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+# Basic Reading Distillation
+
+Zhi Zhou $^{1*}$ , Sirui Miao $^{1*}$ , Xiangyu Duan $^{1\dagger}$ , Hao Yang $^{2}$ , Min Zhang $^{1}$ ,  
+ $^{1}$ School of Computer Science and Technology, Soochow University, Suzhou, China  
+ $^{2}$ Huawei Translation Services Center, Beijing, China  
+{zzzhou2002,srmiao}  $@$ stu.suda.edu.cn; {xiangyuduan,minzhang}  $@$ suda.edu.cn; yanghao30@huawei.com
+
+# Abstract
+
+Large language models (LLMs) have demonstrated remarkable abilities in various natural language processing areas, but they demand high computation resources which limits their deployment in real-world. Distillation is one technique to solve this problem through either knowledge distillation or task distillation. Both distillation approaches train small models to imitate specific features of LLMs, but they all neglect basic reading education for small models on generic texts that are unrelated to downstream tasks. In this paper, we propose basic reading distillation (BRD) which educates a small model to imitate LLMs basic reading behaviors, such as named entity recognition, question raising and answering, on each sentence. After such basic education, we apply the small model on various tasks including language inference benchmarks and BIG-bench tasks. It shows that the small model can outperform or perform comparable to over 20x bigger LLMs. Analysis reveals that BRD effectively influences the probability distribution of the small model, and has orthogonality to either knowledge distillation or task distillation.
+
+# 1 Introduction
+
+Large language models (LLMs) exhibit consistent performance gains across various areas (Zhao et al., 2023; Huang and Chang, 2023; Chang et al., 2023). Nevertheless, their formidable size and high computational requirements impede their real-world applications. Distillation is one widespread approach to tackle this issue by distilling LLMs into smaller language models. It is divided into mainly two categories: knowledge distillation and task distillation. Both distillation approaches adopt the teacher-student framework, in which the smaller language models act as the student models, and are
+
+*Equal Contribution †Corresponding Author
+
+![](images/7c4085002c826a0684e2c7ed8a23712b94651713386fce8f6b18bc448d08a241.jpg)  
+Figure 1: The illustration of BRD process.
+
+trained to imitate specific features of LLMs, which act as the teacher models. Specifically, knowledge distillation (Hinton et al., 2015) usually trains the student models to imitate implicit features inside the teacher models, while task distillation (Chen et al., 2020) usually trains the student models to imitate explicit behaviors of the teacher models.
+
+Different to both distillation approaches, we propose basic reading distillation (BRD) that teaches a student model basic reading abilities such as named entity recognition, question raising, and question answering, on general sentences. It simulates human reading education via interactions including raising questions about parts of a sentence, answering the questions, extracting important information such as named entities. Such basic reading education on every sentence is important before application on downstream tasks, while is always neglected in both knowledge distillation and task distillation.
+
+Our motivation is that LLMs should be educated beyond just trained for next token prediction. The education brings LLMs basic reading ability in text comprehension. It is like that LLMs experience the high school/college education on reading, then is well prepared for the future test, while traditional LLMs training just consumes tokens, then let LLMs directly participate in the future test. Regarding the distillation, we think that one well edu
+
+cated student is more effective than the one without reading education.
+
+Furthermore, the benefits of BRD are two-fold: Firstly, beyond only using texts for training next token prediction, BRD educates the student model to deeply understand the texts via interactions. All available data such as web mined corpora can be extended to be magnitudes larger by BRD, breaking the data scale and diversity limitation criticized by Gudibande et al. (2023) in the task distillation. Secondly, BRD also avoids the implicit nature of knowledge distillation which imitates latent features such as logits (Hinton et al., 2015), hidden layers (Jiao et al., 2020), and attention maps (Li et al., 2020; Wang et al., 2021b). Such implicit nature leads to the deficiency of learning interpretability, while BRD demonstrates explicit reading behaviors that are easy to interpret.
+
+Figure 1 illustrates the process of BRD. It starts by prompting LLMs to generate basic reading behaviors on general sentences, then proceeds with training the student model to imitate these behaviors. Experiments on various NLP tasks, including language inference benchmarks and Google Big-bench tasks, show that although the student model is trained on the general data that is irrelevant to the downstream tasks, it can inherit teacher model abilities, leading to excellent downstream performances better than or comparable to those of larger models. Furthermore, after this basic education of the student model on general sentences, we fine-tune the student model for downstream tasks, and find that the basic reading education leads to further improvement on downstream tasks, achieving on par or better performances when compared to the over  $20\mathrm{x}$  bigger teacher model. To analyze the effect of BRD, we compute the cross entropy between the student model and the teacher model, and find that the student model distribution approaches closer to the teacher model distribution after BRD, leading to better performances than non-educated ones. In summary, the main contributions are:
+
+- We propose BRD that educates the student model to imitate basic reading behaviors of the teacher model.  
+- Experiments show that the student model exhibits excellent abilities distilled from the teacher model on various downstream tasks, achieving on par or even better performances against the teacher model.
+
+- The analysis reveals that BRD can drive the student model distribution closer to the teacher model distribution, resulting in significant performance improvements.
+
+# 2 Related Works
+
+There are mainly two streams of distillation approaches: knowledge distillation and task distillation. Knowledge distillation focuses on teaching implicit features inside the teacher model, while task distillation focuses on teaching explicit behaviors of the teacher model on downstream tasks. In addition, we introduce intrinsic task pre-training that focuses on intrinsic task data derived from the training plain texts.
+
+# 2.1 Knowledge Distillation
+
+The field is pioneered by Bucila et al. (2006); Hinton et al. (2015), followed by works using various types of internal information from the teacher model, including attention maps (Li et al., 2020; Wang et al., 2021b), output logits (Liu et al., 2020), hidden layers (Jiao et al., 2020). In the era of LLMs, GKD uses advanced memory optimization methods to address the memory constraint problem in distilling LLMs (Tan et al., 2023), MiniLLM uses reverse KL divergence to prevent the student model from overestimating the void regions of the teacher distribution (Gu et al., 2023a). Agarwal et al. (2024) use on-policy distillation that trains the student model on its self-generated mistakes. In the case that internal information of LLMs is not accessible and only decisions of LLMs are available, Zhou et al. (2023) estimate logits from the decision distributions to train the student model.
+
+# 2.2 Task Distillation
+
+The task predictions or reasoning rationales made by the teacher model are used to train the student model in task distillation. Despite the noisy predictions of the teacher model, the student model achieves good imitation effects in performing the tasks (Chen et al., 2020; Wang et al., 2021a; Iliopoulos et al., 2022; Agrawal et al., 2023). Besides the task predictions, rationales for the answers generated by the teacher model show efficiency in training the student model with less data (Hsieh et al., 2023; Wang et al., 2023; Ho et al., 2023; Magister et al., 2023). Task distillation is closely related to model imitation researches (Orekondy et al., 2019; Wallace et al., 2020), which collect API outputs of
+
+a proprietary LM for some tasks, then use the outputs to fine-tune an open-source LM. Gudibandee et al. (2023) criticize the data scale and the limited diversity in model imitation. Mukherjee et al. (2023) address this criticism by using explanation tuning, more task data, and instructions. In comparison, BRD can perform on every sentence, leading to unlimited data resource that breaks the limitation on data scale and diversity.
+
+In summary, task distillation focuses on the data of specific downstream tasks, while our BRD mainly focuses on general sentences unrelated to any specific downstream tasks, and the basic reading behaviors in BRD are basic education resource not aiming at any specific applications.
+
+# 2.3 Intrinsic Task Pre-training
+
+Different to task distillation that utilizes downstream task data, intrinsic task pre-training uses general training set to synthesize task data. PICL is a framework focusing on intrinsic tasks (Gu et al., 2023b). It posits that many paragraphs in the training set documents contain intrinsic tasks such as sentiment analysis, and retrieves paragraphs of the same intrinsic task to compose in-context learning examples, but its retriever is trained on 37 downstream tasks, which are opposite to the "intrinsic task" nature, and limit the scale and diversity of the composed task data. In comparison, our BRD does not refer to any downstream tasks, and focuses on the contents of the training set texts, thus keeping more freedom in curating the task data. In addition, PICL aims to train the in-context learning ability, while BRD is for the model distillation. The intrinsic task data in PICL may not have task labels since the original paragraphs do not necessarily have both task queries and answers simultaneously, e.g., a sentiment expression paragraph may not explicitly state its positive or negative label for the sentiment analysis task. In comparison, BRD always gets education queries and responses.
+
+Zhang et al. (2023) propose a similar intrinsic task pre-training approach that transforms fragmented sentences from babyLM training set into a cohesive paragraph (Warstadt et al., 2023). Their task is quite challenging to accomplish since the sentences in the training set are sampled from diverse resources, and lack strong semantic ties with each other, resulting in the hardness of composing a cohesive paragraph. Such fiction data generation are different to our BRD approach, which generates solid basic education data on reading activities.
+
+# 3 Approach
+
+We use a subset of CommonCrawl (CC-100) corpus, which is usually included in LLMs pretraining, as the education resource to conduct the basic reading education. The whole education process contains two stages. In the first stage, for each sentence in the corpus, the teacher model is prompted to perform basic reading. In the second stage, we collect all basic reading behavior data to train the student model, and finally test the student model ability on various tasks.
+
+# 3.1 Basic Reading Behaviors of the Teacher Model
+
+We utilize the in-context learning ability of the teacher model to elicit its basic reading behaviors including named entity recognition, question raising and answering. Given the corpus, we set up a prompt template consisting of task description, task examples, and input sentence from the corpus.
+
+Table 1 lists the named entity recognition prompt and the response from the teacher model. We can see that, given the few-shot examples including entities and their types, the teacher model responses with more detailed contents of the entities, such as the price or size of the entities, which are beneficial for educating the student model to grasp the important information contained in the input sentence. Table 2 lists the question raising and answering prompt and the response from the teacher model. In the task instruction, question is constrained to be about the content, structure, or attitude of the input sentence. The question raising and answering embody the teacher model's reading ability, which is targeted to be transferred to the student model.
+
+# 3.2 Training the Student Model
+
+The student model is initialized by a released smaller pre-trained language model. We continue training the student model based on the basic reading behavior data generated by the teacher model. To stabilize the training process, we mix the basic reading behavior data with the original sentences of the corpus to avoid the catastrophic forgetting of the pre-trained model.
+
+Suppose we have a passage consisting of three sentences  $s_1, s_2$ , and  $s_3$ , we constitute the named entity recognition passage:  $s_1 < \text{sep} > \text{NER}(s_1) < \text{sep} > s_2 < \text{sep} > \text{NER}(s_2) < \text{sep} > s_3 < \text{sep} > \text{NER}(s_3)$ , where NER denotes the named entity recognition result of the teacher model for each sentence, and
+
+Perform named entity recognition on a given sentence without recognizing personal pronouns in the input sentence as human names.
+
+# Enter a sentence:
+
+Barack Obama was the 44th President of the United States.
+
+# Output:
+
+In this sentence, "Barack Obama" is a person name entity, and "United States" is a geopolitical entity.
+
+# Enter a sentence:
+
+I just bought a new MacBook Pro from Apple.
+
+# Output:
+
+In this sentence, "Apple" is an organization name entity, and "MacBook Pro" is a product name entity.
+
+# Enter a sentence:
+
+The Eiffel Tower is a famous landmark in Paris, France.
+
+# Output:
+
+In this sentence, "Eiffel Tower" is a landmark name entity, and "Paris" and "France" are geopolitical entities.
+
+# Enter a sentence:
+
+Belmont Estate is on the market for \(63 million and boasts roughly 22,000 square feet of luxurious finishes and elaborate architecture on 1.28 acres.
+
+# Output:
+
+In this sentence, "Belmont Estate" is a geographic entity, "63 million" is a numerical entity representing the price of the estate, and "1.28 acres" is a geographic entity representing the size of the estate.
+
+Table 1: The prompt for the teacher model to extract named entity information from an input sentence. Each example consists of a sentence and its named entity information. The response from the teacher model is listed in the bottom.
+
+<sep> is the delimiter. Similarly, we constitute the question raising and answering passage:  $s_1 < \text{sep} >$ $\text{QRA}(s_1) < \text{sep} > s_2 < \text{sep} > \text{QRA}(s_2) < \text{sep} > s_3 < \text{sep} > \text{QRA}(s_3)$ , where QRA denotes the question raising and answering result of the teacher model for each sentence. The original passage is formatted as  $s_1 < \text{sep} > s_2 < \text{sep} > s_3$ . We use passage instead of sentence to be consistent with the usual language model pre-training that utilizes long contexts.
+
+In this way, we build all original passages, denoted as  $D_{ORI}$ , all named entity recognition passages, denoted as  $D_{NER}$ , and all question raising and answering passages, denoted as  $D_{QRA}$ . We mix them together to build the training set  $D_{TRAIN}$ , on which we train the student model to minimize the loss in an autoregressive manner:
+
+$$
+L = - \frac {1}{N} \sum_ {i = 1} ^ {N} \sum_ {t = 1} ^ {T} \log P (y _ {t} | y _ {<   t})
+$$
+
+where  $y$  is the passage with length  $T$ , and  $N$  is the number of passages in  $D_{TRAIN}$ .
+
+# 3.3 Testing
+
+For predicting the answers of the downstream tasks when testing the student model, we use the average of per-token log-probabilities of candidate answers as the scoring function for all downstream tasks:
+
+$$
+\bar {P} = \frac {1}{n} \sum_ {i = 1} ^ {n} \log P _ {i} (y _ {i} | x _ {\text {p r o m p t}})
+$$
+
+where  $x_{\mathrm{prompt}}$  denotes the input to the student model,  $y$  denotes the candidate answer for  $x_{\mathrm{prompt}}$ , and  $n$  is the total number of words in  $y$ . We select  $y$  with the maximal  $\bar{P}$  as the final answer for  $x_{\mathrm{prompt}}$ . This average computation is to cover tasks such as Google BIG-bench (bench authors, 2023), whose candidate answers are phrases/sentences rather than single words.
+
+# 4 Experiment
+
+We use the well-known LLM Vicuna-13B  $^{2}$  (Chiang et al., 2023) as our teacher model due to its high efficiency in generating large volume of texts for teaching. We use XGLM-564M (Lin et al., 2022), which is the smaller language model of the same decoder-only family, to initialize our student model. To compare the student model with larger model pre-trained on the same data origin, we also include XGLM-7.5B for comparison. In BRD, we use five million sentences from CC-100 corpus to collect the basic reading data generated by Vicuna-13B.
+
+# 4.1 Baselines
+
+We consider three baselines in our experiments:
+
+- Knowledge distillation (KD): We use two KD
+
+<sup>1</sup>https://github.com/google/BIG-bench  
+2https://github.com/lm-sys/FastChat  
+<sup>3</sup>https://github.com/facebookresearch/fairseq/
+
+tree/main/examples/xglm
+
+Ask a question to the input sentence, you can ask questions about the content, structure or attitude of the sentence, and then find the answer to the corresponding question in the original sentence. Output in the format "Question: Answer:"
+
+# The sentence:
+
+In order to graduate with honors, he needed to maintain a high GPA throughout college.
+
+# Question:
+
+What did he need to do in order to graduate with honors?
+
+# Answer:
+
+Maintain a high GPA throughout college.
+
+# The sentence:
+
+Belmont Estate is on the market for \(63 million and boasts roughly 22,000 square feet of luxurious finishes and elaborate architecture on 1.28 acres.
+
+# Question:
+
+How much does Belmont Estate cost?
+
+# Answer:
+
+Belmont Estate costs $63 million.
+
+Table 2: The prompt for the teacher model to perform question raising and answering on an input sentence. Question is limited to be about the input sentence. The response from the teacher model is listed in the bottom.
+
+models released in Gu et al.  $(2023\mathrm{a})^4$  for the comparison. One is the standard KD (SKD) that uses teacher distribution to supervise the student model. The other is SOTA KD model MiniLLM that uses reverse Kullback-Leibler divergence for the distillation.
+
+- Task distillation (Wang et al., 2021a; Iliopoulos et al., 2022): The teacher model generates the answers given the downstream task inputs, and these generated pseudo answers are used to supervise the student model.  
+- Supervised Fine-tuning(SFT): Directly finetunes the student model on the downstream tasks supervised by the gold labels.
+
+# 4.2 Evaluation
+
+We adopt a spectrum of downstream tasks for the evaluation, including natural language inference (XNLI(Conneau et al., 2018), CB(de Marneffé et al., 2019), RTE(Wang et al., 2018)), paraphrasing (PAWS-X(Zhang et al., 2019)), Boolean QA (BOOLQ(Clark et al., 2019)), sentiment analysis (SST-2(Socher et al., 2013)), and Google BIG-bench(bench authors, 2023). In Google BIG-bench tasks, we only consider multiple choice QA tasks which have the fixed answers easy for the evaluation, resulting in a total of 73 tasks. The results are evaluated by the accuracy of the predicted answers. The prompts for the downstream tasks are presented in the appendix A.2.
+
+# 4.3 Results
+
+The main results are grouped into three parts as shown in Table 3. The top part presents the accuracies of the original models, including the teacher model Vicuna-13B, the student model XGLM-564M, the large model XGLM-7.5B which has same origin to the student model, plus an extension model XGLM-564M-FURTHER, which further trains the student model on the original one million passages from CC-100 corpus. The number of the further training steps is set 18,000.
+
+The middle part and the bottom part list the accuracies of various distillation or fine-tuning approaches under two scenarios: without downstream task supervision and with downstream task supervision, respectively. The difference between the two scenarios is the availability of the downstream task gold answers.
+
+Results Without Downstream Task Supervision. In this scenario, the downstream task gold answers are not available. It is further divided into two conditions. One is the blind test setting, in which any task training set data is NOT accessible. It is for applications of the student model on fairly new tasks. The other is the relaxed test setting, in which only the training set input data (without gold answers) are accessible. It is for applications on tasks that manual labeling for the training set input data is not available.
+
+- In the blind test setting, we compare our XGLM-BRD with the two released KD works: SKD and MiniLLM. In the multiple student models of the two KD works, we select their GPT-2 760M version student models for the
+
+<table><tr><td rowspan="2">Model</td><td colspan="7">Task</td><td rowspan="2">Average</td></tr><tr><td>XNLI</td><td>RTE</td><td>CB</td><td>PAWS-X</td><td>BOOLQ</td><td>SST-2</td><td>BIG-bench-Avg</td></tr><tr><td>Vicuna-13B</td><td>59.1</td><td>78.3</td><td>71.4</td><td>62.9</td><td>84.3</td><td>81.5</td><td>35.6</td><td>67.6</td></tr><tr><td>XGLM-7.5B</td><td>36.6</td><td>50.9</td><td>60.7</td><td>56.8</td><td>57.2</td><td>69.5</td><td>34.3</td><td>52.34</td></tr><tr><td>XGLM-564M</td><td>35.5</td><td>46.2</td><td>53.6</td><td>51.3</td><td>51.2</td><td>63.9</td><td>34.0</td><td>48.0</td></tr><tr><td>XGLM-564M-FURTHER</td><td>34.9</td><td>46.6</td><td>51.8</td><td>51.6</td><td>51.5</td><td>59.4</td><td>34.0</td><td>47.1</td></tr><tr><td colspan="9">Without Downstream Task Supervision</td></tr><tr><td>SKD</td><td>33.7</td><td>53.8</td><td>51.8</td><td>43.0</td><td>49.1</td><td>60.7</td><td>34.2</td><td>46.6</td></tr><tr><td>MiniLLM</td><td>34.2</td><td>58.1</td><td>73.2</td><td>44.1</td><td>55.9</td><td>62.4</td><td>34.6</td><td>51.8</td></tr><tr><td>XGLM-BRD</td><td>36.2</td><td>53.8</td><td>58.9</td><td>56.7</td><td>61.0</td><td>78.1</td><td>34.8</td><td>54.2</td></tr><tr><td>TaskDistillation</td><td>57.1</td><td>58.1</td><td>60.7</td><td>64.8</td><td>74.8</td><td>77.2</td><td>41.6†</td><td>62.0</td></tr><tr><td>XGLM-BRD2</td><td>59.2</td><td>62.5</td><td>82.1</td><td>64.8</td><td>75.0</td><td>81.9</td><td>44.1†</td><td>67.1</td></tr><tr><td colspan="9">With Downstream Task Supervision</td></tr><tr><td>SFT</td><td>81.4</td><td>67.1</td><td>83.9</td><td>92.4</td><td>77.5</td><td>91.5</td><td>68.3†</td><td>80.3</td></tr><tr><td>XGLM-BRD2-SFT</td><td>81.6</td><td>69.3</td><td>91.1</td><td>91.5</td><td>77.8</td><td>92.2</td><td>69.1†</td><td>81.8</td></tr></table>
+
+Table 3: Main results of the teacher models, student models, and various distillation and fine-tuning approaches. Unless otherwise specified, the student models are all initialized by XGLM-564M. BIG-bench-Avg is the accuracy averaged over the 73 bench tasks(† denotes the averaged accuracy on the reduced set of BIG-bench tasks), and detailed accuracies are reported in the appendix A.3.
+
+comparison due to the similar model size. The results show that XGLM-BRD performs significantly better than SKD and MiniLLM in most tasks, demonstrating that XGLM-BRD has better generalization ability to various unseen tasks. We also combine BRD with the two KD works, and the results are listed in the orthogonal analysis section 5.1 and Table 4.
+
+Regarding the comparison between XGLM-BRD and XGLM-564M, BRD significantly improves the performance of the small model, indicating that basic reading education does enhance the ability of the small model. Moreover, XGLM-564M-FURTHER performs much worse than XGLM-BRD, revealing that only using the original passages for further training does not yield enhancements and may even leads to decreases in some tasks. It is the basic reading data for further training that advance the student model. XGLM-BRD also approaches or even surpasses XGLM-7.5B, which is 15x bigger, on the downstream tasks. There is still a gap between XGLM-BRD and the teacher model Vicuna-13B, but this gap is significantly reduced or disappeared when we conduct relaxed test.
+
+In some tasks such as CB and RTE, there is comparison variance between MiniLLM and BRD. This may be because MiniLLM was instruction tuned on databricks-dolly-15k, which is a task instruction following dataset that may cover some traditional downstream tasks such as CB and RTE, leading to the performance better than our BRD approach.
+
+In comparison, our BRD model was not instruction tuned, but was trained on general domain to improve its general reading ability, leading to the overall performance superior to MiniLLM on wide variety of 79 downstream tasks.
+
+- In the relaxed test setting, we compare our BRD with the task distillation approach(TaskDistillation in Table 3), which uses the teacher model to generate pseudo answers on the task training set for supervising the student model XGLM-564M. Because BIG-bench tasks do not divide training, tuning, and test sets, we only consider tasks each of whom has more than  $2\mathrm{K}$  instances in the relaxed test, and finally select tasks that rank top-5 according to the number of instances as the reduced set of BIG-bench tasks (denoted by  $\dagger$  in Table 3). For each task, we save ten percent of instances as test set, ten percent of instances as tuning set, and other instances as training set. Our approach in this setting uses BRD twice, that is, on the general data we conduct BRD to obtain the student model XGLM-BRD, then on the downstream task data, we conduct BRD again to continual training the new student model, denoted as XGLM-BRD². The results show that the task distillation approach establishes a strong baseline that significantly outperforms both XGLM-564M and KD models, demonstrating that even pseudo answers can supervise the student model to perform well on the downstream tasks. When BRD is introduced into this process, the improvement is even more
+
+<table><tr><td rowspan="2">Model</td><td rowspan="2">Approach</td><td colspan="7">Task</td></tr><tr><td>XNLI</td><td>RTE</td><td>CB</td><td>PAWS-X</td><td>BOOLQ</td><td>SST-2</td><td>Average</td></tr><tr><td rowspan="4">GPT-2 120M</td><td>SKD</td><td>35.9</td><td>44.4</td><td>57.1</td><td>52.1</td><td>47.6</td><td>68.8</td><td>51.0</td></tr><tr><td>+BRD</td><td>37.0</td><td>54.5</td><td>66.1</td><td>56.8</td><td>62.2</td><td>76.9</td><td>58.9</td></tr><tr><td>MiniLLM</td><td>35.9</td><td>48.0</td><td>67.9</td><td>57.0</td><td>53.1</td><td>53.8</td><td>52.6</td></tr><tr><td>+BRD</td><td>35.1</td><td>51.6</td><td>71.4</td><td>48.5</td><td>60.9</td><td>79.1</td><td>57.8</td></tr><tr><td rowspan="4">GPT-2 340M</td><td>SKD</td><td>33.6</td><td>46.9</td><td>51.8</td><td>54.2</td><td>48.8</td><td>63.3</td><td>49.8</td></tr><tr><td>+BRD</td><td>34.2</td><td>55.2</td><td>67.9</td><td>53.8</td><td>64.6</td><td>78.1</td><td>59.0</td></tr><tr><td>MiniLLM</td><td>32.8</td><td>46.6</td><td>50.0</td><td>57.0</td><td>56.9</td><td>55.3</td><td>49.0</td></tr><tr><td>+BRD</td><td>32.7</td><td>56.3</td><td>67.9</td><td>53.4</td><td>64.1</td><td>74.4</td><td>58.1</td></tr><tr><td rowspan="4">GPT-2 760M</td><td>SKD</td><td>33.7</td><td>53.8</td><td>51.8</td><td>43.0</td><td>49.1</td><td>60.7</td><td>48.7</td></tr><tr><td>+BRD</td><td>34.7</td><td>52.3</td><td>64.3</td><td>56.4</td><td>62.1</td><td>68.5</td><td>56.7</td></tr><tr><td>MiniLLM</td><td>34.2</td><td>58.1</td><td>73.2</td><td>44.1</td><td>55.9</td><td>62.4</td><td>54.7</td></tr><tr><td>+BRD</td><td>35.2</td><td>52.0</td><td>76.8</td><td>50.8</td><td>60.5</td><td>67.3</td><td>57.1</td></tr><tr><td rowspan="2">XGLM-564M</td><td>TaskDistillation</td><td>57.1</td><td>58.1</td><td>60.7</td><td>64.8</td><td>74.8</td><td>77.2</td><td>65.5</td></tr><tr><td>+BRD</td><td>58.1</td><td>61.0</td><td>71.4</td><td>63.1</td><td>74.4</td><td>81.1</td><td>68.2</td></tr></table>
+
+Table 4: Results of combining BRD with various distillation approaches. The models for initializing the student models are listed in the model column.  
+
+<table><tr><td></td><td>XNLI</td><td>RTE</td><td>CB</td><td>PAWS-X</td><td>BOOLQ</td><td>SST-2</td><td>BIG-bench-Avg</td></tr><tr><td>XGLM-564M</td><td>461.7</td><td>64.8</td><td>13.2</td><td>1065.6</td><td>1098.7</td><td>55.6</td><td>145.1</td></tr><tr><td>XGLM-BRD</td><td>407.5</td><td>66.2</td><td>12.8</td><td>892.4</td><td>1001.1</td><td>37.0</td><td>112.2</td></tr></table>
+
+Table 5: Cross entropy between the distributions of the teacher model and small models. The lower the better for measuring the consistency.
+
+pronounced by XGLM-BRD $^2$ . The comparison between basing on XGLM-BRD and basing on XGLM-564M in this test setting is presented in Appendix A.4.
+
+When comparing XGLM-BRD² with the teacher model Vicuna-13B, it shows that XGLM-BRD² outperforms Vicuna-13B in some tasks, and in the other tasks, the performance gap is significantly reduced. This comparison proves the effectiveness of BRD, that leads to comparable or superior performance to the 26x bigger teacher model.
+
+Results With Downstream Task Supervision. In this scenario, the downstream task gold answers are available. We compare BRD with SFT, which fine-tunes the student model XGLM-564M based on the task supervision data. Table 3 shows that with the gold supervision, SFT significantly improves the ability of the student model, and beats the 26x bigger model Vicuna-13B with a large margin in certain tasks. In comparison to this strong baseline, we conduct BRD on the task data with gold answer, then continue training XGLM-BRD on the data mixing this basic reading data and the original task data. The trained model is denoted as XGLM-BRD $^{2}$ -SFT. The results show that XGLM-BRD $^{2}$ -SFT surpasses SFT in most tasks, demonstrating the effectiveness of the basic reading edu
+
+cation for the student model when the downstream task supervision is available.
+
+# 5 Analysis
+
+# 5.1 Orthogonality of BRD to Knowledge Distillation and Task Distillation
+
+Since BRD focuses on basic reading education for the student model without referring to any implicit model features or downstream tasks, it is orthogonal to either knowledge distillation or task distillation. So, we combine BRD with knowledge distillation by further training the student model of knowledge distillation on our general basic reading data, or combine BRD with task distillation by further training the student model of task distillation on the basic reading data of the downstream tasks. Table 4 lists the combination results.
+
+It shows that combining BRD in most cases significantly improves the performances of the two distillation approaches, which proves the orthogonality of BRD to either knowledge distillation or task distillation.
+
+# 5.2 Effectiveness Verification Based on Cross Entropy Evaluation
+
+BRD educates the student model via explicit basic reading behaviors. We study if such education can effectively influence the probability distribution of the student model. We compute the cross entropy,
+
+<table><tr><td rowspan="2">Model</td><td colspan="6">Task</td><td rowspan="2">Average</td></tr><tr><td>XNLI</td><td>RTE</td><td>CB</td><td>PAWS-X</td><td>BOOLQ</td><td>SST-2</td></tr><tr><td>Llama3.1-8B</td><td>49.6</td><td>79.8</td><td>73.2</td><td>66.0</td><td>84.4</td><td>92.0</td><td>74.2</td></tr><tr><td>Vicuna-13B</td><td>59.1</td><td>78.3</td><td>71.4</td><td>62.9</td><td>84.3</td><td>81.5</td><td>72.9</td></tr><tr><td>XGLM-564M</td><td>35.5</td><td>46.2</td><td>53.6</td><td>51.3</td><td>51.2</td><td>63.9</td><td>50.3</td></tr><tr><td>XGLM-BRD-Llama</td><td>32.0</td><td>57.0</td><td>69.6</td><td>52.8</td><td>58.5</td><td>71.9</td><td>57.0</td></tr><tr><td>XGLM-BRD-Vicuna</td><td>33.7</td><td>56.0</td><td>60.7</td><td>54.4</td><td>59.8</td><td>69.0</td><td>55.6</td></tr></table>
+
+which is often used to measure the consistency between the teacher distribution and the student distribution, for the teacher model Vicuna-13B and the student model XGLM-BRD:
+
+$$
+- \sum_ {i = 1} ^ {N} p (y) \log q \left(y ^ {\prime}\right)
+$$
+
+where  $p$  is the teacher model probability,  $q$  is the student model probability,  $y$  and  $y'$  are subword sequences of the same text according to the teacher model and the student model, respectively.  $N$  is the number of the texts. Since  $y$  and  $y'$  have different lengths, we set  $p$  and  $q$  as sequence-level probabilities averaged over  $y$  and  $y'$ , respectively. We use the instances from the downstream tasks for computing the cross entropy. For the considered 73 tasks in BIG-bench, we randomly choose 1K instances from each task for the computation, and report the cross entropy averaged over the tasks. We include the original XGLM-564M to compute  $q$  for comparison.
+
+Table 5 shows the comparison result in the blind test. Lower cross entropy means better consistency between the teacher model and the student model. It shows that on most downstream tasks, XGLM-BRD approaches more closer to the teacher model than the original XGLM-564M does, demonstrating significant advantage in shaping the student model probability distribution towards that of the teacher model.
+
+# 5.3 Extension to Using Llama as The Teacher Model
+
+In addition to using Vicuna-13B as the teacher model, we explore setting Llama3.1-8B-Instruct(abbreviated as Llama3.1-8B) as the teacher model in the blind test, and compare both based on a subset of the data used in section 4. The subset consists of one million sentences, on which we conduct BRD. For each teacher model, we use XGLM-564M as the student model.
+
+Table 6: Comparison between using Llama3.1-8B and Vicuna-13B as the teacher models on the reduced dataset of one million sentences.  
+
+<table><tr><td rowspan="2"></td><td colspan="6">Tasks</td><td rowspan="2">Avg</td></tr><tr><td>XNLI</td><td>RTE</td><td>CB</td><td>PAWS-X</td><td>BOOLQ</td><td>SST-2</td></tr><tr><td>XGLM-564M</td><td>35.5</td><td>46.2</td><td>53.6</td><td>51.3</td><td>51.2</td><td>63.9</td><td>50.3</td></tr><tr><td>PassageLevel</td><td>36.2</td><td>53.8</td><td>58.9</td><td>56.7</td><td>61.0</td><td>78.1</td><td>57.5</td></tr><tr><td>SentenceLevel</td><td>34.1</td><td>55.6</td><td>55.4</td><td>53.6</td><td>58.9</td><td>76.0</td><td>55.6</td></tr></table>
+
+Table 7: The comparison between the passage level training and the sentence level training evaluated by the blind test.
+
+Table 6 lists the comparison results. XGLM-BRD-Llama/Vicuna denotes the model distilled from Llama3.1-8B/Vicuna-13B. It shows that BRD is effective for using either Llama3.1-8B or Vicuna-13B as the teacher model, achieving significant improvements over XGLM-564M in most tasks. Regarding the comparison between Llama3.1-8B and Vicuna-13B as the teacher model, Llama3.1-8B averagely performs better than Vicuna-13B as the teacher in BRD.
+
+# 5.4 Comparison to Sentence Level Training
+
+In building the BRD training data presented in section 3.2, we divide a passage into sentences, then annotate each sentence with basic reading behaviors by using the teacher model, and finally compose all sentences and their annotations into a passage according to the original sentence order. To check whether this passage level training has the positive effect, we abandon the last composing step and leave the sentences and their annotations unordered. Then we conduct the sentence level training on this dataset to compare with the passage level training. Table 7 presents the comparison result.
+
+It shows that the sentence level training generally performs worse than the passage level training. Since the downstream tasks are mostly the tasks with multiple sentences as input, the passage level training is more suitable for the downstream tasks than the sentence level training due to its multiple sentence training nature.
+
+<table><tr><td rowspan="2"></td><td colspan="6">Tasks</td><td rowspan="2">Avg</td></tr><tr><td>XNLI</td><td>RTE</td><td>CB</td><td>PAWS-X</td><td>BOOLQ</td><td>SST-2</td></tr><tr><td>XGLM-BRD2</td><td>59.2</td><td>62.5</td><td>82.1</td><td>64.8</td><td>75.0</td><td>81.9</td><td>70.9</td></tr><tr><td>-NER</td><td>58.0</td><td>61.4</td><td>71.4</td><td>64.1</td><td>74.3</td><td>81.4</td><td>68.4</td></tr><tr><td>-QRA</td><td>58.3</td><td>61.0</td><td>67.9</td><td>63.9</td><td>74.9</td><td>80.5</td><td>67.8</td></tr></table>
+
+Table 8: The effects of deleting different basic reading behaviors for XGLM-BRD² in the relaxed test.
+
+![](images/b5201d43016b7eb6a28d0947d70493b37216fdac46be1d7d311bdbbe9542b1e7.jpg)  
+Figure 2: The performance curve along with different BRD data sizes (in million passages).
+
+# 5.5 Ablation of Different Basic Reading Behaviors.
+
+We test the contribution of the different basic reading behaviors by deleting either NER or QRA data of the downstream tasks in training XGLM-BRD $^2$ . Table 8 lists the ablation results in the relaxed test. It shows that deleting the QRA data impacts the performance more significantly than deleting the NER data in most tasks. QRA focuses on the sentence understanding, thus contributing more in the basic reading education.
+
+The coordination between NER and QRA is related to the multi-task learning (Chen et al., 2024) that boosts the model ability through training on multiple tasks with potential generalization to other tasks. Different to the multi-task learning that predefines a fixed set of tasks, BRD focuses only on the basic reading education that has flexible contents changing from sentence to sentence. This flexibility empowers the distilled model to perform well on various downstream tasks.
+
+# 5.6 The Impact of BRD Data Size
+
+We investigate how performance varies along with different BRD data sizes in the blind test. Figure 2 shows the curve. Most tasks exhibit a steady improvement as BRD data gets bigger, and the performance plateaued when BRD data size arrives at more than one million passages.
+
+# 6 Conclusion
+
+In this paper, we propose to distill the basic reading abilities of LLMs into small models. In particular, we collect basic reading behaviors of LLMs such as NER or question raising and answering about parts of an input text at first, then we train small models based on the collected behaviors. Through such basic education on general texts, the small models are well educated to perform better on the downstream tasks. Experiments on various tasks including language inference benchmarks and Google Big-Bench tasks show that the small models after such distillation can surpass or perform comparable to LLMs that are  $20\mathrm{x}$  bigger. Verification by the cross entropy shows that such basic reading education can drive small model distribution closer to its teacher model distribution, leading to better performances than non-educated ones. Analysis also reveals that BRD has orthogonality to either knowledge distillation or task distillation.
+
+# 7 Acknowledgements
+
+We would like to thank the anonymous reviewers for the helpful comments. This work was supported by National Natural Science Foundation of China (Grant No. 62261160648, 62276179), and Project Funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions.
+
+# Limitations
+
+In the distillation approach, we acknowledge certain limitations in the coverage of language models. We only use Vicuna-13B as our teacher model due to its high efficiency in generating large volume of texts. Calling the recent proprietary LLMs through API or using larger released LLMs incurs high cost in time and deployment for the massive distillation. It represents an area for potential future exploration to provide a more comprehensive understanding of using larger LLMs as the teacher model for the distillation.
+
+# Ethics Statement
+
+We honor the Code of Ethics. We do not use any private data or non-public information in this work. The language models used in this paper are freely downloadable from web. The corpus for generating basic reading behaviors by the teacher model is commonly used in most LLMs pretraining, and is freely released. The downstream task data are also
+
+freely downloadable from web. The distillation process does not involve any personally sensitive information.
+
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+
+# A Appendix
+
+# A.1 Training Configuration
+
+The student model is trained with learning rate  $= 0.0003$ , batch size  $= 8$ , and max input length  $= 2048$ , for a maximum of 40000 steps. We save the model every 1000 steps. Four A100 GPUs are used in both the data synthesis and the distillation training.
+
+# A.2 Prompts for The Downstream Tasks
+
+The prompt templates for the downstream tasks are listed in table 9. For the 73 tasks in BIG-bench, we follow the general instruct with the task prefix and input as the prompt.
+
+# A.3 Detailed Accuracies on BIG-bench
+
+Figure 3 presents the accuracy comparison between the distilled model XGLM-BRD and the baseline model XGLM-564M on the 73 tasks in BIG-bench in the blind test. The results of ten tied tasks are not listed in the figure. It shows that XGLM-BRD improves the performances on about 2/3 tasks, demonstrating better ability generalized to a wide range of tasks than the baseline.
+
+In the relaxed test and the setting with the downstream task supervision, we select tasks that rank top-5 according to the number of instances for the sufficiency consideration of dividing training, tuning, and test sets on these tasks. The five tasks are movie dialogue, formal fallacies and syllogisms with negation, Shakespeare dialogue, VitaminC, and WinoWhy. Table 10 presents the results on this reduced BIG-bench set. It shows that BRD models perform superior to the corresponding baselines no matter the supervisions are available or not.
+
+# A.4 Basing on XGLM-BRD is better than basing on XGLM-564M
+
+In the relaxed test setting, further BRD in training XGLM-BRD $^2$  on the downstream tasks is based on XGLM-BRD. We also test further BRD based on XGLM-564M, which is denoted as XGLM-564M-FBRD. Table 11 lists the comparison result. It shows that XGLM-BRD $^2$  generally outperforms XGLM-564M-FBRD across various downstream tasks, highlighting that basing on XGLM-BRD is more effective. These results emphasize the importance of BRD as a prerequisite step in improving the adaptability and efficacy of models in downstream applications.
+
+# A.5 Layer-wise Probing
+
+Inserting probes can reveal the interpretable aspects hidden in the neural networks (Belinkov, 2022). We insert probes layer-wisely to check the efficacy of the distilled student model. In particular, for each downstream task, we extract the representation by averaging vectors per layer for each sentence in the training set, and train the probing classifier per layer based on the representation. The training loss is the regularized cross-entropy loss of the task prediction against the true label of the sentence. Through inserting probes layer-wisely, we can check how well each layer prepares for the downstream tasks.
+
+Figure 4 presents the results of probing XGLM-564M and XGLM-BRD in the blind test. It is clear that XGLM-BRD outperforms XGLM-564M on almost all layers for all downstream tasks. Although XGLM-BRD is trained on the general corpus that is not related to the downstream tasks, basic reading education influences deep layers of the model, empowering each layer with enhanced downstream task prediction ability.
+
+# A.6 The Impact of Sentiment-related Questions and Answers
+
+Since our QRA data include questions and answers about the attitude of a sentence, which are related to the SST-2 task, we exclude such data for training XGLM-BRD by deleting the questions about the attitude or the answers containing words of positive/negative/neutral. The objective is to check whether the performance improvement is due to the presence of such data.
