded from  $U$ .
+
+In order to produce fluent conversations with newly generated compositional units, we leverage a pre-trained generation model. Concretely, we pre-train a sequence-to-sequence model in the following steps: (1) randomly select a topical split  $b_{i}$  from the original conversation, (2) get the corresponding set of actions  $A = \{a_{1},\dots,a_{k}\}$  for  $b_{i}$ , (3) mask  $b_{i}$  from the original conversation, (4) take extracted actions  $A$  and unmasked the rest of the conversation as input. Then we use this selected topical split  $b_{i}$  as the target output for the model. For example, the input and output of the pre-trained generation model could be
+
+- Input: we'll meet at arrivals  $\langle \mathrm{s} \rangle$  Corina: Are you at the airport? <mask>  
+- Output: Regina: sure, waiting for K. Jorge: Good! we'll meet at the arrivals then.
+
+where “we’ll meet at arrivals” is the combination of action triples, “</s>” is used to separate triples from conversations, and “<mask>” is what we want to predict as the output. If there are multiple actions, we use ‘|’ token to split them.
+
+# 3.2 Noise-tolerant Training Settings
+
+Our model is trained on two noise-tolerant settings to further boost the performance with limited data. In self-training setting, only the newly generated conversations are incorporated, and a teacher model is utilized to predict pseudo summaries. In joint-training setting, we test the framework with paired data, i.e., with newly generated conversations and summaries.
+
+Algorithm 1: Match topical split and summary sentences  
+Input: A topical split of conversation  $b_i \in C_{topic}$ , a summary  $S$  containing  $n$  sentences, sliding window size interval [a,b]  
+Output: Corresponding summary sentences  $S_{paired}^i$  for  $b_i$   
+1 for  $w = a$  to  $b$  do  
+2 for  $j = 1$  to  $|\mathcal{C}| - w$  do  
+3 cand=  $S_{j,j + w}$   
+4 r(j,w) ← ROUGE(cand, b_i)  
+5 W ← W ∪ cand  
+6 j ← j + w/2  
+7 w ← w + 1  
+8 jbest, wbest ← argmaxj, wr(j, w)  
+9  $S_{paired}^i \gets S_{jbest,(jbest + wbest)}$
+
+Algorithm 2: Self-training  
+1 Train a base model  $f_{\theta}$  with labeled data  $D_{l} = \{(c_{i}^{l},s_{i})\}_{i = 1:n}$    
+2 for  $i = 1$  to  $K$  do   
+3 Predict pseudo summaries  $s_i^u$  for unlabeled conversations  $D_{u} = \{(c_{i}^{u})\}_{i = 1:m}$    
+4 Select a subset of  $S = D_{l}\cup D$  where  $D = \{c_i^u,s_i^u\}_{i = 1:a}$    
+5 train a new model  $f_{\theta}$  on  $S\cup D_l$
+
+# 3.2.1 Self-training with Augmented Data
+
+The detailed algorithm for self-training (He et al., 2019) is displayed in Algorithm 2. Specifically, the algorithm starts with a parallel dataset  $D_{l} = \{(c_{i}^{l}, s_{i})\}_{i=1:n}$  and the unlabeled dataset  $D_{u} = \{(c_{i}^{u})\}_{i=1:m}$  where  $m >> n$ . In a semi-supervised setting, a teacher model  $f_{\theta}$  is first trained on  $D_{l}$ , and is further used to predict pseudo summaries for unlabeled data. The pseudo data  $D$  and  $D_{l}$  are combined and we sample a subset of them for training another model  $f_{\theta'}$ . Here  $\theta$  is the parameter from the teacher model from the last iteration and fixed within the current iteration. This process is iterated for  $K$  times. The unsupervised loss  $L_{u}$  from unlabeled conversations is defined as:
+
+$$
+L _ {u} = - \mathbb {E} _ {c \sim D ^ {u}} \mathbb {E} _ {c ^ {\prime} \sim \mathrm {C o m p o} (c)} \log P \left(f \left(c; \theta^ {\prime}\right) \mid f \left(c ^ {\prime}; \theta\right)\right) \tag {2}
+$$
+
+Note that we choose the number of subset selections so that the total training instances are twice the original dataset.
+
+# 3.2.2 Joint Training with Augmented Pairs
+
+Apart from using unlabeled conversations for self-training, we can also generate pseudo summaries for augmented conversations, and perform joint training to see the effect.
+
+New Summary Generation For each newly generated conversation, we leverage a pre-trained generation model similar to the model described in Section 3.1, and generate a new summary conditioned on summary context and the action triples.
+
+Finally, the model is trained on a combination of the original samples and augmentation samples to obtain a trade-off between regularization and noise injection. The total training objective is:
+
+$$
+L = \mathbb {E} _ {(c, s) \in D ^ {l}} \log P (s | c) + \gamma \mathbb {E} _ {\left(c ^ {\prime}, s ^ {\prime}\right) \in D ^ {\prime}} \log P \left(s ^ {\prime} \mid c ^ {\prime}\right) \tag {3}
+$$
+
+where  $\gamma$  is the weight of the augmented samples.
+
+# 4 Experiments
+
+# 4.1 Datasets
+
+To evaluate the effectiveness of our proposed framework, we conduct experiments on two benchmarks of conversation summarization: SAMSum (Gliwa et al., 2019) and DialogSum (Chen et al., 2021c) which contain open-domain daily-chat conversations and diverse task-oriented conversations for real-life scenario. More detailed data statistics could be found in Table 7 in the Appendix.
+
+# 4.2 Evaluation Metrics and Baselines
+
+Evaluation Metrics We use the standard ROUGE metric $^{1}$  (Lin, 2004) as automatic evaluation metrics, including ROUGE-1, ROUGE-2, and ROUGE-L for both SAMSum and DialogSum datasets. Note that the ROUGE scores might vary with different tookits.
+
+Baselines with different augmentation strategy To demonstrate the superiority of our proposed compositional augmentation over previous data augmentation methods, we take several state-of-the-art and representative data augmentation methods as baseline models. Specifically, they are tailored or suitable for conversation augmentation in different granularity including token-level, sentencelevel and context-level:
+
+- BART (Lewis et al., 2020) is the state-of-the-art pre-trained model for summarization. It also indicates training without augmentation. We use BART-base as well as BART-large as our base models for scalability.
+
+<table><tr><td rowspan="2">Model</td><td colspan="3">1%-147</td><td colspan="3">5%-735</td><td colspan="3">full-14732</td></tr><tr><td>R-1</td><td>R-2</td><td>R-L</td><td>R-1</td><td>R-2</td><td>R-L</td><td>R-1</td><td>R-2</td><td>R-L</td></tr><tr><td>BARTbase</td><td>42.36</td><td>18.63</td><td>38.44</td><td>45.56</td><td>20.44</td><td>41.27</td><td>51.74</td><td>26.46</td><td>48.72</td></tr><tr><td>BARTlarge</td><td>48.26</td><td>22.59</td><td>43.93</td><td>50.01</td><td>23.97</td><td>45.73</td><td>53.12</td><td>27.95</td><td>49.15</td></tr><tr><td colspan="10">self-training</td></tr><tr><td>SRbase</td><td>43.88</td><td>19.96</td><td>39.56</td><td>46.54</td><td>21.60</td><td>41.52</td><td>51.81</td><td>26.44</td><td>48.78</td></tr><tr><td>BTbase</td><td>44.49</td><td>20.14</td><td>40.38</td><td>45.96</td><td>21.74</td><td>41.58</td><td>52.06</td><td>26.32</td><td>49.22</td></tr><tr><td>USbase</td><td>44.74</td><td>20.18</td><td>40.62</td><td>46.28</td><td>22.34</td><td>42.06</td><td>52.24</td><td>26.50</td><td>49.28</td></tr><tr><td>Semi-CODA†</td><td>44.34</td><td>19.22</td><td>41.16</td><td>46.21</td><td>21.02</td><td>42.85</td><td>50.08</td><td>24.62</td><td>46.89</td></tr><tr><td>COMPObase</td><td>45.42↑3.06</td><td>21.23↑2.60</td><td>41.42↑2.98</td><td>48.03↑2.47</td><td>24.00↑3.56</td><td>44.91↑3.64</td><td>52.90↑1.16</td><td>27.03↑0.57</td><td>49.64↑0.92</td></tr><tr><td>COMPOlarge</td><td>49.78↑1.62</td><td>24.65↑2.06</td><td>45.41 ↑1.48</td><td>51.66↑1.65</td><td>26.55↑2.58</td><td>47.59↑1.86</td><td>53.56↑0.44</td><td>28.66↑0.71</td><td>50.04 ↑0.89</td></tr><tr><td colspan="10">joint-training</td></tr><tr><td>SRbase</td><td>42.93</td><td>19.11</td><td>38.86</td><td>45.89</td><td>20.97</td><td>41.40</td><td>51.69</td><td>26.40</td><td>48.74</td></tr><tr><td>BTbase</td><td>43.79</td><td>19.54</td><td>39.21</td><td>45.91</td><td>20.94</td><td>41.17</td><td>51.76</td><td>26.42</td><td>48.70</td></tr><tr><td>USbase</td><td>43.96</td><td>19.67</td><td>39.30</td><td>46.06</td><td>21.54</td><td>41.63</td><td>51.83</td><td>26.49</td><td>48.81</td></tr><tr><td>COMPObase</td><td>44.89↑2.53</td><td>20.64↑2.01</td><td>40.58↑2.14</td><td>47.07↑1.51</td><td>22.56↑2.12</td><td>43.29↑2.02</td><td>52.38↑0.64</td><td>26.69↑0.23</td><td>48.95↑0.23</td></tr><tr><td>COMPOlarge</td><td>49.14↑0.88</td><td>23.45↑0.86</td><td>44.35↑1.42</td><td>51.06↑1.05</td><td>24.67↑0.70</td><td>45.80↑0.07</td><td>53.26↑0.24</td><td>28.32↑0.37</td><td>49.73↑0.58</td></tr></table>
+
+Table 1: Results on SAMSum test set where  $1\%$  (147),  $5\%$  (735) and all (14732) of the conversations and summaries are used for training respectively. COMPO<sub>base</sub> and COMPO<sub>large</sub> denotes COMPO with BART<sub>base</sub> and BART<sub>large</sub>. Better performances in each settings are highlighted. † results reported in (Chen and Yang, 2021a).
+
+- Synonym Replacement (SR) (Kumar et al., 2020; Kobayashi, 2018) is a token-level approach, which keeps the semantic meaning unaffected by replacing a random word in the conversation with its synonyms.  
+- Back Translation (BT) (Chen et al., 2020a; Xie et al., 2019) is a utterance-level method, which firstly translates an selected utterance into an intermediate language, and then translates it back to the original language.  
+- Utterance Swapping (US) (Wang et al., 2021) is a context-level manner, which perturbs discourse relations to create augmented conversations. It first randomly selects two utterances in the conversation, and then swaps them.  
+- Semi-CODA (Chen and Yang, 2021a) is a two-stage noisy self-supervised framework that synthesizes a set of augmentation techniques, including random swapping and deletion, dialogue-acts-guided insertion, and conditional-generation-based substitution.
+
+# 4.3 Implementation Details
+
+During the training process, the encoder and decoder share the same set of parameters, which are initialized using a pre-trained BART (Lewis et al., 2020). The maximum iteration for self-training  $K$  is set to 5. During training, we used a batch size of 16 for 10 iterations with a 3e-5 learning rate. To ensure the model receives the same amount of
+
+data for each training epoch, we replicate the original dataset to the same size as the augmentation datasets in the training stage. It takes around 5 hours to train on 4 A6400 GPUs for a full dataset under self-training, and 1 hour for the limited data setting. For joint training, it takes around 20 minutes for limited data, and 2 hours for full data. Note that the total amount for training (2x of the original samples) is equal for both self-training and joint training. Therefore, it is fair to directly compare those results. We take the average of 5 runs on random seeds for the main results shown in Table 1 and Table 2.
+
+# 4.4 Results
+
+Table 1 and Table 2 show the results on SAMSum and DialogSum $^2$  benchmark datasets under both limited-data and full-data settings. Based on the numbers, we have the following observations:
+
+Different amount of data: When all the labeled data are used for training, COMPO shows performance gains compared to all the baseline methods, suggesting our method's effectiveness as it works well even when a large number of data are used in the training process. With the limited data setting, we can see that performance gains are even larger compared with the full data setting. When less labeled data (i.e.,  $1\%$  of the total data) are incorporated into the training process, the performance increase proves to be larger. Specifically, COMPO achieved an increase of  $7.2\%$  on Rouge-1,  $14.0\%$
+
+<table><tr><td rowspan="2">Model</td><td colspan="3">1%-125</td><td colspan="3">5%-623</td><td colspan="3">full-12460</td></tr><tr><td>R-1</td><td>R-2</td><td>R-L</td><td>R-1</td><td>R-2</td><td>R-L</td><td>R-1</td><td>R-2</td><td>R-L</td></tr><tr><td>BARTbase</td><td>40.11</td><td>14.06</td><td>34.79</td><td>42.27</td><td>15.53</td><td>36.79</td><td>45.86</td><td>19.75</td><td>41.16</td></tr><tr><td>BARTlarge</td><td>41.24</td><td>15.08</td><td>35.56</td><td>43.96</td><td>17.30</td><td>38.23</td><td>47.28</td><td>21.18</td><td>44.83</td></tr><tr><td colspan="10">self-training</td></tr><tr><td>SRbase</td><td>41.08</td><td>14.85</td><td>35.63</td><td>43.27</td><td>16.61</td><td>37.54</td><td>45.93</td><td>19.80</td><td>41.24</td></tr><tr><td>BTbase</td><td>41.38</td><td>15.23</td><td>36.21</td><td>43.24</td><td>16.83</td><td>37.64</td><td>46.00</td><td>19.87</td><td>41.30</td></tr><tr><td>USbase</td><td>41.56</td><td>15.42</td><td>36.18</td><td>43.25</td><td>17.11</td><td>37.50</td><td>46.15</td><td>20.04</td><td>41.35</td></tr><tr><td>COMPObase</td><td>43.13↑3.02</td><td>16.21↑2.15</td><td>37.40↑2.61</td><td>45.34↑3.07</td><td>18.09↑2.56</td><td>38.42↑1.63</td><td>46.81↑0.95</td><td>20.61↑0.86</td><td>42.21↑1.05</td></tr><tr><td>COMPOlarge</td><td>43.61↑2.37</td><td>16.81↑1.73</td><td>37.73↑2.17</td><td>45.80↑1.84</td><td>19.03↑1.73</td><td>39.76↑1.53</td><td>47.94↑0.66</td><td>21.67↑0.49</td><td>45.10↑0.27</td></tr><tr><td colspan="10">joint-training</td></tr><tr><td>SRbase</td><td>40.70</td><td>14.57</td><td>35.22</td><td>42.45</td><td>16.31</td><td>36.73</td><td>45.80</td><td>19.74</td><td>41.21</td></tr><tr><td>BTbase</td><td>40.76</td><td>14.63</td><td>35.42</td><td>42.51</td><td>16.42</td><td>36.69</td><td>45.90</td><td>19.83</td><td>41.26</td></tr><tr><td>USbase</td><td>41.03</td><td>15.12</td><td>35.89</td><td>42.67</td><td>16.59</td><td>36.84</td><td>45.94</td><td>19.87</td><td>41.19</td></tr><tr><td>COMPObase</td><td>41.96↑1.85</td><td>15.80↑1.74</td><td>36.59↑1.80</td><td>43.71↑1.44</td><td>17.27↑1.74</td><td>37.11↑0.32</td><td>46.42↑0.56</td><td>20.21↑0.46</td><td>41.65↑0.49</td></tr><tr><td>COMPOlarge</td><td>42.96↑1.72</td><td>16.53↑1.45</td><td>37.38↑1.82</td><td>44.64↑0.68</td><td>18.38↑1.08</td><td>39.00↑0.77</td><td>47.73↑0.45</td><td>21.42↑0.24</td><td>44.91↑0.08</td></tr></table>
+
+Table 2: Results on DialogSum test set where  $1\%$  (125),  $5\%$  (623) and all (12460) of the conversations and summaries are used for training respectively. COMPO<sub>base</sub> and COMPO<sub>large</sub> denotes COMPO with BART<sub>base</sub> and BART<sub>large</sub>. Better performances in each settings are highlighted.
+
+on Rouge-2, and  $7.8\%$  on Rouge-L compared with BART-base when  $1\%$  of the labeled data is used.
+
+Different backbone models: We also test COMPO's scalability using both the BART<sub>base</sub> and BART<sub>large</sub> as backbone pre-training models. Performance increases for both two PLMs on two datasets. With BART<sub>base</sub>, our method even outperforms BART<sub>large</sub> baseline on SAMSum. With BART<sub>large</sub>, COMPO also achieves consistent performance gains, which means COMPO is scalable to different backbone models. Not surprisingly, the increase is much larger with BART<sub>base</sub>.
+
+Different training settings: COMPO improves the performance of summarization under both self-training and joint-training settings. While self-training (leverage teacher model to predict pseudo summaries and trained for more iterations) surpasses joint-training, we can see that our newly generated summary labels are feasible to improve the performance over baseline models.
+
+Different datasets: Our model also performs well on DialogSum, which is a more abstractive, open-domain, and spoken analogous (Chen et al., 2021c) summarization dataset. We can infer that COMPO has great summarization ability when it comes to more challenging tasks.
+
+# 4.5 Human Evaluation
+
+We conducted human evaluations to assess the summaries generated by different models trained on  $1\%$  (147) conversations from the SAMSum dataset and  $1\%$  (125) conversations from the DialogSum dataset. Specifically, we asked annotators from
+
+Amazon Mechanical  $\mathrm{Turk}^3$  to rank summaries on a scale of 1 (the least preferred) to 3 (the most preferred). Summaries to be ranked are generated from  $BART_{base}$ ,  $\mathrm{COMPO}_{base}$  in self-training (COMPOSF) and joint-training (COMPO-jt) respectively. To avoid bias, we randomly sample summaries generated from 100 conversations for each dataset and perturb them for the workers to rank. Workers were paid  $0.1\$$  for each ranking task. Every summary was ranked by three workers, and the rank for every summary was aggregated by majority voting. The Intra-Class Correlation (Koo and Li, 2016) (ICC1k) was 0.573, indicating moderate agreement. As shown in Figure 3, COMPO-sf and COMPO-jt both surpass the BART-base by a large margin on SAMSum and DialogSum datasets. Additionally, we observe larger gaps in terms of the scores for three models on DialogSum dataset. More details for human evaluation including interface design, scheduling details, and how we process with obtained rank scores could be found in Appendix D. Case studies for these three models could be found in Appendix E, where we provide the original conversation and the ranked three summaries.
+
+# 5 Analysis
+
+# 5.1 Automatic Quality Analysis of Summaries
+
+We adopt a multi-dimensional evaluator (Zhong et al., 2022b) to evaluate the quality of our summaries automatically, in terms of coherence (coh.), consistency (con.), fluency (flu.), and relevance (rel.). Summaries generated with BART<sub>base</sub>,
+
+![](images/45c4793983493c5fbb34f91fd91319403c0e91dd9ecbda98c0de1f187c048d49.jpg)
+
+Figure 3: Human evaluation results in terms of average scores. A larger score indicates better performance.  
+
+<table><tr><td>Model</td><td>coh.</td><td>con.</td><td>flu.</td><td>rel.</td><td>overall</td></tr><tr><td>BARTbase</td><td>0.868</td><td>0.861</td><td>0.909</td><td>0.744</td><td>0.846</td></tr><tr><td>COMPO-jt</td><td>0.873</td><td>0.860</td><td>0.916</td><td>0.763</td><td>0.853</td></tr><tr><td>COMPO-sf</td><td>0.868</td><td>0.867</td><td>0.923</td><td>0.773</td><td>0.858</td></tr></table>
+
+Table 3: Automatic experiment results for the quality of generated summaries in terms of coherence, consistency, fluency, and relevance.
+
+COMPO-sf, and COMPO-jt are taken for comparison. As shown in Table 3, both COMPO-jt and COMPO-sf achieve better results against the baseline model, with  $8\%$  and  $14\%$  improvement on overall scores respectively. We also observe the largest performance increase on relevance. This indicates that summaries generated with COMPO are more factually consistent with conversations and accurately reflect important information.
+
+# 5.2 Transferability to other Datasets
+
+To test whether COMPO is transferable to other input forms and datasets, we conduct experiments on CNN/Dailymail (Hermann et al., 2015), a traditional text summarization dataset from the news report. We treat sentences in articles as utterances in conversations and conduct exactly the same operations for augmentation. Table 4 shows the result on CNN/Dailymail in the limited data setting with only  $1\%$  (2871) data used. Consistent performance is achieved with evaluations in Section 4.4, our introduced COMPO significantly outperforms the baseline models. This verifies an additional generalization ability of our augmentation framework as well as the newly generated labels.
+
+# 5.3 Ablation Studies
+
+To see the effect of different components in COMPO, we conduct ablation studies on SAMSum dataset under the limited data setting, where  $1\%$
+
+<table><tr><td>Model</td><td>R-1</td><td>R-2</td><td>R-L</td></tr><tr><td>BARTbase</td><td>37.63</td><td>15.38</td><td>35.09</td></tr><tr><td>COMPO-jt</td><td>38.58</td><td>16.34</td><td>36.24</td></tr><tr><td>COMPO-sf</td><td>39.50</td><td>16.79</td><td>36.87</td></tr></table>
+
+Table 4: Results on CNN/Dailymail dataset in the limited data setting.  
+
+<table><tr><td>Model</td><td>R-1</td><td>R-2</td><td>R-L</td></tr><tr><td>COMPO</td><td>45.42</td><td>21.23</td><td>41.42</td></tr><tr><td>Selective Retrieval → K-NN</td><td>44.91</td><td>20.67</td><td>40.71</td></tr><tr><td>Actions → Conversation Snippets</td><td>44.86</td><td>20.43</td><td>40.60</td></tr><tr><td>Actions → SRL</td><td>44.17</td><td>19.82</td><td>40.20</td></tr><tr><td>Action Extraction → OpenIE</td><td>45.03</td><td>20.91</td><td>40.96</td></tr><tr><td>COMPO → DialogGPT</td><td>44.30</td><td>20.26</td><td>40.48</td></tr></table>
+
+Table 5: Ablation studies on SAMSum dataset of different components in COMPO.
+
+labeled data are used for training.
+
+Number of iterations  $K$  in self-training We explored how performance changes with the progress of self-training. Specifically, we use the number of iterations to identify. As shown in Table 6, the performance continues to increase until iteration 3, and then starts to fall. This suggests that the model could indeed learn from the teacher model as it generates the pseudo summaries as labels.
+
+Effect of different components We tested the performance of using the traditional OpenIE method for action extraction. As shown in Table 5, COMPO, which leverages more diverse patterns for action extraction and syntactic structure, outperforms OpenIE. More examples of action extraction are listed in Appendix B.
+
+We also conduct experiments with respect to alternative choices of action. Firstly, representations for conversation snippets are directly used for selective retrieval instead of extracted actions. Results show that using conversation snippets underperforms much, and even demonstrates the similar performance of  $BT$ . The potential reason is that directly using conversation snippets may bring some noise such as stopwords, pronouns, etc., instead of focusing on the core idea of a conversation snippet. We also try other structures such as Semantic Role Labeling (SRL) (Carreras and Marquez, 2005), which is known to extract the predicate, theme, and recipient. As shown in Table 5, overall performance is not comparable to actions. We interpret this result from the following aspects: (i) num of SRL (avg 29.80) is far more than actions (avg 12.32) since SRL contains many prevalent but
+
+<table><tr><td>Number</td><td>R-1</td><td>R-2</td><td>R-L</td></tr><tr><td>BARTbase</td><td>42.36</td><td>18.63</td><td>38.44</td></tr><tr><td>Iteration 0</td><td>43.98</td><td>18.97</td><td>39.72</td></tr><tr><td>Iteration 1</td><td>44.17</td><td>19.82</td><td>40.20</td></tr><tr><td>Iteration 2</td><td>44.85</td><td>20.80</td><td>40.77</td></tr><tr><td>Iteration 3</td><td>45.42</td><td>21.23</td><td>41.42</td></tr><tr><td>Iteration 4</td><td>44.75</td><td>20.63</td><td>40.57</td></tr></table>
+
+Table 6: Experiment results regarding different iterations in self-training setting.
+
+noisy verbs such as "am". (ii) average length of the extracted span is very long (sometimes even containing clauses) for SRL (avg 8.37) compared with actions (avg 4.74). Finally, we show the effect of selective retrieval against K-NN search. Unsurprisingly, K-NN search fails to outperform selective retrieval. This is because selective retrieval brings more coverage and diversity.
+
+Augmentation with DialogGPT To investigate how COMPO surpasses model pre-trained on rough data as DA techniques, we experiment with DialogGPT (Zhang et al., 2020b). It is pre-trained on Reddit comment chains, which is easy to collect compared with human-labeled data. We follow the settings in (Feng et al., 2021b) and apply DialogGPT to generate the responses for each selected utterance. Then we treat them as newly augmented data samples for further training. As shown in Table 5, employing DialogGPT underperforms COMPO. The reasons are two folds: (i) DialogGPT fails to consider the structural and compositional information in the conversations, but rather generates plain responses. (ii) DialogGPT is pre-trained without speaker information, and thus may not be sensitive enough to tell the specific actions that happened.
+
+# 6 Conclusion
+
+This paper introduced a simple and effective compositional data augmentation method for abstractive conversation summarization. We leverage the topical view of conversations and treat them as the units for compositional operation. Extensive experiments on benchmark datasets demonstrate that COMPO significantly outperforms prior state-of-the-art baselines in terms of both quantitative and qualitative evaluation, through generating compositional and diverse augmented data. Our method has key implications for designing augmentation techniques for low-resource dialogue-related tasks.
+
+# Limitations
+
+Our work on COMPO is subject to multiple limitations. The first limitation is around its scope when probing compositional operations. We only explored compositional substitution for topical snippets in conversations as an initial effort. However, there are many other types of conversation structures that can be leveraged such as conversation stages or specific discourse acts. Second, we used a set of external tools to process the conversations for augmentation, such as the use of C99 for topic split and action extraction. Although we choose to select widely-used tools with high precision, error cascades are inevitable. Furthermore, our approach may not be applicable to low-resourced languages since these pre-processing tools may not be available even in the first place for these low-resourced contexts. We urge future work to further work on this line of compositional data augmentation without any dependencies on external software.
+
+# Ethics Statement
+
+Despite the recent success of pre-trained language models in abstractive conversation summarization, they mostly rely on large-scale annotated data. This leads to a major concern about the labor-intensive and time-consuming annotating process, which might not be available for small research groups or institutions with relatively fewer resources; we hope that COMPO can be an initial effort in mitigating this issue. Our work also sheds light on a more general framework to deal with data scarcity issues, making summarization systems more applicable to real-world scenarios where annotations are often hard to get. Overall, we do not foresee any major risk or negative societal impact of our work. However, like any other machine learning model, the proposed framework may not be completely accurate and should be used with caution in real-world applications. To encourage reproducibility, we provide our source code in the supplementary material. The details of our framework are described in Section 3. The hyperparameters for our model are discussed in Section 4.1 and Section 4.3. The SAMSum and DialogSum datasets we experiment with are also publicly available resources.
+
+# Acknowledgements
+
+We thank members of the SALT Lab, and reviewers for their helpful feedback.
+
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+
+# A Statistics for Datasets
+
+Here we provide the detailed statistics about the two datasets, SAMSum and DialogSum.
+
+SAMSum contains open-domain daily-chat conversations in English written by linguists, each of which is annotated with summary by language experts. The topics contain arranging meetings, planning travels, chit-chat and so on. There are 14,732 dialogue-summary pairs for training, 818 and 819 instances for validation and test, respectively.
+
+DialogSum is a large-scale dataset for real-life scenario conversations. It contains diverse task-oriented conversations. Specifically, speakers in DialogSum are denoted with \#Person_1# and \#Person_2\#. The public dataset consists of 12,460 training samples. The validation and test set have equal 500 instances.
+
+As could be inferred from Table 7, the number of participants for DialogSum are mostly 2, while SAMSum could have multi-party conversations. Also, the number of turns and reference length in DialogSum is shorter, which means that the information flow in DialogSum are relatively compact.
+
+<table><tr><td rowspan="2">Dataset</td><td rowspan="2">Split</td><td colspan="3">Number of Participants</td><td colspan="3">Number of Turns</td><td colspan="3">Reference Length</td></tr><tr><td>Mean</td><td>Std</td><td>Interval</td><td>Mean</td><td>Std</td><td>Interval</td><td>Mean</td><td>Std</td><td>Interval</td></tr><tr><td rowspan="3">SAMSum</td><td>Train 14732</td><td>2.40</td><td>0.83</td><td>[1,14]</td><td>11.17</td><td>6.45</td><td>[1,46]</td><td>23.44</td><td>12.72</td><td>[2,73]</td></tr><tr><td>Dev 818</td><td>2.39</td><td>0.84</td><td>[2,12]</td><td>10.83</td><td>6.37</td><td>[3,30]</td><td>23.42</td><td>12.71</td><td>[4,68]</td></tr><tr><td>Test 819</td><td>2.36</td><td>0.83</td><td>[2,11]</td><td>11.25</td><td>6.35</td><td>[3,30]</td><td>23.12</td><td>12.20</td><td>[4,71]</td></tr><tr><td rowspan="3">DialogSum</td><td>Train 12460</td><td>2.01</td><td>0.13</td><td>[2,7]</td><td>9.49</td><td>4.16</td><td>[2,65]</td><td>22.87</td><td>10.71</td><td>[5,153]</td></tr><tr><td>Dev 500</td><td>2.01</td><td>0.13</td><td>[2,4]</td><td>9.38</td><td>3.99</td><td>[2,29]</td><td>20.91</td><td>9.76</td><td>[6,56]</td></tr><tr><td>Test 500</td><td>2.01</td><td>0.27</td><td>[2,3]</td><td>9.71</td><td>4.99</td><td>[2,65]</td><td>19.09</td><td>9.20</td><td>[6,84]</td></tr></table>
+
+Table 7: Statistics of the used datasets. Interval denotes the minimum and maximum range.
+
+# B Details for Human Evaluation on Amazon MTurk
+
+The web interface for human evaluation of quality is shown in Figure 4. Given a conversation, we randomly perturb the summaries generated and ask the workers to rank the summaries through the sliders. In principle, we do not accept repeated scores for three summaries since this is a ranking task. However, in practice, we found that there are almost identical summaries and it is difficult for human annotators to distinguish them. Therefore, for those cases (17 samples for SAMSum and 21 samples for DialogSum), we allow repetitive scores. For example, if all three summaries are identical, we will rank them as “1,1,1”. If two of the summaries are identical, we will rank them as “1,2,2” or “1,1,2”.
+
+![](images/5d3b5a10368c4ab5bd2fca4db76be6cdab77195b24add275a07ec739212337ae.jpg)  
+Figure 4: Web interface for human evaluation.
+
+# C Patterns and Examples for Action Extraction
+
+For action extraction, we first use a dependency parser to get the parsing tree, and we select all non-auxiliary verbs as centric tokens. Then we match the syntactic relations between the verbs and other spans/tokens to see if they match the predefined patterns. As shown in Table 9, there are some typical patterns used in the extraction, and their corresponding examples. For example, for pattern  $n_1$ -nsubj- $v_1$ -xcomp- $a / n_2$ , 'nsubj' is the active relation between a noun and a verb. 'xcomp' here indicates open clausal complement or predicative complement.
+
+<table><tr><td>Patterns</td><td>Examples</td></tr><tr><td>n1-nsubj-v1</td><td>Melanie screw up. Lillian call.</td></tr><tr><td>n1-nsubj-v1-dobj-n2</td><td>Layla wait for Rachel. Lucia need haircut.</td></tr><tr><td>n1-nsubj-v1-xcomp-a/n2</td><td>Connor is too tired. Tonight is Opening Night.</td></tr><tr><td>n1-auxcop-n2-advmod</td><td>Sam will be 30 minutes late.</td></tr><tr><td>n1-auxpass-v1</td><td>Tim get injured.</td></tr></table>
+
+# D Examples for Actions Retrieval
+
+In this section, we display different actions retrieved with selective retrieval and traditional kNN method to provide an intuitive view of their effects, and how they influence the final performance of summarization. For each of the actions, top three retrieved samples are listed for both the selected retrieval and kNN method. As can be seen, traditional kNN method usually focus only on word semantics, and is not able to generate diverse results.
+
+Table 8: Typical patterns used and their corresponding examples when we extract actions. Here 'v' is a verb, 'n' is a noun, 'a' is the adjective. All the verbs are in their original form. The other notations are syntactic relations.  
+
+<table><tr><td>Actions</td><td>Selective Retrieval</td><td>kNN</td></tr><tr><td>Gavin have new one everything on external drive</td><td>Noah abandon old computer Sam got 1st credit card Ali need hard drive</td><td>Ali need hard drive Sara have one with normal USB Paul saved file on laptop</td></tr><tr><td>Sonia babysit child Sonia is scared</td><td>Ted have busy day sister has child it continue on</td><td>Martha worry about Anna Drew afraid of wife Naomi worry about Samuel</td></tr><tr><td>medicine are in kitchen green box in kitchen</td><td>fridge smell bad smell come from box Lisa is sick</td><td>It is in fridge green plastic box fell I&#x27;m in drugstore</td></tr></table>
+
+Table 9: Examples for action retrieval using different methods.
+
+# E Examples for Summaries generated from three models mentioned in Section 4.5
+
+We demonstrate several cases for summary generation with BART-base, COMPO-jt, COMPO-sf. We also attach groundtruth summaries for reference in Table 10. For each summary generated, the human evaluation scores (after majority voting) are also provided.
+
+# F Examples for Newly Augmented Data
+
+In this section, we provide several examples for the newly augmented data generated with COMPO, as shown in Table 11. Selected topical split for composioanl operation is highlighted in green.
+
+<table><tr><td colspan="3">Conversations</td></tr><tr><td colspan="3">Riley: Chloe is on tv!! James: On which channel? James: Never mind I&#x27;ve found it. 
+James: What is she doing? I don&#x27;t get it. 
+Riley: This is a programme in which women undergo a complete metamorphosis. 
+Riley: OMG she looks drop dead gorgeous!</td></tr><tr><td>BART-base</td><td>COMPO-sf</td><td>COMPO-jt</td></tr><tr><td>Riley doesn&#x27;t understand Chloe&#x27;s 
+transformation. 
+Human evaluation: 1</td><td>Chloe is on TV. 
+Human evaluation: 3</td><td>James hasn&#x27;t found Chloe on TV. 
+Human evaluation: 2</td></tr><tr><td colspan="3">Conversations</td></tr><tr><td colspan="3">Bob: &lt;file&gt;. I bought this game and I think you should too. 
+Bob: We could play together. Harry: Sorry mate, no money to spend on this 
+Harry: I&#x27;ve got broken car nad shitty job, so for now I can&#x27;t think about such leisure. 
+Bob: Sorry to hear that.</td></tr><tr><td>BART-base</td><td>COMPO-sf</td><td>COMPO-jt</td></tr><tr><td>Bob bought together and 
+Harry should play it 
+Human evaluation: 1</td><td>Bob bought together. 
+Harry doesn&#x27;t want to play it. 
+Human evaluation: 3</td><td>Bob bought this game and 
+he thinks Harry should play together. 
+Human evaluation: 2</td></tr><tr><td colspan="3">Conversations</td></tr><tr><td colspan="3">Rob: &lt;photo&gt;. Not sure if I&#x27;m getting dumber, or this is how it feels like to get older. 
+Tom: What? Rob: I&#x27;m looking at today&#x27;s memes and they mostly refer to things that are either 
+completely stupid, or have no humour value. 
+Tom: Rob, get yourself a girlfriend please. You&#x27;re talking bullshit :D 
+Rob: Ehh. Fuck you.</td></tr><tr><td>BART-base</td><td>COMPO-sf</td><td>COMPO-jt</td></tr><tr><td>Rob is getting older. 
+He wants to get a girlfriend. 
+Human evaluation: 1</td><td>Rob and Tom are looking at 
+today&#x27;s memes and they mostly 
+refer to things that are 
+completely stupid. 
+Human evaluation: 3</td><td>Rob is looking at today&#x27;s memes 
+and they mostly refer to things 
+that are either completely stupid 
+or have no humour value. 
+Human evaluation: 2</td></tr><tr><td colspan="3">Conversations</td></tr><tr><td colspan="3">Paul: Hey Matthew did you find anyone to couch the game Saturday? 
+Matthew: Hey Paul, no still looking. Paul: My plans changed so I can do it if you need 
+Matthew: Ahh yes that be great! thank you. Paul: No problem see you Saturday</td></tr><tr><td>BART-base</td><td>COMPO-sf</td><td>COMPO-jt</td></tr><tr><td>Matthew is looking for someone 
+to couch the game Saturday. 
+Paul is still looking. 
+Human evaluation: 1</td><td>Paul will couch the 
+game Saturday. 
+Human evaluation: 3</td><td>Paul will couch the game Saturday. 
+Matthew is still looking for 
+someone to couch it. 
+Human evaluation: 2</td></tr></table>
+
+Table 10: Examples for action retrieval using different methods.
+
+<table><tr><td>Newly-Generated Data</td><td>Original Data</td></tr><tr><td>Jack: Is Daine with you? 
+Marie: Nope 
+Jack: Sorry, just can&#x27;t find her. 
+Marie: Is everything okay? 
+Jack: Fine, just lost Diane! 
+Jack: I&#x27;m not sure what to do. 
+Marie: Tonight is opening night. 
+Jack: TY!</td><td>Jack: Is Daine with you? 
+Marie: Nope 
+Jack: Sorry, just can&#x27;t find her. 
+Marie: Is everything okay? 
+Jack: Fine, just lost Diane! 
+Marie: LOL! 
+Jack: I&#x27;m sure she just ran out for milk or something. Sorry to bother you! 
+Marie: No problem! If I see her, I&#x27;ll send her your way. 
+Jack: TY!</td></tr><tr><td>Pseudo summary for joint-learning: 
+Jack lost Diane. Jack and Marie will meet tonight 
+for opening night. 
+Newly generated summary for joint-training: 
+Jack&#x27;s looking for Diane. Jack and Marie will go to opening night tonight.</td><td>Summary:Jack&#x27;s looking for Diane. She probably went out to do shopping. Marie will direct Diane to Jack if she sees her.</td></tr><tr><td>Hannah: Hi, I have a problem with my milk 
+Alicia: Sorry, I&#x27;m running late today. 
+Hannah: I don&#x27;t have an allergy but the doctor told me to avoid it 
+Alicia: Ok, I will get you some with no milk</td><td>Alicia: How about some ice cream for desert? 
+Hannah: Milk-free for me please :P 
+Alicia: Are you lactose intolerant? 
+Alicia: I didn&#x27;t know that 
+Hannah: I don&#x27;t have an allergy but the doctor told me to avoid it 
+Alicia: Ok, I will get you some with no milk</td></tr><tr><td>Pseudo summary for joint-learning: 
+Hannah has a problem with her milk. 
+Alicia will get her some with no milk. 
+Newly generated summary for joint-training: 
+Hannah has a problem with her milk. 
+Alicia will get some milk-free one for her.</td><td>Summary: 
+Alicia will get some milk-free ice-cream for Hannah.</td></tr><tr><td>Olivia: Hi Charlie. I&#x27;m looking for a private room. 
+Charlie: It&#x27;s a shared room 
+Olivia: Ah ok. I&#x27;m looking for only a private room. 
+I cannot share it with someone else. Anyway 
+thank you!</td><td>Charlie: Hi. For how long you gonna need a room? 
+Olivia: Hey, I need it till the end of January. 
+Charlie: It&#x27;s a shared room. 
+Olivia: Ah ok. I&#x27;m looking for only a private room. I cannot share it with someone else. Anyway thank you!</td></tr><tr><td>Pseudo summary for joint-learning: 
+Olivia is looking for a private room, 
+and she can&#x27;t share it with someone else. 
+Newly generated summary for joint-training: 
+Olivia is looking for a private room. 
+Olivia can&#x27;t share it with someone else.</td><td>Summary: 
+Olivia needs a private room till the end of January. Charlie says it&#x27;s a shared room. 
+Olivia can&#x27;t share a room.</td></tr></table>
+
+Table 11: Sampled newly augmented data examples for conversations and the summaries.
+
+A For every submission:
+
+A1. Did you describe the limitations of your work? Section 7  
+A2. Did you discuss any potential risks of your work? Section 8  
+A3. Do the abstract and introduction summarize the paper's main claims? Section 1  
+A4. Have you used AI writing assistants when working on this paper? Left blank.
+
+B Did you use or create scientific artifacts?
+
+Section 3.2
+
+B1. Did you cite the creators of artifacts you used? Section 3.2, Section 4  
+B2. Did you discuss the license or terms for use and / or distribution of any artifacts? No response.  
+B3. Did you discuss if your use of existing artifact(s) was consistent with their intended use, provided that it was specified? For the artifacts you create, do you specify intended use and whether that is compatible with the original access conditions (in particular, derivatives of data accessed for research purposes should not be used outside of research contexts)? The original intended use is not found  
+B4. Did you discuss the steps taken to check whether the data that was collected / used contains any information that names or uniquely identifies individual people or offensive content, and the steps taken to protect / anonymize it? Left blank.  
+B5. Did you provide documentation of the artifacts, e.g., coverage of domains, languages, and linguistic phenomena, demographic groups represented, etc.? Left blank.  
+B6. Did you report relevant statistics like the number of examples, details of train / test / dev splits, etc. for the data that you used / created? Even for commonly-used benchmark datasets, include the number of examples in train / validation / test splits, as these provide necessary context for a reader to understand experimental results. For example, small differences in accuracy on large test sets may be significant, while on small test sets they may not be. Appendix A, Section 4
+
+C Did you run computational experiments?
+
+Section 4
+
+C1. Did you report the number of parameters in the models used, the total computational budget (e.g., GPU hours), and computing infrastructure used? Section 4.3
+
+The Responsible NLP Checklist used at ACL 2023 is adopted from NAACL 2022, with the addition of a question on AI writing assistance.
+
+C2. Did you discuss the experimental setup, including hyperparameter search and best-found hyperparameter values?
+
+Section 4.3
+
+C3. Did you report descriptive statistics about your results (e.g., error bars around results, summary statistics from sets of experiments), and is it transparent whether you are reporting the max, mean, etc. or just a single run?
+
+Section 4.3
+
+C4. If you used existing packages (e.g., for preprocessing, for normalization, or for evaluation), did you report the implementation, model, and parameter settings used (e.g., NLTK, Spacy, ROUGE, etc.)?
+
+Section 4.3
+
+D Did you use human annotators (e.g., crowdworkers) or research with human participants?
+
+Section 4.5, Appendix b
+
+D1. Did you report the full text of instructions given to participants, including e.g., screenshots, disclaimers of any risks to participants or annotators, etc.?
+
+Appendix B
+
+D2. Did you report information about how you recruited (e.g., crowdsourcing platform, students) and paid participants, and discuss if such payment is adequate given the participants' demographic (e.g., country of residence)?
+
+Section 4.5
+
+D3. Did you discuss whether and how consent was obtained from people whose data you're using/curating? For example, if you collected data via crowdsourcing, did your instructions to crowdworkers explain how the data would be used?
+
+Section 4.5
+
+D4. Was the data collection protocol approved (or determined exempt) by an ethics review board?
+
+Left blank.
+
+D5. Did you report the basic demographic and geographic characteristics of the annotator population that is the source of the data?
+
+Left blank.

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+# Compositional Generalization without Trees using Multiset Tagging and Latent Permutations
+
+Matthias Lindemann<sup>1</sup> and Alexander Koller<sup>2</sup> and Ivan Titov<sup>1,3</sup>
+
+$^{1}$  ILCC, University of Edinburgh,  $^{2}$  LST, Saarland University,  $^{3}$  ILLC, University of Amsterdam
+
+m.m.lindemann@sms.ed.ac.uk, koller@coli.uni-saarland.de, ititov@inf.ed.ac.uk
+
+# Abstract
+
+Seq2seq models have been shown to struggle with compositional generalization in semantic parsing, i.e. generalizing to unseen compositions of phenomena that the model handles correctly in isolation. We phrase semantic parsing as a two-step process: we first tag each input token with a multiset of output tokens. Then we arrange the tokens into an output sequence using a new way of parameterizing and predicting permutations. We formulate predicting a permutation as solving a regularized linear program and we backpropagate through the solver. In contrast to prior work, our approach does not place a priori restrictions on possible permutations, making it very expressive. Our model outperforms pretrained seq2seq models and prior work on realistic semantic parsing tasks that require generalization to longer examples. We also outperform non-tree-based models on structural generalization on the COGS benchmark. For the first time, we show that a model without an inductive bias provided by trees achieves high accuracy on generalization to deeper recursion depth. $^{1}$
+
+# 1 Introduction
+
+Sequence-to-sequence models have been very successfully applied to many structural tasks in NLP such as semantic parsing. However, they have also been shown to struggle with compositional generalization (Lake and Baroni, 2018; Finegan-Dollak et al., 2018; Kim and Linzen, 2020; Hupkes et al., 2020), i.e. the model fails on examples that contain unseen compositions or deeper recursion of phenomena that it handles correctly in isolation. For example, a model which correctly parses 'Mary knew that Jim slept' should also be able to parse sentences with deeper recursion than it has seen during training such as 'Paul said that Mary knew that Jim slept'. This sort of generalization is easy for humans but challenging for neural models.
+
+![](images/27bf8d3de9e679c7320397d012e876d0481213ac7647e1244e377086d7cfaad2.jpg)  
+Figure 1: We model seq2seq tasks by first predicting a multiset (dashed boxes) for every input token, and then permuting the tokens to put them into order. We realize the permutation using the red edges: if there is an edge from token  $i$  to  $j$ , then  $i$  is the predecessor of  $j$  in the output. Every token is visited exactly once.
+
+In order for a model to generalize compositionally in semantic parsing, it has to identify reusable 'fragments' and be able to systematically combine them in novel ways. One way to make a model sensitive to fragments is to make it rely on a tree that makes the compositional structure explicit. However, this complicates the training because these trees need to be obtained or induced. This is computationally demanding or at least requires structural preprocessing informed by domain knowledge.
+
+In this paper, we propose a two-step sequence-based approach with a structural inductive bias that does not rely on trees: the 'fragments' are multisets of output tokens that we predict for every input token in a first step. A second step then arranges the tokens we predicted in the previous step into a single sequence using a permutation model. In contrast to prior work (Wang et al., 2021; Lindemann et al., 2023), there are no hard constraints on the permutations that our model can predict. We show that this enables structural generalization on tasks that go beyond the class of synchronous context-free languages.
+
+We overcome two key technical challenges in this work: Firstly, we do not have supervision for the correspondence between input tokens and output tokens. Therefore, we induce the correspondence during training. Secondly, predicting permutations without restrictions is computationally challenging. For this, we develop a differentiable GPU-friendly algorithm.
+
+On realistic semantic parsing tasks our approach outperforms previous work on generalization to longer examples than seen at training. We also outperform all other non-tree models on the structural generalization tasks in semantic parsing on COGS (Kim and Linzen, 2020). For the first time, we also show that a model without an inductive bias towards trees can obtain high accuracy on generalization to deeper recursion on COGS.
+
+To summarize, our main contributions are:
+
+- a flexible seq2seq model that performs well on structural generalization in semantic parsing without assuming that input and output are related to each other via a tree structure.  
+- a differentiable algorithm to parameterize and predict permutations without a priori restrictions on what permutations are possible.
+
+# 2 Overview and Motivation
+
+Our approach consists of two stages. In the first stage (multiset tagging), we predict a multiset  $\mathbf{z}_i$  of tokens for every input token  $\mathbf{x}_i$  from the contextualized representation of  $\mathbf{x}_i$ . This is motivated by the observation that input tokens often systematically correspond to a fragment of the output (like slept corresponding to sleep and agent and a variable in Fig. 1). Importantly, we expect this systematic relationship to be largely invariant to phrases being used in new contexts or deeper recursion. We refer to the elements of the multisets as multiset tokens.
+
+In the second stage (permutation), we order the multiset tokens to arrive at a sequential output. Conceptually, we do this by going from left to right over the output and determining which multiset token to put in every position. Consider the example in Fig. 1. For the first output position, we simply select a multiset token (\* in the example). All subsequent tokens are put into position by 'jumping' from the token that was last placed into the output to a new multiset token. In Fig. 1, we jump from  $\star$  to girl (shown by the outgoing red edge from  $\star$ ). This indicates that girl is the successor of  $\star$  in the output and hence the second output token. From
+
+girl we jump to one of the  $x_{1}$  tokens to determine what the third output token is and so on. Since we predict a permutation, we must visit every multiset token exactly once in this process.
+
+The jumps are inspired by reordering in phrase-based machine translation (Koehn et al., 2007) and methods from dependency parsing, where directly modeling bi-lexical relationships on hidden states has proven successful (Kiperwasser and Goldberg, 2016). Note also that any permutation can be represented with jumps. In contrast, prior work (Wang et al., 2021; Lindemann et al., 2023) has put strong restrictions on the possible permutations that can be predicted. Our approach is more flexible and empirically it also scales better to longer inputs, which opens up new applications and datasets.
+
+Setup. We assume we are given a dataset  $\mathcal{D} = \{(\mathbf{x}^1, \mathbf{y}^1), \ldots\}$  of input utterances  $\mathbf{x}$  and target sequences  $\mathbf{y}$ . If we had gold alignments, it would be straightforward to train our model. Since we do not have this supervision, we have to discover during training which tokens of the output  $\mathbf{y}$  belong into which multiset  $\mathbf{z}_i$ . We describe the model and the training objective of the multiset tagging in Section 3. After the model is trained, we can annotate our training set with the most likely  $\mathbf{z}$ , and then train the permutation model.
+
+For predicting a permutation, we associate a score with each possible jump and search for the highest-scoring sequence of jumps. We ensure that the jumps correspond to a permutation by means of constraints, which results in a combinatorial optimization problem. The flexibility of our model and its parametrization come with the challenge that this problem is NP-hard. We approximate it with a regularized linear program which also ensures differentiability. Our permutation model and its training are described in Section 4. In Section 5, we discuss how to solve the regularized linear program and how to backpropagate through the solution.
+
+# 3 Learning Multisets
+
+For the multiset tagging, we need to train a model that predicts the multisets  $\mathbf{z}_1,\ldots ,\mathbf{z}_n$  of tokens by conditioning on the input. We represent a multiset  $\mathbf{z}_i$  as an integer-valued vector that contains for every vocabulary item  $v$  the multiplicity of  $v$  in  $\mathbf{z}_i$ , i.e.  $\mathbf{z}_{i,v} = k$  means that input token  $i$  contributes  $k$  occurrences of output type  $v$ . If  $v$  is not present in multiset  $\mathbf{z}_i$ , then  $\mathbf{z}_{i,v} = 0$ . For example, in Fig. 1,  $\mathbf{z}_{3,\mathrm{sleep}} = 1$  and  $\mathbf{z}_{2,\mathrm{x_1}} = 2$ . As discussed in Sec-
+
+tion 2, we do not have supervision for  $\mathbf{z}_1,\dots ,\mathbf{z}_n$  and treat them as latent variables. To allow for efficient exact training, we assume that all  $\mathbf{z}_{i,v}$  are independent of each other conditioned on the input:
+
+$$
+P (\mathbf {z} \mid \mathbf {x}) = \prod_ {i, v} P (\mathbf {z} _ {i, v} \mid \mathbf {x}) \tag {1}
+$$
+
+where  $v$  ranges over the entire vocabulary.