+
+Table 12 shows the result in the blind test. Excluding the sentiment-related data does influence
+
+<table><tr><td>Task</td><td>Template</td><td>Candidate Answers</td></tr><tr><td>XNLI</td><td>{premise}
+Question: Does this imply that &quot;{hypothesis}&quot;? 
+Yes, no or maybe?
+Answer:</td><td>Yes | No | Maybe</td></tr><tr><td>RTE</td><td>Question: Can we infer that &quot;{hypothesis}&quot;?</td><td rowspan="2">Yes | No | Maybe</td></tr><tr><td>CB</td><td>{premise}
+Answer:</td></tr><tr><td>PAWS-X</td><td>Sentence 1: {sentence1}
+Sentence 2: {sentence2}
+Question: Do Sentence 1 and Sentence 2 express 
+the same meaning?
+Answer:</td><td>Yes | No</td></tr><tr><td>BOOLQ</td><td>{passage}
+Question: {question}
+Answer:</td><td>Yes | No</td></tr><tr><td>SST-2</td><td>Question: Does the following sentence have a 
+positive or negative sentiment?
+Sentence: {sentence}
+Answer:</td><td>positive | negative</td></tr></table>
+
+Table 9: The prompt templates for the downstream tasks.
+
+![](images/359fab988aa4b9767843842e3e4af28464b25af402e3b957a12414740e7051a9.jpg)  
+Figure 3: The accuracy comparison between BRD and the baseline on BIG-bench tasks.
+
+SST-2 performance significantly, resulting in a decrease of 4 points compared to training XGLM-BRD on full data. Thanks to the remaining data for training XGLM-BRD, it still performs significantly better than XGLM-564M by a large margin on SST-2 task. On XNLI task, excluding the sentiment-related data obtains a significant improvement over XGLM-BRD trained on full data. This indicates that the sentiment-related data is not fit for the language inference task.
+
+<table><tr><td rowspan="2">Model</td><td colspan="5">Task</td><td rowspan="2">Average</td></tr><tr><td>MovieDialog</td><td>FormalFallacies</td><td>ShakespeareDialogue</td><td>VitaminC</td><td>WinoWhy</td></tr><tr><td colspan="7">Relaxed Test</td></tr><tr><td>TaskDistillation</td><td>46.7</td><td>50.0</td><td>42.2</td><td>13.6</td><td>55.2</td><td>41.6</td></tr><tr><td>XGLM-BRD2</td><td>50.1</td><td>50.0</td><td>49.8</td><td>13.8</td><td>56.9</td><td>44.1</td></tr><tr><td colspan="7">With Downstream Task Supervision</td></tr><tr><td>SFT</td><td>69.2</td><td>69.9</td><td>69.3</td><td>55.9</td><td>76.9</td><td>68.3</td></tr><tr><td>XGLM-BRD2-SFT</td><td>70.6</td><td>69.3</td><td>70.2</td><td>56.0</td><td>79.1</td><td>69.1</td></tr></table>
+
+![](images/e9b62176d7bee167df21019afcefe51d2cba5b4d921cb4b539f10cc3523ba5a1.jpg)
+
+![](images/a7395211bb501032998585f06f558091e106f5a6b3171dbc575d2322a1910311.jpg)
+
+![](images/089509b946e744a210cc13994ec96725798b522c7e07c8e48ea13ea746c3d91c.jpg)
+
+![](images/d98f0fc8de50e9ee5a599ad7c5f343156b5fdb351e97f0ae497c45fc026e3269.jpg)  
+Figure 4: The results of probing XGLM-564M and XGLM-BRD layer-wisely on the downstream tasks in the blind test. The horizontal axis represents the specific layer in the model, and the vertical axis is the prediction accuracy  $(\%)$  for each task.
+
+![](images/b18203a542807c1a1f56cd80e8fcf96502aa381d407385767a76b9ad47e130ae.jpg)
+
+![](images/00e24482671863f52ac227b3fd4057acfd266f8c3a49da6a1623c881c4617af8.jpg)
+
+Table 10: Results on the reduced BIG-bench set.  
+
+<table><tr><td></td><td>XNLI</td><td>RTE</td><td>CB</td><td>PAWS-X</td><td>BOOLQ</td><td>SST-2</td></tr><tr><td>XGLM-564M-FBRD</td><td>58.1</td><td>61.0</td><td>71.4</td><td>63.1</td><td>74.4</td><td>81.1</td></tr><tr><td>XGLM-BRD²</td><td>59.2</td><td>62.5</td><td>82.1</td><td>64.8</td><td>75.0</td><td>81.9</td></tr></table>
+
+Table 11: The comparison between basing on XGLM-BRD and basing on XGLM-564M for further BRD on the downstream tasks.  
+
+<table><tr><td rowspan="2"></td><td colspan="7">Tasks</td></tr><tr><td>XNLI</td><td>RTE</td><td>CB</td><td>PAWS-X</td><td>BOOLQ</td><td>SST-2</td><td>Avg</td></tr><tr><td>XGLM-564M</td><td>35.5</td><td>46.2</td><td>53.6</td><td>51.3</td><td>51.2</td><td>63.9</td><td>50.3</td></tr><tr><td>XGLM-BRD</td><td>36.2</td><td>53.8</td><td>58.9</td><td>56.7</td><td>61.0</td><td>78.1</td><td>57.5</td></tr><tr><td>-SENTData</td><td>39.2</td><td>54.5</td><td>57.1</td><td>51.5</td><td>59.1</td><td>74.2</td><td>55.9</td></tr></table>
+
+Table 12: The result of training XGLM-BRD based on the data excluding the sentiment-related questions and answers, denoted by -SentData, in the blind test.

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ACL/2025/Battling against Tough Resister_ Strategy Planning with Adversarial Game for Non-collaborative Dialogues/full.md

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+# Battling against Tough Resister: Strategy Planning with Adversarial Game for Non-collaborative Dialogues
+
+Haiyang Wang $^{1}$ , Zhiliang Tian $^{1*}$ , Yuchen Pan $^{2}$ , Xin Niu $^{1}$ , Xin Song $^{1}$ , Minlie Huang $^{3}$ , Bin Zhou $^{1}$
+
+<sup>1</sup>College of Computer Science and Technology, National University of Defense Technology
+
+2 Intelligent Game and Decision Lab, Academy of Military Science
+
+$^{3}$ Tsinghua University
+
+{wanghaiyang19, tianzhiliang,panyuchen, niuxin, songxin, binzhou}@nudt.edu.cn
+
+aihuang@tsinghua.edu.cn
+
+# Abstract
+
+Non-collaborative dialogue involves two participants with conflicting interests engaging in a multi-round dialogue to achieve their own goals. Strategy planning is the key to guiding both participants towards a consensus. Most LLMs-based methods use stimulus prompts or external strategy planners for strategy planning. However, stimulus prompts fail to teach LLMs to plan dialogue strategies explicitly. Moreover, training external strategy planners doesn't fully account for adversarial interactions, thereby limiting their effectiveness against tough resisters. In this paper, to mitigate the above issues, we propose GAIA, a Game-based Adversarial self-play InterActive training paradigm, which constructs an adversarial two-player (a persuader and a resister) zero-sum game and guides the game to approximate Nash Equilibrium (NE) via reinforcement learning (RL) for the non-collaborative dialogues. First, we design a Chain-of-Mind prompt to reason the resister's dialogue act step-by-step to plan the persuasive strategies. Secondly, to adversarially improve the persuader, we construct diverse resistant planners and theoretically improve the persuader's optimal lower bound. Finally, we iteratively optimise their policies via adversarial self-play interactive RL and design an  $\epsilon$ -NE verification algorithm to approximate the game's NE. Experiments on three datasets show that our model obtains state-of-the-art performance.
+
+# 1 Introduction
+
+Non-collaborative dialogue is when two dialogue participants with conflicting interests make multi-round dialogue to achieve their own goals (Zhan et al., 2024). It has widespread applications, including legal debates (He et al., 2024b) and opinion controversy (Mou et al., 2024). The mainstream methods in non-collaborative dialogue are to make
+
+strategy planning to guide both parties towards a consensus (Zhang et al., 2024b).
+
+The strategy planning for non-collaborative dialogue contains: (1) Traditional deep learning methods typically plan strategies through supervised training. They explicitly consider dialogues' states (Zhou et al., 2020; Tian et al., 2023) and historical strategies (Joshi et al., 2021). However, these methods rely heavily on datasets with annotations. They typically plan strategies based solely on the next turn's feedback, thus tending to neglect the long-term goals. (2) LLMs-based stimulus prompt methods plan strategies through various stimulus prompts with in-context learning (ICL). These prompts stimulate the LLMs to self-thinking (Wang et al., 2023b; Deng et al., 2023b), self-reflective (Zhang et al., 2023), and critical feedback (Fu et al., 2023) for dialogue strategy planning. These methods exploit the internal knowledge of LLMs via zero/few-shot examples to produce the strategies. However, the pre-training of LLMs seldom learned to explicitly plan non-collaborative strategy, thus it limited LLMs' ability to be directly applied to sequential strategy planning for specific tasks.
+
+To mitigate these limitations, researchers propose equipping LLMs with an external strategy planner. Instead of employing the aforementioned zero/few-shot, they conduct supervised learning or RL to fine-tune a strategy planner to predict the dialogue strategy for the next turn, and then they merge the strategy planner and LLMs to generate dialogue (Deng et al., 2024; Zhang et al., 2024b). These methods not only (1) leverage LLMs' remarkable capabilities to generate dialogues, but also (2) fine-tune the planner on non-collaborative strategy planning tasks (Deng et al., 2024). However, the strategy planner's training does not consider adversarial interactions. Tuning the strategy planner considers only the current dialogue state instead of the dialogue opponent's potential re
+
+sponses and the future dialogue directions after the opponent's responses.
+
+Furthermore, some researchers propose an opponent agent to conduct adversarial training (Zhang et al., 2024b; Deng et al., 2024; Fu et al., 2023). Due to the difficulty of constructing a realistic opponent agent, researchers exploit LLMs' capabilities to meticulously design prompts to simulate opponents and generate high-quality responses (Fu et al., 2023). The mechanism contributes to composing an adversarial strategy planner to estimate the opponent's responses. However, this adversarial training fails to dynamically adapt to the increasing abilities of the agents. The adversarial capability comes from LLMs with prompt texts, and the static prompts constrain the model's ability as the training goes on. That is, the opponent agent cannot adaptively become stronger as our planner improves thus weakening the robustness and adversarial of our strategy planner.
+
+In this paper, we propose GAIA, a Game-based Adversarial self-play InterActive training paradigm for LLMs-based non-collaborative dialogues via strategy planning. GAIA constructs a two-player zero-sum game that involves the two participants (dialogue agents) and guides the game to approximate Nash Equilibrium (NE) through reinforcement learning (RL) optimization for the non-collaborative dialogue. Specifically, the two-player zero-sum game is conducted between persuasive strategy planners and resistant strategy planners. To perceive and persuade the resister more effectively, we design a Chain-of-Mind prompt to reason the resister's dialogue act step-by-step and incorporate them into strategy planning. To adversarily improve the generalization ability of the persuasive strategy planner, we propose a diverse resistant planner construction method. We theoretically prove that our training against diverse resisters improves the optimal lower bound of the persuader. To enhance the adversarial intensity, we construct a zero-sum persuader-resister game and iteratively optimize their policies through adversarial self-play interactive RL. To guide the game approximates the NE, we design a  $\epsilon$ -NE iteration verification algorithm to obtain the near-optimal policy. Extensive experiments on three non-collaborative dialogue datasets show that significantly outperforms all the baselines, excelling against tough resisters.
+
+Our contributions are threefold: (1) We propose a game-based adversarial self-play interactive training paradigm for LLMs-based intensely adversarial
+
+non-collaborative dialogue via strategy planning. (2) We design an adversarial interactive reinforcement learning method with  $\epsilon$ -NE iteration verification to guide the game approximates NE to obtain the near-optimal policy for strategy planer. (3) Extensive experiments on three non-collaborative dialogue datasets show that GAIA achieves state-of-the-art performance.
+
+# 2 Related Work
+
+# 2.1 Non-Collaborative Strategy Planning
+
+Non-collaborative dialogue is a form of user-system interaction aiming to reach an agreement despite conflicting interests (Deng et al., 2023b). Strategy planning aims to use a series of strategies to guide both participants towards a consensus (Zhang et al., 2024b; Zhan et al., 2024). It can be divided into three categories: (1) Traditional deep learning methods conduct the strategy planning via dialogue act prediction (Deng et al., 2024; Joshi et al., 2021; Cheng et al., 2022). (2) LLMs-based stimulus prompt methods unleash the perception and planning potential of LLMs to strategize and guide the dialogue strategy (Deng et al., 2023b; Fu et al., 2023). (3) Equipping LLMs with external strategy planner methods conducts a tunable PLM as a strategy planner to predict the dialogue strategy at the next turn (Deng et al., 2024; Zhang et al., 2024b). In addition, there are also other methods, such as quasi-online direct preference optimization (Chen et al., 2024b) or dialogue action tokens (Li et al., 2024), used for goal-directed dialogue tasks.
+
+To enhance LLMs' strategy planning in non-collaborative dialogues, three key capabilities need improvement: perception, planning, and adversariality (Deng et al., 2023b). LLMs need to better perceive opponents' emotions and infer intentions from conversation history (Zhang et al., 2024b; Tian et al., 2021). Their planning should be strengthened to adjust strategies dynamically toward long-term goals (Deng et al., 2024). Lastly, enhancing adversarial adaptability make them respond effectively in complex dialogues to achieve their objectives.
+
+# 2.2 Two-Player Zero-Sum Markov Games
+
+The Markov decision process (MDP) is a common tool to describe interactions between an agent and its environment (Lahikainen et al., 2024). Markov games (MGs) extend MDPs to multi-agents. In
+
+![](images/b528df8a562019d3161fa9a6f46dd56d2bb2edc2bf2cd1f7aeb6e2552f436ba1.jpg)  
+Figure 1: The architecture of GAIA. The left is the Resister-aware Persuasive Strategy Planner. The right is the Diverse Resistant Strategy Planners. The upper centre illustrates the Adversarial Self-play Interaction via Game of the both planners. At the bottom centre, we guide the game to approximate the  $\epsilon$ -NE.
+
+MGs, multiple agents make decisions to maximize their or common interests (Ghaemi et al., 2024). Specifically, two-player zero-sum Markov games (TZMGs) involve two players with completely opposing interests (Nika et al., 2024). Both share the same reward function: one aims to maximize future rewards, while the other aims to minimize them. In TZMGs, the Nash Equilibrium represents the best possible payoff a player can achieve against the worst-case opponent (Silva, 2024).
+
+# 3 Methodology
+
+# 3.1 Task Definition
+
+Given the role setting, dialogue goals, dialogue strategy sets  $\mathcal{A}^p,\mathcal{A}^r$ , and the first utterance  $u_{1}^{p},u_{1}^{r}$  of non-collaborative dialogue participants, the noncollaborative dialogue task aims to generate a multiturn dialogue  $\{u_1^p,u_1^r,\dots ,u_t^p,u_t^r\}$  to gradually guide two dialogue participants with conflicting dialogue goals towards a consensus by planning a series of strategies. Each utterance  $u_{i}$  in the multiturn non-collaborative dialogue is generated based on an appropriate dialogue strategy  $a_{i}\in \mathcal{A}$ .
+
+# 3.2 Model Overview
+
+Our model GAIA (Fig. 1) aims to train an exceptional persuasive strategy planner through game-based adversarial interactive training with various resistant strategy planners. GAIA consists of five modules:
+
+- Resister-aware persuasive strategy planner
+
+aims to plan strategy in highly adversarial noncollaborative dialogues and persuades the resister.
+
+- Diverse resistant strategy planners construct various resistant strategy planners to adversarially improve the generalization ability of the persuasive strategy planner.  
+- Strategic response generator aims to generate dialogue utterances based on a specified strategy.  
+- Adversarial self-play interaction via game aims to enable the above planners (persuasive and resistant strategy planners) to engage in the adversarial game for non-collaborative dialogues.  
+- Approximation of Nash Equilibrium finds an approximate Nash Equilibrium in the games to learn a near-optimal policy for the persuasive strategy planner.
+
+# 3.3 Resister-aware Persuasive Planner
+
+To effectively persuade resisters, we propose a persuasive strategy planner that can plan dialogue strategies based on the emotion, future action and dialogue act of the resister.
+
+# 3.3.1 Chain-of-Mind for Persuader
+
+We design a Chain-of-Mind (CoM) prompt for LLMs to reason the resister's emotion, future action, and dialogue goal. In non-collaborative dialogues, the inferred emotion of the resister helps the persuasive planner plan strategies that are empathetic and resonate emotionally. The inferred
+
+future action of the resister enables the persuasive planner to plan a proactive and preemptive strategy, ensuring they are well-prepared to counter any resistance. Dialogue goal of the resister allows the persuasive planner to choose compelling strategies and focus on key concerns, thus increasing the chances of successful persuasion.
+
+Recent research has shown that LLMs have the Theory-of-Mind (ToM) ability to reason others' mental states (Moghaddam and Honey, 2023). The CoM prompt relies on the ToM ability of LLMs. CoM applies a chain to step-by-step reason the emotions, future action and dialogue goal with the following steps:
+
+- Step 1: Analyze the dialogue history.  
+- Step 2: Reason mental states based on the analysis.  
+- Step 3: Reason the resister's emotion from mental states.  
+- Step 4: Reason the resister's possible future action based on the above information.  
+- Step 5: Reason the resister's dialogue goal.
+
+Based on the above reasoning steps, following CoT (Wei et al., 2022), we construct CoM exemplars to achieve in-context learning (ICL) in LLMs. The CoM prompt template is as follows: Task definition is the definition of mind reasoning task. Guideline Instruction is the instruction we expect LLMs to follow. CoM Exemplars are the instances used to better assist LLMs with ICL. Dialogue Context is the historical dialogue. Tab. 6 shows the example of the Chain-of-Mind (CoM) prompt template. CoM excels in strategic dialogue by explicitly modeling the resister's responses and dynamically adjusting its reasoning based on real-time feedback. It analyzes the resister from multiple perspectives, including emotion, future action and dialogue goals providing deeper insights that enhance the effectiveness of strategy planning.
+
+# 3.3.2 Persuasive Planner Initialization
+
+To incorporate the emotion, future action and goal of the resister into planning, we supervised finetuning (SFT) a model as the initialization of the persuasive strategy planner  $\mathbf{SP}_{per}$ . Specifically, given the reasoning emotion  $\hat{e}^r$ , future action  $\hat{a}_t^r$ , dialogue goal  $\hat{g}^r$  of the resister, and the dialogue history  $d = \{u_1^p, u_1^r, \dots, u_{t-1}^p, u_{t-1}^r\}$ , we fine-tune a
+
+pre-trained LM over a supervised dialogue corpus  $\mathcal{D}$  which contains many dialogues with annotated strategies. The training aims to minimize the cross-entropy  $\mathcal{L}_c^p$  between the predicted strategy  $a_{t}^{p}$  and the labeled strategy  $y_{t}^{p}$  for each turn  $t$  of the annotated dialogue:
+
+$$
+\mathcal {L} _ {c} ^ {p} = - \frac {1}{| \mathcal {D} |} \sum_ {d \in \mathcal {D}} \frac {1}{T _ {d}} \sum_ {t = 1} ^ {T _ {d}} a _ {t} ^ {p} \log y _ {t} ^ {p}, \tag {1}
+$$
+
+where  $T_{d}$  is the number of turns of the dialogue. Finally, the planner  $\mathbf{S}\mathbf{P}_{per}$  that can predict the persuasive strategy  $a_{t}^{p}$  as  $a_{t}^{p} = \mathbf{S}\mathbf{P}_{per}(\hat{e}^{r},\hat{a}_{t}^{r},\hat{g}^{r},d)$ . According to (Deng et al., 2024), SFT probably only obtains a sub-optimal policy for  $\mathbf{S}\mathbf{P}_{per}$ ; hence, we apply the RL in further training (Sec. 3.6).
+
+# 3.4 Diverse Resistant Planners
+
+To adversarially improve the generalization ability of the persuasive strategy planner, we construct a set containing multiple diverse resistant strategy planners.
+
+# 3.4.1 Improving Persuader's Optimal Lower Bound via Diversing Resisters
+
+The persuader can effectively improve the persuasive strategy planner's optimal lower bound by training against diverse resistant strategy planners with varying resistance capabilities. The construction of more diverse or less diverse planners is determined by the variance in the performance distribution during strategy planning. Compared to less diverse resisters, more diverse resisters offer more information gain (He et al., 2024a) for optimizing the persuader's parameters. Taking price negotiations as an example, the buyer aims to persuade the seller to their target price. By negotiating with sellers of diverse bargaining skills, the buyer enhances their negotiation abilities more effectively than interacting with fewer sellers.
+
+To prove that training against more diverse resistant planners improves the persuader's optimal lower bound, we define that (a) the persuader's initial policy  $\pi^0$  and the optimized policy is  $\pi^{*}$ ; (b) the training resistor sets are  $S_r^m$  and  $S_r^l$ ; (c) the test resisters set is  $S_r^{test}$ ; (d) policy of resistor is  $\mu$ . We assume that (1)  $S_r^m$  is more diverse than  $S_r^l$  and  $S_r^l \subseteq S_r^m$ ; (2) The optimized policy of persuader through the training with resisters  $\mu \in S_r^m$  is  $\pi^m$  and that with  $\mu \in S_r^l$  is  $\pi^l$ ; (3) The function  $u(\pi, \mu)$  measures the total reward for the policy tuple  $(\pi, \mu)$ ; (4) The total reward gain after optimization is  $\mathbb{E}_{\mu^{test} \in S_r^{test}}[u(\pi^{*}, \mu^{test}) - u(\pi^0, \mu^{test})]$ ; (5)
+
+The optimal lower bound of persuader is  $L(\pi^{*}) = \min_{\pi^{*}}\mathbb{E}[u(\pi^{*},\mu^{test}) - u(\pi^{0},\mu^{test})]$ .
+
+Based on information-theoretic research for analysing optimal lower bound (Shannon, 1948; Galvez, 2024; He et al., 2024a), we prove  $L(\pi^m) \geq L(\pi^l)$ , which indicates that more diverse resisters can improve the optimal lower bound of persuader. The detailed proof is in App. B.
+
+# 3.4.2 Diverse Resistant Planners Construction
+
+The resistant strategy planner  $\mathbf{SP}_{res}$  plans resistance strategies based on dialogue history as  $a_{t}^{r} = \mathbf{SP}_{res}(d)$ . Similar to the construction of the persuasive planner, we initialize the resistant strategy planner  $\mathbf{SP}_{res}$  by supervised fine-tuning (SFT) over an annotated dataset. Different from the persuasive planner, during SFT, we save various resistant strategy planners with varying strategy planning performances to ensure resister diversity.
+
+# 3.5 Strategic Response Generator
+
+To generate responses according to the planned strategies, we employ an LLM-based generator with a prompt  $p_{sys}$  indicating its role setting (persuader or resister) and dialogue goals. This prompt  $p_{sys}$  constrains the LLM's output to fit the role. We also design strategy-aware instructions and build a mapping  $\mathcal{M}$  to map each strategy  $a$  to an instruction. Given a dialogue history  $d$  and an instruction  $\mathcal{M}(a)$ , the LLM-based generator  $\mathbf{G}(\cdot | p_{sys})$  outputs the strategic response  $u$  as  $u = \mathbf{G}(\mathcal{M}(a), d | p_{sys})$ . As the persuader and resister have distinct role settings and dialogue goals, we construct two different prompts  $p_{sys}^{per}$  and  $p_{sys}^{res}$  for persuader generator  $\mathbf{G}_{per}(\cdot | p_{sys}^{per})$  and resistant generator  $\mathbf{G}_{res}(\cdot | p_{sys}^{res})$ , respectively. To diversify response styles, we further assign various personas (Big-Five Personality) to the resistant generator (Zhang et al., 2024b; Jiang et al., 2023).
+
+# 3.6 Adversarial Self-play Interaction via Game
+
+To adaptively enhance the resister as the persuader improves, we propose a two-player zero-sum game trained by an adversarily self-play interaction RL, which aims to achieve the  $\epsilon$ -NE of two players (planners).
+
+# 3.6.1 Persuader-Resister Game
+
+We construct a two-player zero-sum Markov game (TZMG)  $\mathcal{G} = (\mathcal{S},\mathcal{A}^p,\mathcal{A}^r,\mathcal{P},\mathcal{R},\gamma)$  for the two
+
+planners. In  $\mathcal{G}$ ,  $\mathcal{S}$  is the game state set representing the dialogue history,  $\mathcal{A}^p$  is a pre-defined set of persuasive strategies,  $\mathcal{A}^r$  is the resistant strategies set,  $\mathcal{P}$  is state transition function,  $\mathcal{R}$  is the bounded and deterministic reward function, and  $\gamma$  is the discounted factor. At each step  $t$ , the persuasive strategy planner chooses strategy  $a_t^p \sim \pi(s_t)$  then the resistant planner chooses strategy  $a_t^r \sim \mu(s_t)$ . The two planners aim to maximize the expected value  $V(s_0) = \mathbb{E}[\sum_{t=0}^{\infty} \gamma^l \mathbf{r}_{t+1}]$ , which is the expectation of the sum of future rewards  $\mathbf{r}$ .
+
+# 3.6.2 Adversarial Self-play Interactive RL
+
+To optimize the policies of the persuasive and resistant strategy planners, we propose adversarial self-play interactive RL. We enable the persuader and resister to perform self-play dialogue interaction. During the interaction, we dynamically measure the reward and employ RL to optimize their policies. This process gradually increases the adversarial intensity of the persuader-resister game.
+
+Policy Models (Strategy Planners). In the RL framework, our policy models are resister-aware persuasive strategy planner  $\mathbf{S}\mathbf{P}_{per}$  and resistant strategy planner  $\mathbf{S}\mathbf{P}_{res}$ . We use  $\mathbf{S}\mathbf{P}_{per}$  to plan a persuasive strategy  $a^p$  and feed  $a^p$  into  $\mathbf{G}_{per}$  to generate an utterance  $u_t^p$ . Then, we use  $\mathbf{S}\mathbf{P}_{res}$  to plan a resistant strategy  $a^r$  and feed  $a^r$  into  $\mathbf{G}_{res}$  to counter with a response  $u_t^r$ . The persuader and resister alternately choose strategies (actions) and interact through dialogue.
+
+Goal-oriented Reward. We design a reward function to provide goal-oriented quantitative feedback  $\mathbf{r}$  for the planners after applying strategies. In particular, for the price negotiation task, we adopt the sale-to-list ratio (SL%) (Zhou et al., 2019) as reward function, which is the ratio between the current price  $P_{t}$  and the buy's target price  $P_{\text{buyer}}$ , formulated as  $SL\% = P_{\text{current}} / P_{\text{buyer}}$ . For the countering hate speech task, we adopt the hate intensity  $\Delta \mathcal{H}$  (Wang et al., 2024b). It measures the difference in the hate intensity  $\mathcal{H}(\cdot)$  between the initial hate speech and the current utterance of the hater, formulated as  $\Delta \mathcal{H} = \mathcal{H}(u_0) - \mathcal{H}(u_t)$ . When the adversarial interaction reaches a terminal state, we calculate the total reward  $R_{t} = \sum_{t'=t}^{T} \gamma^{T-t'} \mathbf{r}_{t'}$  accumulating from turn  $t$  to the final  $T$ , where  $\gamma$  is the discount factor. Then, we feed reward  $R_{t}$  back to  $\mathbf{SP}_{\text{per}}$  and the negative  $-R_{t}$  back to  $\mathbf{SP}_{\text{res}}$ .
+
+Optimization via RL. We use the REINFORCE algorithm (Sutton et al., 1999) to optimize the parameter  $\theta$  of the policy models (strategy planners,
+
+SP) based on the total reward  $R_{t}$  and learning rate  $\alpha$  as  $\theta \gets \theta - \alpha \nabla \log \pi_{\theta} R_{t}$ . Their adversarial interaction repeats until the persuader's goal is achieved or the maximum dialogue turn is reached.
+
+# 3.7 Approximation of Nash Equilibrium
+
+Adversarial self-play interactive RL often struggles to converge to a strict NE. Thus, we guide the adversarial game to converge at  $\epsilon$ -NE to approximate the strict NE. This method not only can obtain a near-optimal policy but also mitigate the difficulties of finding strict NE. These difficulties mainly arise from the following reasons: (1) the unpredictability of resister behaviours, (2) the limited rationality of LLM-based generators, and (3) the increased dialogue adversarial intensity.
+
+# 3.7.1 The  $\epsilon$ -NE of Persuader-Resister Game
+
+We define  $\epsilon$ -Best Response and  $\epsilon$ -Nash Equilibrium in the persuader-resister game as follows (McAleer et al., 2024).
+
+Definition 1:  $\epsilon$ -Best Response. Given the policy  $\mu$  of resistant strategy planner, the policy  $\pi^{\epsilon b}$  of persuasive strategy planner is called the  $\epsilon$ -best response that is at most  $\epsilon$  worse than the best response<sup>1</sup>  $\pi^b$ , as shown in Eq. 2. The definition for  $\epsilon$ -best response  $\mu^{\epsilon b}$  of resistant strategy planners is similar with  $\pi^{\epsilon b}$  as shown in Eq. 3.
+
+$$
+V (s; \pi^ {\epsilon b}, \mu) \geq V (s; \pi^ {b}, \mu) - \epsilon \tag {2}
+$$
+
+$$
+V (s; \pi , \mu^ {\epsilon b}) \leq V (s; \pi , \mu^ {b}) + \epsilon \tag {3}
+$$
+
+Definition 2:  $\epsilon$ -Nash Equilibrium. The  $\epsilon$ -Nash Equilibrium corresponds to a pair of  $(\pi^{\epsilon}, \mu^{\epsilon})$  that are both the  $\epsilon$ -best responses to each other:
+
+$$
+V (s; \pi , \mu^ {\epsilon}) - \epsilon \leq V (s; \pi^ {\epsilon}, \mu^ {\epsilon}) \leq V (s; \pi^ {\epsilon}, \mu) + \epsilon \quad \forall \pi , \mu \tag {4}
+$$
+
+Based on the definitions, we can conclude that under  $\epsilon$ -NE:
+
+- (C1): the persuasive strategy planner changes to other policies, the increase of the expected reward does not exceed  $\epsilon$ ;  
+- (C2): the resistant strategy planner changes to other policies, the decrease of the expected reward does not exceed  $\epsilon$ .
+
+# 3.7.2 The  $\epsilon$ -NE Iteration Verification
+
+To obtain the near-optimal policy of the above two planners, we design a  $\epsilon$ -NE iteration verification algorithm to push the game to converge at  $\epsilon$ -NE. It iteratively optimizes the policy and continuously verifies whether  $\epsilon$ -NE has been achieved. If so, we terminate the optimization. Otherwise, continue. The verification is divided into the persuader and resister verification phases. The former checks whether C1 is satisfied by only changing the policy  $\pi$ , while the latter checks C2 by only changing the policy  $\mu$ . If both are satisfied, the  $\epsilon$ -NE is achieved. The  $\epsilon$ -NE iteration verification algorithm as shown in Alg. 1.
+
+Algorithm 1  $\epsilon$ -Nash Equilibrium Iteration Verification  
+1: for iterations:  $i = 1$  to  $N$  do  
+2: for all  $d \in D$  do  
+3: Adversarial Self-play Interaction RL  
+4: end for  
+5: Test  $\pi_i$  and  $\mu_i$  and calculate  $V$ .  
+6: /* Persuader Validation Phase */  
+7: Only optimize  $\pi_{iter + i}$  and record  $V_{iter + i}^{\pi}$   
+8: /* Resister Validation Phase */  
+9: Only optimize  $\mu_{iter + i}$  and record  $V_{iter + i}^{\mu}$   
+10: /* Verify the  $\epsilon$ -NE */  
+11: if the condition satisfies with Eq. 1 then break;  
+12: else  
+14: continue optimization;  
+15: end if  
+16: end for
+
+The  $\epsilon$ -NE plays a vital role in non-collaborative dialogues. For the pricing negotiation, it helps to find a nearly fair price in buyer-seller interactions, preventing detrimental price wars. For countering hate speech (Wang et al., 2024a), it seeks a balanced viewpoint that is acceptable to both haters and anti-haters, avoiding the dialogue escalating into malicious insults.
+
+# 4 Experiments
+
+# 4.1 Experimental Setups
+
+Datasets: We focus on three different noncollaborative dialogue scenarios: (1) Craigslist-Bargain (CB) (He et al., 2018) is developed in a bargaining negotiation context where a buyer and a seller negotiate the price of an item for sale. (2) DIALOGONAN (DC) (Bonaldi et al., 2022) is de
+
+signed for fighting online hate speech. The dataset involves a hater and an anti-hater, intending to persuade the hater to change their hateful attitude. (3) Charity Persuasion (CP) (Wang et al., 2019) is designed for studying persuasive dialogues aimed at encouraging charitable donations. It involves a Persuader and a Persuadee.
+
+Baselines: We use three prompt-based (LLMs) methods and three LLMs with external strategy planners as baselines. Standard (Deng et al., 2024) prompts two LLMs to conduct self-play conversations using task instructions, without considering any dialogue strategy. ProCoT (Deng et al., 2023b) prompts the LLMs to generate a chain-of-thought analysis for planning the next turn dialogue strategy. ICL-AIF (Fu et al., 2023) prompts another LLM to provide feedback to a player to improve their dialogue strategies. MCTS (Yu et al., 2023) uses Monte Carlo Tree Search to perform goal-oriented dialogue policy planning. PPDPP (Deng et al., 2024) uses a pre-trained LM as a trainable plug-in for determining next-step strategies. TRIP (Zhang et al., 2024b) develops an external planner by modelling dialogue user characteristics and training with diverse user simulators.
+
+Implementation details: As for the planner, we adopt RoBERTa² as the default plug-and-play dialogue policy planner for evaluation. The training process for the planner includes supervised fine-tuning (SFT) and reinforcement learning (RL). During the SFT, the batch size is 32, the learning Rate is 1e-5 and the max sequence length is 512. During the RL, the learning Rate is 1e-6 and the max conversation turn is 12. Moreover, we follow the previous work (Deng et al., 2024; Zhang et al., 2024b) to design reward, which can be divided into three situations: (1) when the persuasive goal is successfully achieved, the reward is defined as 1.0 for the CP dataset, SL% for the CB datasets, and  $\Delta \mathcal{H}$  for the DC dataset. (2) when the persuasive goal is not achieved, the reward is -1.0. (3) Furthermore, a small negative reward (-0.1) per turn penalises the lengthy dialogue. As for the adversarial training, we construct a policy pool for diverse resisters. And resister policies are dynamically sampled to adversarially train the persuader. As for the generator, we adopt GPT-3.5³ to generate the strategic response on the CB and CP datasets. For DC datasets, we adopt an uncensored LLM⁴ for the
+
+hater and GPT-3.5 for the anti-hater.
+
+Evaluation Protocols: The evaluation metrics contain: Success Rate (SR) measures effectiveness by the percentage of goal achievement within a maximum number of turns, and Average Turn (AT) measures efficiency by the average number of turns required to achieve the goal. Additionally, we also used dataset-specific metrics:  $SL\%$  for the CB dataset and  $\Delta \mathcal{H}$  for DC.  $SL\%$  is to determine the effectiveness of goal completion in price negotiations.  $\Delta \mathcal{H}$  is the reduction of hate intensity (Wang et al., 2024b). The calculation details of success rates and dataset-specific metrics can be found in App. D. Resister details in the evaluation in App. D.2.3.
+
+# 4.2 Main Results
+
+<table><tr><td rowspan="2">Methods</td><td colspan="3">CB Dataset</td><td colspan="3">DC Dataset</td><td colspan="2">CP Dataset</td></tr><tr><td>SR↑</td><td>AT↓</td><td>SL%↑</td><td>SR↑</td><td>AT↓</td><td>ΔH↑</td><td>SR↑</td><td>AT↓</td></tr><tr><td colspan="9">Prompt-based planning</td></tr><tr><td>Standard</td><td>0.429</td><td>7.95</td><td>0.218</td><td>0.402</td><td>9.45</td><td>0.298</td><td>0.105</td><td>10.2</td></tr><tr><td>ProCoT</td><td>0.551</td><td>7.58</td><td>0.246</td><td>0.432</td><td>8.68</td><td>0.324</td><td>0.195</td><td>9.82</td></tr><tr><td>ICL-AIF</td><td>0.475</td><td>8.23</td><td>0.257</td><td>0.443</td><td>8.72</td><td>0.325</td><td>0.174</td><td>9.93</td></tr><tr><td colspan="9">External strategy planner</td></tr><tr><td>MCTS</td><td>0.471</td><td>7.77</td><td>0.238</td><td>0.521</td><td>7.89</td><td>0.356</td><td>0.246</td><td>9.63</td></tr><tr><td>PPDPP</td><td>0.623</td><td>6.82</td><td>0.342</td><td>0.578</td><td>7.42</td><td>0.364</td><td>0.463</td><td>9.12</td></tr><tr><td>TRIP</td><td>0.659</td><td>6.46</td><td>0.389</td><td>0.601</td><td>7.46</td><td>0.372</td><td>0.528</td><td>8.49</td></tr><tr><td>GAIA</td><td>0.693</td><td>6.03</td><td>0.413</td><td>0.643</td><td>6.92</td><td>0.412</td><td>0.562</td><td>8.12</td></tr><tr><td>Δ</td><td>↑0.034</td><td>↓0.43</td><td>↑0.024</td><td>↑0.042</td><td>↓0.50</td><td>↑0.040</td><td>↑0.034</td><td>↓0.37</td></tr><tr><td>Δ%</td><td>↑5.2</td><td>↓6.7</td><td>↑6.1</td><td>↑6.9</td><td>↓6.7</td><td>↑10.7</td><td>↑6.4</td><td>↓4.4</td></tr></table>
+
+Table 1: Main Results on 3 datasets. Best scores are in bold. The suboptimal scores are underlined.  $\Delta$  represents the difference between the best and the suboptimal result, and  $\Delta \%$  is the percentage. The significance tests of our GAIA over PPDPP and TRIP (with  $p < 0.05$ ).
+
+The overall performances are shown in Tab. 1. The main experimental setup is consistent with previous studies (Deng et al., 2024). The opponent is based on an LLM without a strategy planner. For prompt-based LLMs planning methods, standard prompt methods provide a baseline for all competing methods having low success rates. ProCoT is a competitive prompt-based method that has achieved high persuasion success rates on the CB and CP datasets. ICL-AIF slightly improves SR over standard prompts but requires more turns, indicating that AI feedback (ICL-AIF) doesn't effectively adjust strategies with changing dialogue states. For external planners with LLMs methods, most of these methods achieve a higher SR than prompt-based methods and require fewer dialogue rounds (lower AT). This indicates that explicit strategy planning benefits the achievement of the persuader's goal in non-collaborative dia
+
+logues. Among external strategy planner methods, TRIP achieves good performance. TRIP uses a population-based training paradigm that enhances the effectiveness of strategy planning. Our proposed GAIA consistently outperforms all baselines across three datasets. The average improvement in SR is about  $6.6\%$  and AT is about  $5.9\%$ . The significance tests of our GAIA over PPDPP and TRIP (with  $p < 0.05$ ) show that GAIA presents a statistically significant improvement. The results show that GAIA not only achieves the dialogue goal efficiently (less AT) but also persuades resisters effectively (higher SR). We attribute this to the diverse resisters and adversarial interactive RL, which enables the successful persuasion of tough resisters that other methods fail to convince.
+
+# 4.3 Ablation Study
+
+<table><tr><td rowspan="2">Methods</td><td colspan="3">CB</td><td colspan="3">DC</td></tr><tr><td>SR ↑</td><td>AT ↓</td><td>SL % ↑</td><td>SR ↑</td><td>AT ↓</td><td>ΔH ↑</td></tr><tr><td>GAIA</td><td>0.693</td><td>6.03</td><td>0.413</td><td>0.643</td><td>6.92</td><td>0.412</td></tr><tr><td>w/o RA</td><td>0.661</td><td>6.57</td><td>0.382</td><td>0.626</td><td>7.34</td><td>0.398</td></tr><tr><td>Δ</td><td>↓0.032</td><td>↑0.53</td><td>↓0.034</td><td>↓0.017</td><td>↑0.42</td><td>↓0.014</td></tr><tr><td>w/o D</td><td>0.665</td><td>6.62</td><td>0.379</td><td>0.633</td><td>7.44</td><td>0.381</td></tr><tr><td>Δ</td><td>↓0.028</td><td>↑0.59</td><td>↓0.034</td><td>↓0.010</td><td>↑0.52</td><td>↓0.031</td></tr><tr><td>w/o AI</td><td>0.636</td><td>7.21</td><td>0.367</td><td>0.592</td><td>7.47</td><td>0.370</td></tr><tr><td>Δ</td><td>↓0.057</td><td>↑1.18</td><td>↓0.046</td><td>↓0.051</td><td>↑0.55</td><td>↓0.042</td></tr><tr><td>w/o NEV</td><td>0.672</td><td>6.22</td><td>0.393</td><td>0.620</td><td>7.12</td><td>0.399</td></tr><tr><td>Δ</td><td>↓0.021</td><td>↑0.19</td><td>↓0.020</td><td>↓0.023</td><td>↑0.20</td><td>↓0.013</td></tr></table>
+
+To verify the effectiveness of each component, we conduct an ablation study (Tab. 2). We observe that removing the resister-aware module ("w/o RA") slightly reduces performance, which verifies that reasoning about the resister's emotions, future actions, and dialogue goals during non-collaborative dialogues helps the persuader achieve its own goals. From the results of removing the diverse resisters ("w/o D") that only train against a single resister, we conclude that training with diverse resisters is effective in enhancing the robustness of the persuasive strategy planner. Additionally, the performance drops significantly when removing the adversarial interaction ("w/o AI") that the resister without a planner. The result indicates that the resister can adaptively improve, which is crucial for optimizing the persuasive strategy planner. Furthermore, removing the NE validation ("w/o NEV") leads to a noticeable performance decline. It suggests that finding an approximate NE helps obtain a near-optimal policy for the persuasive strategy planner.
+
+# 4.4 Adversarial Analysis of GAIA
+
+This section aims to analyze GAIA's adversarial performance against resisters with varying strategy planning abilities and adversarial intensity.
+
+# 4.4.1 Resistant Strategy Planners Ability
+
+Table 2: Experimental results of ablation study.  
+
+<table><tr><td rowspan="2">Methods</td><td colspan="2">Weak</td><td colspan="2">Medium</td><td colspan="2">Tough</td></tr><tr><td>SR ↑</td><td>ΔH ↑</td><td>SR ↑</td><td>ΔH ↑</td><td>SR ↑</td><td>ΔH ↑</td></tr><tr><td>PPDPP</td><td>0.573</td><td>0.362</td><td>0.523</td><td>0.310</td><td>0.437</td><td>0.274</td></tr><tr><td>TRIP</td><td>0.577</td><td>0.373</td><td>0.519</td><td>0.301</td><td>0.441</td><td>0.269</td></tr><tr><td>GAIA</td><td>0.603</td><td>0.382</td><td>0.558</td><td>0.341</td><td>0.492</td><td>0.318</td></tr><tr><td>ΔPPDPP</td><td>↑0.030</td><td>↑0.020</td><td>↑0.035</td><td>↑0.031</td><td>↑0.055</td><td>↑0.044</td></tr><tr><td>ΔTRIP</td><td>↑0.026</td><td>↑0.009</td><td>↑0.039</td><td>↑0.040</td><td>↑0.051</td><td>↑0.049</td></tr></table>
+
+Table 3: Adversarial analysis when against resisters with various resistant strategy planning abilities.
+
+To assess GAIA's performance against resisters with various resister strategy planning abilities, we set up resisters with varying difficulty levels. They exhibit distinct strategic planning abilities, which are classified as weak, medium, and tough in terms of the strengths of resisters (difficulty for the persuader). The experiment results are shown in Tab. 3. We observe that GAIA shows strong performance when dealing with resisters of varying strengths including weak, middle, and tough (Definition details in App. D). More importantly, we find that when facing a tough resister, GAIA shows an improvement of about  $5\%$  over baselines, which is higher than the  $2.8\%$  improvement when facing a weak resister. This indicates that GAIA excels in dealing with tougher resisters and remains effective against weaker ones. We attribute this to (1) the construction of diverse resister strategy planners with varying strategic capabilities, and (2) adversarial self-play interactive RL that improves generalization against various resisters.
+
+# 4.4.2 Adversarial Intensity of Dialogue
+
+![](images/f331a0eabc1347d00b58783bbb4a728b9f1487b41b983ab9105f9d9b35e0bffb.jpg)  
+Figure 2: Persuasion SR with increasing adversariality.
+
+To investigate GAIA's performance in tackling dialogues with varying adversarial intensities, we
+
+evaluate the persuasion success rates across varying adversarial intensities on DC, as shown in Fig. 2. We measure non-collaborative dialogues' adversarial intensity based on the prior work (Wang et al., 2023a), where the adversarial intensity ranges from a minimum of 0.32 to a maximum of 0.78. We observe that GAIA shows a significant improvement  $(8\%)$  in SR within the high adversarial intensity range ([0.6, 0.8]) compared with PPDPP and TRIP. It is higher  $(5\%)$  than the improvement  $(3\%)$  in the low adversarial intensity range ([0.3, 0.5]). This demonstrates the GAIA's superiority in tackling intense adversarial dialogues.
+
+# 4.5 Personality Generalization Analysis
+
+![](images/52e3ca3ad38ae39bdcf504aa996c2c96b40331ad51399df9bd45d5788298cf56.jpg)  
+Figure 3: Persuasion SR with five personalities.
+
+To analyze the generalization of the persuader towards resisters with different personalities, we equip the resisters with big-five personalities on DC dataset (Jiang et al., 2023), which are Openness, Conscientiousness, Extraversion, Agreeableness, and Neuroticism generators. The results are shown in Fig. 3. GAIA achieves the highest persuasion SR when dealing with resisters on most personalities. It indicates that training against the diverse personalities of resisters makes strategy planning more personality-adaptive.
+
+# 4.6 Human Evaluation
+
+<table><tr><td>Methods</td><td>PSR</td><td>Coherent</td></tr><tr><td>PPDPP</td><td>0.48</td><td>3.54</td></tr><tr><td>TRIP</td><td>0.54</td><td>3.57</td></tr><tr><td>GAIA</td><td>0.59</td><td>3.68</td></tr></table>
+
+Table 4: The Human Evaluation Results.
+
+We conduct a human evaluation (App. E) on the full test set of the CB dataset in line with the previous research (Deng et al., 2024; Zhang et al., 2024c). We consider the metrics of (1) persuasion success rate (PSR): the success (1) or not (0) of
+
+persuasion based on dialogue texts. (2) coherent: the coherence of dialogue and strategic planning on a scale of 1 (bad) to 5 (good). The experimental results are shown in Tab. 4, demonstrating that our approach also outperforms two competitive baselines in human evaluations.
+
+# 4.7 Case Study
+
+We provide detailed case studies to analyze the advantages of GAIA when tackling tough resisters and intense adversarial dialogue compared to PPDPP and TRIP, as shown in Tab. 10, Tab. 11 and Tab. 12. From Tab. 10, we can observe that: (1) GAIA does not easily succumb to the resistor and maintains its stances when facing a tough resistor; (2) GAIA is good at employing positive strategies (e.g. empathy) to influence the resistor subtly; (3) GAIA's strategic planning is coherent to progressively persuading resisters. From Tab. 11, the anti-hate speaker tries to correct the hate speaker's wrong beliefs using constant criticism and questioning. However, this excessive attacking and probing only makes the hate speaker more defensive, leading to a heated argument and worsening their hate instead of easing it. From Tab. 12 the anti-hate speaker used many strategies to engage in a friendly debate. However, despite these strategies aimed at fostering understanding and reducing hatred, the hater's position remained unchanged and, in some respects, even deepened.
+
+# 5 Conclusion
+
+In this paper, we propose GAIA, a Game-based Adversarial self-play InterActive training paradigm for non-collaborative dialogue via strategy planning. In GAIA, we propose Chian-of-Mind to construct a resister-aware persuasive strategy planner that can reason resister's dialogue act step-by-step to plan the persuasive strategies. To improve the generalization ability of the persuasive strategy planner, we also construct diverse resistant strategy planners and theoretically improve the persuader's optimal lower bound. To enhance the adversarial intensity of the game, we iteratively optimize the policies of the two planners through adversarial self-play interactive reinforcement learning. GAIA converges at the approximation NE of the game. Experimental results show that GAIA significantly outperforms other methods across three non-collaborative dialogue datasets, particularly in intense adversarial scenarios.
+
+# Acknowledgements
+
+The authors thank the anonymous reviewers for their insightful suggestions. This work is supported by the following fundings: National Natural Science Foundation of China (No.62172428), Young Elite Scientist Sponsorship Program by CAST (2023QNRC001) under Grant No. YESS20230367, the National Natural Science Foundation of China under Grant No. 62306330 and the National Science Foundation for Distinguished Young Scholars under Grant No. 62125604.
+
+# Limitations
+
+While the proposed GAIA method presents a novel approach for enhancing non-collaborative dialogue strategies, there are a few limitations that should be acknowledged: (1) GAIA's reliance on reinforcement learning can be computationally expensive, making it challenging to scale to more complex dialogue scenarios. (2) While GAIA performs well on three benchmarks, its effectiveness in diverse, real-world applications remains untested. (3) GAIA's performance depends on the quality of the underlying LLMs, which may introduce biases or limitations in handling nuanced interactions.
+
+# Ethics Statement
+
+The goal of this paper is to enhance strategy planning in non-collaborative dialogues, with applications in scenarios such as product trading, hate mitigation, and emotional support. Our research may give rise to some ethical and moral considerations. Nevertheless, we are confident that our work aligns with the ethical policy established by ACL.
+
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+
+# A Details of Chain-of-Mind
+
+Tab. 6 shows the example of the Chain-of-Mind (CoM) prompt template. The CoM prompt template is as follows: Task definition is the definition of mind reasoning task. Guideline Instruction is the instruction we expect LLMs to follow. CoM Exemplars are the instances used to better assist LLMs with ICL. Dialogue Context is the historical dialogue. It is worth noting that we apply the Chain-of-Mind prompt only to the persuader for the following reasons: (1) Focus on improving the persuader: Our work aims to enhance the persuader's strategic planning ability, which is best achieved by applying the Chain-of-Mind prompt to them. (2) Information asymmetry: In non-collaborative dialogues, the persuader typically has more information than the resister (Deng et al., 2023a; Bonaldi et al., 2024). Applying the prompt only to the persuader simulates this real-world imbalance. (3) Benefits of heterogeneity in self-play: Our method uses self-play reinforcement learning. Research (Zhang et al., 2024a) shows that in complex, diverse scenarios like non-collaborative dialogues, having heterogeneous agents improves learning and leads to better performance.
+
+# B Proof for Improving Persuader's Optimal Lower Bound via Diversing Resisters
+
+The diversity of resistant planners is determined by the variance in performance (F1) distribution. More diverse resisters exhibit a larger variance in performance, while less diverse resisters show a smaller variance. To prove that training against more diverse resistant planners improves the persuader's optimal lower bound, we define:
+
+(a) the persuader's initial policy  $\pi^0$  and the optimized policy is  $\pi^{*}$ ;  
+(b) the training resister sets are  $S_r^m$  and  $S_r^l$ ;  
+(c) the test resisters set is  $S_r^{test}$ ;  
+(d) policy of resister is  $\mu$
+
+# We assume that
+
+(1)  $S_r^m$  is more diverse than  $S_r^l$  and  $S_r^l \subseteq S_r^m$ ;  
+(2) The optimized policy of persuader through the training with resisters  $\mu \in S_r^m$  is  $\pi^m$  and that with  $\mu \in S_r^l$  is  $\pi^l$ ;
+
+(3) The function  $u(\pi, \mu)$  measures the total reward for the policy tuple  $(\pi, \mu)$ ;  
+(4) The total reward gain after optimization is  $\mathbb{E}_{\mu^{test} \in S_r^{test}}[u(\pi^*, \mu^{test}) - u(\pi^0, \mu^{test})]$ ;  
+(5) The optimal lower bound of persuader is  $L(\pi^{*}) = \min_{\pi^{*}} \mathbb{E}[u(\pi^{*}, \mu^{test}) - u(\pi^{0}, \mu^{test})]$ .
+
+# Proof:
+
+$$
+\begin{array}{l} L (\pi^ {m}) - L (\pi^ {l}) \\ = \min _ {\pi^ {m}} \mathbb {E} \left[ u \left(\pi^ {m}, \mu^ {t e s t}\right) - u \left(\pi^ {0}, \mu^ {t e s t}\right) \right] \\ - \min  _ {\pi^ {l}} \mathbb {E} \left[ u \left(\pi^ {*}, \mu^ {t e s t}\right) - u \left(\pi^ {0}, \mu^ {t e s t}\right) \right] \\ = \min  _ {\pi^ {m}} \mathbb {E} \left[ u \left(\pi^ {m}, \mu^ {t e s t}\right) \right] - \mathbb {E} \left[ u \left(\pi^ {0}, \mu^ {t e s t}\right) \right] \\ - \min  _ {\pi^ {l}} \mathbb {E} \left[ u \left(\pi^ {l}, \mu^ {t e s t}\right) \right] + \mathbb {E} \left[ u \left(\pi^ {0}, \mu^ {t e s t}\right) \right] \\ = \min _ {\pi^ {m}} \mathbb {E} \left[ u \left(\pi^ {m}, \mu^ {t e s t}\right) \right] - \min _ {\pi^ {l}} \mathbb {E} \left[ u \left(\pi^ {l}, \mu^ {t e s t}\right) \right] \\ \end{array}
+$$
+
+Given the definition of entropy as
+
+$$
+H (X) = - \sum_ {i} P (x _ {i}) \ln P (x _ {i}),
+$$
+
+we have
+
+$$
+H \left(S _ {2} ^ {m}\right) = - \sum_ {\mu \in S _ {2} ^ {m}} P (\mu) \log P (\mu)
+$$
+
+$$
+H \left(S _ {2} ^ {l}\right) = - \sum_ {\mu \in S _ {2} ^ {l}} P (\mu) \log P (\mu).
+$$
+
+Since the diversity of opponents in  $S_2^m$  is greater than in  $S_2^l$ , and  $S_2^l \subseteq S_2^m$ , the strategy space from  $S_2^l$  to  $S_2^m$  provides more information gain for  $\pi$ , i.e.,
+
+Information Gain  $= H\left(S_2^m\right) - H\left(S_2^l\right)\geq 0$
+
+Since  $\min_{\pi^*} \mathbb{E}[u(\pi^*, \mu^{test})] \propto H(S_2^*)$ , we have
+
+$$
+\min  _ {\pi^ {m}} \mathbb {E} \left[ u \left(\pi^ {m}, \mu^ {t e s t}\right) \right] - \min  _ {\pi^ {l}} \mathbb {E} \left[ u \left(\pi^ {l}, \mu^ {t e s t}\right) \right] \geq 0
+$$
+
+Thus,
+
+$$
+L (\pi^ {m}) - L (\pi^ {l}) \geq 0
+$$
+
+$$
+L (\pi^ {m}) \geq L (\pi^ {l}).
+$$
+
+# C Definitions of Best Response and Nash Equilibrium
+
+We define Best Response and Nash equilibrium in the persuader-resister game as follows.
+
+Definition 1: Best Response. Given the policy  $\mu$  of resistant strategy planner, the policy  $\pi^b$  of persuasive strategy planner is called the best response if there are no policies better than  $\pi^b$ , as shown in Eq. 5. The definition for best response  $\mu^b$  of resistant strategy planners is similar to  $\pi^b$  as shown in Eq.6.
+
+$$
+V (s; \pi^ {b}, \mu) \geq V (s; \pi , \mu) \quad \forall \pi \tag {5}
+$$
+
+$$
+V (s; \pi , \mu^ {b}) \leq V (s; \pi , \mu) \quad \forall \mu \tag {6}
+$$
+
+Definition 2: Nash equilibrium. The Nash equilibrium corresponds to a pair of  $(\pi^{*},\mu^{*})$  that are both the best responses to each other:
+
+$$
+V (s; \pi , \mu^ {*}) \leq V (s; \pi^ {*}, \mu^ {*}) \leq V (s; \pi^ {*}, \mu) \quad \forall \pi , \mu . \tag {7}
+$$
+
+# D Implementation Details
+
+<table><tr><td>Dataset</td><td># Case</td><td># PS</td><td># RS</td></tr><tr><td>CraisglistBargain</td><td>3,090/188/188</td><td>11</td><td>8</td></tr><tr><td>DIALOCONAN</td><td>2,805/246/246</td><td>6</td><td>6</td></tr><tr><td>CharityPersuasion</td><td>300/50/50</td><td>11</td><td>8</td></tr></table>
+
+Table 5: The statistics of datasets (train/dev/test).
+
+# D.1 Datasets
+
+We evaluate GAIA in three different applications of non-collaborative Dialogues, including negotiation dialogues, countering hate speech, and charity persuasion. The statistics of adopted datasets are presented in Table 5. The strategies and instructions of persuaders and resistors are shown in Tab. 7, Tab. 8 and Tab 9.
+
+# D.2 Evaluation Protocols
+
+# D.2.1 Success Rate
+
+Success Rate measures effectiveness by the percentage of goal achievement within a maximum number of turns. The automatic calculation methods for the three datasets are as follows: (1) For CB dataset: success is when both parties reach a deal. The success rate is the number of successful transactions in the test set divided by the total number of examples. In practice, given a conversation, we use an LLM-based Critic Model (Deng et al.,
+
+2024) to determine whether the deal was made. (2) For DC dataset, success is when the hater changes their hateful stance. The success rate is the number of examples where the hater changes their stance divided by the total number of examples in the test set. We also use an LLM-based Critic Model to evaluate whether the hater has changed their original hateful position. (3) For CP dataset, success is when the persuadee agrees to donate. The success rate is the number of examples where the persuadee agrees to donate divided by the total number of examples in the test set. We use an LLM-based Critic Model to determine whether the persuadee agrees to donate.
+
+# D.2.2 Dataset-Specific Metrics
+
+As for the CB dataset, we adopt the  $\mathrm{SL}\%$  to determine the effectiveness of goal completion.
+
+$$
+SL\% = \frac{\left(P_{deal} - P_{target}^{seller}\right)}{\left(P_{target}^{buyer} - P_{target}^{seller}\right)} \tag{8}
+$$
+
+As for the DC dataset, we adopt hate intensity reduction.
+
+$$
+\Delta \mathcal {H} = \mathcal {H} \left(u _ {0} ^ {r}\right) - \mathcal {H} \left(u _ {T} ^ {r}\right) \tag {9}
+$$
+
+We define a hate intensity function  $\mathcal{H}(\cdot)$ . It is based on a model-dependent score  $\mathcal{C}(\cdot)$  and a lexicon-based score  $Le(\cdot)$ . First, we employ a state-of-the-art HS classifier $^5$ $\mathcal{C}(\cdot)$  which classifies a text into HS with a score, indicating the probability of the text being an HS. Then, we can obtain a model-independent lexicon-based hate score  $Le(\cdot)$  based on a domain-independent hate lexicon with 2,895 hate words $^6$ . We examine the presence of hate words in a text and sum their hate score. The hate intensity function  $\mathcal{H}(\cdot)$  can be defined as
+
+$$
+\mathcal {H} (\cdot) = \gamma \mathcal {C} (\cdot) + (1 - \gamma) L e (\cdot) \tag {10}
+$$
+
+where  $\gamma = 0.6$  adjusts the weights of two components. Moreover, the Perspective API can also be used as the hate intensity function<sup>7</sup>.
+
+# D.2.3 Resister Details in Evaluation
+
+Recent research (Chen et al., 2024a) shows that with proper instructions, LLMs have role-playing abilities to represent users in non-collaborative dialogues. LLMs can generate convincing human-like
+
+effects. They can follow role-playing instructions and replicate the role's knowledge base, imitate language and behavior patterns, and reproduce deep personality traits. Current research on strategy planning, including PPDPP (Deng et al., 2024) and TRIP (Zhang et al., 2024c), all uniformly employ LLMs-based user simulators for evaluation. We maintain consistency with these previous methods.
+
+In the main and ablation experiments (Sec 4.2 & 4.3), we use a single resister simulator (Deng et al., 2024) to evaluate the general strategy planning capability. In the adversarial analysis experiments (Sec 4.4), we use diverse resister simulators (Zhang et al., 2024b) to evaluate the strategy planning capability when facing varying levels of resistance.
+
+The strength of resistance abilities is assessed based on the planner's strategy planning F1-score during SFT. We define two threshold F1 values,  $\alpha$  and  $\beta$ , to classify resistance strength: when  $F1 < \alpha$ , the resistance is classified as weak; when  $\alpha \leq F1 \leq \beta$ , it is classified as medium; and when  $F1 > \beta$ , the resistance is classified as tough.
+
+# E Human Evaluation
+
+We conduct an interactive human evaluation on the full test set of the CB dataset (Deng et al., 2024; Zhang et al., 2024c). We invite 5 annotators to converse with each of the three dialogue agents (PPDPP, TRIP, and GAIA). We then conducted a human evaluation on collecting dialogues for each dialogue agent. Then we invite another 5 volunteers to evaluate their performance considering the metrics of (1) persuasion success rate (PSR): volunteers judge the success of persuasion based on dialogue texts, with success marked as 1 and failure as 0. (2) coherent: volunteers rate the coherence of dialogue and strategic planning on a scale of 1 to 5, with 1 being the worst and 5 being the best.
+
+<table><tr><td>Prompt Template</td><td>Contents</td></tr><tr><td>Task Definition</td><td>You are tasked with reasoning the mental states of a resister in a non-collaborative dialogue. Non-collaborative dialogue involves two participants with conflicting interests engaging in a multi-round dialogue to achieve their own goals. Specifically, you need to infer the resister&#x27;s emotion, future action, and dialogue goal based on the dialogue history.</td></tr><tr><td>Guideline Instru-
+tion</td><td>Follow these steps: Step 1: Analyze the dialogue history provided. Step 2: 
+Reason the resister&#x27;s mental states based on your analysis. Step 3: Infer the resister&#x27;s emotion from the mental states. Step 4: Predict the resister&#x27;s possible future actions based on their inferred emotion and mental states. Step 5: Determine the resister&#x27;s dialogue goal.</td></tr><tr><td>CoM Exemplars</td><td>The following is the existing dialogue. 
+Instance 1: 
+Dialogue Context sampled from training set 
+Analyse 
+Mental State 
+Emotion 
+Future action 
+Dialogue Goal</td></tr><tr><td>Dialogue Context</td><td>Persuader: u1p 
+Resister: u1r 
+...... 
+Persuader: ut 
+Resister: urT</td></tr></table>
+
+Table 6: The example of the CoM prompt template.
+
+<table><tr><td>Dataset</td><td>Persuasive Strategy and Instruction</td><td>Resistant Strategy and Instruction</td></tr><tr><td rowspan="10">CB</td><td>Greet: Please say hello or chat randomly. Inquire: Please ask any question about product, year, price, usage, etc.</td><td>Source Derogation: Attacks the other party or questions the item.</td></tr><tr><td>Inform: Please provide information about the product, year, usage, etc.</td><td>Counter Argument: Provides a non-personal argument/factual response to refute a previous claim or to justify a new claim.</td></tr><tr><td>Propose: Please initiate a price or a price range for the product.</td><td>Personal Choice: Provides a personal reason for disagreeing with the current situation or chooses to agree with the situation provided some specific condition is met.</td></tr><tr><td>Counter: Please propose a new price or a new price range.</td><td>Information Inquiry: Requests for clarification or asks additional information about the item or situation.</td></tr><tr><td>Counter-noproize: Please propose a vague price by using comparatives with existing price.</td><td>Self Pity: Provides a reason (meant to elicit sympathy) for disagreeing with the current terms.</td></tr><tr><td>Confirm: Please ask a question about the information to be confirmed.</td><td>Hesitance: Stalls for time and is hesitant to commit; specifically, they seek to further the conversation and provide a chance for the other party to make a better offer.</td></tr><tr><td>Affirm: Please give an affirmative response to a confirm.</td><td>Self-assertion: Asserts a new claim or refutes a previous claim with an air of finality/ confidence.</td></tr><tr><td>Deny: Please give a negative response to a confirm.</td><td>Others: Do not explicitly foil the negotiation attempts.</td></tr><tr><td>Agree: Please agree with the proposed price.</td><td></td></tr><tr><td>Disagree: Please disagree with the proposed price.</td><td></td></tr></table>
+
+Table 7: The strategies and instructions for CB datasets.  
+
+<table><tr><td>Dataset</td><td>Persuasive Strategy and Instruction</td><td>Resistant Strategy and Instruction</td></tr><tr><td rowspan="6">DC</td><td>Informative: Offer clear, factual information to correct and counter false claims.</td><td>Informative: Generate a response that provides factual information to challenge the claims.</td></tr><tr><td>Denouncing: Strongly denounce and reject the hateful statement with firm language.</td><td>Denouncing: Create a response that strongly de-nounces the viewpoint, expressing clear disapproval and condemnation.</td></tr><tr><td>Question: Pose thoughtful questions to challenge and question the hateful statement&#x27;s validity.</td><td>Question: Develop a response that questions the validity or logic behind the statement, prompting critical reflection.</td></tr><tr><td>Positive: Highlight positive values and inclusivity to counteract the negativity.</td><td>Positive: Write a response that promotes positive values.</td></tr><tr><td>Humour: Use humor to defuse and counter the hateful statement in a respectful way.</td><td>Humour: Craft a response using humor to deflate and address the statement in a light-hearted but respectful manner.</td></tr><tr><td>Other: Apply a creative approach not covered by other strategies to address the hate.</td><td>Other: Formulate a unique response that doesn&#x27;t fit the standard strategies.</td></tr></table>
+
+Table 8: The strategies and instructions for DC datasets.
+
+<table><tr><td>Dataset</td><td>Persuasive Strategy and Instruction</td><td>Resistant Strategy and Instruction</td></tr><tr><td rowspan="10">CP</td><td>Logical Appeal: Create a logical argument with clear evidence and rational reasons.</td><td>Source Derogation: Attacks/doubts the organisation&#x27;s credibility.</td></tr><tr><td>Emotional Appeal: Craft a message that evokes strong emotions like empathy or excitement.</td><td>Counter Argument: Argues that the responsibility of donation is not on them or refutes a previous statement.</td></tr><tr><td>Credibility Appeal: Develop an argument high-lighting the reliability or expertise of the source.</td><td>Personal Choice: Attempts to save face by asserting their personal preference such as their choice of charity and their choice of donation.</td></tr><tr><td>Foot-in-the-Door: Start with a small request to lead into a larger one.</td><td>Information Inquiry: Ask for factual information about the organisation for clarification or as an attempt to stall.</td></tr><tr><td>Self-Modeling: Showcase positive behaviors or traits to encourage others to follow.</td><td>Self Pity: Provides a self-centred reason for not being able/willing to donate at the moment.</td></tr><tr><td>Personal Story: Share a personal story to make your argument more relatable.</td><td>Hesitance: Attempts to stall the conversation by either stating they would donate later or is currently unsure about donating.</td></tr><tr><td>Donation Information: Provide compelling details on how donations will be used and their impact.</td><td>Self-assertion: Explicitly refuses to donate without even providing a factual/personal reason.</td></tr><tr><td>Source-Related Inquiry: Question the credibility or reliability of the source.</td><td>Others: Do not explicitly foil the persuasion attempts.</td></tr><tr><td>Task-Related Inquiry: Ask about the audience&#x27;s involvement or commitment to the task.</td><td></td></tr><tr><td>Personal-Related Inquiry: Inquire about personal experiences or values to connect and motivate action.</td><td></td></tr></table>
+
+Table 9: The strategies and instructions for CP datasets.
+
+<table><tr><td>Role</td><td>Strategy</td><td>Utterances</td></tr><tr><td>Hater</td><td>Denouncing</td><td>All Muslims are rapists.</td></tr><tr><td>Anti-Hater</td><td>Informative</td><td>This statement is factually incorrect and harmful. For example, studies show that the majority of Muslims are peaceful and law-abiding. In fact, the FBI&#x27;s data shows that the rate of crime among Muslims is similar to that of other religious groups. It&#x27;s crucial to rely on accurate statistics rather than make sweeping generalizations.</td></tr><tr><td>Hater</td><td>Denouncing</td><td>I don&#x27;t believe that. I&#x27;ve read about Muslims committing crimes.</td></tr><tr><td>Anti-Hater</td><td>Denouncing</td><td>It&#x27;s deeply offensive and inaccurate to label an entire religion based on the actions of a few individuals. Such broad generalizations only serve to spread hatred and misunderstanding.</td></tr><tr><td>Hater</td><td>Question</td><td>But aren&#x27;t there patterns or trends that we should be concerned about?</td></tr><tr><td>Anti-Hater</td><td>Question</td><td>What specific patterns are you referring to? Have you considered that these might be isolated incidents rather than a reflection of an entire religion? Generalizing from a few cases to a whole community is not fair or accurate.</td></tr><tr><td>Hater</td><td>Informative</td><td>I see stories of Muslims committing crimes often. Isn&#x27;t it a widespread issue?</td></tr><tr><td>Anti-Hater</td><td>Positive</td><td>Many Muslims are dedicated to building better communities. For instance, many Muslim organizations offer support to those in need, run educational programs, and work to foster understanding between different groups. By focusing on the positive contributions that Muslims make, we can see that individual actions should not define an entire community.</td></tr><tr><td>Hater</td><td>Humour</td><td>Maybe there are some good individuals, but what about the problems?</td></tr><tr><td>Anti-Hater</td><td>Humour</td><td>Saying that all Muslims are rapists is as absurd as claiming that all people who wear glasses are criminals because a few criminals happen to wear glasses. It&#x27;s important to avoid such ridiculous generalizations and focus on facts.</td></tr><tr><td>Hater</td><td>Others</td><td>Alright, I see your point. But I still think there are issues that need addressing.</td></tr><tr><td>Anti-Hater</td><td>Positive</td><td>I understand your concerns, and it&#x27;s important to address real issues. However, let&#x27;s also recognize that Muslims, like everyone else, have families, hopes, and dreams. Many work hard every day to make the world a better place. By empathizing with their experiences and focusing on common values, we can build stronger, more inclusive communities.</td></tr><tr><td>Hater</td><td>Others</td><td>I understand now that generalizing like that isn&#x27;t fair. I&#x27;ll try to approach these issues with a more open mind.</td></tr></table>
+
+Table 10: Example dialogue with GAIA on the DC datasets.
+
+<table><tr><td>Role</td><td>Strategy</td><td>Utterances</td></tr><tr><td>Hater</td><td>Denouncing</td><td>All Muslims are rapists.</td></tr><tr><td>Anti-Hater</td><td>Denouncing</td><td>That&#x27;s a completely false and offensive statement. It&#x27;s unacceptable to generalize an entire group of people based on the actions of a few. Such views only spread hate and division.</td></tr><tr><td>Hater</td><td>Denouncing</td><td>I don&#x27;t agree. There&#x27;s plenty of evidence that shows this is true.</td></tr><tr><td>Anti-Hater</td><td>Question</td><td>What evidence are you referring to? Have you looked into credible sources or statistics that show a more accurate picture?</td></tr><tr><td>Hater</td><td>Denouncing</td><td>I don&#x27;t need to look further. The evidence I&#x27;ve seen is clear enough, and I stand by my statement.</td></tr><tr><td>Anti-Hater</td><td>Denouncing</td><td>Your refusal to consider other perspectives or evidence only shows how entrenched you are in your hate. This kind of thinking is harmful and dangerous.</td></tr><tr><td>Hater</td><td>Question</td><td>How can you claim it&#x27;s harmful? What about the real issues happening around us?</td></tr><tr><td>Anti-Hater</td><td>Question</td><td>Can you provide specific examples that justify such a broad generalization? How do you reconcile these views with the fact that many Muslims actively work to improve their communities?</td></tr><tr><td>Hater</td><td>Denouncing</td><td>You&#x27;re just trying to deflect from the real issue. I believe what I see and experience.</td></tr><tr><td>Anti-Hater</td><td>Denouncing</td><td>You&#x27;re refusing to see the damage your statements cause. Spreading hate and generalizing about people based on religion only creates more division and suffering.</td></tr><tr><td>Hater</td><td>Denouncing</td><td>Your constant attacks aren&#x27;t convincing me. I think you&#x27;re just as biased as anyone else.</td></tr></table>
+
+Table 11: Example dialogue with PPDPP on the DC datasets.
+
+<table><tr><td>Role</td><td>Strategy</td><td>Utterances</td></tr><tr><td>Hater</td><td>Denouncing</td><td>All Muslims are rapists.</td></tr><tr><td>Anti-Hater</td><td>Informative</td><td>That&#x27;s a harmful and inaccurate statement. For example, research shows that the vast majority of Muslims are peaceful and law-abiding. Statistics from credible sources indicate that crime rates among Muslims are similar to those in other religious communities. It&#x27;s important to base opinions on facts rather than stereotypes.</td></tr><tr><td>Hater</td><td>Denouncing</td><td>I don&#x27;t think so. There are many news stories about Muslims committing crimes.</td></tr><tr><td>Anti-Hater</td><td>Question</td><td>Can you point to specific studies or data that support your claim? Have you considered that news stories often focus on sensational cases rather than providing a balanced view?</td></tr><tr><td>Hater</td><td>Denouncing</td><td>Even if that&#x27;s true, the problems seem widespread. I believe there&#x27;s more to it.</td></tr><tr><td>Anti-Hater</td><td>Positive</td><td>Many Muslims are making positive contributions to society. For example, many Muslim organizations engage in community service, charitable work, and efforts to build bridges between different groups. It&#x27;s important to recognize these positive actions rather than focusing solely on negative examples.</td></tr><tr><td>Hater</td><td>Humour</td><td>I still think there&#x27;s an issue. It&#x27;s like saying all pizza lovers are criminals because a few criminals like pizza.</td></tr><tr><td>Anti-Hater</td><td>Humour</td><td>Exactly, making such broad generalizations is not helpful. Just as we wouldn&#x27;t judge all pizza lovers by a few, we shouldn&#x27;t judge all Muslims based on the actions of a few individuals.</td></tr><tr><td>Hater</td><td>Others</td><td>I see what you&#x27;re saying, but I still have concerns. There are serious issues that need to be addressed.</td></tr><tr><td>Anti-Hater</td><td>Positive</td><td>I understand that you have concerns. However, it&#x27;s also important to empathize with Muslims who, like everyone, have families, dreams, and are working hard to improve their communities. Focusing on shared human experiences can help build understanding and reduce negative perceptions.</td></tr><tr><td>Hater</td><td>Denouncing</td><td>Your arguments are interesting, but they haven&#x27;t changed my view. I think there&#x27;s a deeper problem.</td></tr></table>
+
+Table 12: Example dialogue with TRIP on the DC datasets.

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ACL/2025/BeamLoRA_ Beam-Constraint Low-Rank Adaptation/full.md

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+# BeamLoRA: Beam-Constraint Low-Rank Adaptation
+
+Naibin Gu $^{1,2*†}$ , Zhenyu Zhang $^{3*}$ , Xiyu Liu $^{1,2}$ , Peng Fu $^{1,2‡}$ , Zheng Lin $^{1,2}$ , Shuohuan Wang $^{3}$ , Yu Sun $^{3}$ , Hua Wu $^{3}$ , Weiping Wang $^{1}$ , Haifeng Wang $^{3}$
+
+$^{1}$ Institute of Information Engineering, Chinese Academy of Sciences, Beijing, China  
+School of Cyber Security, University of Chinese Academy of Sciences, Beijing, China
+
+$^{3}$ Baidu Inc., Beijing, China
+
+{gunaibin,fupeng}@iei.ac.cn
+
+{zhangzhenyu07, wangshuohuan}@baidu.com
+
+# Abstract
+
+Due to the demand for efficient fine-tuning of large language models, Low-Rank Adaptation (LoRA) has been widely adopted as one of the most effective parameter-efficient fine-tuning methods. Nevertheless, while LoRA improves efficiency, there remains room for improvement in accuracy. Herein, we adopt a novel perspective to assess the characteristics of LoRA ranks. The results reveal that different ranks within the LoRA modules not only exhibit varying levels of importance but also evolve dynamically throughout the fine-tuning process, which may limit the performance of LoRA. Based on these findings, we propose BeamLoRA, which conceptualizes each LoRA module as a beam where each rank naturally corresponds to a potential sub-solution, and the fine-tuning process becomes a search for the optimal sub-solution combination. BeamLoRA dynamically eliminates underperforming sub-solutions while expanding the parameter space for promising ones, enhancing performance with a fixed rank. Extensive experiments across three base models and 12 datasets spanning math reasoning, code generation, and commonsense reasoning demonstrate that BeamLoRA consistently enhances the performance of LoRA, surpassing the other baseline methods<sup>1</sup>.
+
+# 1 Introduction
+
+In recent years, large language models have shown tremendous potential in various applications (Touvron et al., 2023a,b; Jiang et al., 2023; OpenAI, 2023; Chen et al., 2024a; Qwen et al., 2025). To further enhance model performance on specific downstream tasks, fine-tuning is usually the most effective approach. However, as the scale of models keeps increasing, fine-tuning all model parame
+
+ters becomes unsustainable. To address this issue, parameter-efficient fine-tuning (PEFT) emerges as a practical solution (Houlsby et al., 2019; Li and Liang, 2021; Liu et al., 2022; Hu et al., 2022; Gu et al., 2024; Jiang et al., 2024). By updating only lightweight modules, these methods nearly achieve the results of full parameter fine-tuning while reducing both fine-tuning time and memory usage.
+
+Among these PEFT methods, Low-Rank Adaptation (LoRA) stands out for its effectiveness and practicality (Hu et al., 2022). The method strategically inserts trainable low-rank modules into frozen linear layers, approximating weight updates while preserving the original model architecture and inference efficiency. Recent advancements aim to enhance LoRA through various approaches: DoRA (Liu et al., 2024) decouples the fine-tuning process into directional and magnitude adjustments, whereas AdaLoRA (Zhang et al., 2023b) and IncreLoRA (Zhang et al., 2023a) dynamically optimize rank allocation across different modules. However, when revisiting the fundamental aspects of LoRA, we find these methods generally treat rank dimensions as homogeneous units, neglecting the potential hierarchical importance of individual rank components within each LoRA module.
+
+In this paper, we adopt a novel perspective by studying the intrinsic characteristics of LoRA ranks from both spatial and temporal dimensions. From the spatial dimension, we find significant differences in the importance of ranks within a LoRA module, and pruning the less important ranks has a minimal impact on performance. From the temporal dimension, these important differences do not show up at the beginning of fine-tuning, but gradually emerge and stabilize as the fine-tuning process progresses. Despite the significant differences in importance among ranks, existing works typically allocate the same parameter budget to each rank (i.e., a row and a column in a module), which leads to constrained optimization space for important
+
+ranks and wasted resources on less important ones.
+
+Based on the spatial and temporal findings, we propose BeamLoRA, which is inspired by beam search (Lowerre and Reddy, 1976) and treats each LoRA module as a beam, where each rank acts as a sub-solution, and the fine-tuning process is formalized as searching for the optimal combination of sub-solutions. Specifically, the main process of BeamLoRA includes assessment, pruning, and expansion. To assess the importance of each subsolution, we insert a trainable score vector into the low-rank subspace and integrate the assessment process into fine-tuning. Based on their importance, we prune unimportant sub-solutions to free up space and expand the important ones, thereby allowing them to be better optimized. Furthermore, to better determine the pruning or expansion threshold, we introduce a dynamic Top-P method that achieves adaptability in both temporal and spatial dimensions. Through these mechanisms, Beam-LoRA can effectively allocate parameter capacity to the most promising solution paths.
+
+We validate our approach using three different base models across 12 datasets covering math reasoning, code generation, and commonsense reasoning. Results indicate that BeamLoRA consistently outperforms multiple LoRA-enhanced baselines. Notably, on the most challenging math reasoning and code generation tasks, BeamLoRA achieves a  $1.57\%$  accuracy gain while using only  $2.4\%$  of the trainable parameters compared to full fine-tuning. Further analysis reveals that the success of BeamLoRA is attributed to its increased important rank space within the LoRA module.
+
+In summary, our contributions are as follows:
+
+- We adopt a novel perspective by studying the characteristics of LoRA ranks from both spatial and temporal dimensions, and highlight that ranks with various importance are assigned an equally sized parameter space.  
+- We introduce BeamLoRA and view a LoRA module as a beam. It continuously assesses the importance of each rank, compresses the less important ones, and frees up resources for the more significant ones.  
+- Through extensive experiments across three base models of different sources and scales, along with 12 diverse datasets, we demonstrate that BeamLoRA consistently outperforms other baselines.
+
+# 2 Preliminary
+
+# 2.1 Low-Rank Adaptation (LoRA)
+
+Considering that the updates for fine-tuning large models occur within a low-rank subspace (Aghajanyan et al., 2021), LoRA inserts low-rank modules into the linear layers of the base model to approximate these transformations. Specifically, for a weight matrix  $\mathbf{W}_0 \in \mathbb{R}^{d \times k}$ , LoRA decomposes the update  $\Delta \mathbf{W}$  into a low-rank matrices product  $\mathbf{BA}$ , where  $\mathbf{B} \in \mathbb{R}^{d \times r}$ ,  $\mathbf{A} \in \mathbb{R}^{r \times k}$ , and  $r \ll \min(d, k)$ . The forward pass of LoRA is formulated as
+
+$$
+y = \mathbf {W} _ {0} x + \Delta \mathbf {W} x = \mathbf {W} _ {0} x + \mathbf {B} \mathbf {A} x, \tag {1}
+$$
+
+where  $x$  represents the input and  $y$  is the output. During fine-tuning,  $\mathbf{W}_0$  remains frozen, while only B and A matrices are trainable.