+
+Parametrization. We parameterize  $P(\mathbf{z}_{i,v} \mid \mathbf{x})$  as follows. We first pass the input  $\mathbf{x}$  through a pretrained RoBERTa encoder (Liu et al., 2019), where  $\mathrm{ENCODER}(\mathbf{x})$  is the output of the final layer. We then add RoBERTa's static word embeddings from the first, non-contextualized, layer to that:
+
+$$
+\mathbf {h} _ {i} = \operatorname {E N C O D E R} (\mathbf {x}) _ {i} + \operatorname {E M B E D} (\mathbf {x} _ {i}) \tag {2}
+$$
+
+We then pass  $\mathbf{h}_i$  through a feedforward network obtaining  $\tilde{\mathbf{h}}_i = \mathrm{FF}(\mathbf{h}_i)$  and define a distribution over the multiplicity of  $v$  in the multiset  $\mathbf{z}_i$ :
+
+$$
+P (\mathbf {z} _ {i, v} = k | \mathbf {x} _ {i}) = \frac {\exp \left(\tilde {\mathbf {h}} _ {i} ^ {T} \mathbf {w} ^ {v , k} + b ^ {v , k}\right)}{\sum_ {l} \exp \left(\tilde {\mathbf {h}} _ {i} ^ {T} \mathbf {w} ^ {v , l} + b ^ {v , l}\right)} (3)
+$$
+
+where the weights  $\mathbf{w}$  and biases  $b$  are specific to  $v$  and the multiplicity  $k$ . In contrast to standard sequence-to-sequence models, this softmax is not normalized over the vocabulary but over the multiplicity, and we have distinct distributions for every vocabulary item  $v$ . Despite the independence assumptions in Eq. (1), the model can still be strong because  $\mathbf{h}_i$  takes the entire input  $\mathbf{x}$  into account.
+
+Training. The probability of generating the overall multiset  $\mathbf{m}$  as the union of all  $\mathbf{z}_i$  is the probability that for every vocabulary item  $v$ , the total number of occurrences of  $v$  across all input positions  $i$  sums to  $\mathbf{m}_v$ :
+
+$$
+P (\mathbf {m} | \mathbf {x}) = \prod_ {v} P (\mathbf {z} _ {1, v} + \dots + \mathbf {z} _ {n, v} = \mathbf {m} _ {v} | \mathbf {x})
+$$
+
+This can be computed recursively:
+
+$$
+P (\mathbf {z} _ {1, v} + \dots + \mathbf {z} _ {n, v} = \mathbf {m} _ {v} \mid \mathbf {x}) =
+$$
+
+$$
+\sum_ {k} P (\mathbf {z} _ {1, v} = k | \mathbf {x}) P (\mathbf {z} _ {2, v} + \dots \mathbf {z} _ {n, v} = \mathbf {m} _ {v} - k | \mathbf {x})
+$$
+
+Let  $\mathbf{m}(\mathbf{y})$  be the multiset of tokens in the gold sequence  $\mathbf{y}$ . We train our model with gradient ascent to maximize the marginal log-likelihood of  $\mathbf{m}(\mathbf{y})$ :
+
+$$
+\sum_ {(\mathbf {x}, \mathbf {y}) \in \mathcal {D}} \log P (\mathbf {m} (\mathbf {y}) \mid \mathbf {x}) \tag {4}
+$$
+
+Like Lindemann et al. (2023), we found it helpful to initialize the training of our model with high-confidence alignments from an IBM-1 model (Brown et al., 1993) (see Appendix C.3 for details).
+
+Preparation for permutation. The scoring function of the permutation model expects a sequence as input. There is no a priori obvious order for the elements within the individual multisets  $\mathbf{z}_i$ . We handle this by imposing a canonical order  $\mathrm{ORDER}(\mathbf{z}_i)$  on the elements of  $\mathbf{z}_i$  by sorting the multiset tokens by their id in the vocabulary. They are then concatenated to form the input  $\mathbf{z}' = \mathrm{ORDER}(\mathbf{z}_1) \ldots \mathrm{ORDER}(\mathbf{z}_n)$  to the permutation model.
+
+# 4 Relaxed Permutations
+
+After predicting a multiset for every input token and arranging the elements within each multiset to form a sequence  $z'$ , we predict a permutation of  $z'$ .
+
+We represent a permutation as a matrix  $\mathbf{V}$  that contains exactly one 1 in every row and column and zeros otherwise. We write  $\mathbf{V}_{i,j} = 1$  if position  $i$  in  $z^{\prime}$  is mapped to position  $j$  in the output  $y$ . Let  $\mathcal{P}$  be the set of all permutation matrices.
+
+Now we formalize the parametrization of permutations as discussed in Section 2. We associate a score predicted by our neural network with each permutation  $\mathbf{V}$  and search for the permutation with the highest score. The score of a permutation decomposes into a sum of scores for binary 'features' of  $\mathbf{V}$ . We use two types of features.
+
+The first type of feature is active if the permutation  $\mathbf{V}$  maps input position  $i$  to output position  $j$  (i.e.  $\mathbf{V}_{ij} = 1$ ). We associate this feature with the score  $s_{i\mapsto j}$  and use these scores only to model what the first and the last token in the output should be. That is,  $s_{i\mapsto 1}$  models the preference to map position  $i$  in the input to the first position in the output, and analogously  $s_{i\mapsto n}$  models the preference to put  $i$  into the last position in the output. For all output positions  $j$  that are neither the first nor the last position, we simply set  $s_{i\mapsto j} = 0$ .
+
+The second type of feature models the jumps we introduced in Section 2. We introduce a feature that is 1 iff  $\mathbf{V}$  contains a jump from  $k$  to  $i$ , and associate this with a score  $s_{k\curvearrowright i}$ . In order for there to be a jump from  $k$  to  $i$ , the permutation  $\mathbf{V}$  must map input  $i$  to some output position  $j$  ( $\mathbf{V}_{ij} = 1$ ) and it must also map input position  $k$  to output position  $j - 1$  ( $\mathbf{V}_{k,j-1} = 1$ ). Hence, the product  $\mathbf{V}_{k,j-1}\mathbf{V}_{ij}$  is 1 iff there is a jump from  $k$  to  $i$  at output position
+
+$j$ . Based on this, the sum  $\sum_{j} \mathbf{V}_{k,j-1} \mathbf{V}_{ij}$  equals 1 if there is any output position  $j$  at which there is a jump from  $k$  to  $i$  and 0 otherwise. This constitutes the second type of feature.
+
+Multiplying the features with their respective scores, we want to find the highest-scoring permutation under the following overall scoring function:
+
+$$
+\begin{array}{l} \underset {\mathbf {V} \in \mathcal {P}} {\arg \max } \sum_ {i, j} \mathbf {V} _ {i j} s _ {i \rightarrow j} + \\ \sum_ {i, k} s _ {k \curvearrowright i} \left(\sum_ {j} \mathbf {V} _ {k, j - 1} \mathbf {V} _ {i j}\right) \tag {5} \\ \end{array}
+$$
+
+Let  $\mathbf{V}^{*}(s)$  be the solution to Eq. (5) as a function of the scores. Unfortunately,  $\mathbf{V}^{*}(s)$  does not have sensible derivatives because  $\mathcal{P}$  is discrete. This makes  $\mathbf{V}^{*}(s)$  unsuitable as a neural network layer. In addition, Eq. (5) is NP-hard (see Appendix A.1).
+
+We now formulate an optimization problem that approximates Eq. (5) and which has useful derivatives. Firstly, we relax the permutation matrix  $\mathbf{V}$  to a bistochastic matrix  $\mathbf{U}$ , i.e.  $\mathbf{U}$  has non-negative elements and every row and every column each sum to 1. Secondly, note that Eq. (5) contains quadratic terms. As we will discuss in the next section, our solver assumes a linear objective, so we replace  $\mathbf{V}_{k,j-1} \mathbf{V}_{ij}$  with an auxiliary variable  $\mathbf{W}_{ijk}$ . The variable  $\mathbf{W}_{ijk}$  is designed to take the value 1 if and only if  $\mathbf{U}_{i,j} = 1$  and  $\mathbf{U}_{k,j-1} = 1$ . We achieve this by coupling  $\mathbf{W}$  and  $\mathbf{U}$  using constraints. Then, the optimization problem becomes:
+
+$$
+\underset {\mathbf {U}, \mathbf {W}} {\arg \max } \sum_ {i, j} \mathbf {U} _ {i j} s _ {i \mapsto j} + \sum_ {i, j, k} \mathbf {W} _ {i j k} s _ {k \curvearrowright i} \tag {6}
+$$
+
+$$
+\begin{array}{l} \text {s u b j e c t} \quad \sum_ {i} \mathbf {U} _ {i j} = 1 \quad \forall j (6a) \\ \sum_ {j} \mathbf {U} _ {i j} = 1 \quad \forall i (6b) \\ \sum_ {k} \mathbf {W} _ {i j k} = \mathbf {U} _ {i j} \quad \forall j > 1, i (6c) \\ \sum_ {i} \mathbf {W} _ {i j k} = \mathbf {U} _ {k (j - 1)} \forall j > 1, k (6d) \\ \mathbf {U}, \mathbf {W} \geq 0 (6e) \\ \end{array}
+$$
+
+Finally, in combination with the linear objective, the argmax operation still causes the solution  $\mathbf{U}^{*}(s)$  of Eq. (6) as a function of  $s$  to have no useful derivatives. This is because an infinitesimal change in  $s$  has no effect on the solution  $\mathbf{U}^{*}(s)$  for almost all  $s$ .
+
+To address this, we add an entropy regularization term  $\tau (H(\mathbf{U}) + H(\mathbf{W}))$  to the objective Eq. (6), where  $H(\mathbf{U}) = -\sum_{ij}\mathbf{U}_{ij}(\log \mathbf{U}_{ij} - 1)$ , and  $\tau >0$  determines the strength of the regularization. The entropy regularization 'smooths' the solution  $\mathbf{U}^{*}(s)$  in an analogous way to softmax being a smoothed version of argmax. The parameter  $\tau$  behaves analogously to the softmax temperature: the smaller  $\tau$ , the sharper  $\mathbf{U}^{*}(s)$  will be. We discuss how to solve the regularized linear program in Section 5.
+
+Predicting permutations. At test time, we want to find the highest scoring permutation, i.e. we want to solve Eq. (5). We approximate this by using  $\mathbf{U}^{*}(s)$  instead, the solution to the entropy regularized version of Eq. (6). Despite using a low temperature  $\tau$ , there is no guarantee that  $\mathbf{U}^{*}(s)$  can be trivially rounded to a permutation matrix. Therefore, we solve the linear assignment problem with  $\mathbf{U}^{*}(s)$  as scores using the Hungarian Algorithm (Kuhn, 1955). The linear assignment problem asks for the permutation matrix  $\mathbf{V}$  that maximizes  $\sum_{ij}\mathbf{V}_{ij}\mathbf{U}^{*}(s)_{ij}$ .
+
+# 4.1 Parametrization
+
+We now describe how we parameterize the scores  $s$  to permute the tokens into the right order. We first encode the original input utterance  $x$  like in Eq. (2) to obtain a hidden representation  $\mathbf{h}_i$  for input token  $\mathbf{x}_i$ . Let  $a$  be the function that maps  $a(i)\mapsto j$  if the token in position  $i$  in  $z^{\prime}$  came from the multiset that was generated by token  $\mathbf{x}_j$ . For example, in Fig. 1,  $a(6) = 3$  since sleep was predicted from input token slept. We then define the hidden representation  $\mathbf{h}_i^\prime$  as the concatenation of  $\mathbf{h}_{a(i)}$  and an embedding of  $z_{i}^{\prime}$ :
+
+$$
+\mathbf {h} _ {i} ^ {\prime} = \left[ \mathbf {h} _ {a (i)}; \operatorname {E M B E D} \left(z _ {i} ^ {\prime}\right) \right] \tag {7}
+$$
+
+We parameterize the scores for starting the output with token  $i$  as
+
+$$
+s _ {i \mapsto 1} = \mathbf {w} _ {\text {s t a r t}} ^ {T} \operatorname {F F} _ {\text {s t a r t}} \left(\mathbf {h} _ {i} ^ {\prime}\right)
+$$
+
+and analogously for ending it with token  $i$ :
+
+$$
+s _ {i \mapsto n} = \mathbf {w} _ {\text {e n d}} ^ {T} \operatorname {F F} _ {\text {e n d}} \left(\mathbf {h} _ {i} ^ {\prime}\right)
+$$
+
+We set  $s_{i\rightarrow j} = 0$  for all other  $i,j$
+
+We parameterize the jump scores  $s_{k \sim i}$  using Geometric Attention (Csordás et al., 2022) from  $\mathbf{h}_k'$  to  $\mathbf{h}_i'$ . Intuitively, Geometric Attention favours selecting the 'matching' element  $\mathbf{h}_i'$  that is closest to  $\mathbf{h}_k'$  in terms of distance  $|i - k|$  in the string. We refer to Csordás et al. (2022) for details.
+
+![](images/78ce4bb6861700e97f8f8213643a51994788537657623c2695216b7e50cbca4e.jpg)  
+Figure 2: Two possible permutations (represented with red arrows) of  $\mathbf{z}'$  that yield the same result  $\mathbf{y}$ . Only the permutation marked with solid arrows corresponds to the right linguistic relation that will generalize well.
+
+# 4.2 Learning Permutations
+
+We now turn to training the permutation model. At training time, we have access to the gold output  $\mathbf{y}$  and a sequence  $\mathbf{z}'$  from the output of the multiset tagging (see the end of Section 3). We note that whenever  $\mathbf{y}$  (or  $\mathbf{z}'$ ) contains one vocabulary item at least twice, there are multiple permutations that can be applied to  $\mathbf{z}'$  to yield  $\mathbf{y}$ . Many of these permutations will give the right result for the wrong reasons and the permutation that is desirable for generalization is latent. For example, consider Fig. 2. The token agent is followed by the entity who performs the action, whereas theme is followed by the one affected by the action. The permutation indicated by dashed arrows generalizes poorly to a sentence like Emma knew that James slid since slid will introduce a theme role rather than an agent role (as the sliding is happening to James). Thus, this permutation would then lead to the incorrect output know theme Emma ... slide agent James, in which Emma is affected by the knowing event and James is the one who slides something.
+
+In order to train the permutation model in this setting, we use a method that is similar to EM for structured prediction. During training, the model output  $\mathbf{U}^{*}(s)$  and  $\mathbf{W}^{*}(s)$  often represents a soft permutation that does not permute  $\mathbf{z}'$  into  $\mathbf{y}$ . Our goal is to push the model output into the space of (soft) permutations that lead to  $\mathbf{y}$ . More formally, let  $\mathbf{Q} \in \mathcal{Q}(\mathbf{y}, \mathbf{z}')$  be the set of bistochastic matrices such that  $\mathbf{Q}_{i,j} = 0$  iff  $\mathbf{z}_i' \neq \mathbf{y}_j$ . That is, any permutation included in  $\mathcal{Q}(\mathbf{y}, \mathbf{z}')$  leads to the gold output  $\mathbf{y}$  when applied to  $\mathbf{z}'$ .
+
+First, we project the current prediction  $\mathbf{U}^{*}(s)$  and  $\mathbf{W}^{*}(s)$  into  $\mathcal{Q}(\mathbf{y},\mathbf{z}^{\prime})$  using the KL divergence
+
+as a measure of distance (E-step):
+
+$$
+\begin{array}{l} \hat {\mathbf {U}}, \hat {\mathbf {W}} = \underset {\mathbf {U} \in \mathcal {Q} (\mathbf {y}, \mathbf {z} ^ {\prime}), \mathbf {W}} {\arg \min } \operatorname {K L} (\mathbf {U} \| \mathbf {U} ^ {*} (s)) + \tag {8} \\ \operatorname {K L} \left(\mathbf {W} \mid \mid \mathbf {W} ^ {*} (s)\right) \\ \end{array}
+$$
+
+subject to Eq. (6a) to Eq. (6e).
+
+Similar to the M-step of EM, we then treat  $\hat{\mathbf{U}}$  and  $\hat{\mathbf{W}}$  as soft gold labels and train our model to minimize the KL divergence between labels and model:
+
+$$
+\mathrm {K L} (\hat {\mathbf {U}} \mid \mid \mathbf {U} ^ {*} (s)) + \mathrm {K L} (\hat {\mathbf {W}} \mid \mid \mathbf {W} ^ {*} (s))
+$$
+
+Eq. (8) can be solved in the same way as the entropy regularized version of Eq. (6) because expanding the definition of KL-divergence leads to a regularized linear program with a similar feasible region (see Appendix A.3 for details).
+
+# 5 Inference for Relaxed Permutations
+
+Now we describe how to solve the entropy regularized form of Eq. (6) and how to backpropagate through it. This section may be skipped on the first reading as it is not required to understand the experiments; we note that the resulting algorithm (Algorithm 1) is conceptually relatively simple. Before describing our method, we explain the general principle.
+
+# 5.1 Bregman's Method
+
+Bregman's method (Bregman, 1967) is a method for constrained convex optimization. In particular, it can be used to solve problems of the form
+
+$$
+\mathbf {x} ^ {*} = \underset {\mathbf {x} \in C _ {0} \cap C _ {1} \dots \cap C _ {n}, \mathbf {x} \geq \mathbf {0}} {\arg \max } \mathbf {s} ^ {T} \mathbf {x} + \underbrace {\tau H (\mathbf {x})} _ {\text {r e g u l a r i z e r}} \tag {9}
+$$
+
+where  $C_0, \ldots, C_n$  are linear equality constraints,  $H(\mathbf{x}) = -\sum_{i} \mathbf{x}_i (\log \mathbf{x}_i - 1)$  is a form of entropy regularization, and  $\tau$  determines the strength of the regularization. Note that our parameterization of permutations (Eq. (6)) has this form.
+
+Bregman's method is a simple iterative process. We start with the scores  $\mathbf{s}$  and then cyclically iterate over the constraints and project the current estimate  $\mathbf{x}^i$  onto the chosen constraint until convergence:
+
+$$
+\begin{array}{l} \mathbf {x} ^ {0} = \exp {\frac {\mathbf {s}}{\tau}} \\ \mathbf {x} ^ {i + 1} = \underset {\mathbf {x} \in C _ {i \bmod (n - 1)}} {\arg \min } \operatorname {K L} (\mathbf {x} | | \mathbf {x} ^ {i}) \tag {10} \\ \end{array}
+$$
+
+where  $\mathrm{KL}(\mathbf{x}\mid \mathbf{y}) = \sum_{i}\mathbf{x}_{i}\log \frac{\mathbf{x}_{i}}{\mathbf{y}_{i}} -\mathbf{x}_{i} + \mathbf{y}_{i}$  is the generalized KL divergence. We call
+
+Algorithm 1 Bregman's method for Eq. (6) with entropic regularization
+
+function BREGMAN(s,  $\tau$ )
+
+$$
+\mathbf {U} _ {i j} = \exp (\tau^ {- 1} s _ {i \rightarrow j})
+$$
+
+$$
+\mathbf {W} _ {i j k} = \exp (\tau^ {- 1} s _ {k \curvearrowright i})
+$$
+
+while within budget and not converged do
+
+$\mathbf{U}, \mathbf{W} = \mathrm{KL}$  project(U, W; 6a, 6c) with Prop. 2
+
+$\mathbf{U}, \mathbf{W} = \mathrm{KL}$  project(U, W; 6a,6d) with Prop. 2
+
+$\mathbf{U} = \mathrm{KL}$  project (U, 6b) with Prop. 1
+
+end while
+
+return U, W
+
+end function
+
+arg  $\min_{\mathbf{x}\in C}\mathrm{KL}(\mathbf{x}\mid \mathbf{x}^i)$  a KL projection. In order to apply Bregman's method, we need to be able to compute the KL projection arg  $\min_{\mathbf{x}\in C}\mathrm{KL}(\mathbf{x}\mid \mathbf{x}^i)$  for all  $C_0,\ldots ,C_n$  in closed-form. We discuss how to do this for Eq. (6) in the next section.
+
+As an example, consider a problem of the form Eq. (9) with a single linear constraint  $C^{\Delta} = \{\mathbf{x} \mid \sum_{i} \mathbf{x}_{i} = 1\}$ . In this case, Bregman's method coincides with the softmax function. This is because the KL projection  $\mathbf{x}^{*} = \arg \min_{\mathbf{x} \in C^{\Delta}} \mathrm{KL}(\mathbf{x} \parallel \mathbf{y})$  for  $\mathbf{y} > \mathbf{0}$  has the closed-form solution  $\mathbf{x}_{i}^{*} = \frac{\mathbf{y}_{i}}{\sum_{i} \mathbf{y}_{i}}$ .
+
+If we have a closed-form expression for a KL projection (such as normalizing a vector), we can use automatic differentiation to backpropagate through it. To backpropagate through the entire solver, we apply automatic differentiation to the composition of all projection steps.
+
+# 5.2 Bregman's Method for Eq. (6)
+
+In order to apply Bregmans' method to solve the entropy regularized version of Eq. (6), we need to decompose the constraints into sets which we can efficiently project onto. We choose the following three sets here: (i), containing Eq. (6a) and Eq. (6c), and (ii), containing Eq. (6a) and Eq. (6d), and finally (iii), containing only Eq. (6b). We now need to establish what the KL projections are for our chosen sets. For (iii), the projection is simple:
+
+Proposition 1. (Benamou et al. (2015), Prop. 1) For  $\mathbf{A},\mathbf{m} > 0$ , the KL projection  $\arg \min_{\mathbf{U}}\mathrm{KL}(\mathbf{U}\parallel \mathbf{A})$  subject to  $\sum_{j}\mathbf{U}_{ij} = \mathbf{m}_i$  is given by  $\mathbf{U}_{ij}^{*} = \mathbf{m}_{i}\frac{\mathbf{A}_{ij}}{\sum_{j'}\mathbf{A}_{ij'}}$ .
+
+Let us now turn to (i) and (ii). The constraints Eq. (6d) and Eq. (6c) are structurally essentially the same, meaning that we can project onto (ii) in basically the same manner as onto (i). We project onto (i), with the following proposition:
+
+Proposition 2. For  $\mathbf{A},\mathbf{B} > \mathbf{0}$  , the KL projection
+
+$$
+\operatorname * {a r g   m i n} _ {\mathbf {U}, \mathbf {W}} \qquad \mathrm {K L} (\mathbf {U}   |   |   \mathbf {A}) + \mathrm {K L} (\mathbf {W}   |   |   \mathbf {B})
+$$
+
+$$
+\text {s u b j e c t} \quad \sum_ {i} \mathbf {U} _ {i j} = 1 \quad \forall j \tag {11}
+$$
+
+$$
+\sum_ {k} \mathbf {W} _ {i j k} = \mathbf {U} _ {i j} \forall j, i
+$$
+
+is given by:
+
+$$
+\mathbf {U} _ {i j} ^ {*} = \frac {\mathbf {T} _ {i j}}{\sum_ {i ^ {\prime}} \mathbf {T} _ {i ^ {\prime} j}}
+$$
+
+$$
+\mathbf {W} _ {i j k} ^ {*} = \mathbf {U} _ {i j} ^ {*} \frac {\mathbf {B} _ {i j k}}{\sum_ {k ^ {\prime}} \mathbf {B} _ {i j k ^ {\prime}}}
+$$
+
+where  $\mathbf{T}_{ij} = \sqrt{\mathbf{A}_{ij}\cdot\sum_k\mathbf{B}_{ijk}}$
+
+The proof can be found in Appendix A.2. We present the overall algorithm in Algorithm 1, and note that it is easy to implement for GPUs. In practice, we implement all projections in log space for numerical stability.
+
+# 6 Evaluation
+
+# 6.1 Doubling Task
+
+Our permutation model is very expressive and is not limited to synchronous context-free languages. This is in contrast to the formalisms that other approaches rely on (Wang et al., 2021; Lindemann et al., 2023). To evaluate if our model can structurally generalize beyond the synchronous context-free languages in practice, we consider the function  $F = \{(w,ww) \mid w \in \Sigma^{*}\}$ . This function is related to processing challenging natural language phenomena such as reduplication and cross-serial dependencies. We compare our model with an LSTM-based seq2seq model with attention and a Transformer in the style of Csordás et al. (2021) that uses a relative positional encoding. Since the input is a sequence of symbols rather than English, we replace RoBERTa with a bidirectional LSTM and use randomly initialized embeddings. The models are trained on inputs of lengths 5 to 10 and evaluated on longer examples. The results can be found in Fig. 3. All models get perfect or close to perfect accuracy on inputs of length 11 but accuracy quickly deteriorates for the LSTM and the Transformer. In contrast, our model extrapolates very well to longer sequences.
+
+# 6.2 COGS
+
+COGS is a synthetic benchmark for compositional generalization introduced by Kim and Linzen
+
+![](images/d60afb1ec4f5f24df8816b502c7ac477bee7dae20e8c9faad1a4a4f1b8d00f3c.jpg)  
+Figure 3: Accuracy by input length for doubling task.
+
+(2020). Models are tested for 21 different cases of generalization, 18 of which focus on using a lexical item in new contexts (Lex). There are 1000 instances per generalization case. Seq2seq models struggle in particular with the structural generalization tasks (Yao and Koller, 2022), and we focus on those: (i) generalization to deeper PP recursion than seen during training ("Emma saw a hedgehog on a chair in the garden beside the tree..."), (ii) deeper CP recursion ("Olivia mentioned that James saw that Emma admired that the dog slept"), and (iii) PPs modifying subjects when PPs modified only objects in the training data (OS).
+
+We follow previous work and use a lexicon (Akyurek and Andreas, 2021) to map some input tokens to output tokens (see Appendix C.2 for details). We also use this mechanism to handle the variable symbols in COGS.
+
+We report the means and standard deviations for 10 random seeds in Table 1. Our approach obtains high accuracy on CP and PP recursion but exact match accuracy is low for OS. This is in part because our model sometimes predicts semantic representations for OS that are equivalent to the gold standard but use a different order for the conjuncts. Therefore, we report accuracy that accounts for this in Table 2. In both tables, we also report the impact of using a simple copy mechanism instead of the more complex lexicon induction mechanism (-Lex). Our model outperforms all other non-tree-based models by a considerable margin.
+
+Structural generalization without trees. All previous methods that obtain high accuracy on recursion generalization on COGS use trees. Some approaches directly predict a tree over the input (Liu et al., 2021; Weißenhorn et al., 2022), while others use derivations from a grammar for data augmentation (Qiu et al., 2022) or decompose the input along a task-specific parse tree (Drozdov et al., 2022). Our results show that trees are not as important for compositional generalization as their success in the literature may suggest, and that weaker
+
+<table><tr><td>Model</td><td>OS</td><td>CP</td><td>PP</td><td>Lex</td><td>Total</td></tr><tr><td>Q&#x27;22♣</td><td>-</td><td>-</td><td>-</td><td>-</td><td>99</td></tr><tr><td>D&#x27;22♣</td><td>-</td><td>-</td><td>-</td><td>-</td><td>99</td></tr><tr><td>LexLSTM</td><td>0</td><td>0</td><td>1</td><td>96</td><td>82</td></tr><tr><td>Dangle</td><td>0</td><td>14</td><td>14</td><td>98</td><td>85</td></tr><tr><td>Dangle♣</td><td>0</td><td>25</td><td>35</td><td>99</td><td>88</td></tr><tr><td>T5-base♣</td><td>0</td><td>13</td><td>18</td><td>99</td><td>86</td></tr><tr><td>Ours♣</td><td>9±13</td><td>79±11</td><td>85±14</td><td>97±2</td><td>92±2</td></tr><tr><td>Ours♣- Lex</td><td>5±6</td><td>71±26</td><td>82±20</td><td>79±1</td><td>75±2</td></tr></table>
+
+Table 1: Exact match accuracy on COGS by generalization type. ◆refers to models using pretrained transformers, and ◆refers to models implicitly or explicitly using trees. Q'22 is Qiu et al. (2022), D'22 is Drozdov et al. (2022). LexLSTM is the model by Akyurek and Andreas (2021) and Dangle is the model by Zheng and Lapata (2021). We report their results for T5.  
+
+<table><tr><td>Model</td><td>OS</td><td>CP</td><td>PP</td><td>Lex</td><td>Total</td></tr><tr><td>Lear♣</td><td>93</td><td>100</td><td>99</td><td>99</td><td>99</td></tr><tr><td>AM parser♣</td><td>72</td><td>100</td><td>97</td><td>76</td><td>78</td></tr><tr><td>Dangle</td><td>8</td><td>14</td><td>14</td><td>99</td><td>87</td></tr><tr><td>Ours♦</td><td>33±24</td><td>82±11</td><td>91±5</td><td>97±2</td><td>93±2</td></tr><tr><td>Ours♦- Lex</td><td>35±22</td><td>73±27</td><td>92±5</td><td>79±1</td><td>77±2</td></tr></table>
+
+Table 2: Accuracy on COGS when the order of conjuncts is disregarded or established in post-processing. For Lear (Liu et al., 2021) and the AM parser (Groschwitz et al., 2018; Weißenhorn et al., 2022), we report numbers of Weißenhorn et al. (2022).
+
+structural assumptions already reap some of the benefits.
+
+Logical forms with variables. COGS uses logical forms with variables, which were removed in conversion to variable-free formats for evaluation of some approaches (Zheng and Lapata, 2021; Qiu et al., 2022; Drozdov et al., 2022). Recently, Wu et al. (2023) have argued for keeping the variable symbols because they are important for some semantic distinctions; we keep the variables.
+
+# 6.3 ATIS
+
+While COGS is a good benchmark for compositional generalization, the data is synthetic and does not contain many phenomena that are frequent in semantic parsing on real data, such as paraphrases that map to the same logical form. ATIS (Dahl et al., 1994) is a realistic English semantic parsing dataset with executable logical forms. We follow the setup of our previous work (Lindemann et al., 2023) (L'23) and use the variable-free FunQL rep
+
+<table><tr><td>Model</td><td>iid</td><td>Length</td></tr><tr><td>LSTM seq2seq</td><td>75.98±1.30</td><td>4.95±2.16</td></tr><tr><td>Transformer</td><td>75.76±1.43</td><td>1.15±1.41</td></tr><tr><td>BART-base◇</td><td>86.96±1.26</td><td>19.03±4.57</td></tr><tr><td>L&#x27;23♣</td><td>68.26±1.53</td><td>29.91±2.91</td></tr><tr><td>L&#x27;23†♣</td><td>74.15±1.35</td><td>35.41±4.09</td></tr><tr><td>Ours◇</td><td>76.65±1.67</td><td>41.39±13.47</td></tr><tr><td>Ours</td><td>73.93±1.43</td><td>38.79±7.11</td></tr></table>
+
+resentation (Guo et al., 2020). Apart from the usual iid split, we evaluate on a length split, where a model is trained on examples with few conjuncts and has to generalize to longer logical forms with more conjuncts. For a fair comparison with previous work, we do not use the lexicon/copying. We also evaluate a version of our model without RoBERTa that uses a bidirectional LSTM and GloVe embeddings instead. This mirrors the model of L'23.
+
+Table 3 shows mean accuracy and standard deviations over 5 runs. Our model is competitive with non-pretrained models in-distribution, and outperforms all other models on the length generalization. The high standard deviation on the length split stems from an outlier run with  $18\%$  accuracy - the second worst-performing run achieved an accuracy of  $44\%$ . Even without pretraining, our model performs very well. In particular, without grammar-based decoding our model performs on par or outperforms L'23 with grammar-based decoding.
+
+The runtime of the model in L'23 is dominated by the permutation model and it takes up to 12 hours to train on ATIS. Training the model presented here only takes around 2 hours for both stages.
+
+Performance breakdown. In order for our approach to be accurate, both the multiset tagging model and the permutation model have to be accurate. Table 4 explores which model acts as the bottleneck in terms of accuracy on ATIS and COGS. The answer depends on the dataset: for the synthetic COGS dataset, predicting the multisets correctly is easy except for OS, and the model struggles more with getting the permutation right. In contrast, for ATIS, the vast majority of errors can be attributed to the first stage.
+
+Table 3: Accuracy on ATIS.  $\dagger$  indicates grammar-based decoding. L'23 is the model of Lindemann et al. (2023).  
+
+<table><tr><td></td><td></td><td>Freq</td><td>Seq</td><td>Seq/Freq</td></tr><tr><td rowspan="3">COGS</td><td>OS</td><td>50±34</td><td>9±13</td><td>11±15</td></tr><tr><td>CP</td><td>97±5</td><td>79±11</td><td>82±13</td></tr><tr><td>PP</td><td>99±0</td><td>85±14</td><td>85±15</td></tr><tr><td rowspan="2">ATIS</td><td>iid</td><td>77.6±1.4</td><td>76.7±1.7</td><td>98.7±0.5</td></tr><tr><td>Length</td><td>42.2±13.6</td><td>41.4±13.5</td><td>97.8±0.8</td></tr></table>
+
+Table 4: Performance breakdown of the first and second stage. 'Freq' refers to accuracy measured on the predicted multiset; it measures performance of the first stage. 'Seq' measures the accuracy of both stages. 'Seq/Freq' is the percentage of correct predictions given that the multiset is predicted correctly.  
+
+<table><tr><td>Model</td><td>Calendar</td><td>Doc</td><td>Email</td></tr><tr><td>BART-base◇</td><td>36.7±3.0</td><td>0.6±0.3</td><td>20.5±9.8</td></tr><tr><td>L&#x27;23♣</td><td>57.2±19.9</td><td>36.1±5.6</td><td>43.9±3.8</td></tr><tr><td>L&#x27;23†♣</td><td>69.5±13.9</td><td>42.4±5.7</td><td>55.6±2.7</td></tr><tr><td>Ours◇</td><td>74.3±3.5</td><td>57.8±5.5</td><td>60.6±4.8</td></tr><tr><td>Ours</td><td>65.6±2.8</td><td>41.4±4.9</td><td>47.6±4.5</td></tr></table>
+
+Table 5: Accuracy on length splits by domain on Okapi.
+
+# 6.4 Okapi
+
+Finally, we consider the recent Okapi (Hosseini et al., 2021) semantic parsing dataset, in which an English utterance from one of three domains (Calendar, Document, Email) has to be mapped to an API request. We again follow the setup of L'23 and evaluate on their length split, where a model has to generalize to longer logical forms. In contrast to all other datasets we consider, Okapi is quite noisy because it was collected with crowd workers. This presents a realistic additional challenge on top of the challenge of structural generalization.
+
+The results of 5 runs can be found in Table 5. Our model outperforms both BART (Lewis et al., 2020) and the model of L'23. In the comparison without pretraining, our model also consistently achieves higher accuracy than the comparable model of L'23 without grammar-based decoding.
+
+# 7 Related Work
+
+Predicting permutations. Mena et al. (2018) and Lyu and Titov (2018) use variational autoencoders based on the Sinkhorn algorithm to learn latent permutations. The Sinkhorn algorithm (Sinkhorn, 1964) is also an instance of Bregman's method and solves the entropy regularized version of Eq. (6) without the W-term. This parameterization is con
+
+siderably weaker than ours since it cannot capture our notion of 'jumps'.
+
+Wang et al. (2021) compute soft permutations as an expected value by marginalizing over the permutations representable by ITGs (Wu, 1997). This approach is exact but excludes some permutations. In particular, it excludes permutations needed for COGS. In addition, the algorithm they describe takes a lot of resources as it is both  $O(n^{5})$  in memory and compute. Devatine et al. (2022) investigate sentence reordering methods. They use bigram scores, which results in a similar computational problem to ours. However, they deal with it by restricting what permutations are possible to enable tractable dynamic programs. Eisner and Tromble (2006) propose local search methods for decoding permutations for machine translation.
+
+Outside of NLP, Kushinsky et al. (2019) have applied Bregman's method to the quadratic assignment problem, which Eq. (5) is a special case of. Since they solve a more general problem, using their approach for Eq. (6) would require  $O(n^{4})$  rather than  $O(n^{3})$  variables in the linear program.
+
+Compositional generalization. Much research on compositional generalization has focused on lexical generalization with notable success (Andreas, 2020; Akyurek and Andreas, 2021; Conklin et al., 2021; Csordas et al., 2021). Structural generalization remains more challenging for seq2seq models (Yao and Koller, 2022).
+
+Zheng and Lapata (2022) modify the transformer architecture and re-encode the input and partially generated output for every decoding step to disentangle the information in the representations. Structure has also been introduced in models by means of grammars: Qiu et al. (2022) heuristically induce a quasi-synchronous grammar (QCFG, Smith and Eisner (2006)) and use it for data augmentation for a seq2seq model. Kim (2021) introduces neural QCFGs which perform well on compositional generalization tasks but are very compute-intensive. Other works directly parse into trees or graphs inspired by methods from syntactic parsing (Liu et al., 2021; Herzig and Berant, 2021; Weißenhorn et al., 2022; Jambor and Bahdanau, 2022; Petit and Corro, 2023).
+
+Several approaches, including ours, have decoupled the presence or absence of output tokens from their order: Wang et al. (2021) train a model end
+
+to-to-end to permute the input (as discussed above) and then monotonically translate it into an output sequence. Lindemann et al. (2023) also present an end-to-end differentiable model that first applies a 'fertility step' which predicts for every word how many copies to make of its representation, and then uses the permutation method of Wang et al. (2021) to reorder the representation before translating them. Cazzaro et al. (2023) first translate the input monotonically and feed it into a second model. They use alignments from an external aligner to train the first model. The second model is a tagger or a pretrained seq2seq model and predicts the output as a permutation of its input. We compare against such a baseline for permutations in Appendix B, finding that it does not work as well as ours in the compositional generalization setups we consider.
+
+# 8 Conclusion
+
+In this paper, we have presented a flexible new seq2seq model for semantic parsing. Our approach consists of two steps: We first tag each input token with a multiset of output tokens. Then we arrange those tokens into a sequence using a permutation model. We introduce a new method to predict and learn permutations based on a regularized linear program that does not restrict what permutations can be learned. The model we present has a strong ability to generalize compositionally on synthetic and natural semantic parsing datasets. Our results also show that trees are not necessarily required to generalize well to deeper recursion than seen at training time.
+
+# Limitations
+
+The conditional independence assumptions are a limitation for the applicability of our multiset tagging model. For example, the independence assumptions are too strong to apply it to natural language generation tasks such as summarization. From a technical point of view, the independence assumptions are important to be able to induce the latent assignment of output tokens to multisets efficiently. Future work may design multiset tagging methods that make fewer independence assumptions.
+
+While our method for predicting permutations is comparatively fast and only has a memory requirement of  $O(n^{3})$ , inference on long sequences, e.g. with more than 100 tokens, remains somewhat
+
+slow. In future work, we plan to investigate other approximate inference techniques like local search and dual decomposition.
+
+Regarding the importance of trees for compositional generalization, our model has no explicit structural inductive bias towards trees. However, we do not exclude that the pretrained RoBERTa model that we use as a component implicitly captures trees or tree-like structures to a certain degree.
+
+# Acknowledgements
+
+We thank Bailin Wang and Jonas Groschwitz for technical discussions; we thank Hao Zheng for discussions and for providing system outputs for further analysis. We also say thank you to Christine Schäfer and Agostina Calabrese for their comments on this paper.
+
+ML is supported by the UKRI Centre for Doctoral Training in Natural Language Processing, funded by the UKRI (grant EP/S022481/1), the University of Edinburgh, School of Informatics and School of Philosophy, Psychology & Language Sciences, and a grant from Huawei Technologies. IT is supported by the Dutch National Science Foundation (NWO Vici VI.C.212.053).
+
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+
+# A Math Details
+
+# A.1 NP-hardness
+
+We show that Eq. (5) can be used to decide the Hamiltonian Path problem. Let  $G = (V, E)$  be a graph with nodes  $V = \{1, 2, \ldots, n\}$ . A Hamiltonian path  $P = v_1, v_2, \ldots, v_n$  is a path in  $G$  (i.e.,  $(v_i, v_{i+1}) \in E$  for all  $i$ ) such that each node of  $G$  appears exactly once. Deciding if a graph has a Hamiltonian path is NP-complete.
+
+Reduction of Hamiltonian path to Eq. (5). Note that a necessary but not sufficient condition for  $P$  to be a Hamiltonian path is that  $P$  is a permutation of  $V$ . This will be ensured by the constraints on the solution in Eq. (5).
+
+We construct a score function
+
+$$
+s _ {k \curvearrowright i} = \left\{ \begin{array}{l l} 1 & \text {i f} (k, i) \in E \\ 0 & \text {e l s e} \end{array} \right. \tag {12}
+$$
+
+and let  $s_{i \mapsto j} = 0$  for all  $i, j$ . If we find the solution of Eq. (5) for the score function Eq. (12), we obtain a permutation  $P$  of  $V$ , which may or may not be a path in  $G$ . In a path of  $n$  nodes, there are  $n - 1$  edges that are crossed. If the score of the solution is  $n - 1$ , then all node pairs  $(v_i, v_{i+1})$  that are adjacent in  $P$  must have had a score of 1, indicating an edge  $(v_i, v_{i+1}) \in E$ . Therefore,  $P$  must be a Hamiltonian path. If the score of the solution is less than  $n - 1$ , then there is no permutation of  $V$  that is also a path, and hence  $G$  has no Hamiltonian path.
+
+# A.2 Proof of Proposition 2
+
+We now prove Prop. 2 using a very similar technique as Kushinsky et al. (2019). As the constraints
+
+$$
+\begin{array}{l} \operatorname {K L} (\mathbf {x} \mid \mid \mathbf {z}) + \operatorname {K L} \left(\mathbf {Y} ^ {*} (\mathbf {x}) \mid \mid \mathbf {W}\right) \\ = \operatorname {K L} (\mathbf {x} \mid \mid \mathbf {z}) + \sum_ {i, j} \frac {\mathbf {x} _ {i} \mathbf {W} _ {i , j}}{\sum_ {j ^ {\prime}} \mathbf {W} _ {i , j ^ {\prime}}} \left(\log \frac {\frac {x _ {i} \mathbf {W} _ {i , j}}{\sum_ {j ^ {\prime}} \mathbf {W} _ {i , j ^ {\prime}}}}{\mathbf {W} _ {i , j}} - 1\right) \\ = \operatorname {K L} (\mathbf {x} | | \mathbf {z}) + \sum_ {i} \frac {\mathbf {x} _ {i} \sum_ {j} \mathbf {W} _ {i , j}}{\sum_ {j ^ {\prime}} \mathbf {W} _ {i , j ^ {\prime}}} (\log \frac {\mathbf {x} _ {i}}{\sum_ {j ^ {\prime}} \mathbf {W} _ {i , j ^ {\prime}}} - 1) \\ = \sum_ {i} \mathbf {x} _ {i} \left(\log \left(\frac {\mathbf {X} _ {i}}{\mathbf {z} _ {i}}\right) - 1 + \log \frac {\mathbf {x} _ {i}}{\sum_ {j ^ {\prime}} \mathbf {W} _ {i , j ^ {\prime}}} - 1\right) \\ = \sum_ {i} \mathbf {x} _ {i} \left(2 \log \mathbf {x} _ {i} - \log \mathbf {z} _ {i} - \log \left(\sum_ {j ^ {\prime}} \mathbf {W} _ {i, j ^ {\prime}}\right) - 2\right) \\ = 2 \sum_ {i} \mathbf {x} _ {i} (\log \mathbf {x} _ {i} - 1 - \underbrace {\frac {1}{2} (\log \mathbf {z} _ {i} + \log \left[ \sum_ {j ^ {\prime}} \mathbf {W} _ {i , j ^ {\prime}} \right])} _ {\log \mathbf {q} _ {i}}) \\ = 2 \cdot \operatorname {K L} (\mathbf {x} | | \mathbf {q}) \\ \end{array}
+$$
+
+Figure 4: Rewriting the objective function of Eq. (14). We note that the generalized KL divergence  $\mathrm{KL}(\mathbf{x}\mid \mathbf{y}) = \sum_{i}\mathbf{x}_{i}\log \frac{\mathbf{x}_{i}}{\mathbf{y}_{i}} -\mathbf{x}_{i} + \mathbf{y}_{i}$  simplifies to  $\mathrm{KL}(\mathbf{x}\mid \mathbf{y}) = \sum_{i}\mathbf{x}_{i}(\log \frac{\mathbf{x}_{i}}{\mathbf{y}_{i}} -1)$  because we want to find the argmin wrt to  $\mathbf{x}$
+
+in Prop. 2 for any value of  $j$  do not interact with constraints for other values of  $j$ , we can assume w.l.o.g. that  $j$  takes a single value only and drop it in the notation. We want to solve:
+
+$$
+\begin{array}{l} \operatorname * {a r g   m i n} _ {\mathbf {x}, \mathbf {Y}} \qquad \mathrm {K L} (\mathbf {x}   |   |   \mathbf {z}) + \mathrm {K L} (\mathbf {Y}   |   |   \mathbf {W}) \\ \text {s u b j e c t} \quad \sum_ {i} \mathbf {x} _ {i} = 1 \tag {13} \\ \sum_ {k} \mathbf {Y} _ {i k} = \mathbf {x} _ {i} \forall i \\ \end{array}
+$$
+
+We can find  $\mathbf{Y}^{*} = \arg \min_{\mathbf{Y}}\mathrm{KL}(\mathbf{Y}\parallel \mathbf{W})$  subject to  $\sum_{j}\mathbf{Y}_{i,j} = \mathbf{x}_i$  based on Prop. 1:  $\mathbf{Y}_{i,j}^{*} = \frac{\mathbf{x}_{i}\mathbf{W}_{i,j}}{\sum_{j}\mathbf{W}_{i,j}}$ . That is, we can express  $\mathbf{Y}^*$  as a function of  $\mathbf{x}$  (which we write  $\mathbf{Y}^{*}(\mathbf{x})$ ), and therefore our overall problem is now a problem in one variable  $(\mathbf{x})$ :
+
+$$
+\underset {\mathbf {x}} {\arg \min } \quad \mathrm {K L} (\mathbf {x} \mid \mid \mathbf {z}) + \mathrm {K L} \left(\mathbf {Y} ^ {*} (\mathbf {x}) \mid \mid \mathbf {W}\right) \tag {14}
+$$
+
+subject to  $\sum_{i}\mathbf{x}_{i} = 1$
+
+We can now rewrite the objective function as
+
+$$
+\begin{array}{l} \underset {\mathbf {x}} {\arg \min } \quad \operatorname {K L} (\mathbf {x} | | \mathbf {q}) \\ \text {s u b j e c t} \quad \sum_ {i} \mathbf {x} _ {i} = 1 \tag {15} \\ \end{array}
+$$
+
+where  $\mathbf{q}_i = \sqrt{\mathbf{z}_i \cdot \sum_{j'} \mathbf{W}_{i,j'}}$ . This step is justified in detail in Fig. 4.
+
+The rewritten optimization problem has the right form to apply Prop. 1 a second time. We obtain:
+
+$$
+\mathbf {x} _ {i} ^ {*} = \frac {\mathbf {q} _ {i}}{\sum_ {i ^ {\prime}} \mathbf {q} _ {i ^ {\prime}}}
+$$
+
+By plugging this into  $\mathbf{Y}^{*}(\mathbf{x})$ , we obtain the solution to the overall optimization problem.
+
+# A.3 Reduction of Eq. (8) to Eq. (6)
+
+In this section, we show how Eq. (8) can be reduced to a problem of the entropy regularized version of Eq. (6). This is useful because it means we can use Algorithm 1 to solve Eq. (8).
+
+First, we show that computing a KL projection is equivalent to solving an entropy-regularized linear program. Let  $C$  be the feasible region of the linear constraints.
+
+$$
+\begin{array}{l} \underset {\mathbf {x} \in C} {\arg \max} \mathbf {s} ^ {T} \mathbf {x} - \tau \sum_ {i} \mathbf {x} _ {i} (\log \mathbf {x} _ {i} - 1) \\ = \underset {\mathbf {x} \in C} {\arg \min } \tau \sum_ {i} \mathbf {x} _ {i} \left(\log \mathbf {x} _ {i} - \frac {\mathbf {s} _ {i}}{\tau} - 1\right) \\ = \operatorname * {a r g   m i n} _ {\mathbf {x} \in C} \mathrm {K L} (\mathbf {x} | | \exp (\frac {\mathbf {s}}{\tau})) \\ \end{array}
+$$
+
+Due to this, Eq. (8) is equivalent to a linear program that has the same feasible region as Eq. (6) except for the additional constraint  $\mathbf{U} \in \mathcal{Q}(\mathbf{y}, \mathbf{z}^{\prime})$ . Note that  $\mathbf{U} \in \mathcal{Q}(\mathbf{y}, \mathbf{z}^{\prime})$  essentially rules out certain correspondences. Therefore we can approximately enforce  $\mathbf{U} \in \mathcal{Q}(\mathbf{y}, \mathbf{z}^{\prime})$  by masking  $\mathbf{U}^{*}(s)$  such that any forbidden correspondence receives a very low score.
+
+# A.4 Derivation of loss function as ELBO
+
+We now show how the training procedure we use to train our permutation model can be derived from a form of evidence lower bound (ELBO).
+
+Ideally, our permutation model would be a distribution  $P_{\theta}(\mathbf{R}|\mathbf{x},\mathbf{z}^{\prime})$  over permutation matrices  $\mathbf{R}$  and we would maximize the marginal likelihood, i.e. marginalizing over all permutations:
+
+$$
+P (\mathbf {y} | \mathbf {x}, \mathbf {z} ^ {\prime}) = \sum_ {\mathbf {R} \in \mathcal {P}} P _ {\theta} (\mathbf {R} | \mathbf {x}, \mathbf {z} ^ {\prime}) P (\mathbf {y} | \mathbf {z} ^ {\prime}, \mathbf {R}) \tag {16}
+$$
+
+where  $P(\mathbf{y}|\mathbf{z}',\mathbf{R}) = \prod_{j}\sum_{i}R_{ij}\cdot \mathbb{1}(y_{j} = z_{i})$  with 1 being the indicator function.  $P(\mathbf{y}|\mathbf{z}',\mathbf{R})$  returns 1 iff applying the permutation  $\mathbf{R}$  to  $\mathbf{z}'$  results in  $\mathbf{y}$ . Unfortunately, computing Eq. (16) exactly is intractable in general due to the sum over permutation matrices. We instead use techniques from variational inference and consider the following evidence lower bound (ELBO):
+
+$$
+\begin{array}{l} \log P (\mathbf {y} | \mathbf {x}, \mathbf {z} ^ {\prime}) \geq \max  _ {Q} \mathbb {E} _ {\mathbf {R} \sim Q (\mathbf {R} | \mathbf {x}, \mathbf {z} ^ {\prime}, \mathbf {y})} \log P (\mathbf {y} | \mathbf {z} ^ {\prime}, \mathbf {R}) \\ - \operatorname {K L} \left(Q \left(\mathbf {R} \mid \mathbf {x}, \mathbf {z} ^ {\prime}, \mathbf {y}\right) \mid \mid P _ {\theta} \left(\mathbf {R} \mid \mathbf {x}, \mathbf {z} ^ {\prime}\right)\right) \tag {17} \\ \end{array}
+$$
+
+where  $Q(\mathbf{R}|\mathbf{x},\mathbf{z}',\mathbf{y})$  is an approximate variational posterior. We now relax the restriction that  $P(\mathbf{R}|\mathbf{x},\mathbf{z}')$  places non-zero mass only on permutation matrices and use the following definition of  $P_{\theta}(\mathbf{R}|\mathbf{x},\mathbf{z}')$ :
+
+$$
+P _ {\theta} (\mathbf {R} _ {i j} = 1 | \mathbf {x}, \mathbf {z} ^ {\prime}) = \mathbf {U} ^ {*} (s) _ {i j}
+$$
+
+where  $\mathbf{U}^{*}(s)$  is the solution to Eq. (6) with added entropy regularization.