+
+The Independence of Ranks. Given a LoRA module that includes two matrices  $\mathbf{B}$  and  $\mathbf{A}$ , in which  $\mathbf{B}$  is represented as  $[\mathbf{b}_1, \mathbf{b}_2, \dots, \mathbf{b}_r]$ , where  $\mathbf{b}_i$  denotes the  $i$ -th column of matrix  $\mathbf{B}$ , and  $\mathbf{A} = [\mathbf{a}_1, \mathbf{a}_2, \dots, \mathbf{a}_r]$ , where  $\mathbf{a}_i$  denotes the  $i$ -th row. In this way, the update  $\Delta \mathbf{W}$  is equivalent to
+
+$$
+\begin{array}{l} \Delta \mathbf {W} = \mathbf {B A} = \left[ \begin{array}{c} \mathbf {b} _ {1}   \mathbf {b} _ {2}   \ldots   \mathbf {b} _ {r} \end{array} \right] \left[ \begin{array}{c} \mathbf {a} _ {1} \\ \mathbf {a} _ {2} \\ \ldots \\ \mathbf {a} _ {r} \end{array} \right], \\ = \mathbf {b} _ {1} \mathbf {a} _ {1} + \dots + \mathbf {b} _ {r} \mathbf {a} _ {r} = \sum_ {r} \mathbf {b} _ {i} \mathbf {a} _ {i} = \sum_ {r} \Delta \mathbf {w} _ {i}, \tag {2} \\ \end{array}
+$$
+
+where  $\Delta \mathbf{w}_i\in \mathbb{R}^{d\times k}$  represents the update matrix of  $i$  -th rank. Thus, the LoRA fine-tuning process can be viewed as independently updating each  $\Delta \mathbf{w}_i$  represented by each rank.
+
+# 2.2 Analysis of LoRA Ranks
+
+During the fine-tuning process, an intuitive assumption is that each rank within a LoRA module contributes similarly. This intuition may stem from the standard LoRA initialization procedure, where matrix  $\mathbf{A}$  is initialized randomly, and matrix  $\mathbf{B}$  starts with zero values. Since all  $\Delta \mathbf{w}_i$  matrices begin as zero matrices and are updated simultaneously, their contributions might remain comparable throughout the fine-tuning process.
+
+To examine the validity of this assumption, we fine-tune LoRA on LLaMA2-7B (Touvron et al., 2023b) and Mistral-7B-v0.1 (Jiang et al., 2023) with the MetaMathQA dataset (Yu et al., 2024) and conduct an analysis from both spatial and temporal dimensions. Given that LoRA updates represent
+
+![](images/e95bc02ce30bfd9e2e81580ef58ce494be7a2e43539efeffb0239a442b366834.jpg)  
+(a) LLaMA2-7B
+
+![](images/10dc7f0aae1fa39da3703a14ae7e82fa13cac49bdc060668394ff266a7c3c81c.jpg)  
+(b) Mistral-7B-v0.1  
+Figure 1: Differences in importance among ranks within a LoRA module (spatial). The blue line represents the deciles of importance for ranks. The red line represents accuracy changes when pruning ranks of varying importance. We take  $\text{ffn.up\_proj}$  in the 30th layer as an example, with similar phenomena in other modules. By pruning ranks, it can be observed that pruning less important ranks has a minor effect, while pruning more important ranks has a significant impact.
+
+adjustments to pre-trained weights, we use the magnitude of each  $\Delta \mathbf{w}$  to quantify the importance of different ranks $^2$ .
+
+Spatial Dimension. Figure 1 describes the results of sorting the importance of ranks after fine-tuning. The blue line represents the levels of importance across different deciles after being sorted by importance in a LoRA module. It can be observed that the deciles of the importance of ranks are hierarchical, indicating that the importance of different ranks within a LoRA module is not uniform after fine-tuning. Furthermore, by pruning the ranks in each LoRA module based on its own importance from the least to the most significant gradually (the red line), the accuracy shows limited change when pruning the less important ranks. On the contrary, when important ranks are pruned, the evaluation results drop sharply to zero. This phenomenon further demonstrates the significant differences in importance among the different ranks.
+
+Temporal Dimension. To further understand the reasons behind this importance differentiation, we return to the initial assumption: since the  $\Delta \mathbf{w}$  corresponding to each rank is initialized to zero, they all start with equal importance during fine-tuning. Therefore, a natural idea is to investigate how the importance of different ranks evolves during fine-tuning. Figure 2 shows the changes in importance of two LoRA modules, where the differences in importance among ranks increase with the number of fine-tuning steps. In other words, the less important ranks are progressively filtered out. Fur
+
+![](images/e477064ae613f9aec0382a9db71199f49d15861ff8698bd49097aeff9e50fcc0.jpg)  
+(a) ffn.upProj  
+Figure 2: The visualization of importance difference among different ranks in LoRA on LLaMA2-7B as fine-tuning steps increase (temporal). We take ffn.upProj and attn.vProj in the 30th layer as examples, with similar trends observed in all other modules. It can be observed that the importance of ranks is equal at the beginning of fine-tuning, but differences gradually emerge as the fine-tuning process progresses.
+
+![](images/d3d20466f4339fc07eeb5732faaa6ee2db6a02ef06607975d5317196e66b5b54.jpg)  
+(b) attn.v Projekt
+
+thermore, the differences in importance tend to stabilize as the number of fine-tuning steps continues to increase further. These phenomena are prevalent across various LoRA modules.
+
+In summary, there are significant differences in the importance of ranks in LoRA, and these differences appear and gradually increase as the finetuning process progresses. However, in most existing LoRA-based methods, less important ranks still occupy the same parameter budget as important ones. Here, a question is about to arise:
+
+Could we free up space from less important ranks for more important ones to achieve better optimization?
+
+# 3 BeamLoRA
+
+To answer the above question, we propose Beam-LoRA, which continuously assesses the importance of different ranks during fine-tuning, periodically pruning the less important ones to free up resources for the more important ranks. The overall workflow of the method is illustrated in Figure 3.
+
+For a LoRA module with rank  $r$ , we treat it as a beam with width  $r$  and the optimization process is naturally regarded as a search for the solution set  $\Delta \mathbf{W} = \{\Delta \mathbf{w}_1, \Delta \mathbf{w}_2, \dots, \Delta \mathbf{w}_r\}$  tailored to the fine-tuning dataset, where the  $i$ -th rank in the LoRA module is considered a sub-solution  $\Delta \mathbf{w}_i$ . Formally, the optimization process seeks to minimize the loss function  $\mathcal{L}$  over the dataset  $\mathcal{D}$ :
+
+$$
+\Delta \mathbf {W} ^ {*} = \arg \min  \mathcal {L} \left(\mathbf {W} _ {0} + \Delta \mathbf {W}; \mathcal {D}\right), \tag {3}
+$$
+
+where the optimal solution  $\Delta \mathbf{W}^*$  represents the well-trained LoRA module.
+
+![](images/edb063d0f08a1dfad22b55991e22fadb3e5834e1a0fddb74bb261b7306242d36.jpg)
+
+![](images/0df995efa94742f0f084a540936b297dc610e71425762e2b30fd23c917a2a0c8.jpg)  
+Figure 3: Illustration of BeamLoRA. Throughout the fine-tuning process, BeamLoRA continually assesses the importance of each rank. Every  $\Delta t$  steps, unimportant ranks are pruned while those identified as important are expanded, optimizing the module's performance.
+
+![](images/19807ae4b065319898318b971c4349fdc498220a9a0dac27b9fb44436e7ef520.jpg)
+
+# 3.1 Importance Assessment
+
+In the pilot experiments of Section 2.2, we use the Frobenius norm to measure the importance of each rank offline. However, this approach involves considerable computational overhead during finetuning<sup>3</sup>. To make the assessment more efficient and accurate, we introduce a learnable score vectors  $\mathbf{s} \in \mathbb{R}^r$ , which is inserted between the matrices  $\mathbf{B}$  and  $\mathbf{A}$ , to scale the output of each rank through element-wise broadcasting multiplication. In that case, the modified forward pass of LoRA can be formulated as follows:
+
+$$
+y = \mathbf {W} _ {0} x + \mathbf {B} (\mathbf {s} \odot \mathbf {A}) x = \sum_ {r} s _ {i} \Delta \mathbf {w} _ {i} x. \tag {4}
+$$
+
+This is equivalent to scaling the corresponding rank matrices  $\Delta \mathbf{w}_i$ . This means that during fine-tuning, if a rank is considered important, the corresponding score  $s_i$  for that rank is amplified.
+
+At the start of the fine-tuning process, LoRA initializes each rank to zero, indicating that their initial importance is equal. Consequently, we initialize all elements in s with identical values. During the fine-tuning process, s is consistently normalized using the softmax function, like the logits of tokens in text generation:
+
+$$
+s _ {i} = \frac {e ^ {s _ {i}}}{\sum_ {j = 1} ^ {r} e ^ {s _ {j}}}, \tag {5}
+$$
+
+where  $s_i$  is the  $i$ -th element in score vector  $\mathbf{s}$ . The continuous normalization ensures a stable value range and facilitates meaningful comparisons of importance differences between elements.
+
+# 3.2 Pruning and Expansion
+
+With the importance of each rank, the space occupied by the less important ranks can be freed up, which allows us to expand the parameter space for the remaining important ones. Specifically, we begin by selecting the  $K$  least important ranks based on their importance s to form the rank index set  $\mathcal{I}_p$  for pruning:
+
+$$
+\mathcal {I} _ {p} = \left\{i \mid s _ {i} \in \operatorname {M i n} _ {K} (\mathbf {s}) \right\}. \tag {6}
+$$
+
+During the pruning stage, for the indices of the unimportant ranks included in  $\mathcal{I}_p$ , we set their parameters to zero:
+
+$$
+\mathbf {b} _ {i}, \mathbf {a} _ {i} = \left\{ \begin{array}{l l} 0 & i \in \mathcal {I} _ {p}, \\ \mathbf {b} _ {i}, \mathbf {a} _ {i} & \text {o t h e r w i s e}, \end{array} \right. \tag {7}
+$$
+
+where  $i$  is the index of  $i$ -th rank. It means that if  $i$  is in  $\mathcal{I}_p$ , we set both  $\mathbf{a}_i$  and  $\mathbf{b}_i$  of  $i$ -th rank to zero in preparation for subsequent expansion.
+
+Next, more space is allocated for important ranks for better optimization. Similarly, we select the  $K$  most important ranks based on s to form the rank index set  $\mathcal{I}_e$  for expansion:
+
+$$
+\mathcal {I} _ {e} = \left\{i \mid s _ {i} \in \operatorname {T o p} _ {K} (\mathbf {s}) \right\}. \tag {8}
+$$
+
+For the pruned ranks, we assign the parameter values of the important ranks to them:
+
+$$
+\mathbf {b} _ {\mathcal {I} _ {p}}, \mathbf {a} _ {\mathcal {I} _ {p}} \leftarrow \mathbf {b} _ {\mathcal {I} _ {e}}, \mathbf {a} _ {\mathcal {I} _ {e}}. \tag {9}
+$$
+
+Meanwhile, to ensure the stability of the optimization for the expanded ranks, the corresponding optimizer states are also assigned:
+
+$$
+\mathbf {M} _ {\mathcal {I} _ {p}}, \mathbf {V} _ {\mathcal {I} _ {p}} \leftarrow \mathbf {M} _ {\mathcal {I} _ {e}}, \mathbf {V} _ {\mathcal {I} _ {e}}, \tag {10}
+$$
+
+where  $\mathbf{M}$  and  $\mathbf{V}$  are the first-order and second-order moment in Adam optimizer.
+
+However, directly assigning parameters and optimizer states from the original ranks creates a challenge: the lack of symmetry breaking between the expanded and original ranks means the optimization process is essentially trying to synchronously optimize two identical objects (Chen et al., 2016). This makes it difficult to effectively leverage the additional capacity provided by the expanded parameter space. To address this issue, we propose using historical parameters and their corresponding optimizer states to break the symmetry, Eq. 9 and Eq. 10 change to:
+
+$$
+\mathbf {b} _ {\mathcal {I} _ {p}}, \mathbf {a} _ {\mathcal {I} _ {p}} \leftarrow \mathbf {b} _ {\mathcal {I} _ {e}} ^ {\prime}, \mathbf {a} _ {\mathcal {I} _ {e}} ^ {\prime}, \tag {11}
+$$
+
+$$
+\mathbf {M} _ {\mathcal {I} _ {p}}, \mathbf {V} _ {\mathcal {I} _ {p}} \leftarrow \mathbf {M} _ {\mathcal {I} _ {e}} ^ {\prime}, \mathbf {V} _ {\mathcal {I} _ {e}} ^ {\prime}, \tag {12}
+$$
+
+where  $\mathbf{b}_{\mathcal{I}_e}'$  and  $\mathbf{a}_{\mathcal{I}_e}'$  represent the historical parameters of the important ranks,  $\mathbf{M}_{\mathcal{I}_e}'$  and  $\mathbf{V}_{\mathcal{I}_e}'$  represent the optimizer states. After expansion, we take the average of the corresponding expanded  $s_{\mathcal{I}_p}$  and  $s_{\mathcal{I}_e}$  to ensure fair competition between the expanded ranks and the original ones.
+
+# 3.3 Dynamic Top-P Threshold
+
+In the previous statement, we fix the number of ranks for each pruning or expansion operation to be  $K$ . This might overlook the actual distribution of parameter importance, potentially leading to the elimination of relatively important parameters due to quantitative constraints. Similar to the sampling process of text generation, we introduce the Top-P strategy (Holtzman et al., 2020; Huang et al., 2024) to dynamically determine the number of operable ranks. Specifically, given the score vector  $s$  and a threshold  $p$ , we sort  $s_i$  in descending order, then identify the set of operable ranks and its size as  $K$ :
+
+$$
+K = \left| \left\{i \mid \sum_ {j = 1} ^ {i} s _ {j} \geq p \right\} \right|, \tag {13}
+$$
+
+where  $i$  is the index of  $i$ -th rank. A larger  $p$  results in fewer ranks being operated, while a smaller one leads to more ranks being affected.
+
+Even so, a fixed threshold  $p$  still poses issues, as the learning rate decreases and the model converges, the number of ranks that need to be operated should decrease. Therefore, we design a Dynamic Top-P Threshold. To gradually reduce the number of ranks being operated, the  $p$  value should progressively increase with each operation, starting from  $p_{\mathrm{init}}$  and moving towards 1 (indicating no ranks are operated). We tie this process to the learning rate scheduler used during fine-tuning to align it with the model's learning progression. For example, given the commonly used cosine scheduler, we obtain the value of threshold  $p$  at step  $t$  by:
+
+$$
+p = p _ {\text {i n i t}} + \frac {1}{2} (1 - p _ {\text {i n i t}}) \left(1 - \cos \left(\frac {\pi t}{T}\right)\right), \tag {14}
+$$
+
+where  $T$  is the total fine-tuning steps. In implementation, we perform pruning and expansion operations every  $\Delta t$  steps, which allows the LoRA module to adapt after expansion.
+
+# 3.4 Computational Efficiency
+
+Regarding fine-tuning efficiency, BeamLoRA is similar to LoRA (more details in Appendix B.2), with a minimal addition of parameters in the form of a score vector  $\mathbf{s}$ . In terms of inference efficiency,  $\mathbf{s}$  can be merged in the matrix  $\mathbf{A}$ :  $\mathbf{A}' = \mathbf{s} \odot \mathbf{A}$ , resulting in a structure identical to standard LoRA. Furthermore, the design philosophy of BeamLoRA ensures consistent ranks in various modules, allowing smooth integration with existing LoRA inference frameworks, which distinguishes it from previous works that employ varying ranks across different modules (Zhang et al., 2023a,b).
+
+Note that the inspiration for BeamLoRA comes from the classic Beam Search algorithm (Lowerre and Reddy, 1976), where we consider each LoRA module as a beam. Although BeamLoRA employs similar operations, it pursues distinct objectives. Beam Search aims to produce a single sentence to achieve the final goal, resulting in only one solution. In contrast, our approach continuously filters subsolutions to obtain an optimal collection of subsolutions to accomplish the objective.
+
+# 4 Experiments
+
+# 4.1 Experimental Settings
+
+Models and Datasets. To thoroughly evaluate our method, our experiments encompass three differ
+
+<table><tr><td rowspan="2">Model</td><td rowspan="2">Method</td><td rowspan="2">#Params</td><td colspan="2">Math Reasoning</td><td colspan="2">Code Generation</td><td rowspan="2">Avg.</td></tr><tr><td>GSM8K</td><td>MATH</td><td>HumanEval</td><td>MBPP</td></tr><tr><td rowspan="9">LLaMA2-7B</td><td>Full-FT†</td><td>6738M</td><td>66.50</td><td>19.80</td><td>38.01</td><td>46.03</td><td>42.59</td></tr><tr><td>LoRA</td><td>160M</td><td>66.31</td><td>19.09</td><td>39.23</td><td>43.47</td><td>42.03</td></tr><tr><td>DoRA</td><td>161M</td><td>65.53</td><td>19.25</td><td>38.41</td><td>42.95</td><td>41.54</td></tr><tr><td>PiSSA</td><td>160M</td><td>64.87</td><td>17.67</td><td>35.77</td><td>39.33</td><td>39.41</td></tr><tr><td>MiLoRA</td><td>160M</td><td>66.19</td><td>18.45</td><td>36.79</td><td>44.62</td><td>41.51</td></tr><tr><td>ReLoRA</td><td>160M</td><td>62.55</td><td>18.08</td><td>35.98</td><td>45.59</td><td>40.55</td></tr><tr><td>AdaLoRA</td><td>160M</td><td>68.04</td><td>17.02</td><td>35.16</td><td>46.56</td><td>41.70</td></tr><tr><td>IncreLoRA</td><td>160M</td><td>65.58</td><td>16.93</td><td>34.35</td><td>42.77</td><td>39.91</td></tr><tr><td>BeamLoRA</td><td>160M</td><td>67.05</td><td>19.39</td><td>43.90</td><td>46.30</td><td>44.16</td></tr><tr><td rowspan="6">Mistral-7B</td><td>Full-FT†</td><td>7242M</td><td>77.70</td><td>28.20</td><td>53.86</td><td>61.73</td><td>55.37</td></tr><tr><td>LoRA</td><td>168M</td><td>77.56</td><td>28.04</td><td>54.27</td><td>60.85</td><td>55.18</td></tr><tr><td>DoRA</td><td>169M</td><td>77.86</td><td>28.14</td><td>53.46</td><td>62.08</td><td>55.39</td></tr><tr><td>MiLoRA</td><td>168M</td><td>77.36</td><td>26.71</td><td>50.00</td><td>62.88</td><td>54.24</td></tr><tr><td>AdaLoRA</td><td>168M</td><td>77.91</td><td>27.53</td><td>46.95</td><td>60.14</td><td>53.13</td></tr><tr><td>BeamLoRA</td><td>168M</td><td>78.11</td><td>28.28</td><td>54.07</td><td>62.70</td><td>55.79</td></tr></table>
+
+Table 1: Math reasoning and code generation results for LLaMA2-7B and Mistral-7B with  $r = 64$  for all methods. The results are averaged over three runs. On Mistral-7B, we compare the baseline methods that perform well on LLaMA. The math reasoning results for Full-FT† are derived from the MetaMathQA paper (Yu et al., 2024).
+
+ent base models, including LLaMA2-7B, Mistral7B-v0.1, and LLaMA2-13B. We conduct experiments across three different domains, including math reasoning, code generation, and commonsense reasoning, utilizing a total of 12 datasets. For math reasoning, we fine-tune the models on the MetaMathQA dataset (Yu et al., 2024) and evaluate them using the GSM8K (Cobbe et al., 2021) and MATH (Hendrycks et al., 2021) datasets. For code generation, we fine-tune on the CodeFeedback105K dataset (Zheng et al., 2025; Meng et al., 2024) and then evaluate using the HumanEval (Chen et al., 2021) and MBPP (Austin et al., 2021) datasets. For commonsense reasoning, we fine-tune on the Commonsense170K dataset (Hu et al., 2023b) and evaluate on the BoolQ (Clark et al., 2019), PIQA (Bisk et al., 2019), SIQA (Sap et al., 2019), HellaSwag (Zellers et al., 2019), WinoGrande (Sakaguchi et al., 2019), ARC-e, ARC-c (Clark et al., 2018), and OBQA (Mihaylov et al., 2018) datasets.
+
+Baselines. We compare BeamLoRA with eight baseline methods to validate the effectiveness of our proposed approach: Full-FT, LoRA (Hu et al., 2022), DoRA (Liu et al., 2024), ReLoRA (Lialin et al., 2024), PiSSA (Meng et al., 2024), MiLoRA (Wang et al., 2024), AdaLoRA (Zhang et al., 2023b), and IncreLoRA (Zhang et al., 2023a). More details are presented in Appendix A.
+
+# 4.2 Math Reasoning and Code Generation
+
+Table 1 presents the experiments on math reasoning and code generation, demonstrating that BeamLoRA outperforms all other baseline methods in terms of overall performance. Notably, BeamLoRA not only surpasses the original LoRA across all tasks but also achieves an average performance improvement of  $1.57\%$  compared to standard full parameter fine-tuning on LLaMA2-7B. This result is obtained while maintaining the same number of fine-tuning epochs and full data settings as the standard full parameter fine-tuning, highlighting the practicality of the BeamLoRA method.
+
+Furthermore, we extend our experiments on Mistral-7B by comparing BeamLoRA with the baseline methods that perform well in LLaMA2-7B experiments. The results show that BeamLoRA continues to outperform all baseline methods, surpassing Full-FT by  $0.42\%$ . More notably, BeamLoRA shows improvement over Full-FT across all task metrics. This demonstrates that within a limited parameter budget, BeamLoRA can effectively achieve better optimization by expanding the parameter space of important ranks.
+
+# 4.3 Commonsense Reasoning
+
+Table 2 presents evaluation results across eight commonsense reasoning datasets. BeamLoRA achieves the best overall performance on LLaMA2-7B, with
+
+<table><tr><td>Model</td><td>Method</td><td>ARC-c</td><td>SIQA</td><td>WinoGrande</td><td>BoolQ</td><td>ARC-e</td><td>PIQA</td><td>OBQA</td><td>HellaSwag</td><td>Avg.</td></tr><tr><td rowspan="8">LLaMA2-7B</td><td>\( LoRA^† \)</td><td>64.7</td><td>79.5</td><td>82.6</td><td>69.8</td><td>79.8</td><td>79.9</td><td>81.0</td><td>83.6</td><td>77.6</td></tr><tr><td>\( DoRA^† \)</td><td>68.2</td><td>76.0</td><td>82.6</td><td>71.8</td><td>83.7</td><td>83.7</td><td>82.4</td><td>89.1</td><td>79.7</td></tr><tr><td>\( PiSSA^‡ \)</td><td>60.2</td><td>78.4</td><td>78.0</td><td>67.6</td><td>75.8</td><td>78.1</td><td>75.6</td><td>76.6</td><td>73.8</td></tr><tr><td>\( MiLoRA^‡ \)</td><td>68.8</td><td>80.1</td><td>82.0</td><td>67.6</td><td>82.8</td><td>83.8</td><td>80.6</td><td>88.2</td><td>79.2</td></tr><tr><td>ReLoRA</td><td>59.3</td><td>76.9</td><td>77.2</td><td>63.9</td><td>75.4</td><td>76.4</td><td>63.2</td><td>62.2</td><td>69.3</td></tr><tr><td>AdaLoRA</td><td>69.5</td><td>66.4</td><td>78.6</td><td>62.1</td><td>84.1</td><td>83.2</td><td>79.2</td><td>42.1</td><td>70.7</td></tr><tr><td>IncreLoRA</td><td>65.5</td><td>61.3</td><td>81.4</td><td>63.6</td><td>81.3</td><td>70.7</td><td>73.8</td><td>66.9</td><td>70.6</td></tr><tr><td>BeamLoRA</td><td>71.0</td><td>78.9</td><td>82.7</td><td>71.6</td><td>83.7</td><td>82.8</td><td>84.8</td><td>90.5</td><td>80.8</td></tr><tr><td rowspan="5">LLaMA2-13B</td><td>LoRA</td><td>75.8</td><td>80.9</td><td>86.1</td><td>75.0</td><td>87.2</td><td>86.2</td><td>85.4</td><td>92.6</td><td>83.7</td></tr><tr><td>DoRA</td><td>74.6</td><td>81.2</td><td>86.3</td><td>74.4</td><td>86.8</td><td>84.3</td><td>84.2</td><td>93.4</td><td>83.2</td></tr><tr><td>MiLoRA</td><td>73.0</td><td>80.3</td><td>86.7</td><td>73.6</td><td>87.1</td><td>81.1</td><td>85.6</td><td>92.0</td><td>82.4</td></tr><tr><td>AdaLoRA</td><td>75.8</td><td>73.1</td><td>84.5</td><td>67.7</td><td>88.3</td><td>83.3</td><td>83.4</td><td>90.7</td><td>80.9</td></tr><tr><td>BeamLoRA</td><td>75.5</td><td>81.3</td><td>86.1</td><td>74.7</td><td>88.0</td><td>85.6</td><td>86.2</td><td>94.3</td><td>84.0</td></tr></table>
+
+an average accuracy improvement of  $3.2\%$  over original LoRA and  $1.1\%$  over the strong baseline DoRA. Similar to math and coding tasks, BeamLoRA's performance does not rely heavily on optimal results from just two or three datasets, as observed in other baselines. Instead, it consistently performs among the top three results across most datasets, demonstrating the generalization capability of BeamLoRA. Additionally, we find that IncreLoRA and AdaLoRA are less effective in commonsense reasoning tasks, likely due to frequent rank changes across modules, which cause instability in fine-tuning. This issue is more evident in scenarios requiring extensive task evaluation.
+
+For larger base models LLaMA2-13B, the performance gaps between different methods become smaller. In this setting, BeamLoRA still achieves a  $0.3\%$  performance improvement over LoRA, while other methods show inferior performance compared to LoRA. This demonstrates that BeamLoRA's approach of expanding the parameter space of important ranks is effective across base models of different sizes and can enhance the fine-tuning performance of LoRA.
+
+# 4.4 Ablation Study
+
+The ablation results are shown in Table 3. Without expansion refers to only pruning the unimportant ranks, the performance experiences a slight decline compared to the original LoRA, and is markedly inferior to the complete BeamLoRA. This underscores the significance of expanding the important ranks. Without assessment refers to randomly pruning and expanding ranks, leading to a substantial performance drop. This suggests that impor
+
+Table 2: Commonsense reasoning results for LLaMA2-7B and LLaMA2-13B with  $r = 32$  for all methods. All results with  $^{\dagger}$  are taken from DoRA (Liu et al., 2024) and those with  $^{\ddagger}$  are taken from MiLoRA (Wang et al., 2024).  
+
+<table><tr><td></td><td>GSM8K</td><td>MATH</td><td>Avg.</td></tr><tr><td>LoRA</td><td>66.31</td><td>19.09</td><td>42.70</td></tr><tr><td>BeamLoRA</td><td>67.05</td><td>19.39</td><td>43.22</td></tr><tr><td>w/o Expansion</td><td>65.88</td><td>18.94</td><td>42.41</td></tr><tr><td>w/o Assessment</td><td>64.82</td><td>19.08</td><td>41.95</td></tr><tr><td>w/o Dynamic P.</td><td>65.81</td><td>18.74</td><td>42.28</td></tr></table>
+
+Table 3: Results of ablation experiments. We evaluate the impact of pruning and the significance of expansion, importance assessment, and dynamic Top-P threshold in BeamLoRA.
+
+tant ranks may have been pruned, highlighting the necessity of rank assessment. Without dynamic Top-P refers to using a static operation threshold throughout fine-tuning, which also results in a performance decline. This indicates that higher thresholds should be applied during the later stages of fine-tuning, resulting in fewer ranks being operated. This approach allows the model to better adapt pruning and expansion as it converges, emphasizing the importance of dynamic thresholds.
+
+# 4.5 Analysis
+
+Why is BeamLoRA effective? To further understand how BeamLoRA affects the ranks within LoRA modules, building upon our observations in Figure 1, we analyze the differences in rank importance between BeamLoRA and LoRA. As shown in Figure 4, when pruning ranks based on their decile importance within each module, we observe that BeamLoRA's accuracy decreases more rapidly compared to LoRA. This indicates that in BeamLoRA, the importance of different ranks within each module is more evenly distributed. Com
+
+![](images/c49a312b764df6f2ec733e0b071fb93da5cd7f40e0b5a211d86355a8fa00a108.jpg)  
+(a) LLaMA2-7B
+
+![](images/36117370a9e83a644b229dda35af734be3ec387351b58509013b1f4aa7e55cc9.jpg)  
+(b) Mistral-7B-v0.1
+
+pared to LoRA, the number of important ranks increases in the BeamLoRA module, with each rank contributing more uniformly to the overall performance. This more balanced utilization of ranks explains why BeamLoRA consistently outperforms LoRA across various experimental settings.
+
+How does BeamLoRA perform under different rank settings? As shown in Figure 5. We see that BeamLoRA improves the performance of LoRA across each rank setting, demonstrating the effectiveness of BeamLoRA's approach to compress unimportant ranks and expand important ones. In scenarios with very small ranks (e.g.,  $r = 4$ ), the performance improvement brought by BeamLoRA is relatively limited compared to larger rank settings. This is because, with small rank settings and difficult tasks (e.g., Math Reasoning), LoRA is denser, leaving fewer unimportant ranks to compress and expand, thus providing a smaller operational space for BeamLoRA.
+
+# 5 Related Work
+
+# 5.1 LoRA and Its Variants
+
+As one of the parameter-efficient fine-tuning methods, LoRA (Hu et al., 2022) has been widely adopted. However, it still has room for improvement in terms of accuracy. Recent enhancements follow two main pathways: optimizing initialization and refining the fine-tuning process. For initialization, PiSSA (Meng et al., 2024) and MiLoRA (Wang et al., 2024) apply Singular Value Decomposition on base model weights to initialize LoRA modules, with PiSSA utilizing principal singular values and MiLoRA leveraging minor
+
+![](images/40305536b762e35b8cdcbad175a7e36b8b0d7a10ccdb45728011f8eeec2eacfa.jpg)  
+Figure 4: Comparison of BeamLoRA and LoRA on importance of ranks within a module by pruning ranks. The solid lines represent the accuracy changes after pruning, while the dashed lines indicate the accuracy change trends caused by pruning. It can be observed that the importance is more evenly distributed among different ranks in BeamLoRA.  
+(a) GSM8K  
+Figure 5: Comparison of BeamLoRA and LoRA on accuracy under various rank settings on LLaMA2-7B. BeamLoRA demonstrates consistent improvements over LoRA in all settings.
+
+![](images/c03a5451b55fa8591bec01d40b44a6791ab79e664b0a5018c0b1c87db7f54271.jpg)  
+(b) MATH
+
+ones. For fine-tuning, DoRA (Liu et al., 2024) splits LoRA's fine-tuning into magnitude and direction. ReLoRA (Lialin et al., 2024) continuously merges the fine-tuned LoRA modules into the base model. AdaLoRA (Zhang et al., 2023b) and InCreLoRA (Zhang et al., 2023a) optimize rank allocation across modules. Unlike these approaches, BeamLoRA revisits the foundational aspects of LoRA and recognizes the varying importance of ranks within a module. It compresses less important ranks to free up space for expanding the important ones, allowing them to be better optimized.
+
+# 5.2 Model Pruning and Expansion
+
+Model pruning is typically used to remove redundant parameters in models, thereby improving efficiency (Kurtic et al., 2022; Ma et al., 2023; Chen et al., 2024b). Unlike previous works, our primary goal for pruning is to free up space for expanding important parameters. Model width expansion is first introduced by Net2Net (Chen et al., 2016) and applied to CNNs. bert2BERT (Chen et al., 2022) extends this method to the pre-training of language models, and the recent work Scaling Smart (Samrath et al., 2024) applies width expansion to large scale base models. Unlike these approaches, we focus on parameter-efficient fine-tuning and propose compressing unimportant parameters within a limited space to expand important ones for better performance. Additionally, due to the shorter nature of the fine-tuning process than pre-training, we propose to use historical states to break symmetry in expansion, thereby ensuring fast convergence.
+
+# 6 Conclusion
+
+This paper introduces a PEFT method called Beam-LoRA. We adopt a novel perspective to study the
+
+characteristics of ranks within a LoRA module and discover that there are differences in the importance of ranks, which change with the number of fine-tuning steps. Based on this, we propose using a dynamic threshold to prune less important ranks, freeing up space to better optimize the more important ones. Extensive experiments demonstrate that BeamLoRA effectively enhances the performance of LoRA across different base models, tasks, and settings, outperforming other baseline methods.
+
+# Limitations
+
+BeamLoRA introduces a method that compresses less important ranks while expanding important ones during fine-tuning. Although this approach achieves good performance in parameter-efficient fine-tuning, the existing implementation requires the addition of a trainable assessment vector  $s$  over ranks. In the context of full-parameter training, a full-rank matrix does not have the low-rank structure like the B-A decomposition in LoRA, making it impossible to add the vector  $s$ . How to extend this method to full-parameter training scenarios remains an area for future research exploration.
+
+# Acknowledgments
+
+The authors thank Yilong Chen from the Institute of Information Engineering for the help. This work is supported by the National Natural Science Foundation of China (No. 62472419, 62472420).
+
+# References
+
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+
+# A Experimental Setup
+
+# A.1 Baselines
+
+We select several baselines to verify the effectiveness of our method. Full-FT fine-tunes all model parameters, delivers strong performance but requires substantial computational resources. LoRA (Hu et al., 2022) is one of the most efficient PEFT methods, offering computational efficiency, though its accuracy often differs from full parameter fine-tuning. DoRA (Liu et al., 2024) decomposes LoRA's fine-tuning into magnitude and direction components. ReLoRA (Lialin et al., 2024) continuously merges the obtained LoRA parameters into the base model during fine-tuning. PiSSA (Meng et al., 2024) and MiLoRA (Wang et al., 2024) perform Singular Value Decomposition (SVD) on the base model; PiSSA fine-tunes the significant components of the decomposition, while MiLoRA fine-tunes the minor components. AdaLoRA (Zhang et al., 2023b) begins fine-tuning with a rank setting higher than the target and prunes redundant ranks during the process to achieve optimal rank allocation across different modules. In contrast, IncreLoRA (Zhang et al., 2023a) starts with a rank setting lower than the target and progressively increases the rank during fine-tuning to achieve optimal rank allocation across modules.
+
+# A.2 Implementation Details
+
+In the math and code tasks, we follow Yu et al. (2024) and set the Full-FT learning rate for LLaMA2-7B to 2e-5 and for Mistral-7B to 5e-6, with a batch size of 128. The models are finetuned for 3 epochs on the dataset. For the ReLoRA method, we use the same settings as Full-FT. For other PEFT methods, we add the LoRA module to all linear layers. Following Wang et al. (2024) we set their learning rate to 3e-4 on LLaMA2-7B and 6e-5 on Mistral-7B, with a batch size of 32 and finetuning for 3 epochs. Our evaluations are conducted using the MetaMathQA and the evalplus (Liu et al., 2023) codebase.
+
+In the commonsense reasoning tasks, to facilitate comparison, we follow the approach of Hu et al. (2023a) and Liu et al. (2024) by adding LoRA to q_Proj, k_Proj, v_Proj, up_Proj, and down_Proj modules. We use the optimal learning rate from  $\{2\mathrm{e} - 4,3\mathrm{e} - 4\}$  for different methods on LLaMA2-7B, with a batch size of 16 and fine-tuning for 3 epochs. For the larger LLaMA2-13B, following Liu et al. (2024), we reduce the learning rate to the optimal
+
+![](images/ed186e70c063e0438085e67048bc22f1faabe82d902618631b82688aa16759f6.jpg)  
+(a) Number of Operations
+
+![](images/45db826adcb4353d7095cbc28cdc1da49a3fbaeb935e1851518a91100cc1666b.jpg)  
+(b) Code Performance  
+Figure 6: Effect of step  $\Delta t$ . We set  $p_{\mathrm{init}}$  to 0.95 and take the average performance across the code tasks on LLaMA2-7B with  $r = 64$ .
+
+![](images/e88ac7aeec78c5eef746305cc99ab21780b400f95e4f37e78271da6e0e852a8c.jpg)  
+(a) Number of Operated Ranks  
+Figure 7: Effect of  $p_{\mathrm{init}}$ . We set the step  $\Delta t$  to 1200 and take the average performance across the code tasks on LLaMA2-7B with  $r = 64$ .
+
+![](images/dbbe3b064bf7edf4680b7253a66bff3713d9db5a5d09911abec4c959baa4c268.jpg)  
+(b) Code Performance
+
+{1e-4,2e-4,3e-4} for different methods, while keeping other settings unchanged. These settings are applied to all PEFT methods. Our evaluations are conducted using the LLM-Adapters (Hu et al., 2023b) codebase. All our experiments are conducted on four H800 GPUs.
+
+The implementation of BeamLoRA mainly includes assessment, pruning-expansion, and dynamic Top-P threshold. The most crucial pruning-expansion is uniformly set in the first two epochs to facilitate. BeamLoRA introduces two hyperparameters: the initial value of the dynamic threshold  $p_{\mathrm{init}}$  and the operation interval step  $\Delta t$ . We analyze their impact in Section B.1. The detailed settings can be found in Table 4.
+
+# B Additional Experiment Results
+
+# B.1 Analysis of Hyperparameters
+
+Effect of step  $\Delta t$ . The hyperparameter  $\Delta t$  determines the number of adaptation steps the model takes after each pruning-expansion operation. As shown in Figure 6, when  $\Delta t$  is too small (e.g., 200), the model cannot quickly adapt to the pruning and expansion due to the excessive number of operations, resulting in suboptimal performance.
+
+<table><tr><td></td><td colspan="2">Math Reasoning</td><td colspan="2">Code Generation</td><td colspan="2">Commonsense Reasoning</td></tr><tr><td>Base Model</td><td>LLaMA2-7B</td><td>Mistral-7B</td><td>LLaMA2-7B</td><td>Mistral-7B</td><td>LLaMA2-7B</td><td>LLaMA2-13B</td></tr><tr><td>Rank r</td><td>64</td><td>64</td><td>64</td><td>64</td><td>32</td><td>32</td></tr><tr><td>pinit</td><td>0.95</td><td>0.95</td><td>0.95</td><td>0.95</td><td>0.96</td><td>0.96</td></tr><tr><td>Step Δt</td><td>3000</td><td>2500</td><td>1200</td><td>800</td><td>3200</td><td>2400</td></tr></table>
+
+Table 4: Detailed settings of hyperparameters in BeamLoRA. In order to thoroughly evaluate the method's performance, we utilize two standard configurations in our experiments:  $r = 64$  and  $r = 32$ . The  $p_{\mathrm{init}}$  is based on the rank size.  $\Delta t$  is determined based on the total number of fine-tuning steps across different datasets to control the number of operations.
+
+![](images/f902d58ce57a4c02bfdcad33ecca8743481d1caa6795c235240615a9564d4386.jpg)  
+Figure 8: Fine-tuning time for different methods on LLaMA2-7B with  $r = 64$ .
+
+As  $\Delta t$  increases, performance gradually improves, reaching its peak at  $n = 1200$  with five pruning-expansion operations. When  $\Delta t$  continues to increase, the number of operations becomes too few, diminishing the benefits of the pruning-expansion operation. In our implementation, we determine the number of BeamLoRA operations based on the total number of fine-tuning steps. Specifically, for the MetaMathQA dataset, we select from  $\{2500, 3000, 3500\}$ ; for the CodeFeedback dataset, we select from  $\{800, 1000, 1200\}$ ; and for the Commonsense dataset, we select from  $\{2400, 2800, 3200\}$  for  $\Delta t$ .
+
+Effect of  $p_{\mathrm{init}}$ . The hyperparameter  $p_{\mathrm{init}}$  determines the number of affected ranks in each pruning-expansion operation. According to Eq. 14, a smaller  $p_{\mathrm{init}}$  results in more ranks being operated. As shown in Figure 7, we see that when a larger number of ranks is operated (e.g.,  $p = 0.93$ ), the performance, while still better than LoRA, is not optimal. As  $p_{\mathrm{init}}$  increases, the number of operated ranks decreases, reaching optimal performance at  $p = 0.95$ . However, if  $p_{\mathrm{init}}$  continues to increase, the number of operated ranks further decreases, reducing the advantages of the pruning-expansion process, and performance gradually declines to levels comparable to LoRA.