+
+It turns out, in our case, we can easily construct a variational posterior  $Q$  that has zero reconstruction loss (the first term on the right side in Eq. (17)): we can choose any  $Q(\mathbf{R}|\mathbf{x},\mathbf{z}',\mathbf{y}) \in \mathcal{Q}(\mathbf{y},\mathbf{z}')$  where  $\mathcal{Q}(\mathbf{y},\mathbf{z}')$  is the set of bistochastic matrices such that  $Q(\mathbf{R}|\mathbf{x},\mathbf{z}',\mathbf{y})_{i,j} = 0$  iff  $\mathbf{z}_i' \neq \mathbf{y}_j$ . To see that this gives zero reconstruction error, consider position  $j$  in the output: The probability mass is distributed across precisely those positions  $i$  in  $\mathbf{z}'$  where the
+
+![](images/6f553078e2b9763614a0a8181e5c28a0b3f546af1a9fbea5b2943038d71b21b0.jpg)  
+Figure 5: Accuracy on the document domain of Okapi by number of conjuncts in the gold logical form.
+
+<table><tr><td></td><td></td><td>BART perm</td><td>Ours</td></tr><tr><td rowspan="3">COGS</td><td>OS</td><td>16±8</td><td>33±24</td></tr><tr><td>CP</td><td>17±3</td><td>82±11</td></tr><tr><td>PP</td><td>16±5</td><td>91±5</td></tr><tr><td rowspan="2">ATIS</td><td>iid</td><td>77.10±1.61</td><td>76.65±1.67</td></tr><tr><td>Length</td><td>23.81±9.45</td><td>41.39±13.47</td></tr></table>
+
+Table 6: Performance of our permutation model in comparison to using BART for predicting the permutation. We ignore the order of conjuncts for evaluation.
+
+right kind of token lives. In other words, any alignment with non-zero probability will reconstruct the output token at position  $j$ .
+
+Therefore we can use the following lower bound to the log-likelihood:
+
+$$
+\begin{array}{l} \log P (y | \mathbf {x}, \mathbf {z} ^ {\prime}) \geq \tag {18} \\ - \min  _ {Q \in \mathcal {Q} (\mathbf {y}, \mathbf {z})} \operatorname {K L} (Q (\mathbf {R} | \mathbf {x}, \mathbf {z} ^ {\prime}, \mathbf {y}) \mid | P _ {\theta} (\mathbf {R} | \mathbf {x}, \mathbf {z} ^ {\prime})) \\ \end{array}
+$$
+
+During training, we need to compute the gradient of Eq. (18). By Danskin's theorem (Danskin, 1967), this is:
+
+$$
+- \nabla_ {\theta} \mathrm {K L} \left(Q ^ {*} \mid \mid P _ {\theta} (\mathbf {R} | \mathbf {x}, \mathbf {z} ^ {\prime})\right) \tag {19}
+$$
+
+where  $Q^{*}\in \mathcal{Q}(\mathbf{y},\mathbf{z}^{\prime})$  is the minimizer of Eq. (18). Note that  $Q^{*}$  can equivalently be characterised as  $\hat{\mathbf{U}}$  (Eq. (8)).
+
+In practice, we also add  $-\mathrm{KL}(\hat{\mathbf{W}} |\mathbf{W}^{*}(s))$  to our objective in Eq. (18) to speed up convergence; this does not change the fact that we use a lower bound.
+
+# B Additional results and analysis
+
+Okapi. In Fig. 5 we show the accuracy of our model on the document domain in comparison with previous work by number of conjuncts in the logical form.
+
+Permutation baseline. A simpler approach for predicting a permutation of the output  $z'$  from
+
+the multiset tagging is to use a seq2seq model. In order to compare our approach to such a baseline, we concatenate the original input  $x$  with a separator token and  $z'$ . We then feed this as input to a BART-base model which is trained to predict the output sequence  $y$ . At inference time, we use beam search and enforce the output to be a permutation of the input. As detailed in Table 6, this approach works well in-distribution and it also shows a small improvement over finetuning BART directly on the length split of ATIS. However, it does not perform as well as our approach. On COGS, our model outperforms the permutation baseline by an even bigger margin. Unseen variable symbols could be a challenge for BART on COGS which might explain part of the gap in performance.
+
+This approach towards predicting permutations is similar to that of Cazzaro et al. (2023) except that they do not constrain the beam search to permutations. We found that not constraining the output to be a permutation worked worse in the compositional generalization setups.
+
+# C Further model details
+
+# C.1 Parametrization of permutation model
+
+We do not share parameters between the multiset tagging model and the permutation model.
+
+Tokens that appear more than once in the same multiset have the same representation  $\mathbf{h}_i^\prime$  in Eq. (7). In order to distinguish them, we concatenate another embedding to  $\mathbf{h}_i^\prime$ : if the token  $z_i^\prime$  is the  $k$ -th instance of its type in its multiset, we concatenate an embedding for  $k$  to  $\mathbf{h}_i^\prime$ . For example, in Fig. 1,  $z_5^\prime = \times_1$  and it is the second instance of  $\times_1$  in its multiset, so we use the embedding for 2.
+
+We found it helpful to make the temperature  $\tau$  of the scores for Algorithm 1 dependent on the number of elements in the permutation, setting  $\tau = (\log n)^{-1}$ , so that longer sequences have slightly sharper distributions.
+
+Since the permutation model is designed to model exactly permutations, during training,  $z$  and  $y$  must have the same elements. This is not guaranteed because  $z$  is the prediction of the multiset model which may not have perfect accuracy on the training data. For simplicity, we disregard instances where  $z$  and  $y$  do not have the same elements. In practice, this leads to a very small loss in training data for the permutation model.
+
+# C.2 Lexicon mechanism
+
+The lexicon  $L$  is a lookup table that deterministically maps an input token  $x_{i}$  to an output token  $L(x_{i})$ , and we modify the distribution for multiset tagging as follows:
+
+$$
+P ^ {\prime} (\mathbf {z} _ {i, v} = k | \mathbf {x}) = \left\{ \begin{array}{l l} P (\mathbf {z} _ {i, \mathcal {L}} = k | \mathbf {x} _ {i}) & \text {i f} v = L (\mathbf {x} _ {i}) \\ P (\mathbf {z} _ {i, v} = k | \mathbf {x}) & \text {e l s e} \end{array} \right.
+$$
+
+where  $P(\mathbf{z}_{i,v} = k|\mathbf{x})$  is as defined in Eq. (3) and  $\mathcal{L}$  is a special lexicon symbol in the vocabulary.  $P(\mathbf{z}_{i,\mathcal{L}}|\mathbf{x}_i)$  is a distribution over the multiplicity of  $L(\mathbf{x}_i)$ , independent of the identity of  $L(x_{i})$ . We use the 'simple' lexicon induction method by Akyurek and Andreas (2021). Unless otherwise specified during learning,  $L(\mathbf{x}_i) = \mathbf{x}_i$  like in a copy mechanism.
+
+Handling of variables in COGS. For the COGS dataset, a model has to predict variable symbols. The variables are numbered (0-based) by the input token that introduced it (e.g. in Fig. 1, slept, the third token, introduces a variable symbol  $x_{2}$ ). In order to robustly predict variable symbols for sentences with unseen length, we use a similar mechanism as the lexicon look up table: we introduce another special symbol in the vocabulary, Var. If Var is predicted with a multiplicity of  $k$  at  $i$ -th input token, it adds the token  $x_{i-1}$  to its multiset  $k$  times.
+
+# C.3 Initialization of Multiset Tagging model
+
+If there are  $l$  alignments with a posterior probability of at least  $\chi$  that an input token  $i$  produces token  $v$ , we add the term  $\lambda \log P(\mathbf{z}_{i,v} \geq l \mid \mathbf{x})$  to Eq. (4).  $\lambda$  is the hyperparameter determining the strength. This additional loss is only used during the first  $g$  epochs.
+
+# D Datasets and Preprocessing
+
+We show basic statistics about the data we use in Table 7. Except for the doubling task, all our datasets are in English. COGS uses a small fragment of English generated by a grammar, see Kim and Linzen (2020) for details.
+
+Doubling task. For the doubling task, we use an alphabet of size  $|\Sigma| = 11$ . To generate inputs with a specific range of lengths, we first draw a length from the range uniformly at random. The symbols in the input are also drawn uniformly at random and then concatenated into a sequence. Examples of lengths 5 - 10 are used as training, examples of
+
+<table><tr><td>Dataset</td><td>Split/Version</td><td>Train</td><td>Dev</td><td>Test</td></tr><tr><td>Doubling</td><td></td><td>4,000</td><td>500</td><td>1,000</td></tr><tr><td>COGS</td><td></td><td>24,155</td><td>3,000</td><td>21,000</td></tr><tr><td rowspan="2">ATIS</td><td>iid</td><td>4,465</td><td>497</td><td>448</td></tr><tr><td>length</td><td>4,017</td><td>942</td><td>331</td></tr><tr><td rowspan="3">Okapi</td><td>Calendar</td><td>1,145</td><td>200</td><td>1061</td></tr><tr><td>Document</td><td>2,328</td><td>412</td><td>514</td></tr><tr><td>Email</td><td>2,343</td><td>200</td><td>991</td></tr></table>
+
+Table 7: Number of examples per dataset/split.
+
+length 11 are used as development data (e.g. for hyperparameter selection), and examples of length 11 - 20 are used as test data.
+
+# D.1 Preprocessing
+
+COGS. Unlike Zheng and Lapata (2022); Qiu et al. (2022); Drozdov et al. (2022) we do not apply structural preprocessing to the original COGS meaning representation and keep the variable symbols: all our preprocessing is local and aimed at reducing the length of the logical form (to keep runtimes low). We delete any token in  $\{\text{"},\text {"},\text {"}_{-}\text {"},\text {"}(\text {"},\text {"})\text {"},\text {"}x\text {"},\text {"}. \text {"},\text {"};\text {"},\text {"AND"}\}$  as these do not contribute to the semantics and can be reconstructed easily in post-processing. The tokens {"agent", "theme", "recipient", "ccomp", "xcomp", "nmod", "in", "on", "beside"} are always preceded by a ". ." and we merge ". ." and any of those tokens into a single token.
+
+Example:
+
+\* cookie ( x _ 3 ) ; \* table ( x _ 6 ) ; lend . agent ( x _ 1 , Dylan ) AND lend . theme ( x _ 1 , x _ 3 ) AND lend . recipient ( x _ 1 , x _ 9 ) AND cookie . nmod . beside ( x _ 3 , x _ 6 ) AND girl ( x _ 9 )
+
+Becomes
+
+\* cookie 3 \* table 6 lend .agent 1 Dylan lend .theme 1 3 lend .recipient 1 9 cookie .nmod .beside 3 6 girl 9
+
+ATIS. We follow the pre-processing by Lindemann et al. (2023) and use the variable-free FunQL representation as annotated by Guo et al. (2020). We use spacy 3.0.5 (model en_core_web_sm) to tokenize the input.
+
+Okapi. Again, we follow the preprocessing of Lindemann et al. (2023). We use spacy 3.0.5 (model en_core_web_sm) to tokenize both the input utterances and the output logical forms.
+
+# E Details on evaluation metrics
+
+We provide code for all evaluation metrics in our repository.
+
+Doubling. We use exact match accuracy on the string.
+
+COGS. For COGS we use exact match accuracy on the sequence in one evaluation setup. The other evaluation setup disregards the order of conjuncts: we first remove the 'preamble' (which contains all the definite descriptions) from the conjunctions. We count a prediction as correct if the set of definite descriptions in the preamble matches the set of definite descriptions in the gold logical form and the set of clauses in the prediction match the set of clauses in the gold logical form.
+
+ATIS. We allow for different order of conjuncts between system output and gold parse in computing accuracy. We do this by sorting conjuncts before comparing two trees node by node. This is the same evaluation metric as used by Lindemann et al. (2023).
+
+Okapi. We follow Hosseini et al. (2021); Lindemann et al. (2023) and disregard the order of the parameters for computing accuracy. We use a case-insensitive string comparison.
+
+# F Hyperparameters
+
+We use the same hyperparameters for all splits of a dataset. For our model, we only tune the hyperparameters of the multiset tagging model; the permutation model is fixed, and we use the same configuration for all tasks where we use RoBERTa. For model ablations where we use an LSTM instead of RoBERTa, we use the same hyperparameters for Okapi and ATIS, and a smaller model for the doubling task. These configurations were determined by hand without tuning. For BART, we use the same hyperparameter as Lindemann et al. (2023).
+
+We follow the random hyperparameter search procedure of Lindemann et al. (2023) for the multiset tagging models and the LSTM/transformer we train from scratch: we sample 20 configurations and evaluate them on the development set. We run the two best-performing configurations again with a different random seed and pick the one with the highest accuracy (comparing the union of the predicted multisets with the gold multiset). We then train and evaluate our model with entirely different random seeds.
+
+<table><tr><td>Dataset</td><td>Model</td><td>First stage</td><td>Second stage</td></tr><tr><td rowspan="3">Doubling</td><td>LSTM</td><td>5</td><td>-</td></tr><tr><td>Transformer</td><td>3</td><td>-</td></tr><tr><td>Ours</td><td>3</td><td>14*</td></tr><tr><td>COGS</td><td>Ours</td><td>20</td><td>80</td></tr><tr><td rowspan="2">ATIS</td><td>Ours</td><td>30</td><td>50</td></tr><tr><td>Ours/LSTM</td><td>30</td><td>110</td></tr><tr><td rowspan="2">Okapi/Calendar</td><td>Ours</td><td>9</td><td>35</td></tr><tr><td>Ours/LSTM</td><td>5</td><td>30</td></tr><tr><td rowspan="2">Okapi/Email</td><td>Ours</td><td>12</td><td>40</td></tr><tr><td>Ours/LSTM</td><td>9</td><td>40</td></tr><tr><td rowspan="2">Okapi/Document</td><td>Ours</td><td>12</td><td>70</td></tr><tr><td>Ours/LSTM</td><td>10</td><td>55</td></tr></table>
+
+Table 8: Average runtime for train/evaluate on dev and test in minutes. For the doubling task, we note that our model has converged usually after  $\frac{1}{4}$  of the time in the table.  
+
+<table><tr><td>Dataset</td><td>Model</td><td>First stage</td><td>Second stage</td></tr><tr><td rowspan="3">Doubling</td><td>LSTM</td><td></td><td>2.462</td></tr><tr><td>Transformer</td><td></td><td>10.424</td></tr><tr><td>Ours</td><td>0.273</td><td>0.463</td></tr><tr><td>COGS</td><td>Ours</td><td>125.091</td><td>127.16</td></tr><tr><td rowspan="2">ATIS</td><td>Ours</td><td>125.506</td><td>127.119</td></tr><tr><td>Ours/LSTM</td><td>3.345</td><td>1.816</td></tr><tr><td rowspan="2">Okapi/Calendar</td><td>Ours</td><td>124.927</td><td>127.03</td></tr><tr><td>Ours/LSTM</td><td>1.493</td><td>1.876</td></tr></table>
+
+Table 9: Number of parameters in millions in the models we train. This includes the  $124.646\mathrm{m}$  params of RoBERTa when we finetune it.
+
+The chosen hyperparameters along with the search space are provided in the github repository.
+
+# G Number of parameters, computing infrastructure and runtime
+
+We show the number of parameters in the models we train in Table 9.
+
+All experiments were run on GeForce GTX 1080 Ti or GeForce GTX 2080 Ti with 12GB RAM and Intel Xeon Silver or Xeon E5 CPUs.
+
+The runtime of one run contains the time for training, evaluation on the devset after each epoch and running the model on the test set. We show runtimes of the model we train in Table 8. Since we evaluate on 5 random seeds (10 for COGS due to high variance of results), our experiments overall took around 64 hours of compute time on our computing infrastructure.
+
+A For every submission:
+
+A1. Did you describe the limitations of your work?
+
+Limitations, at the end of the paper
+
+A2. Did you discuss any potential risks of your work?
+
+No apparent societal risks.
+
+A3. Do the abstract and introduction summarize the paper's main claims?
+
+Abstract and 1
+
+A4. Have you used AI writing assistants when working on this paper?
+
+Left blank.
+
+B Did you use or create scientific artifacts?
+
+6, Appendix D
+
+B1. Did you cite the creators of artifacts you used?
+
+6
+
+B2. Did you discuss the license or terms for use and / or distribution of any artifacts?
+
+The data we create programmatically is likely too simple to be protected by copyright.
+
+B3. Did you discuss if your use of existing artifact(s) was consistent with their intended use, provided that it was specified? For the artifacts you create, do you specify intended use and whether that is compatible with the original access conditions (in particular, derivatives of data accessed for research purposes should not be used outside of research contexts)?
+
+6
+
+B4. Did you discuss the steps taken to check whether the data that was collected / used contains any information that names or uniquely identifies individual people or offensive content, and the steps taken to protect / anonymize it?
+
+Not applicable. Left blank.
+
+B5. Did you provide documentation of the artifacts, e.g., coverage of domains, languages, and linguistic phenomena, demographic groups represented, etc.?
+
+6, Appendix D
+
+B6. Did you report relevant statistics like the number of examples, details of train / test / dev splits, etc. for the data that you used / created? Even for commonly-used benchmark datasets, include the number of examples in train / validation / test splits, as these provide necessary context for a reader to understand experimental results. For example, small differences in accuracy on large test sets may be significant, while on small test sets they may not be.
+
+6, Appendix D
+
+C Did you run computational experiments?
+
+6
+
+C1. Did you report the number of parameters in the models used, the total computational budget (e.g., GPU hours), and computing infrastructure used?
+
+Appendix H
+
+The Responsible NLP Checklist used at ACL 2023 is adopted from NAACL 2022, with the addition of a question on AI writing assistance.
+
+C2. Did you discuss the experimental setup, including hyperparameter search and best-found hyperparameter values?
+
+6, Appendix G, code submission.
+
+C3. Did you report descriptive statistics about your results (e.g., error bars around results, summary statistics from sets of experiments), and is it transparent whether you are reporting the max, mean, etc. or just a single run?
+
+6, Appendix B
+
+C4. If you used existing packages (e.g., for preprocessing, for normalization, or for evaluation), did you report the implementation, model, and parameter settings used (e.g., NLTK, Spacy, ROUGE, etc.)?
+
+Appendix D
+
+D Did you use human annotators (e.g., crowdworkers) or research with human participants?
+
+Left blank.
+
+D1. Did you report the full text of instructions given to participants, including e.g., screenshots, disclaimers of any risks to participants or annotators, etc.?
+
+No response.
+
+D2. Did you report information about how you recruited (e.g., crowdsourcing platform, students) and paid participants, and discuss if such payment is adequate given the participants' demographic (e.g., country of residence)?
+
+No response.
+
+D3. Did you discuss whether and how consent was obtained from people whose data you're using/curating? For example, if you collected data via crowdsourcing, did your instructions to crowdworkers explain how the data would be used?
+
+No response.
+
+D4. Was the data collection protocol approved (or determined exempt) by an ethics review board?
+
+No response.
+
+D5. Did you report the basic demographic and geographic characteristics of the annotator population that is the source of the data?
+
+No response.

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2023/Compounding Geometric Operations for Knowledge Graph Completion/full.md

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+# Compounding Geometric Operations for Knowledge Graph Completion
+
+Xiou Ge $^{1*}$ , Yun-Cheng Wang $^{1}$ , Bin Wang $^{2}$ , C.-C. Jay Kuo $^{1}$
+
+<sup>1</sup>University of Southern California, Los Angeles, California, USA
+
+$^{2}$ National University of Singapore, Singapore
+
+{xiouge, yunchenw, jckuo}@usc.edu, bwang28c@gmail.com
+
+# Abstract
+
+Geometric transformations including translation, rotation, and scaling are commonly used operations in image processing. Besides, some of them are successfully used in developing effective knowledge graph embedding (KGE). Inspired by the synergy, we propose a new KGE model by leveraging all three operations in this work. Since translation, rotation, and scaling operations are cascaded to form a composite one, the new model is named CompoundE. By casting CompoundE in the framework of group theory, we show that quite a few distanced-based KGE models are special cases of CompoundE. CompoundE extends the simple distance-based scoring functions to relation-dependent compound operations on head and/or tail entities. To demonstrate the effectiveness of CompoundE, we perform three prevalent KG prediction tasks including link prediction, path query answering, and entity typing, on a range of datasets. CompoundE outperforms extant models consistently, demonstrating its effectiveness and flexibility. $^1$
+
+# 1 Introduction
+
+Knowledge graphs (KGs) such as DBpedia (Auer et al., 2007), YAGO (Suchanek et al., 2007), NELL (Carlson et al., 2010), Wikidata (Vrandecic and Krötzsch, 2014), Freebase (Bollacker et al., 2008), and ConceptNet (Speer et al., 2017) have been created and made available to the public to facilitate research on KG modeling and applications. Triples, denoted by  $(h,r,t)$ , are basic elements of a KG, where  $h$  and  $t$  are head and tail entities while  $r$  is the relation connecting them. KG representation learning, also known as knowledge graph embedding (KGE), has been intensively studied in recent years. Yet, it remains one of the most fundamental problems in Artificial Intelligence (AI) research.
+
+KGE is critical to many downstream applications such as question answering (Guu et al., 2015) knowledge integration (Chen et al., 2017), text analysis (Li et al., 2019), entity classification (Zhao et al., 2020; Ge et al., 2022), etc. There are several challenges in the design of good KGE models. Complex relation patterns (e.g. 1-to-N, N-to-1, and N-to-N, antisymmetric, transitive, hierarchical relations, etc.) remain difficult to model. Also, each of extant KGE models has its own strengths and weaknesses. It is desired yet unclear how to design a KGE model that leverages strengths of some models and complements weaknesses of others.
+
+Geometric operations such as translation and rotation belong to the family of affine transformations. These operations have been used to build effective KGE models such as TransE, RotatE, and PairRE. Previous KGEs often use a single type of operation to model all relation patterns with different properties. This could be problematic since each operator may have modeling limitations. A synergy of different transformations may complement the weaknesses of individual operators. In fact, generic compound operations yielded from a cascade of affine transformations find numerous applications in image processing (Pratt, 2013), including image warping (Wolberg, 1990), image morphing (Seitz and Dyer, 1996), and robot motion planning (LaValle, 2006). Motivated by the synergy, we propose a new KGE model to address the above-mentioned challenges. Since translation, rotation, and scaling operations are cascaded to form a compound operation, the proposed KGE model is named CompoundE. Compound operations inherit many desirable properties from the affine group, allowing CompoundE to model complex relations in different KGs.
+
+There are four main contributions of this work. They are summarized below.
+
+- We present a novel KG embedding model called CompoundE, which combines three
+
+fundamental operations in the affine group and offers a wide range of designs.
+
+- It is proved mathematically that CompoundE can handle complex relation types in KG thanks to unique properties of the affine group.  
+- We apply CompoundE to perform three important KG prediction tasks, including link prediction, path query answering, and entity typing on widely adopted KG benchmarking datasets extracted from Freebase, WordNet, Wikidata, and YAGO. CompoundE consistently outperforms prior work.  
+- Against large-scale datasets containing millions of entities under the memory constraint, CompoundE outperforms other benchmarking methods by a big margin with fewer parameters.
+
+The rest of this paper is organized as follows. Recent KGE models for both distance-based and entity-Transformation-based categories are first reviewed in Section 2. Then, we present CompoundE, show its relationship with previous KG embedding models, and explain the reason why it can model complex relations well in Section 3. Experiment details and performance comparisons are given in Section 4. Finally, concluding remarks are given and possible extensions are suggested in Section 5.
+
+# 2 Related Work
+
+# 2.1 Distance-based Models
+
+Distance-based scoring function is a prevailing strategy in optimizing KGE. The main idea is to model a relation as a transformation that places head entity vectors in the proximity of their corresponding tail entity vectors, and vice versa. For a given triple,  $(h,r,t)$ , the goal is to minimize the distance between  $h$  and  $t$  vectors after the transformation introduced by  $r$ . TransE (Bordes et al., 2013) is one of the earlier KGE models that interpret relations between entities as translation operations in the vector space. However, this simple approach is ineffective in modeling 1-to-N, N-to-1, N-to-N, and symmetric relations. To better encode complex relations, TransH (Wang et al., 2014) enables the relation-specific entity representation by projecting each entity to a relation-specific hyperplane. In order to represent symmetric relations, RotatE (Sun et al., 2019) models entities in the complex vector
+
+space and interprets a relation as a rotation instead of a translation. The self-adversarial negative sampling contributes to RotatE's performance improvement as compared to its predecessors. However, RotatE does not handle the hierarchical structure appearing in many KGs. MuRP (Balažević et al., 2019) and ROTH (Chami et al., 2020) leverage the power of hyperbolic curvature to better capture the hierarchical structure in KGs.
+
+# 2.2 Entity-Transformation-based Models
+
+Adding relation-specific transformation to baseline models is another popular line of work. Although TransH (Wang et al., 2014) enables the translation approach to model complex relations, the orthogonal projection prevents the model from encoding inverse and composition relations. Instead, TransR (Lin et al., 2015) models relations and entities in two different spaces. However, the relation-specific transformation is a dense matrix and significantly increase parameter complexity. To alleviate this problem, TransD (Ji et al., 2015) comes up with dynamic mapping matrices using relation and entity projection vectors. Similarly, TranSparse (Ji et al., 2016) enforces the relation projection matrix to be sparse. More recently, PairRE (Chao et al., 2021) performs transformations on both heads and tails. Specifically, head and tail entities had a Hadamard product with their respective weight vectors  $\mathbf{r}^{\mathrm{H}}$  and  $\mathbf{r}^{\mathrm{T}}$ . This elementwise multiplication is nothing but the scaling operation. SFBR (Liang et al., 2021) introduces a semantic filter that includes a scaling and translation component. STaR (Li and Yang, 2022) adopts a similar approach but adds a rotation operator to design the bilinear product matrix for semantic matching scoring functions. ReflectE (Zhang et al., 2022a) models a relation as the Householder reflection. Different composition of geometric operations inspire us to invent CompoundE embedding in this paper.
+
+# 3 Methodology
+
+Translation, rotation, and scaling transformations appear frequently in engineering applications. In image processing, a cascade of translation, rotation, and scaling operations offers a set of image manipulation techniques. Such compound operations can be used to develop a new KGE model called CompoundE. We provide an illustration of CompoundE and comparison with previous KGE in Fig. 1.
+
+![](images/03396f7d7e3d61a6ccd20c457132210eab3691c70672d8ac7cf250e2e7109cab.jpg)  
+Figure 1: An illustration of previous distance-based KGE models and CompoundE.
+
+![](images/77aae4e122fe7182f838f83405587e899ed6de3fb7a0d1eb21ed4f707823602d.jpg)
+
+![](images/c751854ef0b2a92283e333ecdbd081b5f05e7b90b2b748303ef8e28d09d51185.jpg)
+
+![](images/d10041a570036f186f9de62920568c24d6063e23f23b639fdad336271495458a.jpg)
+
+# 3.1 Definition of CompoundE
+
+Three forms of CompoundE scoring function can be written as
+
+- CompoundE-Head
+
+$$
+f _ {r} (h, t) = \left\| \mathbf {T} _ {\mathbf {r}} \cdot \mathbf {R} _ {\mathbf {r}} \cdot \mathbf {S} _ {\mathbf {r}} \cdot \mathbf {h} - \mathbf {t} \right\|, \tag {1}
+$$
+
+- CompoundE-Tail
+
+$$
+f _ {r} (h, t) = \left\| \mathbf {h} - \hat {\mathbf {T}} _ {\mathbf {r}} \cdot \hat {\mathbf {R}} _ {\mathbf {r}} \cdot \hat {\mathbf {S}} _ {\mathbf {r}} \cdot \mathbf {t} \right\|, \tag {2}
+$$
+
+- CompoundE-Complete
+
+$$
+f _ {r} (h, t) = \left\| \mathbf {T} _ {\mathbf {r}} \cdot \mathbf {R} _ {\mathbf {r}} \cdot \mathbf {S} _ {\mathbf {r}} \cdot \mathbf {h} - \hat {\mathbf {T}} _ {\mathbf {r}} \cdot \hat {\mathbf {R}} _ {\mathbf {r}} \cdot \hat {\mathbf {S}} _ {\mathbf {r}} \cdot \mathbf {t} \right\|, \tag {3}
+$$
+
+where  $\mathbf{h},\mathbf{t}$  denote head and tail entity embeddings,  $\mathbf{T_r},\mathbf{R_r},\mathbf{S_r}$  denote the translation, rotation, and scaling operations for the head entity embedding, and  $\hat{\mathbf{T}}_{\mathrm{r}},\hat{\mathbf{R}}_{\mathrm{r}},\hat{\mathbf{S}}_{\mathrm{r}}$  denote the counterparts for the tail entity embedding, respectively. These constituent operators are relation-specific. To generalize, any order or subset of translation, rotation, and scaling component can be a valid instance of CompoundE. Since matrix multiplications are non-commutative, different orders of cascading the constituent operators result in distinct CompoundE operators. Performance difference between these variations are discussed in Section B of the appendix.
+
+# 3.2 CompoundE as An Affine Group
+
+Most analysis in previous work was restricted to the Special Euclidean Group  $\mathbf{SE}(n)$  (Cao et al., 2022). Yet, we will show that CompoundE is not a special Euclidean group but an affine group. To proceed, we first formally introduce the lie group and three special groups as below.
+
+Definition 3.1. A Lie group is a continuous group that is also a differentiable manifold.
+
+Several Lie group examples are given below.
+
+- The real vector space,  $\mathbb{R}^n$ , with the canonical addition as the group operation.  
+- The real vector space excluding zero,  $(\mathbb{R} \backslash \{0\})$ , with the element-wise multiplication as the group operation.  
+- The general linear group,  $\mathbf{GL}_n(\mathbb{R})$ , with the canonical matrix multiplication as the group operation.
+
+Furthermore, the following three special groups are commonly used.
+
+Definition 3.2. The special orthogonal group is defined as
+
+$$
+\mathbf {S O} (n) = \left\{\mathbf {A} \mid \mathbf {A} \in \mathbf {G L} _ {n} (\mathbb {R}), \mathbf {A} ^ {\top} \mathbf {A} = \mathbf {I}, \det  (\mathbf {A}) = 1 \right\}. \tag {4}
+$$
+
+Definition 3.3. The special Euclidean group is defined as
+
+$$
+\mathbf {S E} (n) = \left\{\mathbf {A} \mid \mathbf {A} = \left[ \begin{array}{l l} \mathbf {R} & \mathbf {v} \\ \mathbf {0} & 1 \end{array} \right], \mathbf {R} \in \mathbf {S O} (n), \mathbf {v} \in \mathbb {R} ^ {n} \right\}. \tag {5}
+$$
+
+Definition 3.4. The affine group is defined as
+
+$$
+\mathbf {A} \mathbf {f f} (n) = \left\{\mathbf {M} \middle | \mathbf {M} = \left[ \begin{array}{l l} \mathbf {A} & \mathbf {v} \\ \mathbf {0} & 1 \end{array} \right], \mathbf {A} \in \mathbf {G L} _ {n} (\mathbb {R}), \mathbf {v} \in \mathbb {R} ^ {n} \right\}. \tag {6}
+$$
+
+By comparing Eqs. (5) and (6), we see that  $\mathbf{SE}(n)$  is a subset of  $\mathbf{Aff}(n)$ .
+
+Without loss of generality, consider  $n = 2$ . If  $\mathbf{M} \in \mathbf{Aff}(2)$ , we have
+
+$$
+\mathbf {M} = \left[ \begin{array}{c c} \mathbf {A} & \mathbf {v} \\ \mathbf {0} & 1 \end{array} \right], \mathbf {A} \in \mathbb {R} ^ {2 \times 2}, \mathbf {v} \in \mathbb {R} ^ {2}. \tag {7}
+$$
+
+The 2D translational matrix can be written as
+
+$$
+\mathbf {T} = \left[ \begin{array}{l l l} 1 & 0 & v _ {x} \\ 0 & 1 & v _ {y} \\ 0 & 0 & 1 \end{array} \right], \tag {8}
+$$
+
+<table><tr><td>Dataset</td><td>#Entities</td><td>#Relations</td><td>#Training</td><td>#Validation</td><td>#Test</td><td>Ave. Deg.</td><td>Scale</td></tr><tr><td>ogbl-wikikg2</td><td>2,500,604</td><td>535</td><td>16,109,182</td><td>429,456</td><td>598,543</td><td>12.2</td><td>Large</td></tr><tr><td>FB15k-237</td><td>14,541</td><td>237</td><td>272,115</td><td>17,535</td><td>20,466</td><td>19.74</td><td>Medium</td></tr><tr><td>WN18RR</td><td>40,943</td><td>11</td><td>86,835</td><td>3,034</td><td>3,134</td><td>2.19</td><td>Small</td></tr></table>
+
+Table 1: Link Prediction Datasets Statistics.
+
+while the 2D rotational matrix can be expressed as
+
+$$
+\mathbf {R} = \left[ \begin{array}{c c c} \cos (\theta) & - \sin (\theta) & 0 \\ \sin (\theta) & \cos (\theta) & 0 \\ 0 & 0 & 1 \end{array} \right]. \tag {9}
+$$
+
+It is easy to verify that they are both special Euclidean groups (i.e.  $\mathbf{T} \in \mathbf{SE}(2)$  and  $\mathbf{R} \in \mathbf{SE}(2)$ ). On the other hand, the 2D scaling matrix is in form of
+
+$$
+\mathbf {S} = \left[ \begin{array}{c c c} s _ {x} & 0 & 0 \\ 0 & s _ {y} & 0 \\ 0 & 0 & 1 \end{array} \right]. \tag {10}
+$$
+
+It is not a special Euclidean group but an affine group of  $n = 2$  (i.e.,  $\mathbf{S} \in \mathbf{Aff}(2)$ ).
+
+Compounding translation and rotation operations, we can get a transformation in the special Euclidean group,
+
+$$
+\begin{array}{l} \mathbf {T} \cdot \mathbf {R} = \left[ \begin{array}{l l l} 1 & 0 & v _ {x} \\ 0 & 1 & v _ {y} \\ 0 & 0 & 1 \end{array} \right] \left[ \begin{array}{c c c} \cos (\theta) & - \sin (\theta) & 0 \\ \sin (\theta) & \cos (\theta) & 0 \\ 0 & 0 & 1 \end{array} \right] \tag {11} \\ = \left[ \begin{array}{c c c} \cos (\theta) & - \sin (\theta) & v _ {x} \\ \sin (\theta) & \cos (\theta) & v _ {y} \\ 0 & 0 & 1 \end{array} \right] \in \mathbf {S E} (2). \\ \end{array}
+$$
+
+Yet, if we add the scaling operation, the compound will belong to the Affine group. One of such compound operator can be written as
+
+$$
+\mathbf {T} \cdot \mathbf {R} \cdot \mathbf {S} = \left[ \begin{array}{c c c} s _ {x} \cos (\theta) & - s _ {y} \sin (\theta) & v _ {x} \\ s _ {x} \sin (\theta) & s _ {y} \cos (\theta) & v _ {y} \\ 0 & 0 & 1 \end{array} \right] \in \mathbf {A f f} (2). \tag {12}
+$$
+
+When  $s_x \neq 0$  and  $s_y \neq 0$ , the compound operator is invertible. It can be written in form of
+
+$$
+\mathbf {M} ^ {- 1} = \left[ \begin{array}{c c} \mathbf {A} ^ {- 1} & - \mathbf {A} ^ {- 1} \mathbf {v} \\ \mathbf {0} & 1 \end{array} \right]. \tag {13}
+$$
+
+# 3.3 Relation with Other Distance-based KGE Models
+
+CompoundE is a general form of quite a few distance-based KGE models. That is, we can derive their scoring functions from that of CompoundE by setting translation, scaling, and rotation operations to certain forms. Four examples are given below.
+
+Derivation of TransE (Bordes et al., 2013). We begin with CompoundE-Head and set its rotation
+
+component to identity matrix  $\mathbf{I}$  and scaling parameters to 1. Then, we get the scoring function of TransE as
+
+$$
+\begin{array}{l} f _ {r} (h, t) = \left\| \mathbf {T} _ {\mathbf {r}} \cdot \mathbf {I} \cdot \operatorname {d i a g} (\mathbf {1}) \cdot \mathbf {h} - \mathbf {t} \right\| \tag {14} \\ = \left\| \mathbf {h} + \mathbf {r} - \mathbf {t} \right\|. \\ \end{array}
+$$
+
+Derivation of RotatE (Sun et al., 2019). We can derive the scoring function of RotatE from CompoundE-Head by setting the translation component to I (translation vector  $\mathbf{t} = \mathbf{0}$ ) and scaling component to 1.
+
+$$
+\begin{array}{l} f _ {r} (h, t) = \left\| \mathbf {I} \cdot \mathbf {R} _ {\mathbf {r}} \cdot \operatorname {d i a g} (\mathbf {1}) \cdot \mathbf {h} - \mathbf {t} \right\| \tag {15} \\ = \left\| \mathbf {h} \circ \mathbf {r} - \mathbf {t} \right\|. \\ \end{array}
+$$
+
+Derivation of LinearRE (Peng and Zhang, 2020). We can add back the translation component for the head transformation:
+
+$$
+\begin{array}{l} f _ {r} (h, t) = \left\| \mathbf {T} _ {\mathbf {r}} \cdot \mathbf {I} \cdot \mathbf {S} _ {\mathbf {r}} \cdot \mathbf {h} - \mathbf {I} \cdot \mathbf {I} \cdot \hat {\mathbf {S}} _ {\mathbf {r}} \cdot \mathbf {t} \right\| \tag {16} \\ = \left\| \mathbf {h} \odot \mathbf {r} ^ {\mathbf {H}} + \mathbf {r} - \mathbf {t} \odot \mathbf {r} ^ {\mathbf {T}} \right\|. \\ \end{array}
+$$
+
+Derivation of PairRE (Chao et al., 2021). CompoundE-Complete can be reduced to PairRE by setting both translation and rotation component to I, for both head and tail transformation.
+
+$$
+\begin{array}{l} f _ {r} (h, t) = \left\| \mathbf {I} \cdot \mathbf {I} \cdot \mathbf {S} _ {\mathbf {r}} \cdot \mathbf {h} - \mathbf {I} \cdot \mathbf {I} \cdot \hat {\mathbf {S}} _ {\mathbf {r}} \cdot \mathbf {t} \right\| \tag {17} \\ \mathbf {\Omega} = \left\| \mathbf {h} \odot \mathbf {r} ^ {\mathbf {H}} - \mathbf {t} \odot \mathbf {r} ^ {\mathbf {T}} \right\|. \\ \end{array}
+$$
+
+# 3.4 Properties of CompoundE
+
+With a richer set of operations, CompoundE is more capable of modeling complex relations such as 1-to-N, N-to-1, and N-to-N relations in KG datasets. Modeling these relations are important since more than  $98\%$  of triples in FB15k-237 and WN18RR datasets involves complex relations. The importance of complex relation modeling is illustrated by two examples below. First, there is a need to distinguish different outcomes of relation compositions when modeling non-commutative relations. That is  $r_1 \cdot r_2 \rightarrow r_3$  while  $r_2 \cdot r_1 \rightarrow r_4$ . For instance,  $r_1, r_2, r_3$  and  $r_4$  denote FatherOf, MotherOf, GrandfatherOf and isGrandmotherOf, respectively. TransE and RotatE cannot make such
+
+<table><tr><td>Datasets</td><td colspan="4">FB15K-237</td><td colspan="4">WN18RR</td></tr><tr><td>Metrics</td><td>MRR</td><td>Hits@1</td><td>Hits@3</td><td>Hits@10</td><td>MRR</td><td>Hits@1</td><td>Hits@3</td><td>Hits@10</td></tr><tr><td colspan="9">text-based methods</td></tr><tr><td>SimKGC (Wang et al., 2022)</td><td>0.666</td><td>0.587</td><td>0.717</td><td>0.800</td><td>0.336</td><td>0.249</td><td>0.362</td><td>0.511</td></tr><tr><td>KG-S2S (Chen et al., 2022)</td><td>0.574</td><td>0.531</td><td>0.595</td><td>0.661</td><td>0.336</td><td>0.257</td><td>0.373</td><td>0.498</td></tr><tr><td colspan="9">embedding-based methods</td></tr><tr><td>TransE (Bordes et al., 2013)</td><td>0.294</td><td>-</td><td>-</td><td>0.465</td><td>0.226</td><td>-</td><td>-</td><td>0.501</td></tr><tr><td>DistMult (Yang et al., 2015)</td><td>0.241</td><td>0.155</td><td>0.263</td><td>0.419</td><td>0.430</td><td>0.390</td><td>0.440</td><td>0.490</td></tr><tr><td>ComplEx (Trouillon et al., 2016)</td><td>0.247</td><td>0.158</td><td>0.275</td><td>0.428</td><td>0.440</td><td>0.410</td><td>0.460</td><td>0.510</td></tr><tr><td>RotatE (Sun et al., 2019)</td><td>0.338</td><td>0.241</td><td>0.375</td><td>0.533</td><td>0.476</td><td>0.428</td><td>0.492</td><td>0.571</td></tr><tr><td>ROTH (Chami et al., 2020)</td><td>0.348</td><td>0.252</td><td>0.384</td><td>0.540</td><td>0.496</td><td>0.449</td><td>0.514</td><td>0.586</td></tr><tr><td>PairRE (Chao et al., 2021)</td><td>0.351</td><td>0.256</td><td>0.387</td><td>0.544</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>FieldE (Nayyeri et al., 2021)</td><td>0.36</td><td>0.27</td><td>0.39</td><td>0.55</td><td>0.48</td><td>0.44</td><td>0.50</td><td>0.57</td></tr><tr><td>KGTuner (Zhang et al., 2022b)</td><td>0.352</td><td>0.263</td><td>0.387</td><td>0.530</td><td>0.484</td><td>0.440</td><td>0.506</td><td>0.562</td></tr><tr><td>IAS (Yang et al., 2022)</td><td>0.339</td><td>0.242</td><td>0.374</td><td>0.532</td><td>0.483</td><td>0.467</td><td>0.502</td><td>0.570</td></tr><tr><td>CAKE (Niu et al., 2022)</td><td>0.321</td><td>0.227</td><td>0.355</td><td>0.515</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>CompoundE</td><td>0.357</td><td>0.264</td><td>0.393</td><td>0.545</td><td>0.491</td><td>0.450</td><td>0.508</td><td>0.576</td></tr></table>
+
+Table 2: Filtered ranking of link prediction for FB15k-237 and WN18RR.
+
+distinctions since they are based on commutative relation embeddings. Second, to capture the hierarchical structure of relations, it is essential to build a good model for sub-relations. For example,  $r_1$  and  $r_2$  denote isCapitalCityOf and cityLocatedInCountry, respectively. Logically, isCapitalCityOf is a sub-relation of cityLocatedInCountry because if  $(h, r_1, t)$  is true, then  $(h, r_2, t)$  must be true. We provide mathematical proofs to show that CompoundE is capable of modeling symmetric/antisymmetric, inversion, composition, commutative/non-commutative, transitive, and sub-relations in Section A of the appendix.
+
+Optimization We follow RotatE's negative sampling loss and the self-adversarial training strategy. The loss function of CompoundE can be written as
+
+$$
+\begin{array}{l} L _ {\mathrm {K G E}} = - \log \sigma \left(\zeta_ {1} - f _ {r} (h, t)\right) \\ - \sum_ {i = 1} ^ {n} p \left(h _ {i} ^ {\prime}, r, t _ {i} ^ {\prime}\right) \log \sigma \left(f _ {r} \left(h _ {i} ^ {\prime}, t _ {i} ^ {\prime}\right) - \zeta_ {1}\right), \tag {18} \\ \end{array}
+$$
+
+where  $\sigma$  is the sigmoid function,  $\zeta_{1}$  is a fixed margin hyperparameter,  $(h_i', r, t_i')$  is the  $i$ -th negative triple, and  $p(h_i', r, t_i')$  is the probability of drawing negative triple  $(h_i', r, t_i')$ . Given a positive triple,  $(h_i, r, t_i)$ , the negative sampling distribution is
+
+$$
+p \left(h _ {j} ^ {\prime}, r, t _ {j} ^ {\prime} \mid \left\{\left(h _ {i}, r, t _ {i}\right) \right\}\right) = \frac {\exp \alpha_ {1} f _ {r} \left(h _ {j} ^ {\prime} , t _ {j} ^ {\prime}\right)}{\sum_ {i} \exp \alpha_ {1} f _ {r} \left(h _ {i} ^ {\prime} , t _ {i} ^ {\prime}\right)}, \tag {19}
+$$
+
+where  $\alpha_{1}$  is the temperature of sampling.
+
+# 4 Experiments
+
+# 4.1 Link Prediction
+
+Datasets. We conduct experiments on three widely used benchmarking datasets: ogbl-wikikg2, FB15k-237, and WN18RR. ogbl-wikikg2 is one of Open Graph Benchmark dataset (Hu et al., 2020) extracted from the Wikidata (Vrandecic and Krötzsch, 2014) KG. Its challenge is with designing embedding models that can scale to large KGs. FB15k-237 and WN18RR are extracted from the Freebase (Bollacker et al., 2008) and the WordNet (Miller, 1995), respectively. Inverse relations are removed from both to avoid the data leakage problem. Their main challenge lies in modeling symmetry/antisymmetry and composition relation patterns. The detailed statistics of the three datasets are shown in Table 1.
+
+Evaluation Protocol. To evaluate the link prediction performance of CompoundE, we compute the rank of the ground truth entity in the list of top candidates. Since embedding models tend to rank entities observed in the training set higher, we compute the filtered rank to prioritize candidates that would result in unseen triples. We follow the convention (Wang et al., 2017; Ji et al., 2021) and adopt the Mean Reciprocal Rank (MRR) and Hits@k metrics to compare the quality of different KGE models. Higher MRR and Hits@k values indicate better model performance.
+
+Performance Benchmarking. Tables 2 and 3 show the best performance of CompoundE and other benchmarking models for FB15k-237,
+
+<table><tr><td>Datasets</td><td colspan="3">ogbl-wikikg2</td></tr><tr><td>Metrics</td><td>Dim</td><td>Valid MRR</td><td>Test MRR</td></tr><tr><td>AutoSF+NodePiece</td><td>100</td><td>0.5806</td><td>0.5703</td></tr><tr><td>ComplEx-RP</td><td>50</td><td>0.6561</td><td>0.6392</td></tr><tr><td>TransE</td><td>500</td><td>0.4272</td><td>0.4256</td></tr><tr><td>DistMult</td><td>500</td><td>0.3506</td><td>0.3729</td></tr><tr><td>ComplEx</td><td>250</td><td>0.3759</td><td>0.4027</td></tr><tr><td>RotatE</td><td>250</td><td>0.4353</td><td>0.4353</td></tr><tr><td>PairRE</td><td>200</td><td>0.5423</td><td>0.5208</td></tr><tr><td>TripleRE</td><td>200</td><td>0.6045</td><td>0.5794</td></tr><tr><td>CompoundE</td><td>100</td><td>0.6704</td><td>0.6515</td></tr></table>
+
+Table 3: Filtered ranking of link prediction on ogbl-wikikg2. Best results are in bold and best known published results are underlined.
+
+WN18RR and ogbl-wikikg2 datasets, respectively. The best results are shown in bold fonts whereas the second best are underlined. CompoundE is a competitive model among embedding-based methods across all three datasets. As shown in Table 3, the results of CompoundE are much better than previous KGE models while the embedding dimension and the model parameter numbers are significantly lower for the ogbl-wikikg2 dataset. This implies lower computation and memory costs of CompoundE. We see from Table 2 that CompoundE has achieved significant improvement over distance-based KGE models using a single operation, either translation (TransE), rotation (RotatE), or scaling (PairRE). This confirms that cascading geometric transformations is an effective strategy for designing KG embeddings. In Table 2, we also compare CompoundE with text-based methods for link prediction on FB15k-237 and WN18RR datasets. Note that text-based methods require entity textual descriptions to make meaningful prediction. It is worth noting that CompoundE can still outperform transformer-based approaches significantly for WN18RR dataset, without having access to large amount of pretraining corpus.
+
+Performance on Different Relation Types. To gain insights into the superior performance of CompoundE, we examine the performance of CompoundE on each type of relations. KG relations can be categorized into 4 types: 1) 1-to-1, 2) 1-to-N, 3) N-to-1, and 4) N-to-N. We classify the relations based on the following rule. For each relation,  $r$ , we compute the average number of subject (head) entities per object (tail) entity as  $hpt_r$  and the average number of object entities per subject as
+
+![](images/a5b08a500d6772c997a513f1f6cc6bdee6840cbd9a39902045ce717df2e05ac5.jpg)  
+Figure 2: Distribution of relation embedding values for "friends" relation in FB15k-237, obtained using  $\| \mathbf{S}_{\mathbf{r}}\cdot \mathbf{R}_{\mathbf{r}}\cdot \mathbf{T}_{\mathbf{r}}\cdot \mathbf{h} - \mathbf{t}\|$ .
+
+$tph_{r}$ . Then, with a specific threshold  $\eta$ ,
+
+$$
+\left\{ \begin{array}{l} h p t _ {r} <   \eta \text {a n d} t p h _ {r} <   \eta \Rightarrow r \text {i s 1 - t o - 1} \\ h p t _ {r} <   \eta \text {a n d} t p h _ {r} \geq \eta \Rightarrow r \text {i s 1 - t o - N} \\ h p t _ {r} \geq \eta \text {a n d} t p h _ {r} <   \eta \Rightarrow r \text {i s N - t o - 1} \\ h p t _ {r} \geq \eta \text {a n d} t p h _ {r} \geq \eta \Rightarrow r \text {i s N - t o - N}. \end{array} \right. \tag {20}
+$$
+
+We set  $\eta = 1.5$  as a logical threshold by following the convention. Table 4 compares the MRR scores of CompoundE with benchmarking models on 1-to-1, 1-to-N, N-to-1, and N-to-N relations in head and tail entities prediction performance for the FB15k237 dataset. We see that CompoundE consistently outperforms benchmarking models in all relation categories. The filtered MRR scores on each relation type of the WN18RR dataset are given in Table 5. We observe that CompoundE has a significant advantage over benchmarking models for certain 1-to-N relations such as "member_of_domain_region"  $(+84.8\%)$  and for some N-to-1 relations such as "synset_domain_topic_of"  $(+12.7\%)$ . CompoundE is more effective than previous KGE models in modeling complex relations.