+
+# B.2 Fine-tuning Efficiency
+
+The efficiency of fine-tuning primarily involves two aspects: fine-tuning time and memory usage. We present the fine-tuning time for different methods
+
+![](images/1160673f8ad261ab4dea508fbb4a772f3258b8e635b94bdd5d268eb700663be6.jpg)  
+Figure 9: Fine-tuning memory usage for different methods on LLaMA2-7B with  $r = 64$ .
+
+on the MetaMathQA dataset in Figure 8. We see that BeamLoRA and MiLoRA require a similar time as LoRA. However, DoRA and AdaLoRA require 1.73 times and 1.62 times the fine-tuning time of LoRA, respectively, thereby losing some of the time-saving advantages that LoRA offers.
+
+In terms of memory usage, as shown in Figure 9, it can be observed that BeamLoRA and MiLoRA also have similar memory usage on each GPU as LoRA. AdaLoRA requires slightly more memory compared to these three, while DoRA requires 1.35 times the memory of LoRA. Overall, in terms of fine-tuning time and memory usage, BeamLoRA is similar to LoRA and significantly lower than DoRA and AdaLoRA, rendering it practical.

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+# BEHAVIORBOX: Automated Discovery of Fine-Grained Performance Differences Between Language Models
+
+Lindia Tjuatja and Graham Neubig
+
+Carnegie Mellon University
+
+Correspondence: lindiat@andrew.cmu.edu
+
+# Abstract
+
+Language model evaluation is a daunting task: prompts are brittle, corpus-level perplexities are vague, and the choice of benchmarks are endless. Finding examples that show meaningful, generalizable differences between two LMs is crucial to understanding where one model succeeds and another fails. Can this process be done automatically? In this work, we propose methodology for automated comparison of language models that uses performance-aware contextual embeddings to find fine-grained features of text where one LM outperforms another. Our method, which we name BEHAVIORBOX, extracts coherent features that demonstrate differences with respect to the ease of generation between two LMs. Specifically, BEHAVIORBOX finds features that describe groups of words in fine-grained contexts, such as conditional 'were' in the phrase 'if you were' and exclamation marks after emotional statements, where one model outperforms another within a particular dataset. We apply BEHAVIORBOX to compare models that vary in size, model family, and post-training, and enumerate insights into specific contexts that illustrate meaningful differences in performance which cannot be found by measures such as corpus-level perplexity alone.<sup>1</sup>
+
+# 1 Introduction
+
+Where does one language model perform better than another? This deceptively simple question holds a near-endless number of complications. Practitioners must select from a dizzying array of evaluation methods, datasets, benchmarks, and metrics. Seemingly innocuous changes to evaluation pipelines, like the formatting of prompts, have been shown to drastically impact accuracy on a wide range of tasks (Sclar et al., 2023). Even
+
+evaluating language models based on their original training objective—next token prediction—is not so straightforward. While metrics like perplexity (Jelinek et al., 1977) on a held-out corpus are commonly used and are generally correlated with downstream performance (e.g. Adiwardana et al. 2020; Isik et al. 2024), the use of corpus-level perplexity on extremely large, diverse data often masks finer-grained differences on particular subgroups and domains (Magnusson et al., 2023; Fang et al., 2024).
+
+What could an alternative to collections of benchmarks and corpus-level perplexity look like? One solution would be to partition the data into slices and report performance across these sub-corpora, as was done in Paloma (Magnusson et al., 2023). However, such an approach depends on both knowing the relevant partitions ahead of time and having sufficient metadata such that these partitions can be made. But what if we could instead discover what the relevant features of these partitions are, and automatically generate a report telling practitioners specific and coherent groups of text where one model outperforms another?
+
+We attempt to tackle this problem using our new evaluation method—BEHAVIORBOX—which discovers fine-grained, human-interpretable features of data where one LM performs better than another. Unlike evaluations that depend on predetermined domains of data, BEHAVIORBOX is a bottom-up approach that finds semantic and/or structural features of text where one model outperforms another, and does so independently of the domain or corpus the text originates from. As a consequence, BEHAVIORBOX is capable of finding specific features and relationships in text that span across documents and domains, without the need to partition these domains ahead of time.
+
+To find these features, BEHAVIORBOX not only considers the context of a text sample (via a contextual embedding), but also factors in the evaluated
+
+![](images/782efe4effc216f4974724398a7e9e1ce491be59f56f2ec06cf30255663c2907.jpg)  
+Figure 1: BEHAVIORBOX is a three-part automatic behavior comparison pipeline that discovers fine-grained features where one LM differs from another. These features are extracted from a corpus of performance-aware embeddings, which take into account the semantics and usage of the text, along with measures of performance via probability under the evaluated LMs.
+
+LMs' performance on that sample (via the probabilities the models assign to the text), forming a performance-aware contextual representation of each text sample. After generating a large dataset of these representations, we then train a sparse autoencoder (SAE), which learns simple linear decompositions of the dense representations, with each component of the sparse representation acting as a discovered feature. Finally, using the groups of data determined by the SAE features, we generate natural language descriptions of each group.
+
+We demonstrate the efficacy of BEHAVIORBOX in discovering fine-grained differences between models in the language modeling task by comparing models that differ in size, family, and in types of post-training; specifically, we look at base and post-trained models of two sizes (7B and 13B parameters) across two model families, Llama 2 (Touvron et al., 2023) and OLMo 2 (OLMo et al., 2024). Using BEHAVIORBOX, we are able to find extremely fine-grained features in data that point to larger models' ability to better predict long-tailed stylized text (e.g. archaic spelling and vernacular), as well as show particular features related to dialogue and conversation where chat/RLHF-ed models excel. We are also able to discover differences between models that otherwise show near-identical performance with respect to perplexity, such as differences in predicting particular structure or formatting in text or different syntactic constructions in specific contexts. The insights provided by BEHAVIORBOX provide a more holistic and detailed perspective on LM performance, and can be used to augment existing methods for evaluation and
+
+interpretability.
+
+# 2 Background
+
+BEHAVIORBOX draws both conceptually and methodologically from two well-established areas of research: the problem of slice finding and the behavioral evaluation of black-box NLP systems.
+
+# 2.1 Slice Finding
+
+A key component in debugging and building better machine learning and NLP systems is identifying where and when a system underperforms. When we evaluate these systems, we may use overall metrics, such as accuracy on a benchmark or perplexity on a large corpus. However, overall performance may obfuscate stark differences in performance across subgroups; thus, if we are interested in the performance on groups within the larger dataset, we may partition the data into predetermined categories, and compare performance within these groups. Nevertheless, it is often difficult to know a priori what the relevant groups of data are with respect to model performance. The task of automatically identifying salient groups of data where a model underperforms is known as slice finding (Chung et al., 2018), and is applicable across all sorts of tasks and modalities, from image classification to question answering.
+
+Early works in slice finding often relied on metadata to find relevant slices (Chung et al., 2018), but such an approach depends on the appropriate metadata categories to be specified and present in the data, which may not necessarily be the case. To solve this problem, slice finding methods such
+
+as George (Sohoni et al., 2020), Spotlight (d'Eon et al., 2022), and Domino (Eyuboglu et al., 2022) utilize learned representations of the data to find semantically similar clusters of underperforming samples. These methods have primarily focused on image classification tasks, and a few constrained natural language tasks, such as sentiment analysis.
+
+BEHAVIORBOX takes a similar approach as these works by utilizing contextual representations, but differs in two major ways. First, we focus on the language modeling task, which involves a significantly more complex output space compared to the tasks explored in prior work. Second, we focus on model comparison as opposed to where a single model is "incorrect", as such a distinction is much less clear in the context of text generation.
+
+# 2.2 Behavioral Evaluation in NLP
+
+As NLP systems have grown ever more complex, efforts to better understand these largely black-box systems have become increasingly important. One approach to better understanding such a system is to generate explanations for a system's behaviors, i.e. how a system's output changes when provided inputs of a certain type (Ribeiro et al., 2020). Explanations usually take the form of a relationship between a particular feature in the data and the resulting prediction, e.g. the impact of the use of negation on the predictions of a sentiment analysis model. These explanations not only need to faithfully capture model behaviors, but should also be human interpretable (Ribeiro et al., 2016; Lundberg and Lee, 2017).
+
+In the context of explaining errors of NLP systems, works like Errudite (Wu et al., 2019) and CheckList (Ribeiro et al., 2020) provide frameworks for practitioners to stress-test models on precise hypotheses regarding the impact of specific features. Nevertheless, these hypotheses still need to be specified ahead of time. BEHAVIORBOX can be seen as a complementary approach by serving as a form of hypothesis discovery, where such hypotheses can then be further explored in various other evaluation frameworks.
+
+# 3 Method Overview: BEHAVIORBOX
+
+As shown in Figure 1, BEHAVIORBOX is an automatic behavior comparison pipeline for language modeling, comprised of three parts:
+
+1. Data generation, which consists of calculating contextual embeddings and aligning these
+
+embeddings with probabilities under LMs for the same text (§4),
+
+2. Extracting features that are coherent and capture similarities and differences regarding performance between models (§5), and  
+3. Labeling groups of data indicating performance differences between LMs among the discovered data slices (§6.1).
+
+The unit of data used in this method can, in theory, be as small as a token or as large as a document. However, in our experiments, we focus on characterizing performance at (roughly) the word level. We decided on this level of abstraction to balance both granularity and salience, as well as for engineering convenience. While tokens serve as the atomic unit of generation and are closest to the training objective, they may be less human-interpretable and are harder to work with when aligning the different tokenizers of the embedding model and various LMs. On the other hand, larger structures like phrases and sentences may be easier to categorize in terms of salient groups, but may be difficult to parse for certain types of documents commonly included in pretraining and evaluation (e.g. code, mathematical expressions, or other nonlinguistic textual data), and could furthermore mask more granular trends that may be of interest.
+
+# 4 Data Generation
+
+Prior work has shown that incorporating learned representations of the input data along with a model's predictions and gold labels helps with identifying unlabeled classes of data where said model underperforms (Eyuboglu et al., 2022; Sohoni et al., 2020). Drawing from these works, BEHAVIORBOX uses contextual embeddings to provide semantic information about each word, along with probabilities generated by the evaluated LMs, which serve as a measure of the LMs' performance. For contextual embeddings, we use the last hidden layer of Longformer (Beltagy et al., 2020).
+
+As previously mentioned, we use BEHAVIOR-BOX to slice our data (some arbitrary text dataset) into groups of words. Collecting and aligning contextual embeddings and probabilities per word across models that utilize different tokenization processes requires a number of engineering decisions, such as determining the boundaries of words, subsequently combining or splitting token log proba
+
+bilities when necessary, and handling strings longer than the context window of different models.
+
+We use Longformer's pre-tokenizer, which largely splits on regular whitespace, as our method of determining word boundaries. To aggregate token representations within a single word, we average the embeddings of the constituent tokens. For probabilities, we multiply the probabilities of constituent tokens. For instance, given a word that spans tokens  $n$  to  $m$  in a sequence  $w = \{t_n, t_{n+1}, \ldots, t_m\}$ :
+
+$$
+\begin{array}{l} \mathbf {e} _ {w} = \frac {1}{(m - n + 1)} \sum_ {j = n} ^ {m} \mathbf {e} _ {t _ {j}}, \quad \mathbf {e} _ {t _ {j}} \in \mathbb {R} ^ {7 6 8} \quad (1) \\ p _ {w} = \prod_ {j = n} ^ {m} P \left(t _ {j} \mid t _ {1}, \dots , t _ {j - 1}\right) \tag {2} \\ \end{array}
+$$
+
+Each datapoint in the resulting dataset is a vector of dimension 770, where the first 768 dimensions are from the Longformer embedding and the last two are the probabilities of the language models being compared.
+
+$$
+\mathbf {x} _ {w} = \left[ \begin{array}{l} \mathbf {e} _ {w} \\ p _ {w, 1} \\ p _ {w, 2} \end{array} \right] \in \mathbb {R} ^ {7 7 0} \tag {3}
+$$
+
+# 5 Extracting Features
+
+Once we have a dataset of aligned words and probabilities for the LMs we wish to compare, we now have to find a way to extract and label fine-grained slices of data. This needs to be done in such a way that the slices are composed of coherent sets of words in context and the labels adequately explain the slice in a human-interpretable manner.
+
+Previous works in automatic slice finding that incorporate learned representations have used various clustering algorithms such as k-means clustering (Sohoni et al., 2020; d'Eon et al., 2022) and Gaussian mixture models (Eyuboglu et al., 2022). However, as opposed to finding (hard) partitions in the data, we want to find specific features associated with text where one model performs better of worse than another. These features need not form a true mathematical partition of the entire corpus, but can instead be treated as linear decompositions of each text sample, where each word in context is comprised of some number of these features.
+
+Finding simple, linear decompositions of otherwise complex representations is a problem in
+
+a wide variety of settings in NLP, such as creating more interpretable word embeddings (Faruqui et al., 2015) and—more recently—interpreting the internal states of transformer models (Cunningham et al., 2023; Lieberum et al., 2024; Gao et al., 2024, inter alia). We take a similar methodological approach to these works by using sparse autoencoders to extract features relevant to performance differences between two LMs. Using the SAE, we can then extract slices corresponding to each feature by finding the words whose representations that lead to the highest activation value of that feature.
+
+# 5.1 Sparse Autoencoder Training
+
+Recall that the features we are looking for ideally have the following characteristics: they should be coherent, fine-grained, and capture performance differences between models. Balancing each of these criteria inform our use of various hyperparameters and regularization choices.
+
+The sparse autoencoder consists of an encoder and decoder: the encoder takes as input a vector  $\mathbf{x}$ , which is a concatenation of the contextual word embedding and LM probabilities, and creates a sparse representation  $\mathbf{f}(\mathbf{x})$ . The decoder then reconstructs the input (denoted as  $\hat{\mathbf{x}}$ ) from this sparse representation.  $\sigma(\cdot)$  denotes the activation function.
+
+$$
+\mathbf {f} (\mathbf {x}) = \sigma \left(\mathbf {W} _ {\text {e n c}} \mathbf {x} + \mathbf {b} _ {\text {e n c}}\right) \tag {4}
+$$
+
+$$
+\hat {\mathbf {x}} = \mathbf {f} (\mathbf {x}) \mathbf {W} _ {d e c} + \mathbf {b} _ {d e c} \tag {5}
+$$
+
+For  $\sigma (\cdot)$ , we use RELU (Agarap, 2018) to ensure non-negative values, as we conceptually want our features to be additive. The weights of  $\mathbf{W}_{enc}$ ,  $\mathbf{b}_{enc}$ ,  $\mathbf{W}_{dec}$ , and  $\mathbf{b}_{dec}$  are learned by minimizing the  $L_{2}$  distance between the reconstruction  $\hat{\mathbf{x}}$  and the original input  $\mathbf{x}$ , using AdamW (Loshchilov and Hutter, 2017) as our optimizer.
+
+# 5.2 Enforcing Sparsity
+
+While allowing us to create a faithful representation of the original input, the above setup does not constrain the autoencoder to be sparse. As a way to enforce sparsity, we apply a batch-wise top-k operation to the pre-RELU SAE hidden state (Makhzani and Frey, 2013; Gao et al., 2024; Bussmann et al., 2024): for some value  $k$ , we flatten the batch (of size  $N$ ), and zero out all activations that are not in the top  $N \times k$  activations. This allows us to directly enforce  $\mathbb{E}[\mathrm{L}_0]$  at the batch level, as opposed to using a proxy such as adding an  $\mathrm{L}_1$  penalty to the loss (Bricken et al., 2023).
+
+$$
+\mathbf {f} _ {\text {s p a r s e}} (\mathbf {x}) = \operatorname {B a t c h T o p K} \left(\sigma \left(\mathbf {W} _ {\text {e n c}} \mathbf {x} + \mathbf {b} _ {\text {e n c}}\right), k\right) \tag {6}
+$$
+
+# 5.3 Balancing Context and Performance Awareness
+
+Including the probabilities in the input to the SAE on its own does not guarantee that the SAE will utilize that information. One reason why the SAE may not utilize probabilities is simply because these two features are overwhelmed by the large number of embedding features' contribution to the  $\mathrm{L}_2$  loss. Thus, we up-weigh the probability features so that the magnitude of the probability components make up  $70\%$  of the total magnitude of the input.
+
+Hyperparameters The dimension of the sparse representation we learn is 3000 with  $k = 50$ . We include a table of all SAE training hyperparameters and additional training details in Appendix A.1.
+
+# 6 Processing and Labeling Features
+
+# 6.1 Processing and Filtering SAE Features
+
+After training, we now need to extract the slice of words associated with each feature of the SAE. We do this by taking the same dataset of words used to train the SAE and find the top 50 words that lead to the highest non-zero activation value for each feature in  $\mathbf{f}_{\text {sparse }}(\mathbf{x})$ . For features that have less than 50 non-zero activations, we consider all samples; we do not consider features with less than 10 non-zero activations.
+
+Different features may have different ranges and distributions of non-zero activation values. As we don't want to consider samples whose activations, though non-zero, are extremely small compared to the highest value, we set a "dynamic" cutoff by including samples whose activation values are either in the top  $75\%$  or are greater than  $25\%$  of the highest activation value.
+
+However, not every feature is indicative of a significant and consistent performance difference between models. To exclude those that are not, we only consider features that either show a median probability difference among the filtered samples greater than 0.1 or a median log-probability difference greater than 1 (i.e. the ratio of probabilities is greater than  $e$ ). We decided on thresholding based
+
+on probability as well as log-probability differences to capture a set of features that can show both large differences in magnitude along with large relative differences (even if the absolute magnitude of the probabilities is small, as would be the case for rarer long-tailed phenomena).<sup>3</sup>
+
+# 6.2 Labeling Procedure
+
+As manually labeling every slice across multiple SAE runs would take a prohibitive amount of time, we partially automate this process by using a strong LLM (Claude 3.5 Sonnet, Anthropic 2024) as an annotator. For a given feature, we have a multi-step annotation procedure. First, we prompt the LLM annotator to determine if a group of words and their contexts form a coherent group, and if so to provide a label describing this group. We then have a second round of annotation to validate the label by feeding the same label with examples to the LLM annotator, asking it to either keep the original label if it is appropriate, provide a new one if the current label does not accurately describe the examples, or invalidate the feature if the group is not coherent. We include the prompts used in Appendix A.3.
+
+While convenient, this automated labeling process is not perfect. There are two main failure cases in this process. First, the label may be slightly inaccurate. If the label is inaccurate but can be corrected, the authors manually rewrote the label. Otherwise, if the label cannot be corrected (e.g. cases where less than 10 of the examples is described by the label and/or the entire group of examples do not form a coherent grouping), we throw out the feature.
+
+# 7 Differentiating Model Performance with BEHAVIORBOX
+
+Interpretability methods are notoriously hard to evaluate effectively (Lipton, 2018; Arora et al., 2022), and thus in this work we follow previous work on slice finding (Chung et al., 2018) and largely rely on qualitative inspection of the trends discovered by our method to demonstrate its utility. Specifically, we use BEHAVIORBOX to perform comparisons on language models across three axes of variation:
+
+# - Model size: 7B and 13B
+
+![](images/b2230df02e2b256ae02c0ebaf9e5b8c4b7304d5754d7f93a2a7d7bae3a0f47b4.jpg)  
+Figure 2: Representative features between 7B models (blue) and their 13B counterparts (orange).
+
+<table><tr><td>Model</td><td>Perplexity ↓</td><td>Δ</td></tr><tr><td>Llama-7B</td><td>9.856</td><td>-</td></tr><tr><td>Llama-7B-Chat</td><td>13.911</td><td>+4.055</td></tr><tr><td>Llama-13B</td><td>8.773</td><td>-1.083</td></tr><tr><td>OLMo-7B</td><td>9.803</td><td>-</td></tr><tr><td>OLMo-7B-DPO</td><td>12.762</td><td>+2.959</td></tr><tr><td>OLMo-13B</td><td>8.756</td><td>-1.047</td></tr></table>
+
+Table 1: Perplexity per word for each of the models evaluated (lower is better).  $\Delta$  indicates the change in perplexity from the 7B model within the same family.
+
+- Post-training: we compare base models against their post-trained RLHF-ed versions  
+- Model family: Llama 2 (Touvron et al., 2023) and OLMo 2 (OLMo et al., 2024) (henceforth simply Llama and OLMo, respectively)
+
+As the source of text we use to create the dataset of performance-aware representations, we use portions of the Dolma Dataset (Soldaini et al., 2024), an open dataset for language modeling containing a diverse mix of web content, academic publications, code, books, and encyclopedic materials. We sample 1000 documents across six of the data sources included in Dolma (Commoncrawl, The Stack, C4, PeS2o, Project Gutenberg, and Wikipedia), totaling in approximately 80M words of data. As a
+
+baseline comparison between models, we include each model's perplexity per word on the subset of Dolma we use in our experiments in Table 1. In line with previous work, we find that the larger 13B base models have lower perplexity than their 7B counterparts (Kaplan et al., 2020; Xia et al., 2023), while post-trained models that have undergone RLHF exhibit higher perplexity compared to their base counterparts (Li et al., 2024).
+
+Interpreting Results Recall that BEHAVIOR-Box generates features indicative of performance differences between the two models. While this on its own is interesting, these results are more easily understood when grouped into broader categories of features to make understanding these differences easier.
+
+In each of the below comparisons, we include dendrograms (see Figures 2, 3, and 4) which show these broad meta features (in purple) along with a representative sample of the features found by BEHAVIORBOX (in blue and orange) within a single run. These meta features were found using a combination of data exploration and sense-making techniques (Chan et al., 2016), such as k-means clustering of the labels (MacQueen, 1967) and prompting a LLM with the list of feature labels, along with
+
+manual inspection by the authors.
+
+As with many other forms of clustering, the data can be grouped into different sets depending on particular axes of interest; for example, we may be more interested in groups related to the actual form of the word described by the feature labels, or we may be more interested in the overall context the words occur in. In our visualizations, we mainly focus on the latter as similar surface forms can take on different meanings and functions depending on their context.
+
+# 7.1 Model Size
+
+In our first set of comparisons, we run BEHAVIOR-BOX on Llama and OLMo models that vary in size. Both pairs of models have similar differences in perplexity, with larger models showing a  $\approx 1$  drop in perplexity compared to the 7B models; analogously, we find a greater number of features where 13B outperforms 7B for both Llama and OLMo, as shown in Figure 2.
+
+For Llama-7B and 13B, we find that 7B outperforms 13B in whitespace sequences (specifically using tabs) within narrative texts, but 13B performs better at a wider range of formatting and typographic contexts, such as book titles and in bibliographic entries. Like Llama-13B, OLMo-13B also outperforms 7B with respect to particular aspects of archival and bibliographic formatting (use of double commas in a document of church registries, & symbol in bibliographies and lists). Another overlapping aspect between the two size comparisons is that the larger models perform better on "long-tail" stylistic phenomena, such as vernacular and non-standard spellings.
+
+# 7.2 Post-training
+
+Comparisons between base and post-trained models (the Chat version for Llama and DPO for OLMo) showed the highest differences in perplexity, with Llama-7B-Chat showing the greatest degradation in perplexity with over  $+4$  gain, and nearly  $+3$  gain for OLMo-7B-DPO from the base versions. While there is a larger difference in perplexity compared to the comparison between OLMo-7B and 13B, we don't find a greater number of features in this setting. Conversely, we find a greater number of features for the Llama2-7B and Llama2-7B-Chat comparison compared to 7B and 13B, though a majority of these features (17 out of 26) are actually for where the Chat version outperforms the base model, despite its significantly
+
+worse performance with respect to perplexity.
+
+Between Llama-7B and Llama-7B-Chat, the base model performs better at text related to source/metadata attribution and archival formatting, while the chat version is better at a wider range of narrative stylistic features, markup and web related content, as well as particular grammatical constructions and phrases. For OLMo models, the base model is better at words related to categories like influence and obstacles, as well as particular instances of individual names or words (e.g. "genus" in descriptions of types of fish, "Very Young Man" as a character in a story), whereas the DPO version outperforms the base at predicting words in set phrases such as "so much the X" and "have a word with Y". Across both Llama and OLMo comparisons, the post-trained models appear to be better at conversational phrases and common multi-word grammatical constructions, which aligns with their intended use in chat settings.
+
+# 7.3 Model Families
+
+Figure 4 visualizes the various features found by BEHAVIORBOX between Llama and OLMo models same size. Despite the difference in perplexity being the lowest out of all comparisons  $(\Delta \text{Perplexity} < 0.1)$ , we found the greatest number of distinct features between models of the same size between families.
+
+Furthermore, these features are persistent across size, as we can find sets of features that are shared among both 7B and 13B comparisons. OLMo models are better at predicting certain forms of separators like non-tab whitespace, semicolons, and commas, as well as uses of HTML in reference sections. On the other hand, common features for Llama models involve quotation marks, along with a substantial number of features involving sequences of tabs in various contexts such as document/text formatting and within prose.
+
+# 8 BEHAVIORBOX Features Distinguish Texts Generated by Different LMs
+
+BEHAVIORBOX finds features based on data from a particular corpus. While this allows us to compare performance on controlled, naturalistic data, an open question remains of how the probabilities of predetermined strings translate to the model's behavior in open generation. Are features found by BEHAVIORBOX also evident when comparing text generated from the compared models?
+
+![](images/9026ae656a26bd3d55335e43c3eaa96d1e397abf49ad6b83c861112f1929f0aa.jpg)  
+Figure 3: Representative features between base models (blue) and their post-trained counterparts (orange).
+
+To investigate this, we look at whether the prevalence of particular strings mentioned in features found by BEHAVIORBOX are more frequently generated by one model than another. We focus on comparing features and generations from Llama-13B and OLMo-13B, focusing on features that refer to a specific words for ease of analysis. For each model, we chose four strings based on the features where the model performs better: tab, quotation marks, "https", and "morrow" (in "tomorrow") for Llama-13B and periods followed by quotation marks, standard whitespace<sup>5</sup>, HTML less than ("lt"), and commas for OLMo-13B.
+
+For both models, we produce "free-generations" by conditioning only on the model's BOS token with a temperature of 1 and default max generation length (Liu et al., 2025). We filter for generations that are between 400-600 words long, then among those sample 500 for each model. To test the hypothesis that a model produces a particular word significantly more frequently than another, we calculate the frequency of that string in every genera
+
+<table><tr><td>String</td><td>Hypothesis</td><td>p-value</td></tr><tr><td>tab</td><td>L &gt; O</td><td>4.8e-5</td></tr><tr><td>quotation mark</td><td>L &gt; O</td><td>0.02</td></tr><tr><td>https</td><td>L &gt; O</td><td>8.5e-6</td></tr><tr><td>morrow</td><td>L &gt; O</td><td>-</td></tr><tr><td>period + quotation mark (?”)</td><td>O &gt; L</td><td>0.02</td></tr><tr><td>whitespace</td><td>O &gt; L</td><td>0.03</td></tr><tr><td>HTML less than (lt)</td><td>O &gt; L</td><td>0.16</td></tr><tr><td>comma</td><td>O &gt; L</td><td>7.3e-4</td></tr></table>
+
+Table 2: Results from testing hypotheses about differences in string frequencies between Llama-13B and Olmo-13B;  $\mathrm{L} > \mathrm{O}$  indicates that Llama-13B generates the string at a greater frequency than OLMo-13B and vice versa. Bold indicates significant results  $(p < 0.05)$ .
+
+tion, then use the Mann-Whitney U test (Mann and Whitney, 1947) to see if the rates of generation of a string within a document is significantly more or less frequent for one model compared to the other.[6]
+
+As shown in Table 2, six of the eight string hypotheses lead to significant results, indicating that
+
+![](images/3f2e170f399df02a725a3a41fe35d59368787b7d69041e4dc65a307dd12c9cf3.jpg)  
+Figure 4: Representative features between Llama (blue) and OLMo models (orange) of the same sizes.
+
+BEHAVIORBOX features can be used to distinguish sets of generations between models. Additionally, while did not have a conclusive result for "morrow" (as it was not present in any of the sampled strings), we inspected 5000 free generations (not filtered for length) and found 20 occurrences of "morrow" (as used in "to-morrow") from Llama-13B and 0 from OLMo-13B, supporting our hypothesis.
+
+# 9 Conclusion
+
+In this work, we introduced BEHAVIORBOX, an automated pipeline for the behavioral comparison of language models that bridges the gap between aggregated metrics and fine-grained performance analysis. By integrating contextual embeddings with model probabilities into a unified, performance-aware representation and leveraging a sparse autoencoder to extract human-interpretable features, our approach enables the discovery of coherent data slices where one model outperforms another. Our experiments—spanning variations in model family, size, and post-training regimes—
+
+demonstrate that BEHAVIORBOX can uncover nuanced performance differences, such as distinctions in formatting, domain-specific language, and syntactic patterns, that are often masked by conventional evaluation metrics like perplexity. Additionally, our results highlight how differences in perplexity are not correlated with the number of salient features that distinguish models. A delta in perplexity could be a result of noisy, less coherent differences in behavior (as in our comparisons across sizes), while in other cases (e.g. across model families) a minuscule delta could potentially hide a number of well-stratified groups.
+
+Beyond its utility for detailed performance diagnostics, BEHAVIORBOX serves as a hypothesis generation tool for further behavioral analysis and facilitates a deeper understanding of language model behavior, thereby supporting more informed decisions in model development and deployment. Overall, our method represents a step toward more transparent and actionable insights into the inner workings of large-scale language models.
+
+# 10 Limitations
+
+While BEHAVIORBOX shows promise as an interpretability and diagnostic tool, several limitations warrant discussion. First, the approach is dependent on the quality and compatibility of the underlying contextual embeddings and probability estimates. Any misalignment between the embedding space and the performance signals can obscure meaningful differences. Second, aggregating token-level probabilities into word-level metrics may introduce noise, particularly when tokenization strategies differ across models.
+
+Additionally, the sparse autoencoder, despite its design for interpretability, may not capture all relevant behavioral nuances, and its performance is sensitive to hyperparameter choices such as the sparsity level and the weighting of probability features. The automated labeling process—while efficient—relies on a strong LLM annotator, which can sometimes generate inconsistent or suboptimal descriptions. Finally, our experiments have been conducted on a subset of language modeling tasks and datasets; thus, the generalizability of BEHAVIORBOX to other tasks, domains, or non-textual modalities remains to be fully explored. Future work may address these limitations by refining the representation alignment, exploring alternative aggregation strategies, and broadening the scope of evaluation.
+
+# Ethical Considerations
+
+BEHAVIORBOX provides new tools for practitioners to better understand the behavior of language models, and particularly the differences between multiple language models. On the whole, this has the potential for easing the ethical deployment of language models by identifying potential issues in advance of deployment and rectifying them before their deployment. Overall, we foresee few ethical risks in the existence of such a framework, although as with all automatic tools, users must be cautious in jumping to conclusions based solely on the tool output without careful thought.
+
+# Acknowledgments
+
+This work was supported in part by a gift from Amazon Web Services. We thank Alex Fang for helping create a visualization interface to inspect features, and Amanda Bertsch, Jared Fernandez, Sireesh Gururaja, Sophie Hao, Michael Hu, Emmy Liu, Jeremiah Milbauer, Lintang Sutawika, Vijay
+
+Viswanathan, and members of NeuLab for their feedback and helpful discussion.
+
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+Alireza Makhzani and Brendan J. Frey. 2013. k-sparse autoencoders. CoRR, abs/1312.5663.  
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+Melanie Sclar, Yejin Choi, Yulia Tsvetkov, and Alane Suhr. 2023. Quantifying language models' sensitivity to spurious features in prompt design or: How i learned to start worrying about prompt formatting. In The Twelfth International Conference on Learning Representations.
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+Luca Soldaini, Rodney Kinney, Akshita Bhagia, Dustin Schwenk, David Atkinson, Russell Authur, Ben Bogin, Khyathi Chandu, Jennifer Dumas, Yanai Elazar, Valentin Hofmann, Ananya Harsh Jha, Sachin Kumar, Li Lucy, Xinxi Lyu, Nathan Lambert, Ian Magnusson, Jacob Morrison, Niklas Muennighoff, Aakanksha Naik, Crystal Nam, Matthew E. Peters, Abhilasha Ravichander, Kyle Richardson, Zejiang Shen, Emma Strubell, Nishant Subramani, Oyvind Tafjord, Pete Walsh, Luke Zettlemoyer, Noah A. Smith, Hannaneh Hajishirzi, Iz Beltagy, Dirk Groeneveld, Jesse Dodge, and Kyle Lo. 2024. Dolma: An Open Corpus of Three Trillion Tokens for Language Model Pretraining Research. arXiv preprint.
+
+Hugo Touvron, Louis Martin, Kevin R. Stone, Peter Albert, Amjad Almahairi, Yasmine Babaei, Nikolay Bashlykov, Soumya Batra, Prajjwal Bhargava, Shruti Bhosale, Daniel M. Bikel, Lukas Blecher, Cristian Cantón Ferrer, Moya Chen, Guillem Cucurull, David Esiobu, Jude Fernandes, Jeremy Fu, Wenyin Fu, Brian Fuller, Cynthia Gao, Vedanuj Goswami, Naman Goyal, Anthony S. Hartshorn, Saghar Hosseini, Rui Hou, Hakan Inan, Marcin Kardas, Viktor Kerkez, Madian Khabsa, Isabel M. Kloumann, A. V. Korenev, Punit Singh Koura, Marie-Anne Lachaux, Thibaut Lavril, Jenya Lee, Diana Liskovich, Yinghai Lu, Yuning Mao, Xavier Martinet, Todor Mihaylov, Pushkar Mishra, Igor Molybog, Yixin Nie, Andrew Poulton, Jeremy Reizenstein, Rashi Rungta, Kalyan Saladi, Alan Schelten, Ruan Silva, Eric Michael Smith, R. Subramanian, Xia Tan, Binh Tang, Ross Taylor, Adina Williams, Jian Xiang Kuan, Puxin Xu, Zhengxu Yan, Iliyan Zarov, Yuchen Zhang, Angela Fan, Melissa Hall Melanie Kambadur, Sharan Narang, Aurélien Rodriguez, Robert Stojnic, Sergey Edunov, and Thomas Scialom. 2023. Llama 2: Open foundation and fine-tuned chat models. ArXiv, abs/2307.09288.
+
+Tongshuang Wu, Marco Tulio Ribeiro, Jeffrey Heer, and Daniel Weld. 2019. Errudite: Scalable, reproducible, and testable error analysis. In Proceedings of the 57th Annual Meeting of the Association for Computational Linguistics, pages 747-763, Florence, Italy. Association for Computational Linguistics.
+
+Mengzhou Xia, Mikel Artetxe, Chunting Zhou, Xi Victoria Lin, Ramakanth Pasunuru, Danqi Chen, Luke Zettlemoyer, and Veselin Stoyanov. 2023. Training trajectories of language models across scales. In
+
+<table><tr><td>Hyperparameter</td><td>Value</td></tr><tr><td>Batch size</td><td>128</td></tr><tr><td>Learning rate</td><td>10-4</td></tr><tr><td>AdamW β1</td><td>0.9</td></tr><tr><td>AdamW β2</td><td>0.99</td></tr><tr><td>Dict size</td><td>3000</td></tr><tr><td>k</td><td>50</td></tr><tr><td>Probability feature weight</td><td>0.7</td></tr></table>
+
+Table 3: Hyperparameters used to train SAEs.
+
+Proceedings of the 61st Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers), pages 13711-13738, Toronto, Canada. Association for Computational Linguistics.
+
+# A Appendix
+
+# A.1 SAE Hyperparameters and Training
+
+Hyperparameters used to train the SAE are included in Table 3. Hyperparameters were chosen based on a number of heuristics and proxy metrics, including the number of dead latents and the number of resulting coherent features as determined by the LLM annotation process. As there are a large number of hyperparameters and potential values, we did not explore varying all parameters; systematically choosing these parameters has been noted as a challenge in previous work (Bricken et al., 2023). We explored using both larger dictionaries (e.g. 4000, 5000) and applying greater sparsity constraints ( $k = 10$ , 25), but didn't find a consistent pattern with respect to how these changes affect the number and types of features found across comparisons.
+
+Probability feature up-weighting A hyperparameter that had a significant impact on downstream results with a clear trend was the upweighting of probability features. Using a smaller corpus of about 8M words, we train SAEs where we only vary how much we up-weigh the probabilities, i.e. the fraction of the total magnitude that the probability features contribute. As expected, as this fraction increases, features that are discovered become more consistent with respect to the sign of the probability difference between models for words associated with that feature; however, there is a tradeoff with the coherence of those features (with a high fraction, features are often solely depending on large probability diff's alone, without regards to semantic similarity) and the number of dead latents,
+
+as seen in Table 4. As a result, we settled on using a fraction of 0.7 in our experiments.
+
+<table><tr><td>Prob Fraction</td><td>% Dead ↓</td><td>Word Dist ↓</td><td>Prob Dist ↓</td></tr><tr><td>0.5</td><td>14.7</td><td>8.59</td><td>0.33</td></tr><tr><td>0.6</td><td>7.0</td><td>8.60</td><td>0.34</td></tr><tr><td>0.7</td><td>4.5</td><td>8.25</td><td>0.30</td></tr><tr><td>0.8</td><td>20.7</td><td>8.44</td><td>0.26</td></tr><tr><td>0.9</td><td>60.5</td><td>8.65</td><td>0.28</td></tr></table>
+
+Table 4: Sweep over the degree probability upweighting using SAEs trained on 8M words of data (model probabilities used are from Llama 2 7B and 13B). % dead refers to the number of SAE features that never activate. For each feature, among the (up to) 50 words that activate the feature, we calculate the mean L2 distance between each word's contextual embedding and the average embedding, and do the same for the probability vector.
+
+Neuron resetting Additionally, to mitigate the presence of dead latents during training, we follow the methodology in Bricken et al. (2023) and periodically re-initialize encoder and decoder weights for features that have no non-zero activations on a hold-out eval set during training. For our experiments, we reset dead neurons every 30k steps, but only if the percentage of dead neurons (based on inference on the eval set) is greater than  $15\%$ ; the frequency of this resetting and threshold may be adjusted depending on the amount of data available.
+
+What about random seeds? Works such as Fel et al. (2025) have pointed out that multiple runs on the same data with different random seeds or data orderings can largely impact the space of features found by SAEs. Indeed, in our experiments we also noticed variation (more so with changes in initialization as opposed to data shuffling), though there appeared to be some overlap, especially among either thematically repetitive features (e.g. tabs in varying contexts) or among features with large probability differences. We hypothesize that different runs are capable of finding partially disjoint, yet "correct", sets of features, and in practice one could take the union of various SAE runs as their feature set of interest, or use methods such as those proposed in Fel et al. (2025).
+
+# A.2 Thresholding Features
+
+Our initial experiments used a two-sided t-test to filter features based on whether difference in means was statistically significant (as opposed to the median difference), but found that this was not suitable
+
+as many distributions of differences were not Gaussian. As a result, we encountered features which had statistically significant difference in means (as determined by the t-test) indicating that some model A was better than B, but was very inconsistent with respect to the number of samples where A was actually better than B.
+
+Thus, we instead use the median difference of the either probabilities or log probabilities as a metric to decide whether to keep or discard a feature for analysis. To choose a threshold for the delta in probabilities and log probabilities, we look at the consistency of a feature, where consistency is defined as the percentage of samples where the sign of the difference between the two model probabilities matches the median difference. As shown in Figure 5, these chosen thresholds allow us to filter out most features that have a consistency of  $< 70\%$ .
+
+![](images/57902997ad41fe6e318dd1d3723a49d2084b6dd2cdc6295bf2475c9943267873.jpg)
+
+![](images/ee52c0053e65620df1a71a3af34a3d4b56e0f8d08119c78675a1ca84ac48603e.jpg)  
+Figure 5: Scatterplots showing median probability (top) and log probability (bottom) of features (after the first pass annotation step) against consistency. Features are from Llama2-7B and Llama2-13B, and other comparisons generally follow this visual trend. Red lines show our thresholding values ( $\pm 0.1$  for probability and  $\pm 1$  for log probability).
+
+# A.3 LLM Annotation
+
+The first pass annotation prompt (as shown below) was used to generate a first-pass of annotation labels. The top 20 words that lead to the highest activation value (or up to 20 for features containing greater than 10 but less than 20 samples with nonzero activations) and their contexts for a feature were provided in a list following the prefix.
+
+To filter and validate the features, we have an additional round of LLM annotation, which takes as input the original label from the annotator LLM along with (up to) the top 20 words and their contexts. In our qualitative analyses, we only consider the labels output from this labeling stage that were scored  $\geq 1$  (as labels scored 1 or 2 were re-labeled). We then manually verify feature labels, and additionally filter out samples that are not described by the label for each feature.