+
+In Fig. 2, we visualize relation embedding for the "friend" relation in FB15k-237 by plotting the histogram of translation, rotation, and scaling parameter values. Since "friend" is a symmetric relation, we expect the translation value to be close to zero, which is consistent with Fig. 2 (a). Also, since "friend" is an N-to-N relation, we expect the Compound operation to be singular. Actually, most of the scaling values are zero as shown in Fig. 2 (c). They support our theoretical analysis of CompoundE's properties.
+
+# 4.2 Path Query Answering
+
+Path query is important since it is often desired to perform complex queries on knowledge graph. For example, one might ask "where did Michelle Obama's spouse live in?" To obtain the answer, a
+
+<table><tr><td>Task</td><td colspan="4">Predicting Head</td><td colspan="4">Predicting Tail</td></tr><tr><td>Type</td><td>1-to-1</td><td>1-to-N</td><td>N-to-1</td><td>N-to-N</td><td>1-to-1</td><td>1-to-N</td><td>N-to-1</td><td>N-to-N</td></tr><tr><td>TransE</td><td>0.492</td><td>0.454</td><td>0.081</td><td>0.252</td><td>0.485</td><td>0.072</td><td>0.740</td><td>0.367</td></tr><tr><td>RotatE</td><td>0.493</td><td>0.471</td><td>0.088</td><td>0.259</td><td>0.491</td><td>0.072</td><td>0.748</td><td>0.370</td></tr><tr><td>PairRE</td><td>0.496</td><td>0.476</td><td>0.117</td><td>0.274</td><td>0.492</td><td>0.073</td><td>0.763</td><td>0.387</td></tr><tr><td>CompoundE</td><td>0.501</td><td>0.488</td><td>0.123</td><td>0.279</td><td>0.497</td><td>0.074</td><td>0.783</td><td>0.394</td></tr></table>
+
+Table 4: Filtered MRR on four relation types of FB15k-237.  
+
+<table><tr><td>Relation</td><td>Type</td><td>TransE</td><td>RotatE</td><td>Ours</td></tr><tr><td>similar_to</td><td>1-to-1</td><td>0.294</td><td>1.000</td><td>1.000</td></tr><tr><td>verb_group</td><td>1-to-1</td><td>0.363</td><td>0.961</td><td>0.974</td></tr><tr><td>member_meronym</td><td>1-to-N</td><td>0.179</td><td>0.259</td><td>0.254</td></tr><tr><td>has_part</td><td>1-to-N</td><td>0.117</td><td>0.200</td><td>0.200</td></tr><tr><td>member_of_domain_usage</td><td>1-to-N</td><td>0.113</td><td>0.297</td><td>0.309</td></tr><tr><td>member_of_domain_region</td><td>1-to-N</td><td>0.114</td><td>0.217</td><td>0.401</td></tr><tr><td>hypernym</td><td>N-to-1</td><td>0.059</td><td>0.156</td><td>0.179</td></tr><tr><td>instance_hypernym</td><td>N-to-1</td><td>0.289</td><td>0.322</td><td>0.351</td></tr><tr><td>synset_domain_topic_of</td><td>N-to-1</td><td>0.149</td><td>0.339</td><td>0.382</td></tr><tr><td>also Seeing</td><td>N-to-N</td><td>0.227</td><td>0.625</td><td>0.629</td></tr><tr><td>derivationally_related_form</td><td>N-to-N</td><td>0.440</td><td>0.957</td><td>0.956</td></tr></table>
+
+model first need to correctly predict the fact that (Michelle Obama, spouse, Barack Obama), and then predict (Barack Obama, livedIn, Chicago). CompoundE has the property to perform well on this task since it is capable of modeling the noncommutative relation compositions.
+
+In Path Query Answering (PQA), a tuple  $(s, P, t)$  is given, where  $s$  and  $t$  denote the source and target entities and  $P = \{r_1, \dots, r_k\}$  denotes the relation path consisting of a sequence of relations that links  $s \rightarrow r_1 \rightarrow r_2 \dots \rightarrow r_k \rightarrow t$ . PQA tests that after traversing through the relation path from a given source entity, whether the model is able to predict the correct target entity. During testing, the ground truth  $t$  is hidden and we compute the score for all candidate target entities and evaluate the quantile of ground truth, which is the fraction of irrelevant candidates that's ranked lower than the ground truth. Mean quantile of all test paths are reported. In particular, type match paths are excluded since those are trivial for prediction. Specifically, we use both the KG triples and sampled paths with length  $|P| \in \{2, 3, 4, 5\}$  to train the embedding, which is also referred to as the "comp" setting (Guu et al., 2015). We use CompoundE to perform PQA on the Freebase and WordNet datasets prepared by (Guu et al., 2015). Statistics of these two datasets are shown in Table 10. Performance comparison with previous models on the PQA task under the "comp"
+
+setting is shown in Table 6. Results show that CompoundE is very competitive for the PQA task among pure embedding models.
+
+Table 5: Filtered MRR on each relation type of WN18RR.  
+
+<table><tr><td></td><td colspan="2">WordNet</td><td colspan="2">Freebase</td></tr><tr><td></td><td>MQ</td><td>H@10</td><td>MQ</td><td>H@10</td></tr><tr><td>Bilinear</td><td>0.894</td><td>0.543</td><td>0.835</td><td>0.421</td></tr><tr><td>TransE</td><td>0.933</td><td>0.435</td><td>0.880</td><td>0.505</td></tr><tr><td>DistMult</td><td>0.904</td><td>0.311</td><td>0.848</td><td>0.386</td></tr><tr><td>RotatE</td><td>0.947</td><td>0.653</td><td>0.901</td><td>0.601</td></tr><tr><td>Rotate3D</td><td>0.949</td><td>0.671</td><td>0.905</td><td>0.621</td></tr><tr><td>CompoundE</td><td>0.951</td><td>0.674</td><td>0.913</td><td>0.650</td></tr></table>
+
+Table 6: Performance comparison for path query answering.
+
+# 4.3 KG Entity Typing
+
+KG Entity typing predicts class labels for nodes in knowledge graph. Entity type provides semantic signals for information extraction tasks such as relation extraction (Yaghoobzadeh et al., 2017), entity linking (Gupta et al., 2017; Choi et al., 2018) and coreference resolution (Durrett and Klein, 2014). Entity typing is challenging since each entity may be associated with a large number of type labels. We show that CompoundE can also be effective for performing entity typing.
+
+We perform entity typing using CompoundE embedding on the FB15k-ET and YAGO43k-ET dataset prepared by (Moon et al., 2017). Statistics of these datasets are shown in Table 9. In addition to RDF triples  $(h, r, t)$ , entity and entity type pairs  $(e, t)$  are added to these entity typing datasets. Since the type can be interpreted as "isA" relationship between  $e$  and  $t$ , we add a "type" relation between the  $e$  and  $t$  pair and treat that as a special triple. Performance comparison with existing work is shown in Table 7. The optimal configuration is shown in Table 13. Similar to link prediction, we also report the MRR and Hits@ $k$  scores. Results show that CompoundE achieves significant improvement over other models especially for the YAGO43k-ET dataset, even without giving special
+
+<table><tr><td>Datasets</td><td colspan="4">FB15k-ET</td><td colspan="4">YAGO43k-ET</td></tr><tr><td>Metrics</td><td>MRR</td><td>H@1</td><td>H@3</td><td>H@10</td><td>MRR</td><td>H@1</td><td>H@3</td><td>H@10</td></tr><tr><td>TransE (Bordes et al., 2013)</td><td>0.45</td><td>31.51</td><td>51.45</td><td>73.93</td><td>0.21</td><td>12.63</td><td>23.24</td><td>38.93</td></tr><tr><td>TransE-ET (Moon et al., 2017)</td><td>0.46</td><td>33.56</td><td>52.96</td><td>71.16</td><td>0.18</td><td>9.19</td><td>19.41</td><td>35.58</td></tr><tr><td>ETE (Moon et al., 2017)</td><td>0.50</td><td>38.51</td><td>55.33</td><td>71.93</td><td>0.23</td><td>13.73</td><td>26.28</td><td>42.18</td></tr><tr><td>HMGCN (Jin et al., 2019)</td><td>0.51</td><td>39.02</td><td>54.75</td><td>72.36</td><td>0.25</td><td>14.21</td><td>27.34</td><td>43.69</td></tr><tr><td>ConnectE (Zhao et al., 2020)</td><td>0.59</td><td>49.55</td><td>64.32</td><td>79.92</td><td>0.28</td><td>16.01</td><td>30.85</td><td>47.92</td></tr><tr><td>CORE (Ge et al., 2022)</td><td>0.60</td><td>48.91</td><td>66.30</td><td>81.60</td><td>0.35</td><td>24.17</td><td>39.18</td><td>54.95</td></tr><tr><td>AttEt (Zhuo et al., 2022)</td><td>0.62</td><td>51.66</td><td>67.68</td><td>82.13</td><td>0.35</td><td>24.43</td><td>41.31</td><td>56.48</td></tr><tr><td>CompoundE</td><td>0.64</td><td>52.49</td><td>71.88</td><td>85.89</td><td>0.48</td><td>36.36</td><td>55.80</td><td>70.31</td></tr></table>
+
+Table 7: Entity typing performance comparison for FB15k-ET and YAGO43k-ET datasets. Best result are in bold and second best result are underlined.
+
+treatment to the representation of entity types. This observation supports the claim that CompoundE is strongly capable of representing entity semantics.
+
+# 4.4 Complexity Analysis.
+
+We compare the computational complexity of CompoundE and several popular KGE models in Table 8. The last column gives the estimated number of free parameters used by different models to achieve the best performance for the ogbl-wikikg2 dataset. CompoundE cuts the number of parameters at least by half while achieving much better performance. In the table,  $n$ ,  $m$ , and  $d$  denote the entity number, the relation number, and their embedding dimension, respectively. Since  $n \gg m$  in most datasets, we can afford to increase the complexity of relation embedding for better link prediction result without significantly increasing the overall space complexity. In Fig. 3, we compare the MRR scores of CompoundE and previous SOTA embedding models on the ogbl-wikikg2 dataset under different dimension settings  $d \in \{10, 20, 50, 100, 150, 200, 250, 300\}$ . CompoundE significantly outperforms benchmarking methods, even under low dimension setting.
+
+Hyperparameters. We conduct two sets of controlled experiments to find the best model configurations for ogbl-wikikg2, FB15k-237, and WN18RR datasets. For the first set, we evaluate the effect of different combinations of learning rates and embedding dimensions while keeping other hyperparameters constant. For the second set, we evaluate the effect of different combinations of the training batch size and the negative sample size, while keeping other hyperparameters constant. The optimal model configurations for three datasets are given in Table 11 of the appendix.
+
+![](images/37924a8cb9f7c597d46553484d3829d7a4f65731b6421111f58ba68ebbbc0a21.jpg)  
+Figure 3: MRR scores on ogbl-wikikg2 dataset.
+
+# 5 Conclusion and Future Work
+
+A new KGE model called CompoundE was proposed in this work. We showed that quite a few distance-based KGE models are special cases of CompoundE. Extensive experiments were conducted for three different knowledge graph prediction tasks including link prediction, path query answering, and entity typing. Competitive experimental results demonstrate the effectiveness of CompoundE. We also mathematically prove the properties of CompoundE and its capability of modeling different relation patterns. We also explain the performance difference of different CompoundE forms, especially for the complex relation patterns.
+
+We are interested in exploring two topics as future extensions. First, we may consider more complex operations in CompoundE. For example, there is a recent trend to extend 2D rotations to 3D rotations for rotation-based embeddings such as RotatE3D (Gao et al., 2020), SU2E (Yang et al., 2020). It is worthwhile to explore CompoundE3D. Second, CompoundE is expected to be useful in many
+
+<table><tr><td>Model</td><td>Ent. emb.</td><td>Rel. emb.</td><td>Scoring Function</td><td>Space</td><td># Params</td></tr><tr><td>TransE</td><td>h, t ∈ Rd</td><td>r ∈ Rd</td><td>-||h + r - t||1/2</td><td>O((m+n)d)</td><td>1251M</td></tr><tr><td>ComplEx</td><td>h, t ∈ Cd</td><td>r ∈ Cd</td><td>Re(∑Kk=1Rkhkτk)</td><td>O((m+n)d)</td><td>1251M</td></tr><tr><td>RotatE</td><td>h, t ∈ Cd</td><td>r ∈ Cd</td><td>-||h ∘ r - t||</td><td>O((m+n)d)</td><td>1250M</td></tr><tr><td>PairRE</td><td>h, t ∈ Rd</td><td>rH, rT ∈ Rd</td><td>-||h ⊙ rH - t ⊙ rT||</td><td>O((m+n)d)</td><td>500M</td></tr><tr><td>CompoundE-Head</td><td>h, t ∈ Rd</td><td>T[;, d-1], diag(S) ∈ Rd, θ ∈ Rd/2</td><td>-||T · R(θ) · S · h - t||</td><td>O((m+n)d)</td><td>250.1M</td></tr><tr><td>CompoundE-Tail</td><td>h, t ∈ Rd</td><td>T[;, d-1], diag(S) ∈ Rd, θ ∈ Rd/2</td><td>-||h - T · R(θ) · S · t||</td><td>O((m+n)d)</td><td>250.1M</td></tr><tr><td>CompoundE-Complete</td><td>h, t ∈ Rd</td><td>T/T[;, d-1], diag(S/hatS) ∈ Rd, θ ∈ Rd/2</td><td>-||T · R(θ) · S · h - T · R(θ) · S·t||</td><td>O((m+n)d)</td><td>250.3M</td></tr></table>
+
+Table 8: Complexity comparison of KGE models.
+
+downstream tasks. This conjecture has to be verified. If this is the case, CompoundE can offer a low memory solution to these tasks in realistic settings.
+
+# Limitations
+
+Similar to many knowledge graph embedding models, our proposed method is yet to handle link prediction under inductive settings. One possible future extension is to leverage entity description information to generate textual features and use CompoundE as a decoder to handle unseen entities. Also, the affine operators we use are limited to translation, rotation, and scaling and this may limit the number of different relation patterns we can handle. In the future, we can include all affine transformations and investigate their difference. Also, because we use 2D givens rotation matrix, the embedding dimension setting needs to be a factor of 2. We can explore higher dimensional transformations such as 3D transformations and compare the modeling power.
+
+# Acknowledgment
+
+The authors acknowledge the Center for Advanced Research Computing (CARC) at the University of Southern California for providing computing resources that have contributed to the research results reported within this publication. URL: https://carc.usc.edu.
+
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+
+# A Properties of CompoundE
+
+Let  $\mathbf{M}$  and  $\hat{\mathbf{M}}$  denote the compound operation for the head and tail entity embeddings, respectively. In the following, we will prove nine properties of CompoundE.
+
+Proposition A.1. CompoundE can model 1-N relations.
+
+Proof. A relation  $r$  is an 1-N relation iff there exist at least two distinct tail entities  $t_1$  and  $t_2$  such that  $(h, r, t_1)$  and  $(h, r, t_2)$  both hold. Then we have:
+
+$$
+\begin{array}{l} \mathbf {M} \cdot \mathbf {h} = \hat {\mathbf {M}} \cdot \mathbf {t _ {1}}, \quad \mathbf {M} \cdot \mathbf {h} = \hat {\mathbf {M}} \cdot \mathbf {t _ {2}} \end{array} \tag {21}
+$$
+
+$$
+\hat {\mathbf {M}} \cdot (\mathbf {t _ {1}} - \mathbf {t _ {2}}) = 0
+$$
+
+Since  $\mathbf{t_1} \neq \mathbf{t_2}$ , CompoundE can model 1-N relations when  $\hat{\mathbf{M}}$  is singular.
+
+Proposition A.2. CompoundE can model N-1 relations.
+
+Proof. A relation  $r$  is an N-1 relation iff there exist at least two distinct head entities  $h_1$  and  $h_2$  such that  $(h_1, r, t)$  and  $(h_1, r, t)$  both hold. Then we have:
+
+$$
+\mathbf {M} \cdot \mathbf {h} _ {1} = \hat {\mathbf {M}} \cdot \mathbf {t}, \quad \mathbf {M} \cdot \mathbf {h} _ {2} = \hat {\mathbf {M}} \cdot \mathbf {t} \tag {22}
+$$
+
+$$
+\mathbf {M} \cdot (\mathbf {h} _ {1} - \mathbf {h} _ {2}) = 0
+$$
+
+Since  $\mathbf{h}_1\neq \mathbf{h}_2$  , CompoundE can model N-1 relations when M is singular.
+
+Proposition A.3. CompoundE can model N-N relations.
+
+Proof. By the proof for Prop.A.1 and A.2, N-N relations can be modeled when both  $\mathbf{M}$  and  $\hat{\mathbf{M}}$  are singular.
+
+Proposition A.4. CompoundE can model symmetric relations.
+
+Proof. A relation  $r$  is a symmetric relation iff  $(h, r, t)$  and  $(t, r, h)$  holds simultaneously. Then we have:
+
+$$
+\begin{array}{l} \mathbf {M} \cdot \mathbf {h} = \hat {\mathbf {M}} \cdot \mathbf {t} \Longrightarrow \mathbf {h} = \mathbf {M} ^ {- 1} \hat {\mathbf {M}} \cdot \mathbf {t} \\ \mathbf {M} \cdot \mathbf {t} = \hat {\mathbf {M}} \cdot \mathbf {h} \Longrightarrow \mathbf {M} \cdot \mathbf {t} = \hat {\mathbf {M}} \mathbf {M} ^ {- 1} \hat {\mathbf {M}} \cdot \mathbf {t} \\ \mathbf {M} \hat {\mathbf {M}} ^ {- 1} = \hat {\mathbf {M}} \mathbf {M} ^ {- 1} \tag {23} \\ \end{array}
+$$
+
+Therefore, CompoundE can model symmetric relations when  $\mathbf{M}\hat{\mathbf{M}}^{-1} = \hat{\mathbf{M}}\mathbf{M}^{-1}$ .
+
+Proposition A.5. CompoundE can model antisymmetric relations.
+
+Proof. A relation  $r$  is a antisymmetric relation iff  $(h, r, t)$  holds but  $(t, r, h)$  does not. By similar proof for Proposition A.4, CompoundE can model symmetric relations when  $\mathbf{MM}^{-1} \neq \hat{\mathbf{MM}}^{-1}$ .
+
+Proposition A.6. CompoundE can model inversion relations.
+
+Proof. A relation  $r_2$  is the inverse of relation  $r_1$  iff  $(h, r_1, t)$  and  $(t, r_2, h)$  holds simultaneously. Then we have:
+
+$$
+\begin{array}{l} \mathbf {M} _ {1} \cdot \mathbf {h} = \hat {\mathbf {M}} _ {1} \cdot \mathbf {t} \Longrightarrow \mathbf {h} = \mathbf {M} _ {1} ^ {- 1} \hat {\mathbf {M}} _ {1} \cdot \mathbf {t} \\ \mathbf {M} _ {2} \cdot \mathbf {t} = \hat {\mathbf {M}} _ {2} \cdot \mathbf {h} \Rightarrow \mathbf {M} _ {2} \cdot \mathbf {t} = \hat {\mathbf {M}} _ {2} \mathbf {M} _ {1} ^ {- 1} \hat {\mathbf {M}} _ {1} \cdot \mathbf {t} \\ \hat {\mathbf {M}} _ {2} ^ {- 1} \mathbf {M} _ {2} = \mathbf {M} _ {1} ^ {- 1} \hat {\mathbf {M}} _ {1} \tag {24} \\ \end{array}
+$$
+
+Therefore, CompoundE can model inversion relations when  $\hat{\mathbf{M}}_2^{-1}\mathbf{M}_2 = \mathbf{M}_1^{-1}\hat{\mathbf{M}}_1$ .
+
+Proposition A.7. CompoundE can model relation compositions.
+
+Proof.  $r_3$  is a composition of  $r_1$  and  $r_2$  iff  $(e_1, r_1, e_2), (e_2, r_2, e_3)$ , and  $(e_1, r_3, e_3)$  hold simultaneously. Then we have:
+
+$$
+\begin{array}{l} \mathbf {M} _ {1} \cdot \mathbf {e} _ {1} = \hat {\mathbf {M}} _ {1} \cdot \mathbf {e} _ {2} \Longrightarrow \mathbf {e} _ {1} = \mathbf {M} _ {1} ^ {- 1} \hat {\mathbf {M}} _ {1} \cdot \mathbf {e} _ {2} \\ \mathbf {M} _ {2} \cdot \mathbf {e} _ {2} = \hat {\mathbf {M}} _ {2} \cdot \mathbf {e} _ {3} \Longrightarrow \mathbf {e} _ {3} = \hat {\mathbf {M}} _ {2} ^ {- 1} \mathbf {M} _ {2} \cdot \mathbf {e} _ {2} \\ \mathbf {M} _ {\mathbf {3}} \cdot \mathbf {e} _ {\mathbf {1}} = \hat {\mathbf {M}} _ {\mathbf {3}} \cdot \mathbf {e} _ {\mathbf {3}} \\ \end{array}
+$$
+
+$$
+\begin{array}{l} \mathbf {M} _ {3} \mathbf {M} _ {1} ^ {- 1} \hat {\mathbf {M}} _ {1} \cdot \mathbf {e} _ {2} = \hat {\mathbf {M}} _ {3} \hat {\mathbf {M}} _ {2} ^ {- 1} \mathbf {M} _ {2} \cdot \mathbf {e} _ {2} \\ \hat {\mathbf {M}} _ {3} ^ {- 1} \mathbf {M} _ {3} = (\hat {\mathbf {M}} _ {2} ^ {- 1} \mathbf {M} _ {2}) (\hat {\mathbf {M}} _ {1} ^ {- 1} \mathbf {M} _ {1}) \tag {25} \\ \end{array}
+$$
+
+Therefore, CompoundE can model relations composition when  $\hat{\mathbf{M}}_3^{-1}\mathbf{M}_3 = (\hat{\mathbf{M}}_2^{-1}\mathbf{M}_2)(\hat{\mathbf{M}}_1^{-1}\mathbf{M}_1)$ .
+
+![](images/6938d6c9694a34341266f88372857f4e18d11d4eaf1a5c255de02b0632cdac21.jpg)
+
+Proposition A.8. CompoundE can model both both commutative and non-commutative relations.
+
+Proof. Since the general form of affine group is non-commutative, our proposed CompoundE is non-commutative i.e.
+
+$$
+\left(\mathbf {M} _ {1} \hat {\mathbf {M}} _ {1} ^ {- 1}\right) \left(\mathbf {M} _ {2} \hat {\mathbf {M}} _ {2} ^ {- 1}\right) \neq \left(\mathbf {M} _ {2} \hat {\mathbf {M}} _ {2} ^ {- 1}\right) \left(\mathbf {M} _ {1} \hat {\mathbf {M}} _ {1} ^ {- 1}\right) \tag {26}
+$$
+
+where each  $\mathbf{M}$  consists of translation, rotation, and scaling component. However, in special cases, when our relation embedding has only one of the translation, rotation, or scaling component, then the relation embedding becomes commutative again.
+
+Proposition A.9. CompoundE can model transitive relations.
+
+Proof.  $r$  is a transitive relation iff  $(e_1, r, e_2)$ ,  $(e_2, r, e_3)$ , and  $(e_1, r, e_3)$  hold simultaneously. Consider the CompoundE variant, and let  $\mathbf{R} = \hat{\mathbf{R}}$ ,  $\mathbf{S}$  be a idempotent matrix.
+
+$$
+\begin{array}{l} f _ {r} (h, t) = \left\| \mathbf {S} \cdot \mathbf {R} \cdot \mathbf {h} - \hat {\mathbf {R}} \cdot \mathbf {t} \right\| \\ = \left\| \mathbf {R} \cdot \left(\mathbf {R} ^ {- 1} \mathbf {S} \mathbf {R} \cdot \mathbf {h} - \mathbf {t}\right) \right\| \tag {27} \\ \mathbf {\Omega} = \left\| \mathbf {R} ^ {- 1} \mathbf {S} \mathbf {R} \cdot \mathbf {h} - \mathbf {t} \right\| \\ \end{array}
+$$
+
+Let  $\mathbf{M}_r = \mathbf{R}^{-1}\mathbf{S}\mathbf{R}$ . Then it is easy to see that
+
+$$
+\begin{array}{l} \mathbf {M} _ {r} \cdot \mathbf {M} _ {r} \cdot \dots \cdot \mathbf {M} _ {r} \\ = \left(\mathbf {R} ^ {- 1} \mathbf {S R}\right) \cdot \left(\mathbf {R} ^ {- 1} \mathbf {S R}\right) \dots \dots \left(\mathbf {R} ^ {- 1} \mathbf {S R}\right) \tag {28} \\ = \mathbf {R} ^ {- 1} \mathbf {S} \mathbf {R} \\ = \mathbf {M} _ {r} \\ \end{array}
+$$
+
+Therefore, CompoundE can model transitive relations.
+
+Proposition A.10. CompoundE can model subrelations.
+
+Proof. A relation  $r_1$  is a sub-relation of  $r_2$  if  $(h, r_2, t)$  implies  $(h, r_1, t)$ . Without loss of generality, suppose our compounding operation takes the following form
+
+$$
+\mathbf {M} = \mathbf {T} \cdot \mathbf {R} \cdot \mathbf {S}, \hat {\mathbf {M}} = \hat {\mathbf {T}} \cdot \hat {\mathbf {R}} \cdot \hat {\mathbf {S}}, \tag {29}
+$$
+
+and suppose
+
+$$
+\mathbf {T} _ {1} = \mathbf {T} _ {2}, \hat {\mathbf {T}} _ {1} = \hat {\mathbf {T}} _ {2},
+$$
+
+$$
+\mathbf {R} _ {1} = \mathbf {R} _ {2}, \hat {\mathbf {R}} _ {1} = \hat {\mathbf {R}} _ {2}, \tag {30}
+$$
+
+$$
+\mathbf {S} _ {1} = \gamma \mathbf {S} _ {2}, \hat {\mathbf {S}} _ {1} = \gamma \hat {\mathbf {S}} _ {2}, \gamma \leq 1.
+$$
+
+With these conditions, we can compare the CompoundE scores generated by  $(h,r_1,t)$  and  $(h,r_2,t)$  as follows:
+
+$$
+\begin{array}{l} f _ {r _ {1}} (h, t) - f _ {r _ {2}} (h, t) \\ = \| \mathbf {T} _ {1} \cdot \mathbf {R} _ {1} \cdot \mathbf {S} _ {1} \cdot \mathbf {h} - \hat {\mathbf {T}} _ {1} \cdot \hat {\mathbf {R}} _ {1} \cdot \hat {\mathbf {S}} _ {1} \cdot \mathbf {t} \| - \\ \left\| \mathbf {T} _ {2} \cdot \mathbf {R} _ {2} \cdot \mathbf {S} _ {2} \cdot \mathbf {h} - \hat {\mathbf {T}} _ {2} \cdot \hat {\mathbf {R}} _ {2} \cdot \hat {\mathbf {S}} _ {2} \cdot \mathbf {t} \right\| \\ = \left\| \mathbf {T} _ {2} \cdot \mathbf {R} _ {2} \cdot (\gamma \mathbf {S} _ {2}) \cdot \mathbf {h} - \hat {\mathbf {T}} _ {2} \cdot \hat {\mathbf {R}} _ {2} \cdot (\gamma \hat {\mathbf {S}} _ {2}) \cdot \mathbf {t} \right\| - \\ \left\| \mathbf {T} _ {2} \cdot \mathbf {R} _ {2} \cdot \mathbf {S} _ {2} \cdot \mathbf {h} - \hat {\mathbf {T}} _ {2} \cdot \hat {\mathbf {R}} _ {2} \cdot \hat {\mathbf {S}} _ {2} \cdot \mathbf {t} \right\| \\ = \| \gamma (\mathbf {T} _ {2} \cdot \mathbf {R} _ {2} \cdot \mathbf {S} _ {2} \cdot \mathbf {h} - \hat {\mathbf {T}} _ {2} \cdot \hat {\mathbf {R}} _ {2} \cdot \hat {\mathbf {S}} _ {2} \cdot \mathbf {t}) \| - \\ \left\| \mathbf {T} _ {2} \cdot \mathbf {R} _ {2} \cdot \mathbf {S} _ {2} \cdot \mathbf {h} - \hat {\mathbf {T}} _ {2} \cdot \hat {\mathbf {R}} _ {2} \cdot \hat {\mathbf {S}} _ {2} \cdot \mathbf {t} \right\| \leq 0 \tag {31} \\ \end{array}
+$$
+
+This means that  $(h,r_1,t)$  generates a smaller error score than  $(h,r_2,t)$ . If  $(h,r_2,t)$  holds,  $(h,r_1,t)$  must also hold. Therefore,  $r_1$  is a sub-relation of  $r_2$ .
+
+# B Performance comparison for different variations of CompoundE
+
+We investigate the performance difference of CompoundE variants. Specifically, the different forms of CompoundE have visible difference in different relation types. We conduct experiment on YAGO3-10 dataset and compare the performance of CompoundE-left, CompoundE-right, CompoundE-Complete for 1-to-1, 1-to-N, and N-to-1 relations. In particular, when evaluating the 1-to-N relations, we focus on predicting  $(?,r,t)$  while for N-to-1 relations we focus on predicting  $(h,r,?)$  to correctly reflect the performance on respective relation types. Performance comparison is shown in 4. We observe that for CompoundE-Complete has advantage over other forms for 1-to-1 relations. CompoundE-left and CompoundE-right are the better performing forms for 1-to-N and N-to-1 relations respectively. This observation is consistent with the discussion of the modeling capability of CompoundE. It still remains a question that how different order of operator composition will affect the performance of CompoundE and we will address that in future work.
+
+# C Visualization of Embedding
+
+We provide a 2D  $t$ -SNE visualization of the entity embedding generated by CompoundE for FB15k-237 in Fig. 5. Each entity is colored with its respective entity type. As shown in the figure, some entity type class are well separated while others are not. This scatter plot shows that entity representations
+
+extracted by CompoundE can capture the semantics of the entity. Thus, their embeddings can be used in various downstream tasks such as KG entity typing and similarity based recommendations.
+
+Besides the histograms shown in the main paper, we add more plots to visualize CompoundE relation embedding values. In Fig. 6, we show the embedding values for the "friends" relation in the FB15k-237. We use the CompoundE-Complete variant  $(\| \mathbf{S_r}\cdot \mathbf{R_r}\cdot \mathbf{T_r}\cdot \mathbf{h} - \hat{\mathbf{S}}_r\cdot \hat{\mathbf{R}}_r\cdot \hat{\mathbf{T}}_r\cdot \mathbf{t}\|)$  to generate the embedding. We plot the translation and scaling components for both the head and the tail. We only show a single plot for the rotation component since the rotation parameter is shared between the head and the tail. Different from the CompoundE-head  $(\| \mathbf{S_r}\cdot \mathbf{R_r}\cdot \mathbf{T_r}\cdot \mathbf{h} - \mathbf{t}\|)$ , we see two modes (instead of only one mode) in CompoundE-Complete's plots. One conjecture for this difference is that CompoundE-Complete has a pair of operations on both the head and the tail, the distribution of values need to have two modes to maintain the symmetry. Similar to CompoundE-head, the scaling parameters of CompoundE-Complete have a large amount of zeros to maintain the singularity of compounding operators and help learn the N-to-N complex relations.
+
+Fig. 7 and Fig. 8 display the histogram of relation embeddings for "instance_hypernym" relation and "similar_to" relation in WN18RR, respectively. The real (in blue) and the imaginary (in orange) parts are overlaid in each plot. Notice that "instance_hypernym" is an antisymmetric relation while "similar_to" is a symmetric relation. This relation pattern is reflected on the embedding histogram since the translation and the scaling histograms for the head and the tail are different in "instance_hypernym". In contrast, the translation and scaling histograms for the head and the tail are almost identical in "similar_to".
+
+# D Datasets
+
+The path query dataset can be obtained from the link. The original github repo has the MIT license. The entity typing dataset can be found here. Statistics of these datasets are shown in Table 9 and
+
+$^{2}$ https://worksheets.codalab.org/works/heets/0xfcace41fdeec45f3bc6ddb31107b829f  
+3https://github.com/kelvinguu/travers ing-knowledge-graphs  
+4https://github.com/cmoon2/knowledge_graph/tree/master/datasets
+
+<table><tr><td rowspan="2">Dataset</td><td rowspan="2">#Ent</td><td rowspan="2">#Rel</td><td rowspan="2">#Type</td><td colspan="3">#KG Triples</td><td colspan="3">#Entity Type Pairs</td></tr><tr><td>#Train</td><td>#Valid</td><td>#Test</td><td>#Train</td><td>#Valid</td><td>#Test</td></tr><tr><td>FB15k-ET</td><td>14,951</td><td>1,345</td><td>3,851</td><td>483,142</td><td>50,000</td><td>59,071</td><td>136,618</td><td>15,749</td><td>15,780</td></tr><tr><td>YAGO43k-ET</td><td>42,335</td><td>37</td><td>45,182</td><td>331,687</td><td>29,599</td><td>29,593</td><td>375,853</td><td>42,739</td><td>42,750</td></tr></table>
+
+Table 9: Entity Typing Datasets Statistics.  
+
+<table><tr><td rowspan="2">Dataset</td><td rowspan="2">#Ent</td><td rowspan="2">#Rel</td><td colspan="3">#KG Triples</td><td colspan="3">#Path</td></tr><tr><td>#Train</td><td>#Valid</td><td>#Test</td><td>#Train</td><td>#Valid</td><td>#Test</td></tr><tr><td>WordNet</td><td>38,551</td><td>11</td><td>110,361</td><td>2,602</td><td>10,462</td><td>2,129,539</td><td>11,277</td><td>46,577</td></tr><tr><td>Freebase</td><td>75,043</td><td>13</td><td>316,232</td><td>5,908</td><td>23,733</td><td>6,266,058</td><td>27,163</td><td>109,557</td></tr></table>
+
+Table 10: Path Query Answering Datasets Statistics.
+
+![](images/4c0dc789cb4e3b96fd4501cb5196dc5c61a6667ee0497c67657729db9761e79c.jpg)  
+(a) 1 to 1
+
+![](images/5fc2234d2eee1c153e0f2ef5c9d317b6330317504652ebd9caf06648458c687e.jpg)  
+(b) 1 to n  
+Figure 4: Comparing the performance of different CompoundE forms.
+
+![](images/4a02d79dc3615fba49a1d19f842d7297b1af18acbbe6900052d971b266e0fcb2.jpg)  
+(c) n to 1
+
+![](images/7de5439f99a69263f0998aef01179895169987e209a5d7a3a6f3b600af37a92d.jpg)  
+Figure 5:  $t$ -SNE visualization of entity embedding in the 2D space for some major entity types in FB15K-237.
+
+Table 10.
+
+# E Implementation and Optimal Configurations
+
+To form relation specific transformation matrices for high dimensional entity vectors, we can first cascade translation, rotation, and scaling operator to yield a compound operator  $\mathbf{O}_{\mathbf{r},\mathbf{i}} = \mathbf{T}_{\mathbf{r},\mathbf{i}}\cdot \mathbf{R}_{\mathbf{r},\mathbf{i}}\cdot \mathbf{S}_{\mathbf{r},\mathbf{i}}$  In the actual implementation, we use the operator's representation in regular Cartesian coordinate instead of the homogeneous coordinate. Furthermore,
+
+a high-dimensional relation operator can be represented as a block diagonal matrix in the form of
+
+$$
+\mathbf {M} _ {\mathbf {r}} = \operatorname {d i a g} \left(\mathbf {O} _ {\mathbf {r}, 1}, \mathbf {O} _ {\mathbf {r}, 2}, \dots , \mathbf {O} _ {\mathbf {r}, \mathbf {n}}\right), \tag {32}
+$$
+
+where  $\mathbf{O}_{\mathbf{r},\mathbf{i}}\in \mathbb{R}^{2\times 2}$  is the compound operator of the  $i$  -th block.
+
+In our implementation, we normalize all entity embeddings to unit vectors before applying compound operations. The optimal configurations of CompoundE are given in Table 11. The implementation of the rotation operation in the optimal CompoundE configuration for the WN18RR dataset is adapted from RotatE.
+
+All experiments were conducted on a NVIDIA V100 GPU with 32GB memory. GPUs with larger memory such as NVIDIA A100 (40GB), NVIDIA A40 (48GB) are only needed for hyperparameter sweep when the dimension, the negative sample size, and the batch size are high. We should point out that such settings are not essential for CompoundE to obtain good results. They were used to search for the optimal configurations. We have considered the following set of numbers as our parameter search space to obtain the best performance we can for each dataset and tasks.
+
+Link Prediction.
+
+Table 11: Optimal Configurations for Link Prediction Tasks.  $B$  denotes the batch size and  $N$  denotes the negative sample size.  
+
+<table><tr><td>Dataset</td><td>CompoundE Variant</td><td>#Dim</td><td>lr</td><td>B</td><td>N</td><td>α</td><td>ζ</td></tr><tr><td>ogbl-wikikg2</td><td>||h - \(\hat{\mathbf{S}}\cdot\hat{\mathbf{T}}\cdot\hat{\mathbf{R}}\cdot\mathbf{t}\)||</td><td>100</td><td>0.005</td><td>4096</td><td>250</td><td>1</td><td>7</td></tr><tr><td>FB15k-237</td><td>||S·R·T·h - \(\hat{\mathbf{S}}\cdot\hat{\mathbf{R}}\cdot\hat{\mathbf{T}}\cdot\mathbf{t}\)||</td><td>600</td><td>0.00005</td><td>1024</td><td>125</td><td>1</td><td>6</td></tr><tr><td>WN18RR</td><td>||R·S·T·h - \(\hat{\mathbf{S}}\cdot\hat{\mathbf{T}}\cdot\mathbf{t}\)||</td><td>500</td><td>0.00007</td><td>1024</td><td>256</td><td>0.5</td><td>6</td></tr></table>
+
+Table 12: Optimal Configurations for Path Query Answering.  $B$  denotes the batch size and  $N$  denotes the negative sample size.  
+
+<table><tr><td>Dataset</td><td>CompoundE Variant</td><td>#Dim</td><td>lr</td><td>B</td><td>N</td><td>α</td><td>ζ</td></tr><tr><td>Freebase</td><td>||S·T·R·h - t||</td><td>1500</td><td>0.00002</td><td>1024</td><td>256</td><td>1</td><td>6</td></tr><tr><td>WordNet</td><td>||S·T·R·h - t||</td><td>1000</td><td>0.00005</td><td>1024</td><td>256</td><td>1</td><td>6</td></tr></table>
+
+![](images/1512c4400b7f3a68116db6461f9e5df5d5527babeadbbaf2e91730778cf615cd.jpg)  
+(a)
+
+![](images/147821b0de6081bbe7e6ea495644e66a4e62d34bd924878afc1e446a97e51a9f.jpg)  
+(b)
+
+![](images/30e914604c5f2f872f2ac15c91240412aad553d8cab36db843401692dce423d4.jpg)  
+(a)
+
+![](images/130663364aad436c520eb9923696a8a15c21cad20d6c0bfddf78b8cdd8685ab7.jpg)  
+(b)
+
+![](images/6085da517ec6482fbc7a1393569f81f4d3f1840306aafda5e045c6a46003f7c8.jpg)  
+(c)
+
+![](images/9a52eadc700efd0e140718ad738450356a63b0b683888b943885982952d33afe.jpg)  
+(d)
+
+![](images/273e8dc6a6b8592193f5fdbdc13e4cd2b53b82b5b56c665e57c10d399a7626f8.jpg)  
+(c)
+
+![](images/7fa7e497f75e3797b61acdac6edef9e4f600dc069c0e6299c8955b57da561e2d.jpg)  
+(d)
+
+![](images/323ad692fbb1ea35de517f28370be78b554f9aa70964038212f1a1d36a5adc33.jpg)  
+(e)
+
+# Wikig2
+
+-  $d \in \{50, 100, 150, 200, 250, 300, 400\}$  
+-  $lr \in \{0.0005, 0.001, 0.005, 0.01\}$  
+-  $\zeta \in \{5,6,7,8,9\}$  
+- batch  $\in$  {256, 512, 1024, 2048}  
+- negative sample  $\in$  {256, 512, 1024, 2048}
+
+FB15k-237
+
+![](images/a9b1ccb93fe461782b344d7142b14fd5ae55b4d04d305ac4ff84f4d403795db6.jpg)  
+Figure 6: FB15k-237 "friends" relation embedding obtained using  $\| \mathbf{S} \cdot \mathbf{R} \cdot \mathbf{T} \cdot \mathbf{h} - \hat{\mathbf{S}} \cdot \hat{\mathbf{R}} \cdot \hat{\mathbf{T}} \cdot \mathbf{t} \|$ : (a) distribution of head translation values, (b) distribution of tail translation values, (c) distribution of head scaling values, (d) distribution of tail scaling values, and (e) distribution of rotation angle values.
+
+![](images/2c995291a36af09187bc5fa9f05e94ae23ff0a62482adf9168b0c47231d2c840.jpg)  
+Figure 7: WN18RR "instance_hypernym" relation: (a) distribution of head translation values, (b) distribution of tail translation values, (c) distribution of head scaling values, and (d) distribution of tail scaling values.  
+(b)
+
+![](images/6fb7b21f8653d145972425ff5e7355a1b17832453b6b92b7342884c6ae07d0de.jpg)  
+(a)  
+(c)  
+Figure 8: WN18RR "similar_to" relation: (a) distribution of head translation values, (b) distribution of tail translation values, (c) distribution of head scaling values, and (d) distribution of tail scaling values.
+
+![](images/c723bd58f8b2eaaff6dedd5af4e8dbf0c8bb4c0e197679a9b65b3927f832374b.jpg)  
+(d)
+
+Table 13: Optimal Configurations for Entity Typing.  $B$  denotes the batch size and  $N$  denotes the negative sample size.  
+
+<table><tr><td>Dataset</td><td>CompoundE Variant</td><td>#Dim</td><td>lr</td><td>B</td><td>N</td><td>α</td><td>ζ</td></tr><tr><td>FB15k-ET</td><td>||R·T·S·h - \(\hat{R}\) ·\(\hat{T}\) ·\(\hat{S}\) ·t||</td><td>1500</td><td>0.00005</td><td>2048</td><td>512</td><td>1</td><td>10</td></tr><tr><td>YAGO43k-ET</td><td>||h - \(\hat{T}\) ·\(\hat{S}\) ·\(\hat{R}\) ·t||</td><td>1000</td><td>0.00005</td><td>1024</td><td>256</td><td>1</td><td>6</td></tr></table>
+
+$d\in \{100,200,300,400\}$  
+-  $lr \in \{0.00001, 0.00005, 0.0001, 0.0005\}$  
+-  $\zeta \in \{4,5,6,7,8,9\}$  
+- batch  $\in$  {256, 512, 1024, 2048}  
+- negative sample  $\in$  {256, 512, 1024, 2048}
+
+# WN18RR
+
+$d\in \{100,200,300,400\}$  
+-  $lr \in \{0.00001, 0.00005, 0.0001, 0.0005\}$  
+-  $\zeta \in \{5,6,7,8,9\}$  
+- batch  $\in$  {256, 512, 1024, 2048}  
+- negative sample  $\in$  {256, 512, 1024, 2048}
+
+# Path Query Answering.
+
+Freebase
+
+-  $d \in \{500, 1000, 1500, 2000\}$  
+-  $lr \in \{0.00001, 0.00002, 0.00005, 0.0001\}$  
+-  $\zeta \in \{6,9,12,15\}$  
+- batch  $\in$  {512, 1024}  
+- negative sample  $\in$  {256, 512}
+
+# WordNet
+
+-  $d \in \{500, 1000, 1500, 2000\}$  
+-  $lr \in \{0.00001, 0.00002, 0.00005, 0.0001\}$  
+-  $\zeta \in \{6,9,12,15\}$  
+- batch  $\in$  {512, 1024}  
+- negative sample  $\in$  {256, 512}
+
+# Entity typing.
+
+# FB15k-ET
+
+$d\in \{500,1000,1500\}$  
+-  $lr \in \{0.00001, 0.00005, 0.0001, 0.0005\}$
+
+$\zeta \in \{8,9,10,11\}$  
+- batch  $\in$  {1024, 2048, 4096, 8192}  
+- negative sample  $\in$  {256, 512, 1024, 2048}
+
+# YAGO43k-ET
+
+-  $d \in \{500, 1000, 1500\}$  
+-  $lr \in \{0.00001, 0.00005, 0.0001, 0.0005\}$  
+-  $\zeta \in \{19,20,21,22\}$  
+- batch  $\in$  {1024, 2048}  
+- negative sample  $\in$  {256, 512}
+
+# F Comparing CompoundE and STaR
+
+The main difference between CompoundE and STaR is that STaR embedding uses a bilinear product and adopts a semantic matching approach while CompoundE's scoring function is a distance-based metric. Because of this, the optimization strategy for CompoundE is the self-adversarial negative sampling loss whereas STaR uses the regularized cross-entropy loss. More importantly, CompoundE embedding has clear and intuitive geometric interpretations whereas the design of STaR is less intuitive since it is unclear what composition of operators means in the context of a bilinear product. We also shed light on the superior capability of CompoundE to model relation compositions and entity semantics through PQA and entity typing experiments. Lastly, we can incorporate reflection and shear operators below who also belong to the affine operator family. The reflection matrix can be defined as
+
+$$
+\mathbf {F} = \left[ \begin{array}{c c c} \cos (\phi) & \sin (\phi) & 0 \\ \sin (\phi) & - \cos (\phi) & 0 \\ 0 & 0 & 1 \end{array} \right], \tag {33}
+$$
+
+And the shear matrices on two different directions can be defined as
+
+$$
+\mathbf {H} _ {x} = \left[ \begin{array}{c c c} 1 & \tan (\psi_ {x}) & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{array} \right], \tag {34}
+$$
+
+<table><tr><td>Datasets</td><td colspan="6">ogbl-wikikg2</td></tr><tr><td rowspan="2">Metrics</td><td rowspan="2">Dim</td><td>Valid</td><td colspan="4">Test</td></tr><tr><td>MRR</td><td>MRR</td><td>Hit@1</td><td>Hit@3</td><td>Hit@10</td></tr><tr><td>||h - \hat{S} \cdot \hat{T} \cdot \hat{R} \cdot t||</td><td>100</td><td>0.6704</td><td>0.6515</td><td>0.5843</td><td>0.6781</td><td>0.7872</td></tr><tr><td>||h - \hat{S} \cdot \hat{T} \cdot \hat{F} \cdot \hat{R} \cdot t||</td><td>100</td><td>0.6694</td><td>0.6509</td><td>0.5844</td><td>0.6760</td><td>0.7865</td></tr><tr><td>||h - \hat{S} \cdot \hat{H}_{x} \cdot \hat{H}_{y} \cdot \hat{T} \cdot \hat{R} \cdot t||</td><td>100</td><td>0.6701</td><td>0.6539</td><td>0.5865</td><td>0.6805</td><td>0.7906</td></tr></table>
+
+Table 14: Preliminary comparison after adding reflection and shear operators.
+
+$$
+\mathbf {H} _ {y} = \left[ \begin{array}{c c c} 1 & 0 & 0 \\ \tan (\psi_ {y}) & 1 & 0 \\ 0 & 0 & 1 \end{array} \right], \tag {35}
+$$
+
+We have done preliminary experiments on Wikikg2 but reflection and shear operators and result is shown in Table 14. We will further improve the result in the future.
+
+A For every submission:
+
+A1. Did you describe the limitations of your work?
+
+Second last, before Acknowledgement
+
+A2. Did you discuss any potential risks of your work?
+
+Not applicable. Left blank.
+
+A3. Do the abstract and introduction summarize the paper's main claims?
+
+Section 1
+
+A4. Have you used AI writing assistants when working on this paper?
+
+Left blank.
+
+B Did you use or create scientific artifacts?
+
+Section 4.1
+
+B1. Did you cite the creators of artifacts you used?
+
+Section 4.1
+
+B2. Did you discuss the license or terms for use and / or distribution of any artifacts?
+
+Not applicable. Left blank.
+
+B3. Did you discuss if your use of existing artifact(s) was consistent with their intended use, provided that it was specified? For the artifacts you create, do you specify intended use and whether that is compatible with the original access conditions (in particular, derivatives of data accessed for research purposes should not be used outside of research contexts)?
+
+Not applicable. Left blank.
+
+B4. Did you discuss the steps taken to check whether the data that was collected / used contains any information that names or uniquely identifies individual people or offensive content, and the steps taken to protect / anonymize it?
+
+Not applicable. Left blank.
+
+B5. Did you provide documentation of the artifacts, e.g., coverage of domains, languages, and linguistic phenomena, demographic groups represented, etc.?
+
+Section 4.1
+
+B6. Did you report relevant statistics like the number of examples, details of train / test / dev splits, etc. for the data that you used / created? Even for commonly-used benchmark datasets, include the number of examples in train / validation / test splits, as these provide necessary context for a reader to understand experimental results. For example, small differences in accuracy on large test sets may be significant, while on small test sets they may not be.
+
+Table 1 and appendix D
+
+C Did you run computational experiments?
+
+Section 4
+
+C1. Did you report the number of parameters in the models used, the total computational budget (e.g., GPU hours), and computing infrastructure used?
+
+Table 7, and appendix E
+
+The Responsible NLP Checklist used at ACL 2023 is adopted from NAACL 2022, with the addition of a question on AI writing assistance.
+
+C2. Did you discuss the experimental setup, including hyperparameter search and best-found hyperparameter values?  
+Appendix E  
+C3. Did you report descriptive statistics about your results (e.g., error bars around results, summary statistics from sets of experiments), and is it transparent whether you are reporting the max, mean, etc. or just a single run? Left blank.  
+C4. If you used existing packages (e.g., for preprocessing, for normalization, or for evaluation), did you report the implementation, model, and parameter settings used (e.g., NLTK, Spacy, ROUGE, etc.)? Not applicable. Left blank.
+
+D Did you use human annotators (e.g., crowdworkers) or research with human participants? Left blank.
+
+D1. Did you report the full text of instructions given to participants, including e.g., screenshots, disclaimers of any risks to participants or annotators, etc.? Not applicable. Left blank.  
+D2. Did you report information about how you recruited (e.g., crowdsourcing platform, students) and paid participants, and discuss if such payment is adequate given the participants' demographic (e.g., country of residence)? Not applicable. Left blank.  
+D3. Did you discuss whether and how consent was obtained from people whose data you're using/curating? For example, if you collected data via crowdsourcing, did your instructions to crowdworkers explain how the data would be used? Not applicable. Left blank.  
+D4. Was the data collection protocol approved (or determined exempt) by an ethics review board? Not applicable. Left blank.  
+D5. Did you report the basic demographic and geographic characteristics of the annotator population that is the source of the data? Not applicable. Left blank.

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