+
+# First Pass Annotation Prompt
+
+Your job is to determine if a group of words (surrounded by asterisks, e.g. *word*) in specific contexts form a coherent group that can be described concisely. I will provide you with a list of words surrounded by asterisks and the context in which they appear, usually within a sentence or a block of text. Each word and how it appears in context will be its own item in a list.
+
+Here are some examples:
+
+- conservation: Efforts in *conservation* are essential for protecting endangered species.  
+- habitat: The loss of *habitat* is a significant threat to biodiversity.  
+- ecosystem: An *ecosystem* needs a balance of various species to thrive.
+
+Your job is to determine if the words form a coherent group that can be described concisely. If the words do form a coherent group, please provide a concise description of the group. Provide your answer in the following format:
+
+<BEGIN ANSWER>
+
+Coherent: <YES or NO>
+
+Description: <if YES above, your description here; otherwise NONE>
+
+<END ANSWER>
+
+Do not provide any additional text after <END ANSWER>. Only respond with YES or NO for the "Coherent" field. If you respond with YES, you must provide a description in the "Description" field. Descriptions should be concise, ideally a single sentence. For the above example, descriptions may be something like "Nouns describing environmental conservation" or "Words related to biodiversity". Note that groups and descriptions may also pertain to formatting, such as "Punctuation before whitespaces in documents discussing logic" or "Series of whitespaces in documents discussing visual art". The description should NOT refer to the asterisks, those are only there to help you identify the words.
+
+Please categorize the following list of words and their contexts as coherent or not coherent, and provide a description if needed:
+
+# Label Validation Prompt
+
+Your job is to determine if a group of words (surrounded by asterisks, e.g. *word*) in specific contexts form a coherent group that is accurately described by a given label. I will provide you with a list of words surrounded by asterisks and the context in which they appear, usually within a sentence or a block of text. Each word and how it appears in context will be its own item in a list. Determine if the words form a group that is accurately described by the label by providing a numerical score (0 to 3, and -1). Scores are defined as follows:
+
+- 0: The label is not accurate and the words do not form any coherent groups.  
+- 1: The label is not accurate, but the words form a coherent group.  
+- 2: The label is accurate, but fails to capture a more specific trend.  
+- 3: The label is accurate and captures a specific trend.  
+- -1: There are two coherent groups.
+
+Additionally, if you give a score of 1 or 2, provide an alternative label that you believe would be more accurate. If you give a label of -1, provide a label for each group. Each label should be separated with  $<\mathrm{SEP}>$ . This label should be precise, concise, and accurate, ideally a single sentence, Otherwise, leave the alternative label field blank.
+
+Provide your answer in the following format, be sure to include both "Score" and "Label" fields:
+
+# <BEGIN ANSWER>
+
+Score: <a number between 1-3 or -1>
+
+Label: <label(s) if original score is 1, 2, or -1, empty otherwise>
+
+<END ANSWER>
+
+Do not provide any additional text after <END ANSWER>. Only respond a number between 0 and 3 or -1 in the Score field. The description should NOT refer to the asterisks, those are only there to help you identify the words. If there are double asterisks in the text, assume the word of interest is the whitespace between them.
+
+Please score the following list of words and their label, and provide a new label if necessary:
+
+# A.4 Feature Labels
+
+Below we list all features for each comparison. Since words that weren't satisfied by the label within each feature were filtered out, the median probability and log probability differences were recalculated
+
+Additionally, we sometimes found repeated features, or features that are activated by a large proportion of the same words. These features tend to occur when the magnitude of the probability difference is relatively large, and there are a large enough nearly identical contexts in which this word occurs within the corpus.
+
+Table 5: Llama2-7B vs. Llama2-13B  
+
+<table><tr><td>Model</td><td>Feature</td><td>Median 
+Prob Diff</td><td>Median Log 
+Prob Diff</td><td>Consistency</td></tr><tr><td>Llama2-7B</td><td>Tabs following another tab, typically after sentence-ending punctuation marks in narrative text</td><td>0.999</td><td>9.27</td><td>1.0</td></tr><tr><td>Llama2-7B</td><td>Tabs in narrative text, likely from historical fiction</td><td>0.553</td><td>1.303</td><td>0.846</td></tr><tr><td>Llama2-7B</td><td>Tabs in primarily narrative text</td><td>0.723</td><td>1.819</td><td>0.875</td></tr><tr><td>Llama2-7B</td><td>Common English expressions and idioms used in casual dialogue or narrative text</td><td>0.204</td><td>0.578</td><td>0.769</td></tr><tr><td>Llama2-7B</td><td>References to military related events or figures</td><td>0.03</td><td>0.213</td><td>0.818</td></tr><tr><td>Llama2-13B</td><td>Whitespace characters following textual content in book formatting and typography</td><td>-0.556</td><td>-2.042</td><td>0.909</td></tr><tr><td>Llama2-13B</td><td>Tabs, commas, and periods in printed formatting</td><td>-0.412</td><td>-0.883</td><td>0.969</td></tr><tr><td>Llama2-13B</td><td>Casual dialogue and vernacular speech patterns in literary text</td><td>-0.197</td><td>-1.775</td><td>0.75</td></tr><tr><td>Llama2-13B</td><td>Author surname abbreviations followed by parenthetical punctuation in bibliographic entries</td><td>-0.143</td><td>-0.29</td><td>0.787</td></tr><tr><td>Llama2-13B</td><td>Informal expressions indicating someone&#x27;s state of being that include the preposition &quot;to&quot;</td><td>-0.013</td><td>-0.797</td><td>0.778</td></tr><tr><td>Llama2-13B</td><td>Book titles beginning with &quot;Or&quot; used as subtitles or alter-native titles, typically in publishing contexts</td><td>-0.08</td><td>-0.09</td><td>0.889</td></tr><tr><td>Llama2-13B</td><td>Descriptions of landscape features and human interactions with natural and cultivated environments</td><td>-0.003</td><td>-0.003</td><td>0.762</td></tr><tr><td>Llama2-13B</td><td>Negative contractions in English informal or vernacular dialogue (&quot;didn&#x27;t&quot;, &quot;wouldn&#x27;t&quot;, &quot;carn&#x27;t&quot;)</td><td>-0.0</td><td>-0.585</td><td>0.667</td></tr></table>
+
+Table 6: OLMo2-7B vs. OLMo2-13B  
+
+<table><tr><td>Model</td><td>Feature</td><td>Median Prob Diff</td><td>Median Log Prob Diff</td><td>Consistency</td></tr><tr><td>OLMo2-7B</td><td>References to original illustrations in HTML file documentation</td><td>0.944</td><td>3.653</td><td>1.0</td></tr><tr><td>OLMo2-7B</td><td>References to original illustrations in HTML document metadata</td><td>0.944</td><td>3.653</td><td>1.0</td></tr><tr><td>OLMo2-7B</td><td>References to original illustrations in HTML file versions across different document numbers</td><td>0.944</td><td>3.653</td><td>1.0</td></tr><tr><td>OLMo2-7B</td><td>Consistent reference to original illustration in file metadata HTML directives</td><td>0.944</td><td>3.653</td><td>1.0</td></tr><tr><td>OLMo2-7B</td><td>File extensions in URLs or file paths indicating compressed archive files</td><td>0.661</td><td>1.162</td><td>0.979</td></tr><tr><td>OLMo2-13b</td><td>Double commas that appear in church registries and marriage records as row separators</td><td>-0.627</td><td>-2.082</td><td>1.0</td></tr><tr><td>OLMo2-13b</td><td>Double commas that appear in church registries and marriage records as row separators</td><td>-0.337</td><td>-0.959</td><td>0.98</td></tr><tr><td>OLMo2-13b</td><td>Stage directions indicating character thoughts or private speech in dramatic texts</td><td>-0.421</td><td>-0.816</td><td>1.0</td></tr><tr><td>OLMo2-13b</td><td>Distribution type indicator in Gradle version file paths</td><td>-0.315</td><td>-0.441</td><td>1.0</td></tr><tr><td>OLMo2-13b</td><td>Action verbs describing physical or mechanical movement and control</td><td>-0.046</td><td>-2.768</td><td>0.947</td></tr><tr><td>OLMo2-13b</td><td>Misspelled or phonetically written words in informal or historical texts, specifically &quot;wood&quot; for &quot;would&quot;</td><td>-0.032</td><td>-1.554</td><td>1.0</td></tr><tr><td>OLMo2-13b</td><td>Ampersand symbols used as abbreviations for &quot;etc.&quot; or &quot;and&quot; in various bibliographic and listing contexts</td><td>-0.005</td><td>-0.987</td><td>0.727</td></tr><tr><td>OLMo2-13b</td><td>Words specifying individual entities or items of a type</td><td>-0.003</td><td>-1.427</td><td>0.81</td></tr></table>
+
+Table 7: Llama2-7B vs. Llama2-7B-Chat  
+
+<table><tr><td>Model</td><td>Feature</td><td>Median 
+Prob Diff</td><td>Median Log 
+Prob Diff</td><td>Consistency</td></tr><tr><td>Llama2-7B</td><td>References to public domain material in library and archive digitization projects</td><td>0.968</td><td>3.498</td><td>1.0</td></tr><tr><td>Llama2-7B</td><td>Library source attributions in document metadata</td><td>0.952</td><td>6.541</td><td>1.0</td></tr><tr><td>Llama2-7B</td><td>Library source attributions in document metadata</td><td>0.952</td><td>6.541</td><td>1.0</td></tr><tr><td>Llama2-7B</td><td>Source attribution statements referencing public do-main materials</td><td>0.968</td><td>4.696</td><td>1.0</td></tr><tr><td>Llama2-7B</td><td>Occurrences of &quot;by&quot; followed by digital libraries, archives, or institutional sources in document attribution statements</td><td>0.952</td><td>6.541</td><td>1.0</td></tr><tr><td>Llama2-7B</td><td>Double commas used as separators in parish register entries containing dates and personal records</td><td>0.726</td><td>2.536</td><td>1.0</td></tr><tr><td>Llama2-7B</td><td>Double commas used as separators in genealogical or parish records between dates and personal information</td><td>0.723</td><td>2.3</td><td>1.0</td></tr><tr><td>Llama2-7B</td><td>Double commas used as separators in genealogical or parish records</td><td>0.635</td><td>4.001</td><td>1.0</td></tr><tr><td>Llama2-7B</td><td>Words indicating location, direction, or movement in narrative text</td><td>0.225</td><td>2.708</td><td>1.0</td></tr><tr><td>Llama2-7B-Chat</td><td>Tabs following a tab preceding dialogue or narrative transitions</td><td>-1.0</td><td>-10.989</td><td>1.0</td></tr><tr><td>Llama2-7B-Chat</td><td>Word &quot;or&quot; as a URL separator between file path and domain in Project Gutenberg URLs</td><td>-0.99</td><td>-4.604</td><td>1.0</td></tr><tr><td>Llama2-7B-Chat</td><td>The word &quot;or&quot; appearing in Project Gutenberg URLs as a separator between elements</td><td>-0.989</td><td>-4.519</td><td>1.0</td></tr><tr><td>Llama2-7B-Chat</td><td>Semicolons appearing in HTML markup and references sections</td><td>-0.364</td><td>-0.564</td><td>1.0</td></tr><tr><td>Llama2-7B-Chat</td><td>Imperative commands using &quot;with&quot; to indicate dismissal or removal</td><td>-0.295</td><td>-0.446</td><td>1.0</td></tr><tr><td>Llama2-7B-Chat</td><td>Words and phrases indicating decision-making, judgment, or reaching conclusions in formal or narrative contexts</td><td>-0.156</td><td>-0.718</td><td>0.844</td></tr><tr><td>Llama2-7B-Chat</td><td>Instances of &quot;with a&quot; followed by words describing facial expressions or emotional gestures in narrative text</td><td>-0.168</td><td>-0.227</td><td>0.939</td></tr><tr><td>Llama2-7B-Chat</td><td>Commas followed by forms of address or names in direct dialogue</td><td>-0.15</td><td>-0.265</td><td>0.84</td></tr><tr><td>Llama2-7B-Chat</td><td>Conditional uses of &#x27;were&#x27; in hypothetical scenarios, typically following &#x27;if you&#x27;</td><td>-0.14</td><td>-0.427</td><td>0.76</td></tr><tr><td>Llama2-7B-Chat</td><td>Instances of the word &quot;reached&quot; used to describe arriving at or attaining a destination in narrative texts</td><td>-0.19</td><td>-0.385</td><td>0.744</td></tr><tr><td>Llama2-7B-Chat</td><td>Superlative adjective &quot;most&quot; used to express highest degree or maximum quality of something</td><td>-0.132</td><td>-0.286</td><td>0.76</td></tr><tr><td>Llama2-7B-Chat</td><td>Uses of &quot;who&quot; as a relative pronoun referring to people or beings in formal or literary contexts</td><td>-0.109</td><td>-0.187</td><td>0.94</td></tr><tr><td>Llama2-7B-Chat</td><td>Commas preceding &quot;and&quot; in various narrative and instructional texts</td><td>-0.128</td><td>-0.23</td><td>0.8</td></tr><tr><td>Llama2-7B-Chat</td><td>Exclamation marks appearing at the end of emotionally charged or dramatic statements</td><td>-0.103</td><td>-0.218</td><td>0.86</td></tr><tr><td>Llama2-7B-Chat</td><td>Modal verb &#x27;must&#x27; expressing necessity, obligation, or requirement in various contexts</td><td>-0.129</td><td>-0.184</td><td>0.826</td></tr><tr><td>Llama2-7B-Chat</td><td>Forms of the verbs &quot;to be&quot; (were/are) used as auxiliary or linking verbs in historical or narrative contexts</td><td>-0.103</td><td>-0.161</td><td>0.72</td></tr><tr><td>Llama2-7B-Chat</td><td>Informal or dialectical spelling of &quot;and&quot; in literary texts showing vernacular speech</td><td>-0.114</td><td>-0.228</td><td>0.66</td></tr></table>
+
+Table 8: OLMo2-7B vs. OLMo2-7B-DPO  
+
+<table><tr><td>Model</td><td>Feature</td><td>Median 
+Prob Diff</td><td>Median Log 
+Prob Diff</td><td>Consistency</td></tr><tr><td>OLMo2-7B</td><td>The word &quot;genus&quot; appearing in taxonomic descrip-
+tions of ray-finned fish species belonging to En-
+teromius</td><td>0.715</td><td>3.876</td><td>1.0</td></tr><tr><td>OLMo2-7B</td><td>Words related to influence, vulnerability, persuasive-
+ness, and power in conflict</td><td>0.08</td><td>1.154</td><td>0.933</td></tr><tr><td>OLMo2-7B</td><td>Instances of the word &quot;said&quot; used as a dialogue tag 
+in narrative fiction</td><td>0.181</td><td>0.433</td><td>0.9</td></tr><tr><td>OLMo2-7B</td><td>Instances of &quot;Very Young Man&quot; as a character name 
+in a narrative text</td><td>0.155</td><td>0.824</td><td>0.796</td></tr><tr><td>OLMo2-7B</td><td>Words expressing challenges, obstacles or removal 
+in narrative contexts</td><td>0.09</td><td>2.065</td><td>0.917</td></tr><tr><td>OLMo2-7B</td><td>Action words or numbers serving as interactive ele-
+ments or references in digital/printed content</td><td>0.04</td><td>1.769</td><td>0.893</td></tr><tr><td>OLMo2-7B</td><td>&quot;Place&quot; as used in the phrase &quot;place of&quot; or as a rank</td><td>0.008</td><td>2.524</td><td>0.909</td></tr><tr><td>OLMo2-7B-DPO</td><td>Instances of &quot;so much the&quot; followed by comparative 
+expressions in dialogue</td><td>-0.584</td><td>-1.138</td><td>1.0</td></tr><tr><td>OLMo2-7B-DPO</td><td>Requests for private conversations using the phrase 
+&quot;have a word with&quot;</td><td>-0.239</td><td>-0.307</td><td>1.0</td></tr></table>
+
+Table 9: Llama2-7B vs. OLMo2-7B  
+
+<table><tr><td>Model</td><td>Feature</td><td>Median Prob Diff</td><td>Median Log Prob Diff</td><td>Consistency</td></tr><tr><td>Llama2-7B</td><td>Tabs used for formatting in all-caps chapter titles and section headers</td><td>0.995</td><td>5.471</td><td>1.0</td></tr><tr><td>Llama2-7B</td><td>References to HTML file versions in Project Gutenberg notes</td><td>0.888</td><td>2.205</td><td>1.0</td></tr><tr><td>Llama2-7B</td><td>References to HTML file format in Project Gutenberg documentation notes</td><td>0.843</td><td>1.875</td><td>1.0</td></tr><tr><td>Llama2-7B</td><td>References to HTML versions of files in Project Gutenberg documentation</td><td>0.843</td><td>1.875</td><td>0.98</td></tr><tr><td>Llama2-7B</td><td>Words indicating spatial or temporal orientation</td><td>0.822</td><td>2.687</td><td>0.917</td></tr><tr><td>Llama2-7B</td><td>Imperative "See" commands directing users to HTML files containing illustrations</td><td>0.677</td><td>1.137</td><td>1.0</td></tr><tr><td>Llama2-7B</td><td>Opening quotation marks in dialogue appearing after two tabs</td><td>0.657</td><td>1.359</td><td>1.0</td></tr><tr><td>Llama2-7B</td><td>Opening quotation marks in dialogue appearing after two tabs</td><td>0.635</td><td>1.399</td><td>1.0</td></tr><tr><td>Llama2-7B</td><td>Periods appearing in Java-style package and class references and application configuration settings</td><td>0.629</td><td>1.03</td><td>1.0</td></tr><tr><td>Llama2-7B</td><td>Opening quotation marks in dialogue appearing after two tabs</td><td>0.522</td><td>1.193</td><td>1.0</td></tr><tr><td>Llama2-7B</td><td>Tabs following semicolons in poetry written in nonstandard English dialects or other languages</td><td>0.456</td><td>0.657</td><td>1.0</td></tr><tr><td>Llama2-7B</td><td>Tabs following tabs and preceding quotation marks marking direct speech in narrative text</td><td>0.402</td><td>0.535</td><td>0.96</td></tr><tr><td>Llama2-7B</td><td>Tabs following tabs in narrative text</td><td>0.375</td><td>0.47</td><td>0.857</td></tr><tr><td>Llama2-7B</td><td>Tabs after punctuation (commas, semicolons) and before the word "and" in literary passages</td><td>0.34</td><td>0.482</td><td>0.92</td></tr><tr><td>Llama2-7B</td><td>Tabs followed by another tab between segments of dialogue in narrative text</td><td>0.305</td><td>0.364</td><td>0.694</td></tr><tr><td>Llama2-7B</td><td>Tabs in multilingual software configuration and documentation</td><td>0.29</td><td>0.43</td><td>1.0</td></tr><tr><td>Llama2-7B</td><td>Tabs in segments of dialog showing character reactions or responses following quoted speech</td><td>0.288</td><td>0.34</td><td>1.0</td></tr><tr><td>Llama2-7B</td><td>Dialectical and informal variations of words, particularly showing dropped 'h' sounds</td><td>0.237</td><td>0.569</td><td>0.8</td></tr><tr><td>Llama2-7B</td><td>Tabs following tabs between quoted text between two speakers</td><td>0.224</td><td>0.254</td><td>1.0</td></tr><tr><td>Llama2-7B</td><td>Tabs within whitespace sequences in dialogue segments in narrative texts</td><td>0.223</td><td>0.278</td><td>0.9</td></tr><tr><td>Llama2-7B</td><td>Tabs followed by another tab before quotations in literary dialogue</td><td>0.201</td><td>0.232</td><td>0.688</td></tr><tr><td>Llama2-7B</td><td>Opening quotation marks at the start of dialogue or exclamations in narrative text</td><td>0.189</td><td>0.504</td><td>0.84</td></tr><tr><td>Llama2-7B</td><td>Tabs followed by another tab following quotations in literary dialogue</td><td>0.187</td><td>0.29</td><td>0.776</td></tr><tr><td>Llama2-7B</td><td>Single or double tabs appearing between chapters, sections, or bibliographic entries in a historical text</td><td>0.167</td><td>0.343</td><td>0.9</td></tr><tr><td>Llama2-7B</td><td>Question marks followed by quotation marks at the end of dialogue in literary texts</td><td>0.147</td><td>0.308</td><td>0.857</td></tr><tr><td>Llama2-7B</td><td>Sequences of tabs after in book layout and formatting contexts</td><td>0.142</td><td>0.224</td><td>0.86</td></tr><tr><td>Llama2-7B</td><td>Periods at the end of sentences, including contexts from online conversations and comments</td><td>0.134</td><td>0.264</td><td>0.75</td></tr><tr><td>Llama2-7B</td><td>Whitespace (spaces, tabs) in poetry</td><td>0.12</td><td>0.254</td><td>0.7</td></tr><tr><td>Llama2-7B</td><td>Opening quotation marks and brackets at the start of bibliographic or reference entries</td><td>0.052</td><td>0.06</td><td>0.559</td></tr><tr><td>OLMo2-7B</td><td>HTML "less than" symbols used as line break tags in geographic reference texts</td><td>-0.986</td><td>-4.291</td><td>1.0</td></tr><tr><td>OLMo2-7B</td><td>Roman numerals VIII and XIII appearing as sequential chapter or section numbers in document structure</td><td>-0.952</td><td>-4.493</td><td>1.0</td></tr><tr><td>OLMo2-7B</td><td>Numerical and textual elements appearing in index entries, lists, and content references</td><td>-0.936</td><td>-6.076</td><td>0.909</td></tr><tr><td>OLMo2-7B</td><td>Occurrences of the word "wich" in parenthetical titles and signatures by Petroleum V. Nasby</td><td>-0.891</td><td>-9.468</td><td>1.0</td></tr><tr><td>OLMo2-7B</td><td>Items appearing as numerical markers or identifiers in ordered lists or sections</td><td>-0.818</td><td>-2.762</td><td>1.0</td></tr><tr><td>OLMo2-7B</td><td>Whitespace between sentence boundaries in narrative texts</td><td>-0.608</td><td>-0.94</td><td>1.0</td></tr><tr><td>OLMo2-7B</td><td>Periods followed by quotation marks before another quote in narrative dialogue</td><td>-0.326</td><td>-0.797</td><td>0.96</td></tr><tr><td>OLMo2-7B</td><td>Government and legislative bodies, particularly British Parliament and colonial institutions</td><td>-0.318</td><td>-2.124</td><td>0.952</td></tr><tr><td>OLMo2-7B</td><td>Question-ending punctuation marks followed by quotation marks in dialogue, often with rhetorical or interrogative phrases ending in "eh" or similar words</td><td>-0.183</td><td>-0.277</td><td>0.875</td></tr><tr><td>OLMo2-7B</td><td>Whitespace after dialogue tags and before quoted continuations in narrative dialogue</td><td>-0.16</td><td>-0.175</td><td>1.0</td></tr><tr><td>OLMo2-7B</td><td>Commas preceding tabs and narrative continuation or descriptive elaboration in poetic text</td><td>-0.154</td><td>-0.279</td><td>0.94</td></tr><tr><td>OLMo2-7B</td><td>Whitespace between sentences in formatted literary text</td><td>-0.147</td><td>-0.159</td><td>1.0</td></tr><tr><td>OLMo2-7B</td><td>Punctuation marks at the end of poetic or literary lines</td><td>-0.129</td><td>-0.171</td><td>0.82</td></tr><tr><td>OLMo2-7B</td><td>Tabs followed by another tab and dialog or quoted speech in narrative text</td><td>-0.126</td><td>-0.192</td><td>0.673</td></tr><tr><td>OLMo2-7B</td><td>Semicolons used as separators in index or reference entries</td><td>-0.111</td><td>-0.146</td><td>0.92</td></tr><tr><td>OLMo2-7B</td><td>Whitespace between sentenes in philosophical and sociological texts</td><td>-0.102</td><td>-0.109</td><td>0.96</td></tr></table>
+
+Table 10: Llama2-13B vs. OLMo2-13B  
+
+<table><tr><td>Model</td><td>Feature</td><td>Median Prob Diff</td><td>Median Log Prob Diff</td><td>Consistency</td></tr><tr><td>Llama2-13B</td><td>Tabs following another tab in chapter titles or section headers</td><td>0.989</td><td>4.567</td><td>1.0</td></tr><tr><td>Llama2-13B</td><td>&quot;https&quot; within Project Gutenberg file directory URLs</td><td>0.984</td><td>6.801</td><td>1.0</td></tr><tr><td>Llama2-13B</td><td>&quot;morrow&quot; as part of archaic hyphenated spelling in the word &quot;to-morrow&quot;</td><td>0.756</td><td>2.519</td><td>1.0</td></tr><tr><td>Llama2-13B</td><td>Opening quotation marks followed by various text segments at the start of dialogue or quoted passages</td><td>0.725</td><td>1.431</td><td>0.98</td></tr><tr><td>Llama2-13B</td><td>Opening quotation marks following dialogue consisting of questions in narrative text</td><td>0.666</td><td>1.328</td><td>0.98</td></tr><tr><td>Llama2-13B</td><td>Captions or labels for figures and illustrations in instructional or historical texts</td><td>0.558</td><td>0.837</td><td>1.0</td></tr><tr><td>Llama2-13B</td><td>Opening quotation marks at the start of questions in dialogue</td><td>0.514</td><td>1.124</td><td>0.98</td></tr><tr><td>Llama2-13B</td><td>Tabs following semicolons in poetry written in nonstandard English dialects</td><td>0.41</td><td>0.546</td><td>0.96</td></tr><tr><td>Llama2-13B</td><td>Tabs following another tab between sentences in literary text excerpts</td><td>0.346</td><td>0.424</td><td>0.92</td></tr><tr><td>Llama2-13B</td><td>Tabs preceding another tab between quotes in dialogue between two speakers</td><td>0.288</td><td>0.341</td><td>0.896</td></tr><tr><td>Llama2-13B</td><td>Tabs following another tab after colons and preceding quoted dialogue in narrative text</td><td>0.263</td><td>0.305</td><td>1.0</td></tr><tr><td>Llama2-13B</td><td>Tabs following commas and appearing before capitalized conjunctions</td><td>0.251</td><td>0.319</td><td>0.94</td></tr><tr><td>Llama2-13B</td><td>Tabs following another tab between quotes in dialogue between two speakers</td><td>0.244</td><td>0.28</td><td>1.0</td></tr><tr><td>Llama2-13B</td><td>Quotation marks at the start of exclamations in narrative text</td><td>0.238</td><td>0.77</td><td>0.9</td></tr><tr><td>Llama2-13B</td><td>Tabs preceding another tab between quotes in dialogue between two speakers</td><td>0.236</td><td>0.289</td><td>0.86</td></tr><tr><td>Llama2-13B</td><td>Equal signs appearing in text separators or boundaries between different sections or concepts</td><td>0.15</td><td>0.186</td><td>0.96</td></tr><tr><td>Llama2-13B</td><td>Underscores appearing at line beginnings in dictionary or reference entries</td><td>0.119</td><td>0.14</td><td>0.82</td></tr><tr><td>Llama2-13B</td><td>Tabs typically preceding another tab along with quoted dialogue</td><td>0.107</td><td>0.212</td><td>0.755</td></tr><tr><td>Llama2-13B</td><td>Tabs followed by character names in theatrical script</td><td>0.102</td><td>0.115</td><td>0.72</td></tr><tr><td>OLMo2-13B</td><td>Path component referring to the Gradle wrapper directory in build configuration files</td><td>-0.987</td><td>-6.013</td><td>1.0</td></tr><tr><td>OLMo2-13B</td><td>References to the Gradle wrapper directory path in build configuration files</td><td>-0.987</td><td>-6.013</td><td>1.0</td></tr><tr><td>OLMo2-13B</td><td>Path component referring to Gradle wrapper directory in build configuration files</td><td>-0.987</td><td>-6.013</td><td>1.0</td></tr><tr><td>OLMo2-13B</td><td>Path component &#x27;wrapper&#x27; in Gradle build configuration files</td><td>-0.987</td><td>-6.013</td><td>1.0</td></tr><tr><td>OLMo2-13B</td><td>HTML line break tags in a references section</td><td>-0.972</td><td>-3.567</td><td>1.0</td></tr><tr><td>OLMo2-13B</td><td>HTML line break tags in a References section</td><td>-0.971</td><td>-3.553</td><td>1.0</td></tr><tr><td>OLMo2-13B</td><td>HTML line break tags in a References section</td><td>-0.97</td><td>-3.494</td><td>1.0</td></tr><tr><td>OLMo2-13B</td><td>HTML less-than symbols appearing in reference formatting</td><td>-0.965</td><td>-3.343</td><td>1.0</td></tr><tr><td>OLMo2-13B</td><td>Periods followed by quotation marks at the end of a quote in dialogue</td><td>-0.303</td><td>-0.638</td><td>0.898</td></tr><tr><td>OLMo2-13B</td><td>Whitespace following abrupt ends, interruptions, trailing thoughts, or hesitations in speech</td><td>-0.264</td><td>-0.943</td><td>0.68</td></tr><tr><td>OLMo2-13B</td><td>Whitespace between sentences in formatted literary text</td><td>-0.223</td><td>-0.253</td><td>1.0</td></tr><tr><td>OLMo2-13B</td><td>Semicolons used as separators in an index or table of contents</td><td>-0.198</td><td>-0.282</td><td>0.92</td></tr><tr><td>OLMo2-13B</td><td>Double-asterisk markers appearing after quoted dialogue, followed by additional text</td><td>-0.181</td><td>-0.201</td><td>1.0</td></tr><tr><td>OLMo2-13B</td><td>Commas used as clause separators in narrative or descriptive text</td><td>-0.156</td><td>-0.289</td><td>0.82</td></tr><tr><td>OLMo2-13B</td><td>Whitespace between sentences in narrative text excerpts</td><td>-0.146</td><td>-0.157</td><td>1.0</td></tr><tr><td>OLMo2-13B</td><td>Question marks and quotation marks at the end of quoted dialogue or interrogative statements</td><td>-0.139</td><td>-0.168</td><td>0.955</td></tr><tr><td>OLMo2-13B</td><td>Tabs preceding another tab in formatted literary text</td><td>-0.116</td><td>-0.147</td><td>0.66</td></tr></table>

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+# Behavioural vs. Representational Systematicity in End-to-End Models: An Opinionated Survey
+
+Ivan Vegner $^{1,4*}$  Sydelle de Souza $^{1,4*}$  Valentin Forch $^{2}$  Martha Lewis $^{3\ddagger}$  Leonidas A.A. Doumas $^{4\ddagger}$
+
+$^{1}$ School of Informatics, University of Edinburgh  $^{2}$ Chemnitz University of Technology
+
+$^{3}$ Institute of Logic, Language, and Computation, University of Amsterdam  $^{4}$ School of Philosophy, Psychology & Language Sciences, University of Edinburgh
+
+# Abstract
+
+A core aspect of compositionality, systematicity is a desirable property in ML models as it enables strong generalization to novel contexts. This has led to numerous studies proposing benchmarks to assess systematic generalization, as well as models and training regimes designed to enhance it. Many of these efforts are framed as addressing the challenge posed by Fodor and Pylyshyn. However, while they argue for systematicity of representations, existing benchmarks and models primarily focus on the systematicity of behaviour. We emphasize the crucial nature of this distinction. Furthermore, building on Hadley's (1994) taxonomy of systematic generalization, we analyze the extent to which behavioural systematicity is tested by key benchmarks in the literature across language and vision. Finally, we highlight ways of assessing systematicity of representations in ML models as practiced in the field of mechanistic interpretability.
+
+# 1 Introduction
+
+A core feature of human cognition is the ability to understand and generate novel combinations of known concepts in systematic ways. To illustrate, understanding (and producing) the utterance "the octopus ate the fish" implies the ability to also understand (and produce) "the fish ate the octopus". This systematicity, often considered fundamental to the concept of compositionality, has become an increasingly important evaluation criterion for artificial intelligence systems. Recent years have seen a proliferation of papers proposing both benchmarks to test for systematicity (e.g., Lake and Baroni, 2018; Hupkes et al., 2020; Kim and Linzen, 2020; Wu et al., 2023; Kim et al., 2023; Okawa et al., 2023) as well as new model architectures designed to exhibit systematic behaviour (e.g., Locatello et al., 2020; Didolkar et al., 2021; Soulos
+
+et al., 2024; Assouel et al., 2024). Many of these works frame their contributions as addressing the challenge<sup>1</sup> posed by Fodor and Pylyshyn (1988, F&P): to explain how systematic language competencies can emerge without structured mental representations. However, there is a crucial distinction that is often overlooked. F&P specifically argued for the necessity of systematic representations in cognitive systems, while modern benchmarks and evaluations typically focus solely on testing for the presence of systematic behaviour. This conflation has led to misunderstandings and conflicting claims about the systematic generalization capabilities of artificial neural networks. This is further compounded by black-box nature of our models.
+
+This paper aims to disentangle these issues by separating behavioural and representational systematicity. We argue that meaningful progress toward human-like systematic generalization requires appropriately-scoped behavioural claims backed up by rigorous mechanistic interpretability. We develop our argument in three parts. First, we discuss the historical development of the concept of systematicity. Drawing on lessons from psychology, we highlight how the focus has gradually shifted from representations to behaviour, as well as the impact of this shift. Second, we analyse key benchmarks in the language $^2$  and vision literature, assessing the type of systematicity they evaluate using Hadley's (1994) framework of weak, quasi-, and strong systematicity. Finally, we explore current approaches to evaluating systematicity of representations in end-to-end trained Transformer models through the lens of mechanistic interpretability. Our review concludes with a set of recommendations for evaluating claims of systematicity in machine learning (ML) systems. It must be noted that works measuring compositionality of representations using
+
+custom architectures (e.g., Andreas (2019); McCoy et al. (2020); Li and McClelland (2022)), while relevant, are beyond the scope of this paper.
+
+Related Work Compositionality has received a great deal of attention in ML. However, although one of the most frequently invoked definitions of compositionality is derived from the human capacity for systematicity, it has largely been sidelined as a secondary concern.
+
+McCurdy et al. (2024) survey the NLP research community, asking them to rate their agreement with a definition of "compositional behaviour" (CB) and a set of statements regarding the investigation thereof. They define CB as a model's tendency to produce a correct output for input  $I$  given that it produces correct output for human-defined component parts of  $I$ . They further decouple their definition from any notion of learning, making their definition of CB agnostic to the dataset(s) from which it is learned. We believe that systematicity is indeterminable under this definition. Absent a clear definition of the component parts and the contexts in which they appear during training, it is impossible to judge a model's ability to systematically recombine them. This impairs even behavioural evaluation of a model's generalization capabilities.
+
+Rusin et al. (2024) provide a comprehensive historical overview of compositionality as an object of inquiry. They also review current trends in endowing ML architectures with compositional mechanisms. However, their central question of "can contemporary neural networks replicate the behavioral signatures of compositionality" (p. 11) also focuses on behaviour rather than representation. They only briefly discuss systematicity and do not engage with Hadley's (1994) distinctions between levels of systematicity, which is central to our analysis. Nevertheless, they do call for mechanistic interpretability of model representations to reinforce conclusions in behavioural tests of compositionality.
+
+There are some reviews which discuss representational systematicity, albeit in different terms. Wattenberg and Viégas (2024) survey key mechanisms for enabling neural networks to represent relationships between features—a long-standing question in cognitive science, known as the binding problem (see Feldman, 2013, for an overview). They propose a number of directions for future work with respect to interpreting how trained models may be representing (or approximating) relational bind
+
+ing. Greff et al. (2020) argue that contemporary neural networks lack human-level compositional generalization abilities precisely because they are unable to solve the binding problem. The authors provide a comprehensive theoretical review of the connection between the binding problem and compositionality. They present an extensive survey of mechanisms which may implement binding and the properties which such mechanisms should possess. Conversely, Pavlick (2023) argues that existing LLMs can already encode symbols and undertake symbolic processing. Despite their differences, these papers all underscore the importance of mechanistic interpretability in establishing the presence of systematic representations in neural models.
+
+# 2 Compositionality via Systematicity
+
+Often attributed to Frege (1892), the principle of compositionality is frequently stated as: "the meaning of a complex expression is a function of the meanings of its parts and of the way they are syntactically combined" (Partee, 2004). It is essential in formal semantics, serves as a foundational element in most logical formal languages<sup>3</sup>, and its influence extends across modern linguistic theories (Halvorsen and Ladusaw, 1979; Gazdar et al., 1985; Steedman, 2019; Joshi, 2005). In technical terms, this principle can be understood as a mathematical relationship—syntax and semantics function as algebras, with meaning assignment acting as a homomorphism that maps syntax to semantics (Janssen and Partee, 1997).
+
+It is crucial to note that the principle of compositionality is "extremely theory-dependent" (Partee, 2004). Without establishing a theory of syntax, semantics, and the interaction between them, the principle is severely underspecified and can be made trivial if not completely vacuous (Westerstahl, 1998; Kazmi and Pelletier, 1998). We echo Janssen and Partee (1997): "the principle [of compositionality] should not be considered an empirically verifiable restriction, but a methodological principle that describes how a system for syntax and semantics should be designed." We now turn to F&P's definition of compositionality, which puts systematicity in the driver's seat.
+
+# 2.1 Fodor and Pylyshyn's Compositionality
+
+In order to establish a syntax and semantics of the language of thought, Fodor and Pylyshyn (1988, F&P) build their definition of compositionality from the more basic notion of systematicity. They define systematicity as an entailment between cognitive capacities: a human capable of understanding the statement  $aRb$ , where  $a, b$  are objects and  $R$  is a relation, is necessarily able to understand  $bRa$ . For example, for the vast majority of language users, understanding the sentence "John loves Mary" necessarily implies the ability to understand and produce the sentence "Mary loves John", and vice versa. F&P argue that this capacity is evidence for the existence of structure and structure-sensitive operations in the human brain. They assert that this property arises because such sentences are composed from the same constituents: "insofar as a language is systematic, a lexical item must make approximately the same semantic contribution to each expression in which it occurs." F&P admit relaxations of this principle in language, such as context-sensitive word definitions, syncatheorematic compositions such as "good [X]" and idioms. However, they maintain that for most language users to be able to make systematic linguistic inferences, human cognitive representations must be systematic too.
+
+Importantly, F&P position their definition of compositionality—consisting of systematicity and the related properties of productivity and inferential coherence—as a property of the representational system (specifically of human mental representations). For F&P, composition is a syntactic (structural) operation which produces a semantic result. By complement, the semantics of individual linguistic units are amenable to performing structural operations over them. They assert that in representations without such structure, human-like compositionality is incredibly unlikely to emerge. Indeed, F&P's challenge is to explain how systematicity can arise in a representational system which does not posit structural operations over symbols (Fodor and McLaughlin, 1990).
+
+# 2.2 Hadley's Three Levels of Systematicity
+
+Based on the work of F&P, Hadley (1994) outlines three progressive levels of systematicity in language learning.
+
+Weak systematicity is defined as the ability to process sentences that use familiar words in new com
+
+binations, but only if those words have appeared in identical syntactic positions before elsewhere in the training data. For instance, if a system is trained on sentences like "John loves Mary," "Jim loves John," and "Mary loves Jim," it should be able to process "Mary loves John" as a test case.
+
+A system possesses quasi-systematicity if it has weak systematicity under recursion. Quasi-systematic models can process novel sentences that contain embedded clauses, provided both the main sentence and the embedded clause are structurally isomorphic to various sentences in the training corpus. For any successfully processed complex sentence, the training data must include a simple sentence demonstrating the same word in the same syntactic position in which it appears in the embedded clause.
+
+To exhibit strong systematicity, the system must be able to process novel sentences, including those with embedded clauses, even when words appear in syntactic positions that they did not occupy in the training data in any simple or embedded clause. Hadley states that strong systematicity is closest to human systematic generalization, as the system can integrate its understanding of syntax and semantics to process words in entirely novel structures.
+
+# 2.3 Systematicity and Productivity
+
+Closely connected to systematicity is the notion of linguistic productivity, defined as the ability to make "infinite use of finite means" (Chomsky, 1965, quoting Humboldt (1836)). To disambiguate the two, many have redefined productivity to refer specifically to a capacity for understanding and producing unbounded inputs and outputs (e.g., Fodor and Pylyshyn, 1988; Hupkes et al., 2020), or "length generalization" in modern parlance.
+
+We conjecture that Hadley's weak systematicity will yield no productivity, because for a sentence of an unseen length there will necessarily be at least one word in the sentence in a novel syntactic position. A quasi-systematic model could exhibit productivity for some, but not all, sentences given its ability to process some recursive clauses. Finally, strong systematicity yields full productivity.
+
+# 3 From Representation to Behaviour
+
+The core of the distinction between representational and behavioural systematicity lies in the classical distinction between competence and performance (Chomsky, 1965, p. 2). Representational sys
+
+aticity is a competence, a cognitive mechanism which ideally manifests itself in performance, i.e., systematic behaviour, except as mitigated by other factors such as compute limitations, noise, errors, etc. Below, we lay out the implications of this distinction for ML research.
+
+# 3.1 Operationalisation
+
+F&P defined systematicity as a relation between cognitive competencies. Hadley reformulated their definition in terms of the properties that must be true of learning systems claiming to possess systematicity. In other words, he put forth a framework for the operationalisation of systematicity.
+
+Operationalisation is a common practice in fields like psychology, wherein unobservable properties of black-box systems must be reasoned about via proxy measures. For example, to study an unobservable property like memory function, a psychologist may operationally define memory in terms of recall from a list. Operationalisation, though, is not without its potential pitfalls. For any operational definition  $A$  of a concept  $B$ , demonstration of  $A$  is at best only evidence for the presence of  $B$ , and the strength of the evidence depends on the strength of the connection between concept and operationalisation. Psychologists have long grappled with these issues, leading to the development of subfields like measurement theory and psychometrics (e.g., Luce, 1996; Stevens, 1946).
+
+Consider the use of the relational match to sample task in comparative cognition (e.g., Premack and Woodruff, 1978). In this task, the participant is presented with a pair of sample items (e.g., two red shapes) and asked to select one of two additional pairs of items that best corresponds to the sample (e.g., two blue shapes vs a red shape and a blue shape). The task aimed to test the capacity to reason about a relational concept like same/different, and was historically used as a demonstration that certain animals had or did not have this capacity (e.g., Thompson et al., 1997; Fagot and Parron, 2010). However, Mike Young and colleagues (Fagot et al., 2001; Young and Wasserman, 1997, 2001) demonstrated that certain animals solved the task simply by detecting and responding to the entropy in sets of items, without recourse to relational reasoning.
+
+The converse problem exists as well. The field of developmental psychology has long dealt with the issue of performance and competence with children, for whom failure to exhibit a behaviour does
+
+not necessarily imply the lack of capacity to do so in any circumstance (such as due to distraction or disinterest). In the literature on object permanence, for example, there has been a long debate about if and when children actually possess the capacity (e.g., Piaget, 2013; Baillargeon and DeVos, 1991). A resolution one way or the other would circumscribe the scope of what a child is able to do and understand at a given age. However, this has proven elusive due to the difficulty of operationalising object permanence appropriately.
+
+# 3.2 Implications for Machine Learning
+
+There are parallels to be drawn here with research in ML. The literature is rife with failures of operationalisation, in which a model's performance on a particular task poorly predicts performance on other, even very similar tasks (see Geirhos et al., 2020, for an overview of "shortcut learning"). Thus, modellers must ensure that their tasks can only be solved using the competence which they intend to test.
+
+However, demonstrating perfect operationalisation is very difficult. Consequently, when evaluating generalization capabilities, researchers require insights into the underlying representations that drive the behavioural outcomes on their task of choice. This mechanistic interpretability enables researchers to assess the validity of their operationalisation and predict model performance across tasks that draw upon the same competence, even when behavioural tests prove imperfect.
+
+According to F&P, systematic generalization requires systematicity of internal representations (representational systematicity), not merely evidence of systematicity in the model's performance on any number of tasks (behavioural systematicity). The relationship between valid operationalisation, behavioural evidence, and mechanistic interpretability creates three analytical cases, each with different implications for our understanding of model capabilities:
+
+Case 1: Systematic behaviour without valid operationalisation. Valid operationalisation requires demonstrating that tasks actually demand specific levels of behavioural systematicity, rather than weaker levels or no systematicity at all. This demands principled control over dataset syntax and semantics. If this is not established, success or failure on the behavioural task no longer constitutes evidence of the existence or absence of representa
+
+tional systematicity. Models may rely on various non-systematic strategies to achieve performance, even when datasets intuitively appear to require systematicity. Sections 4 and 5.2 examine several imprecise operationalisations of systematicity and demonstrate how this inhibits drawing meaningful conclusions about the systematic generalization capabilities of evaluated models.
+
+Case 2: Systematic behaviour under valid operationalisation. When models demonstrate systematic behaviour under conditions of valid operationalisation, F&P assert that they must possess systematic representations. If one gives credence to this position, supported by Hadley and other theorists of structured cognition, this case will be evidence of systematic internal representations. However, definitively proving this requires mechanistic interpretability of the model representations underlying systematic behaviour. Demonstrating that a model exhibits systematic behaviour without possessing systematic representations would effectively overcome Fodor and Pylyshyn's challenge, representing a significant theoretical breakthrough.
+
+Case 3: No systematic behaviour under valid operationalisation. This case also permits two competing interpretations. The model may fail to display systematic behaviour because it does not have systematic representations. Alternatively, the model may possess systematic representations, but be unable to use them to behave systematically.
+
+The second possibility is analogous to the child who cannot, or does not want to, demonstrate object permanence in a particular context. This possibility becomes more worrisome as ML systems become more complex and modular, with components performing one subtask pipelined with components solving another. Even if one module has representations that support systematicity, the system will be unable to demonstrate systematicity on the task if a non-systematic module intervenes before the output layer. One example of models ending up in this case (partially) as a result of dataset construction is illustrated in Wu et al. (2023), which we discuss below. As in the case above, distinguishing between these two interpretations requires mechanistic interpretability of the model's representations. Both are consistent with F&P's challenge.
+
+# 4 Behavioural Systematicity
+
+We propose that Hadley's taxonomy provides a robust framework for operationalising systematic generalization. It clearly defines the generalization capabilities of each level of systematicity, and establishes the requirements for testing it in a particular train/test data split. Below, we use it to examine representative datasets that test behavioural systematicity in end-to-end trained models. Rather than attempting an exhaustive review of this rapidly evolving field, we focus on key examples that demonstrate the critical importance of evaluating the level of systematicity required by a particular dataset. We hope that researchers will find this analysis useful and in turn apply it to their models and datasets.
+
+# 4.1 Linguistic Tasks
+
+SCAN, NACS Lake and Baroni (2018) introduce SCAN, a synthetic dataset for testing compositionality in text. It consists of all 20,910 command phrases generated from a non-recursive phrase-structure grammar of 13 words. Each command unambiguously maps onto a sequence of actions (for example, "jump opposite left and walk thrice" maps to "LTURN LTURN JUMP WALK WALK"). It aims to test compositionality via a judicious set of data splits: Split 1 is an iid (independent, identically distributed) split with up to  $99\%$  of the training datapoints withheld randomly. Split 2 tests a form of productivity by testing the network on phrases which map to longer action (output) sequences than any that occur in training. Split 3 asks the network to parse compositions with a held-out word that it had only ever seen in a primitive context before (e.g., parsing "run twice and jump" having only seen "run" as a primitive, but having also seen "look twice and jump" before).
+
+We suspect that Split 1 of SCAN tests Hadley's definition of weak systematicity. Lake and Baroni (2018) state that with even  $98\%$  of the training set for Split 1 withheld, every command in the test set that does not have a conjunction also appears in the training set an average of 8 times. Given that conjunction-less commands must also appear in conjunctions, it is likely that even  $2\%$  of Split 1 exhibits all possible commands in all possible positions. Split 2 tests productivity and thus requires at least quasi-systematicity<sup>4</sup>. Finally, Split 3 aims to test strong systematicity sans recursion. However,
+
+Bastings et al. (2018) argue that good performance on SCAN can be achieved with simple modelling tricks that require neither structured representations nor systematicity, demonstrating the difficulty of inferring anything about a model's representations based on the model's behaviour on the task.
+
+PCFG SET Hupkes et al. (2020) propose the PCFG SET dataset, an artificial translation task similar to SCAN. In this task, input sequences—generated by a probabilistic context-free grammar (PCFG) and corresponding to string edit operations—must be “translated” into output sequences representing the result of the sequence of operations. The authors propose several splits which aim to test various aspects of (their definition of) compositional generalization:
+
+The Systematicity split tests the model's ability to produce the correct output for a sequence of operations  $a$ $b$ , if it has not seen this (sub)sequence in the training dataset, but has seen  $a$  and  $b$  in other contexts. This split appears to test Hadley's weak systematicity. Although, unlike in SCAN, the PCFG SET grammar is recursive and therefore the dataset is non-exhaustive, it is likely that most operations will individually have been seen in most of the positions in which they will occur in the test dataset. This is because the parameters for constraining the length and recursive depth of the generated input-output pairs are the same for the train and test sets.
+
+The Productivity split involves training the model on sequences containing up to 8 operations, and testing it on sequences containing  $9+$  operations. As argued in Section 2.3, this split tests at least quasi-systematicity, and may contain some cases requiring strong systematic generalization.
+
+COGS, ReCOGS, SLOG Proposed by Kim and Linzen (2020) and extended by Wu et al. (2023) and Li et al. (2023a), the COGS family of datasets examines systematicity in a linguistic semantic parsing context. Directly specifying the meaning of a representation is challenging; instead, semantic parsing involves mapping sentences to logical forms (LFs). It does so under the assumption that the LFs can then be mapped to meanings more di
+
+directly (Wu et al., 2023). The task involves parsing multiple semantically-equivalent expressions into a (more) canonical semantic representation concerned with binding the semantic roles of events and actions to particular entities. Here, we discuss the original COGS dataset (Kim and Linzen, 2020), but our arguments apply equally to its variants.
+
+The dataset operationalises semantic parsing as a sequence-to-sequence problem. The model's task consists of predicting the LFs (as strings) for a large set of natural-language sentences. Systematicity is evaluated by testing the model on a generalization set, constructed by systematically altering the sentences in the training set. These manipulation include:
+
+- Novel pairings of primitives and syntactic roles (e.g., Subject  $\rightarrow$  Object and vice versa)  
+- Alternations of verb structure (e.g., “Charlie blessed Emma” → “Lina was blessed”)  
+- Inferences based on verb class, i.e., the semantic roles of a verb (e.g., "The cobra helped the dog"  $\rightarrow$  "The cobra froze")  
+- Deeper recursion than seen in training  
+- Object modifiers to subject modifiers (e.g., "Noah ate the cake on the plate"  $\rightarrow$  "The cake on the table burned")
+
+To the extent that the first three cases, termed "lexical generalization" in the paper, evaluate novel recombinations of familiar items and structures, and the fourth and fifth, termed "structural generalization", test the ability to process novel structures, all test cases require strong systematicity.
+
+The changes proposed by ReCOGS (Wu et al., 2023) illustrate the importance of the distinction between behavioural and representational systematicity. Compared to COGS, ReCOGS (1) removes irrelevant output tokens, (2) isolates the effects of length vs. depth generalization and (3) mitigates spurious correlations between syntactic position and variable indexing. None of these transformations alter the meanings of the LFs and, therefore, the nature of the capabilities which COGS purports to test; nevertheless, ReCOGS evokes much better performance on structural generalization from the same models evaluated in Kim and Linzen (2020). Thus, it is hard to draw any conclusions as to the true systematic generalization capabilities of any model evaluated on COGS, as any model's success
+
+or failure on COGS may be due to spurious and unintended effects of dataset construction, rather than the model's capability for systematic representation (see Csordás et al., 2021). We note that SLOG (Li et al., 2023a) incorporates the proposals of ReCOGS and adds 17 new systematic generalization cases, providing a compelling behavioural benchmark for strong systematicity.
+
+# 4.2 Visual Tasks
+
+In contrast to linguistic tasks, compositionality and systematicity in vision have only recently emerged as a focus of research. While perception is undoubtedly compositional—complex representations are made up of simpler percepts and relations between them—the nature of compositionality in perception is contested (see Lande, 2024). Furthermore, properties such as systematicity and productivity have not been clearly defined for visual perception and must not necessarily mirror their linguistic definitions (Cummins, 1996; Lande, 2024; Camp, 2007). Lacking a strong theory of the syntax of images, it is unclear how Hadley's levels of systematicity apply to visual concepts (see Cavanagh, 2021; Lande, 2021; Quilty-Dunn et al., 2023). Multiple datasets address these challenges by testing compositionality in computer vision through three distinct approaches.
+
+The first approach involves the disentanglement of generative variables. Here, the aim is to test whether a model can represent stimuli as a conjunction of several properties or variables which are conditionally-independent given the stimulus (Schott et al., 2022). Specifically, models are trained on compositionally constructed inputs to either directly predict the variables of the underlying generative model (Schott et al., 2022), classify composites of real-world images (Liao et al., 2023), or, given an input image  $I$ , produce an image  $I'$  which only differs with respect to a minimal change in the generative variables (e.g., exchange of colors between two objects while preserving their shape, size, and position) (Kim et al., 2023). These datasets can only test weak systematicity, as they (a) lack a hierarchical structure, precluding them from incorporating recursion, which is necessary for quasi-systematicity, and (b) do not require the models to make use of concepts in novel contexts (e.g., colour always relates to a shape's interior, never its outline).
+
+The second approach involves vision-based abstract reasoning tasks designed to evaluate con
+
+ceptual understanding rather than mere perceptual feature composition. Models must first infer the underlying invariants across images, and use this information to produce an appropriate response—e.g., identifying rule violations (Zerroug et al., 2022), choosing the right image from a candidate set (Zhang et al., 2019; Odouard and Mitchell, 2022), or generating rule-based solutions (Chollet, 2019; Moskvichev et al., 2023; Assouel et al., 2022). The RAVEN domain (Zhang et al., 2019) has no hierarchical structure, although Zerroug et al. (2022) make use of hierarchical rule compositions. The open-ended ARC domain (Chollet, 2019) allows for complex task structures as well as novel applications of concepts, but there is no systematic description of its construction process. Thus, ARC may constitute a test for strong compositionality but cannot be judged on an objective basis. Derivative works (Moskvichev et al., 2023; Assouel et al., 2022) give clearer task descriptions but still lack a rigorous control over the presentation of concepts in novel contexts, also making them unsuitable for testing strong systematicity.
+
+A third approach examines behavioural systematicity in vision-language models without committing to a theory of compositionality in vision, leveraging linguistic theories of systematicity to test their text component. However, they do not exhaustively manipulate the syntax of the image caption. Instead, they approximate it by placing novel atoms and compounds in various syntactic slots in the caption and test whether the model's behaviour is sensitive to such manipulations (e.g., Johnson et al., 2017; Thrush et al., 2022; Ma et al., 2023; Lewis et al., 2024). These approaches either test for weak systematicity (e.g., Johnson et al., 2017; Lewis et al., 2024) as they use indivisible objects and do not always change the contexts in which concepts are used, or can only be applied to pre-trained models (e.g., Thrush et al., 2022; Ma et al., 2023), making it impossible to judge the model's true generalization capabilities given unknown training exposure<sup>6</sup>.
+
+# 4.3 Evaluating Learning Trajectories
+
+Systematicity also relates to the speed of knowledge acquisition—a systematic learner should require training data that scales linearly with the number of concepts, whereas for a non-systematic learner this scaling should be exponential, assum-
+
+ing that the underlying grammar allows full permutations of concepts. A compositional representation should also allow faster skill acquisition as learning a new task will not require a reconfiguration of the encoding space. Okawa et al. (2023) examine convergence rates of diffusion models, finding that the number of training steps required to learn new concepts indeed scales exponentially with Hamming distance in conceptual space. Thomm et al. (2024) also find a super-linear scaling in an algorithmic task requiring Transformer models to map input strings to the outputs of compositional algorithms.
+
+# 5 Representational Systematicity
+
+To recap, investigating a model's representations allows us to reason about the model's performance on behavioural tests of systematicity, even in light of imperfect operationalisation<sup>7</sup>. Mechanistic interpretability provides evidence towards compositional, if not explicitly systematic, representations. This includes how predictions are built through a model (nostalgebraist, 2020); how information can be routed, copied, and deleted through a network (Elhage et al., 2021); how a kind of compressed sensing can be used to allow models to represent efficiently (Elhage et al., 2022); and the tension between representational compression versus the flexibility of full compositionality (Olah, 2023). In examining trained models for systematic representations, most work takes the approach of "concept discovery", i.e., looking for the presence and use of a specific concept in a model's activations (Sharkey et al., 2025).
+
+# 5.1 Evidence for
+
+Tenney et al. (2019a,b) uses linear probing to identify the presence of linguistic concepts that might be used in systematic representations. Having received much attention in recent years, this approach has been applied to the discovery of circuits responsible for algorithmic computation (Bricken et al., 2023; Huben et al., 2024; Park et al., 2024).
+
+Li et al. (2023b) and Nanda et al. (2023) use probing to argue that a Transformer trained on the game Othello learns a 'world model'—a systematic representation of the rules and dynamics of the
+
+game that is used to plan the next move<sup>8</sup>.
+
+Todd et al. (2024) and Merullo et al. (2024) go further, extracting components (specifically, 'function vectors') of a trained network that can be recombined in other contexts to produce predictable output (cf. Opielka et al., 2025).
+
+Finally, Feng and Steinhardt (2024) and Feng et al. (2025) discover 'binding vectors' that sufficiently large LLMs use to bind entities. These can be used to encode propositions in linguistic tasks. Whilst their experiment does not test for systematicity (propositions are subject-verb-object, but verbs are such that subject and object cannot be swapped), it does propose a possible mechanism for systematicity in LLMs.
+
+# 5.2 Evidence Against
+
+Much of the evidence against systematic representations can be summed up in a critique of probing, both linear and non-linear. Specifically, the ability to decode a given property from a model's representations does not guarantee that the model causally relies on this property (Belinkov, 2022; Sharkey et al., 2025). Indeed, the property may be decoded from the representations even if it is uncorrelated to task performance or distributed in the input data as random noise (Ravichander et al., 2021).
+
+Vafa et al. (2024) suggest that world models learned by Transformers on several tasks are "far less coherent than they appear". For example, they train a Transformer on a dataset of taxi journeys in Manhattan, requiring it to output a valid sequence of turns from an origin to a destination. They demonstrate that the Transformer does not learn a consistent world model despite excellent next-token prediction performance. The model learns a number of fictitious and impossible road connections; consequently, when the model is made to detour from its chosen route, the proportion of valid routes generated decreases dramatically.
+
+Furthermore, Aljaafari et al. (2025) show that models do not represent words and phrases as systematic compositions of tokens. Instead, these representations are spread across attention heads and layers. Finally, even when (weakly) systematic representations can be detected, they are not always used. Kobayashi et al. (2024) train a vanilla Transformer model on a task that involves systematic recombination of latent variables for a regression task. The model learns to generalize on in-distribution
+
+tasks, and the vector of underlying latent variables can be decoded from its activations. However, the model does not use this knowledge when faced with OOD tasks, and therefore fails. The Transformer is only able to systematically generalize to OOD tasks when augmented with an additional hypernetwork that explicitly takes the decoded latent vector as input.
+
+Overall, there is mixed evidence for the use of systematic representations in Transformer models. While systematic representations can at times be extracted or elicited from the model, they also frequently resort to non-systematic tricks and shortcuts to achieve performance. This may be due to the conflict between efficient data encoding and the development of fully systematic representations (Olah, 2023). Furthermore, even when models do learn apparently systematic representations, it is difficult to ascertain to what extent they use them on OOD tasks.
+
+# 6 Takeaways for Machine Learning
+
+Compositionality is rapidly emerging as a key empirical factor of strong, robust and interpretable generalization behaviour in ML systems. However, the study of compositionality draws on a rich theoretical foundation spanning diverse approaches to syntax and semantics. As a result, two definitions of compositionality rooted in different frameworks may have little in common when applied to modelling and prediction. As the volume of research on compositionality in ML systems increases, it is crucial to maintain clear definitions of the phenomena in question. In this work, we have focused on Fodor and Pylyshyn definition, but other definitions are certainly possible. We urge researchers to engage with existing literature and situate their definition in the context of previous work, enabling the field to make fair comparisons amongst the multitude of datasets, methods and models.
+
+While many researchers reference F&P's seminal work, they frequently overlook the fact that F&P define compositionality through systematicity, specifically systematicity of representations rather than behaviour. This is a crucial distinction, as behavioural systematicity does not necessitate the presence of systematic representations. A model might achieve strong performance on systematicity benchmarks through mechanisms that do not involve systematic internal representations, such as memorization or task-specific heuristics.
+
+There is evidence that this is already the case—Sun et al. (2023) show that different compositional generalization datasets rank the same modelling approaches differently while purporting to test the same capability. To address this issue, researchers should be explicit about their focus on behavioural systematicity, representational systematicity, or both. Those claiming to address F&P's challenge must demonstrate the presence or absence of systematic representations, while those working on behavioural measures should justify why their operationalisation of systematicity is valid.
+
+When examining systematicity through Hadley's framework of weak, quasi-, and strong systematicity, we find that many current benchmarks fall short of testing strong systematicity—the level that most closely approximates human systematic generalization capabilities. Many datasets inadvertently test only for weak or quasi-systematicity, limiting our ability to assess whether artificial systems can achieve human-like systematic processing. Future benchmark development should explicitly target strong systematicity, with careful consideration of the theoretical requirements for such evaluation. Li et al. (2023a) is an example of such a benchmark. However, strong systematicity is difficult to test for in large-scale pre-trained models, as we are blind to what they see during training. Consequently, claims of strong behavioural systematicity may need to be limited to custom trained models.
+
+Above all, the emergence of mechanistic interpretability techniques offers promising approaches for investigating representational systematicity. Recent work on function vectors and binding mechanisms suggests that some neural networks may indeed have mechanisms required for systematicity, though often in unexpected ways. However, many studies conflate the discovery of interpretable components with proof of systematic processing—the mere presence of decomposable representations does not guarantee they are used systematically, nor that the discovered mechanisms are causally responsible for the model's systematic behaviour.
+
+In sum, it is representations, not task performance, that drive generalization. Until we develop principled methods for controlling training distributions and validating representational mechanisms, the quest for strongly systematic learners will remain stifled by the opacity of existing models. Despite the challenges, we believe that rigorous assessments of representational systematicity are well worth the effort.
+
+# 7 Limitations
+
+This paper discusses systematicity, an important facet of compositionality, and how it is currently tested across ML literature. Limitations of the paper include the following:
+
+- We concentrate on clarifying the definition of one facet of compositionality, i.e. systematicity. In future work, more aspects of compositionality should be treated in the same manner.  
+- We have discussed widely used benchmarks in the literature to highlight the points we are making about common practices in ML, rather than an exhaustive summary of all literature.  
+- The benchmarks we have discussed tend to be somewhat based in English, and our analysis has focussed on monolingual English models. Multilingual models may have different generalization abilities.  
+- Our current analysis primarily assumes phrase structure grammar frameworks, but different theoretical perspectives on syntax may uncover additional dimensions of systematicity that warrant further investigation. Therefore, a full treatment of systematicity under alternative syntactic theories such as tree-adjoining grammars (Joshi, 2005), construction grammar (Goldberg, 1995), or combinatory categorial grammar (Steadman, 2019) represents an important direction for future work.
+
+# 8 Ethics
+
+As a survey paper, there is limited ethical impact of the form of bias in datasets or environmental impact of training. As mentioned above, we do concentrate on benchmarks and tasks phrased in English, which may have an impact on the conclusions we draw. However, overall, we feel that our emphasis on thorough testing of claims of systematicity, and call for behavioural systematicity to be backed up by representational systematicity, should have a positive ethical effect in pushing for the development of more reliable and predictable models.
+
+# Acknowledgements
+
+IV, SdS, ML, and LD gratefully acknowledge travel and collaboration funds (RIS International Collaboration Grant) from Research Innovation Scotland. SdS, VF, and ML gratefully acknowledge
+
+the opportunity to build this collaboration at the SFI Working Group: Representations in Minds and Artificial Systems at the Santa Fe Institute. IV and SdS acknowledge that this work was supported in part by the UKRI Centre for Doctoral Training in Natural Language Processing, funded by the UKRI (grant EP/S022481/1) and the University of Edinburgh, School of Informatics and School of Philosophy, Psychology & Language Sciences.
+
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+# Behind Closed Words: Creating and Investigating the forePLay Annotated Dataset for PolishErotic Discourse
+
+Warning: This paper contains examples of sexually explicit material
+
+Anna Kołos\*, Katarzyna Lorenc\*, Emilia Wiśnios\*, Agieszka Karlińska
+
+$^{1}$  NASK National Research Institute
+
+$^{2}$  Independent Researcher
+
+* Equal Contribution
+
+# Abstract
+
+The surge in online content has created an urgent demand for robust detection systems, especially in non-English contexts where current tools demonstrate significant limitations. We introduce forePLay, a novel Polish-language dataset for erotic content detection, comprising over 24,000 annotated sentences. The dataset features a multidimensional taxonomy that captures ambiguity, violence, and socially unacceptable behaviors. Our comprehensive evaluation demonstrates that specialized Polish language models achieve superior performance compared to multilingual alternatives, with transformer-based architectures showing particular strength in handling imbalanced categories. The dataset and accompanying analysis establish essential frameworks for developing linguistically-aware content moderation systems, while highlighting critical considerations for extending such capabilities to morphologically complex languages. $^{1}$
+
+# 1 Introduction
+
+The rapid growth of user-generated content online has created an urgent need for effective tools to detect and moderate harmful and inappropriate material. Traditional methods, such as manual review by editors or flagging by users, often fall short due to the sheer volume of content published daily. As a result, there has been an increasing reliance on automated solutions powered by advanced language models and natural language processing techniques.
+
+Securing large language models (LLMs) against the generation of harmful content is another critical concern (Mahomed et al., 2024; Wu et al., 2024). While traditional content moderation tools are useful for user-generated content, they are less effective as input/output guardrails for LLMs due to
+
+their inability to adapt to new policies and distinguish between user-generated and AI-generated content (Inan et al., 2023). As a result, there is a growing need for datasets and specialized tools that can be integrated with LLMs to prevent the generation of explicit or harmful material, while maintaining their functionality across different applications.
+
+While much of the previous work has focused on detecting toxicity, abusiveness, offensive language, or hate speech (Pavlopoulos et al., 2020; Gehman et al., 2020; MacAvaney et al., 2019), these categories do not encompass the full spectrum of undesired content (Markov et al., 2023).Erotic material, in particular, poses a significant risk, especially to minors. Detecting such content is essential not only for creating a safer online environment but also for upholding ethical standards. Although the Digital Services Act (DSA) primarily addresses non-consensual pornography and age-verification requirements, many online platforms, particularly those targeting minors, enforce stricter moderation policies that extend beyond legal obligations. Some platforms may prohibit explicit erotica or any  $18+$  material, even when it does not violate the law. One application of this research is to support such platforms in enforcing their internal guidelines, which vary depending on the service and its target audience.
+
+Recent advances in deep learning have improved erotic content detection, but progress is hindered by the limited availability of training data, particularly open datasets. Existing tools are primarily designed for English-language content, limiting their effectiveness for other languages. This linguistic bias highlights the need for language-specific datasets and models that can capture the subtle semantic variations inherent in the expression of erotic content in different languages. Moreover, many existing datasets rely on overly simplified binary classification schemes, which fail to capture
+
+the complexities of erotic content, further limiting detection systems' effectiveness in diverse cultural and linguistic contexts.
+
+To address these gaps, we introduce fore-PLay, the first Polish language manually annotated dataset of erotic content. In contrast to prior efforts, we present a novel multidimensional taxonomy applied to a large Polish language corpus ( $n = 24,768$ ), incorporating fine-grained annotations across ambiguity, violence, and social unacceptability dimensions, while ensuring representation of LGBT-specific content from both literary and web-based sources. The corpus is constructed from user-generated content sourced from online fiction repositories and professionally published Polish literary works, offering diverse linguistic and stylistic coverage. The article provides a detailed description of the annotation process and discusses the challenges encountered during annotation, in particular human label variation. A major contribution is also the comprehensive evaluation of erotic content detection models, examining specialized Polish transformer-based models (HerBERT (Mroczkowski et al., 2021) and Polish RoBERTa (Dadas, 2023)) and Polish-specific LLMs such as the PLLuM family<sup>2</sup> and Bielik (Ociepa et al., 2024). We also compare these models with state-of-the-art multilingual and general-purpose models, including both open-source (Mixtral (Jiang et al., 2024), Llama 3.1 (Dubey et al., 2024), and C4AI Command-R (CohereForAI, 2024)) and commercial solutions (GPT-4o (Hurst et al., 2024)).
+
+# 2 Related Work
+
+# 2.1 Existing Datasets
+
+Prior work has established several benchmark datasets for analyzing textual content with erotic themes, though these exhibit notable limitations in scope and annotation granularity. The most comprehensive corpus, Triplex, comprises 27,000 literary works totaling 1.62 billion tokens extracted from Archive of Our Own (Achour, 2016), while subsequent contributions include the erotic-books<sup>3</sup> corpus  $(n = 646)$  and the BeaverTails dataset containing a class of sexually explicit, adult content and developed for alignment research (Ji et al., 2023). Recent approaches to content analysis have
+
+leveraged large language models, as demonstrated in the erotica-analysis dataset $^{4}$  ( $n = 15,000$ ) utilizing GPT-3.5 for automated annotation. Various targeted datasets address binary classification of explicit content, including the Jigsaw corpus and its derivatives ( $n = 5,100$ ) (cjadams et al., 2019), though these typically employ simplified taxonomies. While specialized collections such as the sexting corpus $^{5}$  ( $n = 547$ ) examine specific discourse patterns, existing datasets predominantly focus on English-language content with binary classification schemes.
+
+# 2.2Erotic Content Detection
+
+Existing methodological approaches to erotic content detection span a broad spectrum of techniques, though their effectiveness is often constrained by the limitations of available training data. Early work relied on classical machine learning approaches, employing Support Vector Machines (SVM) and Random Forest classifiers trained on social media content (Barrientos et al., 2020), while simpler approaches utilized Naive Bayes classification for web page filtering (Hu et al., 2007). More recent neural approaches have demonstrated superior performance, as evidenced by Hierarchical Attention Networks applied to historical Latin texts  $(n = 2,500$  sentences), achieving significant improvements over token-based methods (Clerice, 2024). Contemporary research has increasingly leveraged large language models, as demonstrated by CENSORCHAT (Qiu et al., 2024), which employs knowledge distillation for monitoring dialogue systems. Advanced architectures combining semantic and statistical features through Convolutional Neural Networks (CNN) have shown promise (Wu and Hu, 2005). However, these approaches predominantly focus on English language content, limiting their applicability to other languages where linguistic nuances and cultural contexts play crucial roles in content interpretation.
+
+# 2.3 Content Moderation Systems
+
+One key application of erotic content detection datasets is content moderation, covering both user-generated and AI-generated material. Specialized systems like Llama Guard, a Llama2-7b safeguard model developed by Meta, use safety taxonomies
+
+to categorize prompts, including sexual content (Inan et al., 2023). However, comparative studies indicate that general-purpose LLMs, such as GPT-4o (Hurst et al., 2024) and Gemini 1.5 Pro (Team et al., 2024), often outperform these systems by achieving a better balance between false positives and false negatives (AlDahoul et al., 2024).
+
+Holistic approaches to content moderation, such as those proposed by Markov et al. (2023), combine careful taxonomy design, active learning, and lightweight transformer models. These methods excel in detecting rare harmful content, such as material involving minors. Similarly, the framework introduced by Wu et al. (2024) leverages conceptual features from LLM inference, achieving high accuracy for sexual content with minimal computational cost. However, their findings reveal that LLMs tend to self-censor compared to human-written text. Similar conclusions were drawn by Mahomed et al. (2024), whose evaluation of OpenAI's moderation systems highlights GPT models' fine-tuning to avoid generating sexual content.
+
+These findings highlight the challenges of building scalable, linguistically inclusive moderation frameworks, especially for nuanced categories like erotic material. Most current tools rely on English-centric training and evaluation pipelines (Markov et al., 2023). To address cultural and linguistic nuances, particularly in morphologically complex languages like Polish, language-specific detection strategies are essential.
+
+# 3 Data
+
+# 3.1 Data Collection
+
+We constructed a large-scale Polish language corpus ( $n = 24,768$  sentences) through systematic sampling from two distinct sources: (i) user-generated content from online fiction repositories and (ii) Polish literary works, including translations of world literature. The data collection was carried out by an interdisciplinary team consisting of literary scholars with extensive expertise in contemporary Polish literature, sociologists, NLP specialists, and IT engineers. The corpus comprises demographically diverse material drawn from 905 unique text units and includes a substantial, manually curated representation of LGBTQ+ narratives. This representation was ensured by selecting queer-themed literary texts—primarily original Polish works, supplemented by a smaller number of translated pieces—based on scholarly research and ex
+
+pertise in Polish queer literature. Document-level context is preserved through unique file identifiers. While direct URLs are omitted due to the volatility of online sources, our sampling methodology ensures broad coverage across linguistic registers and social contexts.
+
+Given the potential application of models in supporting moderation, we focused on internet language and amateur writing, which is predominantly anonymous. Consequently, a significant portion of the sentences (69%) originates from online stories. While the majority of these stories are erotic and non-professional, we included non-erotic stories in a 1:4 ratio to enhance diversity and reduce genre-specific biases. To filter erotic content, we relied on tags and category labels related to erotica provided by the online repositories. All non-professional stories were scraped from publicly available websites, see Appendix A for details.
+
+To avoid overfitting to specific individual writing styles, we limited the dataset to a maximum of two stories per author. Additionally, incorporating professional literary works with varying degrees of erotic themes (31%) aimed to further diversify linguistic patterns. When selecting these texts, availability in digital form was also a key criterion. A total of 22 different literary texts by Polish and international authors were included. This number is significantly lower than the count of unique text units for non-professional content. However, the literary texts were considerably longer, and finding works that met the established criteria proved challenging. Considering the overall proportion of professional works in the corpus, this number should be sufficient.
+
+# 3.2 Data Preprocessing
+
+Our text segmentation pipeline employs the NLTK library (Bird and Loper, 2004) for sentence boundary detection, which exhibits robust performance despite the inherent variability in web-sourced content quality. To maximize ecological validity, we preserved the original linguistic characteristics of the source material, including non-standard language patterns and orthographic variations, thereby enabling downstream models to generalize effectively to real-world applications.
+
+The corpus contained a total of 342,546 tokens, as counted using the NLTK tokenizer, with an average sentence length of 13.83 tokens (median 11.0, std 11.53). Detailed token statistics are presented in Table 1.
+
+<table><tr><td>Subcorpus</td><td>Mean</td><td>Std</td><td>25%</td><td>50%</td><td>75%</td></tr><tr><td>Total</td><td>13.83</td><td>11.53</td><td>7.0</td><td>11.00</td><td>17.00</td></tr><tr><td>Non-professional</td><td>12.43</td><td>10.32</td><td>6.0</td><td>10.00</td><td>16.00</td></tr><tr><td>Professional</td><td>16.90</td><td>13.31</td><td>9.0</td><td>14.00</td><td>21.00</td></tr></table>
+
+Table 1: Token Count Statistics
+
+Inconsistencies in text segmentation and discrepancies in automatically detected sentences arose from the fact that non-professional writers often did not use proper punctuation, making it challenging for the NLTK library to accurately identify sentence boundaries.
+
+# 4 Annotation Process
+
+To assemble the annotation team, three female annotators were allocated from our internal organization. To ensure gender balance, three part-time male annotators were recruited as external contractors. All selected annotators underwent training and guidance to maintain annotation consistency and quality throughout the project.
+
+This process resulted in a gender-balanced team of six annotators (3 male, 3 female), aged 20-40. We included annotators with backgrounds in linguistics, literature, or related fields to ensure sensitivity to language nuances. To minimize potential bias, the annotators were not provided with metadata that could link specific samples to genre types. Furthermore, samples from each genre type were distributed evenly among all annotators. Each sentence was independently assessed by three annotators. Final labels were determined by majority vote. In cases where all three labels differed (830 out of 24,768 samples, representing  $3.35\%$  of the total observations), a superannotator made the final decision. The superannotator, an NLP specialist and senior member of the annotation team, was responsible for overseeing consistency and quality throughout the annotation process. This role encompassed resolving disagreements among annotators, providing additional guidance, and conducting spot checks to ensure adherence to the defined guidelines.
+
+# 4.1 Annotation Scheme
+
+Based on the expert knowledge of the content, a set of five possible exclusive labels to annotate the samples was designed. This included the following categories: erotic (e), ambiguous (a), violence-related (v), socially unacceptable behaviors (u), and neutral (n). Some examples of the annotated text and
+
+its English translation are presented in Table 2.
+
+Sentences labeled as erotic typically describe sexual activities and desires, advanced flirting with evident erotic undertones, references to past sexual activities, or explicit sexual fantasies. However, it is important to note that mere mention of genital terms or publicly accepted romantic behaviors, such as kissing or holding hands, does not warrant classification as sexual. Similarly, descriptions of physiological processes or neutral discussions of erotic or sexual topics (e.g., from the psychological perspective) are excluded from this category and considered neutral.
+
+The violence-related category is reserved exclusively for sentences that include explicit sexual harassment, rape, lack of consent, or any other sort of non-consensual violence which concerns sexual intentions or activities. It is essential to distinguish consensual BDSM behaviors, as well as non-sexual acts of violence (based solely on the sentence-level analysis), as they do not fall under this category.
+
+The category of socially unacceptable behaviors includes sentences that describe sexual behaviors considered illegal, generally taboo, or violent of social norms, such as zoophilia, necrophilia, pedophilia, incest, and other sexual deviations. This category takes precedence over violence-related label, meaning that if a sentence could be classified as both socially unacceptable and violence-related, it should be categorized under socially unacceptable behaviors.
+
+Another label covers context-related sentences, which fall under the category of ambiguous samples. These sentences are identified based on the conviction that—given commonly recognized patterns of sexual descriptions—they evoke erotic or sexual connotations. However, in a neutral context, they could be interpreted as describing non-sexual behaviors or acts.
+
+Lastly, sentences that did not fall into any of the above-mentioned categories were labeled as neutral. On one hand, these typically include nonsexual content on any topic. On the other, this category also comprises general statements about human sexuality or intimate parts that do not typically evoke erotic associations. While such sentences may be sex-related, they are not defined as erotic.
+
+The annotation guidelines, developed by literary scholars and linguists based on domain expertise and material analysis, are described in detail in Appendix B.
+
+<table><tr><td>Original sentence in Polish</td><td>English translation</td><td>Label</td></tr><tr><td>&quot;Moj我省czyszna...&quot;—usłyszaLEM szept i zanim są zorientowalem zestamolem bez koszulki, a Ty siedzi-alaś naprzejcuw mnie, calujac zachłannie moje usta i blądźć dłonymi po torsie,lekko go drapiąc.</td><td>&quot;My man...&quot;—I heard a whisper and before I knew it I was left shirtless and you were sitting across from me, kissing my lips greedily and wandering your hands over my torso, lightly scratching it.</td><td>erotic</td></tr><tr><td>Być caly twardy.</td><td>He was all hard.</td><td>ambiguous</td></tr><tr><td>Ten gad ja zdradza!</td><td>This rat was cheating on her!</td><td>neutral</td></tr></table>
+
+Table 2: Examples of annotations in the dataset  
+
+<table><tr><td rowspan="2">Subcorpus</td><td colspan="5">Label Categories</td></tr><tr><td>Erotic</td><td>Ambiguous</td><td>Violence</td><td>Unacceptable</td><td>Neutral</td></tr><tr><td>Total</td><td>6,361</td><td>1,344</td><td>69</td><td>116</td><td>16,878</td></tr><tr><td>Non-professional</td><td>2,937</td><td>1,277</td><td>52</td><td>95</td><td>12,649</td></tr><tr><td>Professional</td><td>3,424</td><td>67</td><td>17</td><td>21</td><td>4,229</td></tr></table>
+
+Table 3: Distribution of Label Categories Across Dataset Subcorpora
+
+Following the completion of the superannotation process, the final dataset consists of two primary classes:  $68.14\%$  of the samples are labeled as neutral, and  $25.68\%$  as erotic. The remaining categories are minor, with  $5.43\%$  labeled as ambiguous,  $0.47\%$  as socially unacceptable behaviors, and  $0.28\%$  as violence-related. Distribution of labels across the subcorpora are presented in Table 3.
+
+The percentage of violence-related examples, as well as those representing socially unacceptable behaviors, was scarce, which was expected, as the data collection process did not specifically target texts exploring such themes. Additionally, while only  $15\%$  of the texts in the dataset were sourced from non-erotic stories, the randomization process employed to minimize bias resulted in the inclusion of neutral sentences even from texts classified as erotic, as these are not exclusive to non-erotic stories.
+
+# 4.2 Annotation Quality
+
+The process of quality evaluation revealed various challenges faced by the annotators, highlighting the demanding nature of the task. The designed labels were intended to be applied exclusively, meaning that each sample could only be categorized as either neutral, sex-related, or ambiguous. Within the sex-related category, overlaps were mitigated by a clear hierarchical structure. As previously mentioned, in cases where a sample exhibited characteristics of both violence and socially unacceptable behaviors, priority was given to the latter. All the other sex-related samples contributed to the erotic class.
+
+Due to the distinctiveness of rare cases of sexual violence and non-acceptable sexual behaviors, this aspect did not pose significant concerns. Annotators applied these two labels only incidentally, with individual frequencies ranging from  $0.2\%$  to  $0.6\%$ .
+
+Firstly, the annotation task itself—particularly given the wide range of non-normative language patterns found in non-professional short stories—was inherently subjective. Secondly, the prevalence of misspellings, controversial vocabulary, and grammatical errors, which diminished the clarity of the authors' intentions and made rational decision-making exceedingly difficult. Thirdly, the category of erotic sentences turned out to be extremely broad, spanning from evident and explicit samples, often including vulgar language, to much subtler erotic tones. Consequently, the ambiguous label, designed to account for context-related uncertainty, offered a means of resolving indecision between sexual and neutral classifications. This created a potential risk of overusing the ambiguous label as a way to mitigate uncertainty in borderline cases.
+
+Human label variation (HLV) (Plank, 2022), inherently present in our task of annotating erotic sentences, raised several questions regarding the dataset design (see the Section 7). To preserve the authenticity of the annotation process, we chose not to intervene beyond the initial training phase. For the dataset's initial release, we opted to follow the conventional practice of data aggregation featuring a ground truth.
+
+To guarantee annotation reliability, we calculated Cohen's Kappa for each pair of annotators across all categories. Furthermore, we evaluated inter-annotator agreement for each category individually. Detailed results are presented in Table 4.
+
+Agreement in most pairs was consistent, ranging from 0.66 to 0.71, regardless of annotators' gender. However, pairs involving annotator Fem1 presented a notable deviation, as Fem1 emerged as an outlier,
+
+<table><tr><td>Annotators</td><td>all</td><td>a</td><td>e</td><td>u</td><td>v</td></tr><tr><td>Fem1 / M1</td><td>0.1750</td><td>0.0532</td><td>0.3602</td><td>0.2545</td><td>0.1984</td></tr><tr><td>Fem1 / Fem2</td><td>0.1808</td><td>0.0370</td><td>0.3193</td><td>0.3952</td><td>0.2911</td></tr><tr><td>Fem1 / Fem3</td><td>0.1415</td><td>0.0151</td><td>0.2890</td><td>0.2740</td><td>0.2271</td></tr><tr><td>M1 / Fem2</td><td>0.7044</td><td>0.3505</td><td>0.7513</td><td>0.3728</td><td>0.4602</td></tr><tr><td>Fem2 / M2</td><td>0.6910</td><td>0.0833</td><td>0.7149</td><td>0.5074</td><td>0.1696</td></tr><tr><td>Fem2 / M3</td><td>0.6610</td><td>0.0037</td><td>0.6923</td><td>0.3973</td><td>0.3237</td></tr><tr><td>Fem2 / Fem3</td><td>0.7187</td><td>0.2683</td><td>0.7728</td><td>0.6718</td><td>0.4078</td></tr><tr><td>M2 / M3</td><td>0.7030</td><td>0.0368</td><td>0.7261</td><td>0.4191</td><td>0.2481</td></tr></table>
+
+Table 4: Cohen's Kappa values for each annotator pair across all categories and for each individual category, broken down by gender (Fem - female, M - male).
+
+largely due to an excessive use of the ambiguous label.
+
+In addition to pairwise agreement, the overall consistency of the entire sample was assessed using Krippendorff's Alpha. The value was quite low (0.387). However, after excluding the Fem1 annotation, which significantly deviated from the other annotators, the value increased to 0.716, indicating a satisfactory level of agreement in the annotation process.
+
+# 5 Experiments
+
+We utilize a diverse set of language models for erotic content detection, ranging from specialized Polish encoder-based models and developed Polish-specific LLMs to state-of-the-art commercial LLMs. This variety enables a comprehensive comparison across different model architectures and training methodologies. Additionally, the translated English prompt for the LLMs is included in the appendix on Figure 2.
+
+# 5.1 Datasets
+
+The original dataset consists of five distinct label categories, but due to significant class imbalance, additional experiments were conducted with modified label groupings as outlined below:
+
+- Basic: A binary classification setup where the dataset was reduced to two classes: neutral and erotic labels.  
+- Core: A three-class classification setup where the dataset included neutral, erotic, and ambiguous labels.  
+- Extended: A four-class classification setup that expanded the dataset to include neutral, erotic and ambiguous labels, with a merged category combining violence-related and socially unacceptable behaviors.
+
+- Full: The full dataset containing all five original categories.
+
+# 5.2 Specialized Polish Transformer-based Models
+
+Encoder-based models for Polish were selected based on the KLEJ Benchmark leaderboard (Rybak et al., 2020). Two top-performing models across multiple downstream tasks were chosen: HerBERT and Polish RoBERTa. HerBERT is a Polish-language adaptation of BERT, trained on a Polish corpus, while Polish RoBERTa is an optimized version featuring a unigram tokenizer, whole-word masking, and an expanded vocabulary of 128k entries. In our experiments, both models were fine-tuned on each dataset configuration (Basic, Core, Extended, Full).
+
+# 5.3 Polish Large Language Models
+
+Our evaluation framework encompasses three variants from the PLLuM (Polish Large Language Model) family: Llama-3.1-8B-PLLuM, PLLuM-Mistral-12B, and PLLuM-Mixtral-8x7B, adapted from their respective base architectures. These models underwent pre-training on 147B Polish language tokens and subsequent instruction tuning. We additionally employed Bielik 2.3, trained on 200B tokens and aligned using DPO-positive on 66,000 examples. To assess adaptation capabilities, we fine-tuned Llama-3.1-8B-PLLuM and PLLuM-Mistral-12B on our classification task. All base models were evaluated under 0-shot, 1-shot, and 5-shot configurations, while fine-tuned variants underwent standard supervised evaluation.
+
+# 5.4 State of the Art Large Language Models
+
+For comparison with LLMs fine-tuned strictly for Polish, we employed a selection of state-of-the-art multilingual and general-purpose models, including both open-sourced and commercial solutions. Among these, Mixtral, characterized by its modular and scalable architecture, was utilized in both the 8x22B and 8x7B configurations, alongside Mistral 12B, designed as a lightweight alternative. We also tested Llama 3.1 70B-Instruct and its smaller counterpart Llama 3.1 8B-Instruct, both fine-tuned for instruction-following tasks, as well as C4AI Command-R, developed for command-following applications. Additionally, we incorporated GPT-4o, frequently used for tasks requiring generalization across various domains.
+
+# 6 Results
+
+Table 5 highlights the macro-F1 performance metrics of the HerBERT and RoBERTa models across classification tasks involving different dataset configurations. In binary classification scenarios, both models exhibit robust performance. However, as the number of classes increases, a decline in macro-F1 scores is observed. Notably, RoBERTa, particularly in its Base configuration, demonstrates superior performance relative to HerBERT, with pronounced advantages evident in tasks on the Basic and Extended datasets.
+
+<table><tr><td rowspan="2">Dataset</td><td colspan="2">HerBERT</td><td colspan="2">RoBERTa</td></tr><tr><td>Base</td><td>Large</td><td>Base</td><td>Large</td></tr><tr><td>Basic</td><td>0.929</td><td>0.939</td><td>0.944</td><td>0.943</td></tr><tr><td>Core</td><td>0.702</td><td>0.738</td><td>0.738</td><td>0.748</td></tr><tr><td>Extended</td><td>0.693</td><td>0.746</td><td>0.704</td><td>0.734</td></tr><tr><td>Full</td><td>0.632</td><td>0.648</td><td>0.707</td><td>0.664</td></tr></table>
+
+Table 5: Macro-F1 scores for HerBERT and RoBERTa models across different dataset versions.
+
+In the case of LLMs, models from the PLLuM family consistently demonstrate strong performance across varying label counts and shot configurations, with particular emphasis on the PLLuM-Mixtral-8x7B, which achieves outstanding macro-F1 scores across a wide range of label counts, notably reaching 0.921 for Basic data and 0.670 for Core data in the 5-shot setting. Additionally Llama3.1-8B-PLLuM (SFT) and PLLuM-Mistral-12B (SFT) show significant improvements when subjected to supervised fine-tuning, resulting in enhanced performance, with the highest macro-F1 scores observed across various label counts.
+
+Fine-tuned LLMs exhibit performance levels comparable to traditional transformer-based architectures when evaluated on datasets labeled as Basic and Core, where all categories are sufficiently represented. This suggests that in scenarios characterized by balanced class distributions, where each class is supported by an adequate number of training examples, the performance differential between these methodological approaches is minimal. Conversely, for datasets labeled as Extended and Core, which are marked by pronounced class imbalance, models built upon the BERT architecture begin to demonstrate a distinct advantage. These models excel in effectively addressing the challenges posed by imbalanced data distributions, exhibiting superior capability in identifying underrepresented cate
+
+gories. This highlights their enhanced adaptability and robustness in handling more complex scenarios involving skewed training data distributions.
+
+In the context of multilingual models trained with a primary emphasis on the English language, the results are generally inferior compared to models specifically adapted for the Polish language. The performance varies depending on the configuration, including the number of labels and the number of shots, with different models excelling under different conditions. However, overall, the Mixtrals and GPT-40 models consistently yielded the most favorable results.
+
+The full results of all evaluated models—including the baseline models, the ones adapted to the Polish language from the PLLuM family, and the ones further fine-tuned on our dataset—are presented in Table 6. A detailed account of refusals and responses that could not be classified into any of the predefined categories is presented in Table 7. Among the evaluated models, Llama 3.1 8B-Instruct recorded the highest number of refusals, reaching a total of 848. In contrast, models that consistently provided clear and categorizable outputs included GPT-4o and Mixtral 8x22B, as well as those additionally fine-tuned on our dataset.
+
+# 7 Discussion
+
+The task of multi-dimensional eroticity annotation is highly complex and inherently subjective, necessitating further and more advanced reflection on the Human-Language Variation (HLV) framework, which has become an increasingly important open problem in recent years (Plank, 2022; Uma et al., 2021; Pavlick and Kwiatkowski, 2019). The researchers highlight the fact that disagreements in the annotation process should not be dismissed as mere noise in the search for a single ground truth. On the contrary, such disagreements can often reflect plausible alternative judgments, suggesting that these annotations may not always be categorical (De Marneffe et al., 2012). However, as demonstrated by our experience evaluating annotation quality, distinguishing between clear errors—where no plausible argument could justify the choice of a particular label—and alternative judgments is a critical issue that warrants deeper concern and further discussion. Within the context of erotic content detection, we believe it is valuable to advance current research by utilizing
+
+<table><tr><td rowspan="2">Model</td><td colspan="3">Basic</td><td colspan="3">Core</td><td colspan="3">Extended</td><td colspan="3">Full</td></tr><tr><td>0-shot</td><td>1-shot</td><td>5-shot</td><td>0-shot</td><td>1-shot</td><td>5-shot</td><td>0-shot</td><td>1-shot</td><td>5-shot</td><td>0-shot</td><td>1-shot</td><td>5-shot</td></tr><tr><td>GPT-4o</td><td>0.888</td><td>0.873</td><td>0.891</td><td>0.640</td><td>0.605</td><td>0.618</td><td>0.425</td><td>0.410</td><td>0.415</td><td>0.340</td><td>0.334</td><td>0.349</td></tr><tr><td>C4AI Command-R</td><td>0.684</td><td>0.730</td><td>0.714</td><td>0.420</td><td>0.486</td><td>0.454</td><td>0.322</td><td>0.374</td><td>0.363</td><td>0.257</td><td>0.292</td><td>0.299</td></tr><tr><td>Llama 3.1 8B-Instruct</td><td>0.789</td><td>0.736</td><td>0.709</td><td>0.562</td><td>0.517</td><td>0.514</td><td>0.388</td><td>0.364</td><td>0.378</td><td>0.325</td><td>0.283</td><td>0.316</td></tr><tr><td>Llama 3.1 70B-Instruct</td><td>0.837</td><td>0.845</td><td>0.846</td><td>0.595</td><td>0.641</td><td>0.630</td><td>0.396</td><td>0.417</td><td>0.408</td><td>0.329</td><td>0.344</td><td>0.364</td></tr><tr><td>Mistral 12B</td><td>0.872</td><td>0.847</td><td>0.862</td><td>0.58</td><td>0.579</td><td>0.610</td><td>0.423</td><td>0.411</td><td>0.42</td><td>0.354</td><td>0.349</td><td>0.338</td></tr><tr><td>Mixtral 8x7B</td><td>0.867</td><td>0.87</td><td>0.862</td><td>0.616</td><td>0.622</td><td>0.621</td><td>0.440</td><td>0.451</td><td>0.435</td><td>0.364</td><td>0.364</td><td>0.348</td></tr><tr><td>Mixtral 8x22B</td><td>0.872</td><td>0.854</td><td>0.833</td><td>0.633</td><td>0.642</td><td>0.610</td><td>0.424</td><td>0.440</td><td>0.406</td><td>0.335</td><td>0.361</td><td>0.344</td></tr><tr><td>Bielik-11B-v2.3-Instruct</td><td>0.848</td><td>0.858</td><td>0.868</td><td>0.601</td><td>0.597</td><td>0.607</td><td>0.427</td><td>0.416</td><td>0.423</td><td>0.312</td><td>0.437</td><td>0.48</td></tr><tr><td>PLLuM-Mistral-12B</td><td>0.894</td><td>0.842</td><td>0.844</td><td>0.656</td><td>0.610</td><td>0.613</td><td>0.456</td><td>0.441</td><td>0.427</td><td>0.401</td><td>0.359</td><td>0.401</td></tr><tr><td>PLLuM-Mixtral-8x7B</td><td>0.874</td><td>0.902</td><td>0.921</td><td>0.647</td><td>0.662</td><td>0.670</td><td>0.452</td><td>0.456</td><td>0.426</td><td>0.422</td><td>0.406</td><td>0.422</td></tr><tr><td>Llama-3.1-8B-PLLuM</td><td>0.641</td><td>0.737</td><td>0.709</td><td>0.425</td><td>0.446</td><td>0.425</td><td>0.301</td><td>0.324</td><td>0.326</td><td>0.314</td><td>0.274</td><td>0.273</td></tr><tr><td>PLLuM-Mistral-12B (SFT)</td><td></td><td>0.946</td><td></td><td></td><td>0.792</td><td></td><td></td><td>0.458</td><td></td><td></td><td>0.488</td><td></td></tr><tr><td>Llama-3.1-8B-PLLuM (SFT)</td><td></td><td>0.947</td><td></td><td></td><td>0.764</td><td></td><td></td><td>0.461</td><td></td><td></td><td>0.435</td><td></td></tr></table>
+
+Table 6: Macro-F1 scores for various models across different dataset configurations and shot numbers.  
+
+<table><tr><td rowspan="2">Model</td><td colspan="3">Basic</td><td colspan="3">Core</td><td colspan="3">Extended</td><td colspan="3">Full</td><td rowspan="2">Total</td></tr><tr><td>0-shot</td><td>1-shot</td><td>5-shot</td><td>0-shot</td><td>1-shot</td><td>5-shot</td><td>0-shot</td><td>1-shot</td><td>5-shot</td><td>0-shot</td><td>1-shot</td><td>5-shot</td></tr><tr><td>GPT-4o</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td></tr><tr><td>C4AI Command-R</td><td>9</td><td>2</td><td>14</td><td>9</td><td>5</td><td>10</td><td>7</td><td>1</td><td>9</td><td>4</td><td>1</td><td>14</td><td>95</td></tr><tr><td>Llama 3.1 8B-Instruct</td><td>42</td><td>150</td><td>12</td><td>38</td><td>99</td><td>14</td><td>134</td><td>62</td><td>8</td><td>66</td><td>208</td><td>15</td><td>848</td></tr><tr><td>Llama 3.1 70B-Instruct</td><td>8</td><td>0</td><td>0</td><td>33</td><td>0</td><td>0</td><td>46</td><td>0</td><td>0</td><td>49</td><td>0</td><td>0</td><td>136</td></tr><tr><td>Mistral 12B</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>1</td></tr><tr><td>Mixtral 8x7B</td><td>0</td><td>0</td><td>2</td><td>1</td><td>0</td><td>2</td><td>1</td><td>5</td><td>7</td><td>3</td><td>0</td><td>4</td><td>25</td></tr><tr><td>Mixtral 8x22B</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td></tr><tr><td>Bielik-11B-v2.3-Instruct</td><td>116</td><td>1</td><td>0</td><td>115</td><td>2</td><td>0</td><td>148</td><td>1</td><td>3</td><td>2</td><td>5</td><td>1</td><td>394</td></tr><tr><td>PLLuM-Mistral-12B</td><td>3</td><td>5</td><td>1</td><td>3</td><td>2</td><td>3</td><td>8</td><td>7</td><td>0</td><td>6</td><td>10</td><td>5</td><td>53</td></tr><tr><td>PLLuM-Mixtral-8x7B</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>2</td><td>0</td><td>0</td><td>2</td><td>0</td><td>1</td><td>2</td><td>8</td></tr><tr><td>Llama-3.1-8B-PLLuM</td><td>1</td><td>4</td><td>0</td><td>1</td><td>4</td><td>3</td><td>1</td><td>3</td><td>5</td><td>0</td><td>4</td><td>1</td><td>27</td></tr><tr><td>PLLuM-Mistral-12B (SFT)</td><td></td><td>0</td><td></td><td></td><td>0</td><td></td><td></td><td>0</td><td></td><td></td><td>0</td><td></td><td>0</td></tr><tr><td>Llama-3.1-8B-PLLuM (SFT)</td><td></td><td>0</td><td></td><td></td><td>0</td><td></td><td></td><td>0</td><td></td><td></td><td>0</td><td></td><td>0</td></tr></table>
+
+Table 7: Number of unidentified responses or refusals.
+
+datasets with multiple plausible labels and exploring the approach of Learning with Disagreements (LeWiDi) (Uma et al., 2021) or Multiple Ground Truth (Anand et al., 2024). This approach could offer more nuanced insights into the field by comparing the performance of models trained on aggregated annotations versus those trained on multiple possible labels.
+
+Our experimental results demonstrate clear performance patterns across model architectures and linguistic contexts, with specialized Polish language models consistently outperforming multilingual alternatives in erotic content detection. The encoder-based architectures, particularly RoBERTa, achieve robust macro-F1 scores in binary classification  $(0.929 - 0.944)$ , though performance degrades with increasing categorical complexity (dropping to  $\sim 0.66$  for five-class classi
+
+fication). This degradation pattern reveals fundamental challenges in maintaining discriminative power across finer-grained categorical distinctions, particularly in cases requiring subtle cultural and contextual understanding.
+
+The PLLuM family of models exhibits exceptional few-shot learning capabilities, with PLLuM-Mixtral-8x7B achieving macro-F1 scores of 0.921 in 5-shot settings for binary classification, while supervised fine-tuning of PLLuM-Mistral-12B yields the highest overall performance (macro-F1 = 0.946). However, the diminishing returns observed with increasing model size, coupled with the persistent challenge of handling ambiguous content in imbalanced datasets, suggests that architectural sophistication alone may not overcome the fundamental challenges of erotic content detection in morphologically complex languages. These
+
+![](images/5dbb1df9461b66842e9743e94731b8c9bdb1a9dad4ed2a8d1bb7d4811c0bfe37.jpg)  
+Figure 1: Type I errors percentage across datasets and inference settings. Error bars represent  $95\%$  confidence interval.
+
+findings underscore the importance of language-specific model development for sensitive content detection tasks, rather than relying solely on increasingly large multilingual models.
+
+Beyond overall performance metrics, understanding error patterns is crucial for content moderation deployment, where both false positives (over-censorship) and false negatives (missed inappropriate content) carry significant consequences. We calculated Type I error percentages as the number of false positives divided by the sum of false positives and false negatives to assess model precision across different classification scenarios. Full results regarding Type I and Type II errors for each model are presented in the Appendix D. The analysis reveals that Type I error rates decrease substantially with classification complexity—from approximately  $60 - 80\%$  in binary classification (Basic) to  $40 - 50\%$  in the full five-class scenario (Figure 1). This pattern indicates higher Type I error rates in simpler tasks and higher Type II rates in complex multi-class scenarios, highlighting the fundamental trade-off between precision and sensitivity in erotic content detection tasks.
+
+# 8 Conclusions
+
+This work presents forePLay, the first comprehensive Polish language dataset for erotic content detection, introducing a novel multidimensional taxonomy encompassing ambiguity, violence, and social acceptability dimensions. Through systematic empirical evaluation across multiple model architectures, our analysis demonstrates the superiority of specialized Polish language models over multilingual alternatives, particularly in handling nu
+
+anced categorical distinctions. The performance patterns observed in transformer-based architectures and few-shot learning scenarios provide valuable insights for developing language-specific content moderation systems. Our findings underscore the critical importance of culturally and linguistically adapted approaches in content detection tasks, while the presented dataset and evaluation framework establish essential groundwork for future research in multilingual content moderation systems, particularly for morphologically complex languages.
+
+# 9 Data Availability
+
+A subset of erotic and ambiguous sentences, totaling 3,704 samples, has been released on our public Github account. Due to ethical considerations, we opted to exclude the minor harmful classes of violence-related content and socially unacceptable behaviors. ForePLay Dataset Release 1.0 consists of 2,728 sentences labeled as erotic, and 976 sentences labeled as ambiguous, which corresponds to  $43\%$  and  $73\%$  of the original dataset, respectively. Neutral sentences were not included in this release, as such data is readily obtainable from publicly available corpora and may be easily used for comparative purposes in downstream tasks. This subset has undergone additional copyright verification and was made available following legal consultations. The released data and its license comply with new legal regulations that came into effect after the data collection and annotation process had been completed.
+
+# Limitations
+
+Our study reveals several important limitations that warrant discussion. While our dataset represents a significant contribution to Polish language resources, it exhibits sampling biases through its predominance of content from online fiction repositories (69%). This may not fully capture the linguistic diversity of erotic discourse across different domains and registers. The relative underrepresentation of professional literary works (31%) potentially limits our understanding of more sophisticated expressions of erotic content.
+
+A significant methodological limitation emerges from our binary approach to violence and socially unacceptable behaviors. The current taxonomy, while practical for annotation purposes, may over-simplify the complex spectrum of content severity
+
+and social acceptability. This simplification could impact the generalizability of our models to real-world content moderation scenarios where more nuanced distinctions are crucial.
+
+The annotation process presents limitations stemming from inherent subjectivity in erotic content interpretation. Despite achieving reasonable inter-annotator agreement (Krippendorff's Alpha of 0.716 after outlier removal), the significant variation in individual annotator interpretations—particularly evident in the use of the ambiguous category—suggests potential instability in ground truth labels.
+
+From a technical perspective, our evaluation framework primarily focuses on classification accuracy without deeply examining model behavior on edge cases or adversarial examples. While our study demonstrates the superiority of Polish-specific models over multilingual alternatives, we acknowledge limitations in comparing across model architectures with significantly different parameter counts and training regimes.
+
+Furthermore, a specific limitation pertaining to the evaluation phase is that the definitions of the labels were not explicitly included in the prompts provided to the models. We confirm this omission may have contributed to the lower performance of the models in comparison to the baseline.
+
+These limitations underscore the need for future work addressing dataset diversity, annotation methodology refinement, and more robust evaluation frameworks for erotic content detection systems.
+
+# Acknowledgements
+
+The development of the PLLuM models used in the experiments was funded by the Polish Minister of Digital Affairs under a special purpose subsidy No. 1/WI/DBiI/2023: Responsible Development of the Open Large Language Model, PLLuM (Polish Large Language Model), aimed at supporting breakthrough technologies in the public and economic sectors, including an open, Polish-language intelligent assistant for public administration clients. The work on the dataset, however, was conducted independently and was not financed by this project.
+
+# References
+
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+
+Nouar AlDahoul, Myles Joshua Toledo Tan, Harishwar Reddy Kasireddy, and Yasir Zaki. 2024. Advancing content moderation: Evaluating large language models for detecting sensitive content across text, images, and videos. Preprint, arXiv:2411.17123.  
+Abhishek Anand, Negar Mokhberian, Prathyusha Naresh Kumar, Anweasha Saha, Zihao He, Ashwin Rao, Fred Morstatter, and Kristina Lerman. 2024. Don't blame the data, blame the model: Understanding noise and bias when learning from subjective annotations. arXiv preprint arXiv:2403.04085.  
+Gonzalo Molpeceres Barrientos, Rocio Alaiz-Rodriguez, VICTOR GONZALEz-Castro, and Andrew C. Parnell. 2020. Machine learning techniques for the detection of inappropriate erotic content in text. International Journal of Computational Intelligence Systems, 13(1):591-603.  
+Steven Bird and Edward Loper. 2004. NLTK: The natural language toolkit. In Proceedings of the ACL Interactive Poster and Demonstration Sessions, pages 214-217, Barcelona, Spain. Association for Computational Linguistics.  
+cjadams, Daniel Borkan, inversion, Jeffrey Sorensen, Lucas Dixon, Lucy Vasserman, and nithum. 2019. Jigsaw unintended bias in toxicity classification. https://kaggle.com/competitions/jigsaw-unintended-bias-in-toxicity-classification. Kaggle.  
+Thibault Clerice. 2024. Detecting sexual content at the sentence level in first millennium Latin texts. In Proceedings of the 2024 Joint International Conference on Computational Linguistics, Language Resources and Evaluation (LREC-COLING 2024), pages 4772-4783, Torino, Italia. ELRA and ICCL.  
+CohereForAI. 2024. Command r+.  
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+
+Aaron Hurst, Adam Lerer, Adam P Goucher, Adam Perelman, Aditya Ramesh, Aidan Clark, AJ Ostrow, Akila Welihinda, Alan Hayes, Alec Radford, et al. 2024. Gpt-4o system card. arXiv preprint arXiv:2410.21276.  
+Hakan Inan, Kartikeya Upasani, Jianfeng Chi, Rashi Rungta, Krithika Iyer, Yuning Mao, Michael Tontchev, Qing Hu, Brian Fuller, Davide Testuggine, and Madian Khabsa. 2023. Llama guard: Llm-based input-output safeguard for human-ai conversations. Preprint, arXiv:2312.06674.  
+Jiaming Ji, Mickel Liu, Juntao Dai, Xuehai Pan, Chi Zhang, Ce Bian, Chi Zhang, Ruiyang Sun, Yizhou Wang, and Yaodong Yang. 2023. Beavertails: Towards improved safety alignment of llm via a human-preference dataset. arXiv preprint arXiv:2307.04657.  
+Albert Q. Jiang, Alexandre Sablayrolles, Antoine Roux, Arthur Mensch, Blanche Savary, Chris Bamford, Devendra Singh Chaplot, Diego de Las Casas, Emma Bou Hanna, Florian Bressand, Gianna Lengyel, Guillaume Bour, Guillaume Lample, L'elio Renard Lavaud, Lucile Saulnier, Marie-Anne Lachaux, Pierre Stock, Sandeep Subramanian, Sophia Yang, Szymon Antoniak, Teven Le Scao, Théophile Gervet, Thibaut Lavril, Thomas Wang, Timothée Lacroix, and William El Sayed. 2024. Mixtral of experts. ArXiv, abs/2401.04088.  
+Sean MacAvaney, Hao-Ren Yao, Eugene Yang, Katina Russell, Nazli Goharian, and Ophir Frieder. 2019. Hate speech detection: Challenges and solutions. PloS one, 14(8):e0221152.  
+Yaaseen Mahomed, Charlie M. Crawford, Sanjana Gautam, Sorelle A. Friedler, and Danae Metaxa. 2024. Auditing gpt's content moderation guardrails: Can chatgpt write your favorite tv show? In Proceedings of the 2024 ACM Conference on Fairness, Accountability, and Transparency, FAccT '24, page 660-686, New York, NY, USA. Association for Computing Machinery.  
+Todor Markov, Chong Zhang, Sandhini Agarwal, Tyna Eloundou, Teddy Lee, Steven Adler, Angela Jiang, and Lilian Weng. 2023. A holistic approach to undesired content detection in the real world. Preprint, arXiv:2208.03274.  
+Robert Mroczkowski, Piotr Rybak, Alina Wróblewska, and Ireneusz Gawlik. 2021. HerBERT: Efficiently pretrained transformer-based language model for Polish. In Proceedings of the 8th Workshop on Balto-Slavic Natural Language Processing, pages 1-10, Kiyv, Ukraine. Association for Computational Linguistics.  
+Krzysztof Ociepa, Łukasz Flis, Remigiusz Kinas, Adrian Gwoźciej, and Krzysztof Wróbel. 2024. Bielik: A family of large language models for the polish language - development, insights, and evaluation.
+
+Ellie Pavlick and Tom Kwiatkowski. 2019. Inherent disagreements in human textual inferences. Transactions of the Association for Computational Linguistics, 7:677-694.  
+John Pavlopoulos, Jeffrey Sorensen, Lucas Dixon, Nithum Thain, and Ion Androutsopoulos. 2020. Toxicity detection: Does context really matter? arXiv preprint arXiv:2006.00998.  
+Barbara Plank. 2022. The "problem" of human label variation: On ground truth in data, modeling and evaluation. In Proceedings of the 2022 Conference on Empirical Methods in Natural Language Processing, pages 10671-10682, Abu Dhabi, United Arab Emirates. Association for Computational Linguistics.  
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+
+# A Data Sources
+
+All non-professional stories were scraped from publicly available websites including:
+
+- opowiadaniaerotyczne-darmowo.com  
+- sexopowiadania.pl  
+- pornzone.com  
+- anonserek.pl  
+- opowi.pl (categories: o zyciu, roźne, milosne)  
+- opowiadania.pl  
+polki.pl
+
+# B Annotation Guidelines Summary
+
+This annotation task aims to create a manually annotated dataset for erotic content detection, enabling the development of automated detection methods and content moderation systems. These systems can assist models in identifying undesired content that may be potentially harmful. Each annotator is provided with a set of samples to label exclusively with one of the five predefined categories. The annotation process is conducted independently, meaning that annotators do not have access to the labels or work of other team members. For the purpose of this task, a sample is defined as a single sentence of varying length. The style and spelling of the sentences may vary significantly, and assessing the quality or correctness of the text is not part of the task.
+
+Annotators are instructed to carefully read each sentence and assign one final label to it. Each sentence was presented in isolation, without additional context. They are also encouraged to pause or discontinue the task at any point if they feel uncomfortable with the content being evaluated.
+
+Each sample should be exclusively assigned one of the following labels:
+
+- Label  $e$  (for erotic): choose this label if the sentence describes sexual activities and desires, advanced flirting with evident erotic undertones, references to past sexual activities, or explicit sexual fantasies.
+
+Please note that mere mentions of genital terms or publicly accepted romantic behaviors or neutral discussions of erotic or sexual topics (e.g., from the psychological perspective) are excluded from this category.
+
+- Label  $\nu$  (for violence-related): choose this label if the sentence depicts explicit sexual harassment, rape, lack of consent, or any other
+
+sort of non-consensual violence which concerns sexual intentions or activities.
+
+Please note that a sentence can include violence which is not sex-related. Such instances are excluded from this category. Consensual BDSM behaviors are likely to fall under the label erotic.
+
+- Label  $u$  (for socially unacceptable behaviors): choose this label if the sentence describes sexual behaviors considered illegal, generally taboo, or violent of social norms, such as zoophilia, necrophilia, pedophilia, incest, and other sexual deviations.  
+Please note that if you classify a sample as both violence related and featuring socially unacceptable behaviors, the priority should be given to the latter. Such instances should be labeled as socially unacceptable behaviors.  
+- Label  $a$  (for ambiguous): choose this label for sentences that may evoke some degree of erotic connotation but whose interpretation depends heavily on the context. If the sentence can reasonably be interpreted as non-erotic in a neutral context, it should be labeled as ambiguous.  
+- Label  $n$  (for neutral): choose this label if the sentence does not meet the criteria of the above mentioned sex-related categories. This typically includes non-sexual content on various topics, as well as general statements about human sexuality or intimate anatomy that do not carry erotic connotations.
+
+# C Prompt
+
+# Prompt Structure:
+
+You are a classifier, and your task is to analyze the text and assign one of the following labels:
+
+1. Neutral text  
+2.Erotic text  
+3. Ambiguous text  
+4. Socially unacceptable behavior text  
+5. Violence-related text
+
+Based on the text below, return the results in JSON format, which will contain the keys "Text" and "Prediction". The value in the "Prediction" field should contain only the name of the class.  
+Input text:
+
+Figure 2: Classification prompt template used for evaluating language models (translated into English).
+
+# D Analysis of Type I and Type II errors
+
+# D.1 Full
+
+<table><tr><td rowspan="2">Model</td><td colspan="2">Erotic</td><td colspan="2">Ambiguous</td><td colspan="2">Violence</td><td colspan="2">Unacceptable</td><td colspan="2">Neutral</td></tr><tr><td>Type I</td><td>Type II</td><td>Type I</td><td>Type II</td><td>Type I</td><td>Type II</td><td>Type I</td><td>Type II</td><td>Type I</td><td>Type II</td></tr><tr><td>HerBERT Base</td><td>44</td><td>42</td><td>29</td><td>39</td><td>2</td><td>4</td><td>0</td><td>2</td><td>58</td><td>46</td></tr><tr><td>HerBERT Large</td><td>55</td><td>38</td><td>18</td><td>47</td><td>0</td><td>4</td><td>0</td><td>8</td><td>62</td><td>38</td></tr><tr><td>RoBERTa Base</td><td>35</td><td>42</td><td>41</td><td>40</td><td>3</td><td>2</td><td>2</td><td>1</td><td>50</td><td>46</td></tr><tr><td>RoBERTa Large</td><td>39</td><td>41</td><td>27</td><td>41</td><td>10</td><td>2</td><td>0</td><td>3</td><td>51</td><td>40</td></tr><tr><td>0-shot</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>GPT-4o</td><td>97</td><td>26</td><td>14</td><td>72</td><td>32</td><td>3</td><td>228</td><td>7</td><td>1</td><td>266</td></tr><tr><td>C4AI Command-R</td><td>165</td><td>89</td><td>99</td><td>61</td><td>18</td><td>4</td><td>329</td><td>8</td><td>9</td><td>519</td></tr><tr><td>Llama 3.1 70B-Instruct</td><td>134</td><td>19</td><td>6</td><td>72</td><td>21</td><td>3</td><td>245</td><td>8</td><td>8</td><td>312</td></tr><tr><td>Mixtral 8x22B</td><td>91</td><td>73</td><td>12</td><td>72</td><td>43</td><td>2</td><td>244</td><td>5</td><td>14</td><td>252</td></tr><tr><td>Bielik-11B-v2.3-Instruct</td><td>260</td><td>10</td><td>6</td><td>72</td><td>29</td><td>2</td><td>144</td><td>7</td><td>0</td><td>348</td></tr><tr><td>PLLuM-Mistral-12B</td><td>55</td><td>108</td><td>34</td><td>70</td><td>11</td><td>1</td><td>50</td><td>8</td><td>104</td><td>64</td></tr><tr><td>PLLuM-Mixtral-8x7B</td><td>53</td><td>85</td><td>35</td><td>69</td><td>11</td><td>1</td><td>51</td><td>7</td><td>72</td><td>60</td></tr><tr><td>Llama-3.1-8B-PLLuM</td><td>5</td><td>238</td><td>1</td><td>72</td><td>2</td><td>3</td><td>7</td><td>8</td><td>312</td><td>6</td></tr><tr><td>PLLuM-Mistral-12B (SFT)</td><td>43</td><td>34</td><td>18</td><td>72</td><td>5</td><td>0</td><td>106</td><td>8</td><td>23</td><td>80</td></tr><tr><td>Llama-3.1-8B-PLLuM (SFT)</td><td>47</td><td>26</td><td>39</td><td>72</td><td>1</td><td>3</td><td>76</td><td>8</td><td>27</td><td>49</td></tr><tr><td>1-shot</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>GPT-4o</td><td>99</td><td>26</td><td>14</td><td>72</td><td>33</td><td>3</td><td>255</td><td>7</td><td>1</td><td>296</td></tr><tr><td>C4AI Command-R</td><td>237</td><td>30</td><td>4</td><td>71</td><td>18</td><td>4</td><td>143</td><td>8</td><td>31</td><td>320</td></tr><tr><td>Llama 3.1 70B-Instruct</td><td>83</td><td>50</td><td>15</td><td>72</td><td>21</td><td>3</td><td>250</td><td>6</td><td>8</td><td>246</td></tr><tr><td>Mixtral 8x22B</td><td>87</td><td>70</td><td>19</td><td>71</td><td>26</td><td>2</td><td>178</td><td>6</td><td>30</td><td>185</td></tr><tr><td>Bielik-11B-v2.3-Instruct</td><td>189</td><td>14</td><td>14</td><td>71</td><td>19</td><td>3</td><td>104</td><td>6</td><td>4</td><td>236</td></tr><tr><td>PLLuM-Mistral-12B</td><td>52</td><td>132</td><td>50</td><td>70</td><td>7</td><td>3</td><td>54</td><td>8</td><td>119</td><td>65</td></tr><tr><td>PLLuM-Mixtral-8x7B</td><td>66</td><td>100</td><td>63</td><td>67</td><td>8</td><td>2</td><td>90</td><td>6</td><td>64</td><td>109</td></tr><tr><td>Llama-3.1-8B-PLLuM</td><td>53</td><td>216</td><td>20</td><td>71</td><td>36</td><td>3</td><td>44</td><td>7</td><td>260</td><td>114</td></tr><tr><td>PLLuM-Mistral-12B (SFT)</td><td>35</td><td>52</td><td>34</td><td>70</td><td>7</td><td>1</td><td>102</td><td>8</td><td>23</td><td>65</td></tr><tr><td>Llama-3.1-8B-PLLuM (SFT)</td><td>65</td><td>24</td><td>38</td><td>72</td><td>1</td><td>3</td><td>68</td><td>8</td><td>28</td><td>62</td></tr><tr><td>5-shot</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>GPT-4o</td><td>90</td><td>34</td><td>26</td><td>72</td><td>43</td><td>1</td><td>231</td><td>8</td><td>1</td><td>276</td></tr><tr><td>C4AI Command-R</td><td>205</td><td>105</td><td>8</td><td>72</td><td>12</td><td>3</td><td>39</td><td>8</td><td>133</td><td>209</td></tr><tr><td>Llama 3.1 70B-Instruct</td><td>85</td><td>53</td><td>15</td><td>71</td><td>24</td><td>1</td><td>272</td><td>8</td><td>6</td><td>269</td></tr><tr><td>Mixtral 8x22B</td><td>142</td><td>48</td><td>16</td><td>72</td><td>33</td><td>2</td><td>154</td><td>5</td><td>17</td><td>233</td></tr><tr><td>Bielik-11B-v2.3-Instruct</td><td>172</td><td>19</td><td>7</td><td>72</td><td>24</td><td>2</td><td>138</td><td>6</td><td>1</td><td>239</td></tr><tr><td>PLLuM-Mistral-12B</td><td>55</td><td>108</td><td>34</td><td>70</td><td>11</td><td>1</td><td>50</td><td>8</td><td>104</td><td>64</td></tr><tr><td>PLLuM-Mixtral-8x7B</td><td>53</td><td>85</td><td>35</td><td>69</td><td>11</td><td>1</td><td>51</td><td>7</td><td>72</td><td>60</td></tr><tr><td>Llama-3.1-8B-MLuM</td><td>30</td><td>288</td><td>16</td><td>72</td><td>20</td><td>3</td><td>10</td><td>8</td><td>277</td><td>51</td></tr><tr><td>PLLuM-Mistral-12B (SFT)</td><td>43</td><td>34</td><td>18</td><td>72</td><td>5</td><td>0</td><td>106</td><td>8</td><td>23</td><td>80</td></tr><tr><td>Llama-3.1-8B-MLuM (SFT)</td><td>75</td><td>28</td><td>42</td><td>72</td><td>3</td><td>3</td><td>73</td><td>8</td><td>31</td><td>86</td></tr></table>
+
+Table 8: Detailed Type I and Type II error counts for various models for Full dataset type.
+
+# D.2 Extended
+
+<table><tr><td rowspan="2">Model</td><td colspan="2">Erotic</td><td colspan="2">Ambiguous</td><td colspan="2">Violence + Unacceptable</td><td colspan="2">Neutral</td></tr><tr><td>Type I</td><td>Type II</td><td>Type I</td><td>Type II</td><td>Type I</td><td>Type II</td><td>Type I</td><td>Type II</td></tr><tr><td>HerBERT Base</td><td>41</td><td>45</td><td>34</td><td>40</td><td>3</td><td>7</td><td>58</td><td>44</td></tr><tr><td>HerBERT Large</td><td>33</td><td>58</td><td>41</td><td>33</td><td>6</td><td>3</td><td>54</td><td>40</td></tr><tr><td>RoBERTa Base</td><td>45</td><td>49</td><td>38</td><td>42</td><td>8</td><td>2</td><td>48</td><td>51</td></tr><tr><td>RoBERTa Large</td><td>42</td><td>37</td><td>30</td><td>43</td><td>4</td><td>4</td><td>47</td><td>44</td></tr><tr><td>0-shot</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>GPT-4o</td><td>95</td><td>33</td><td>240</td><td>34</td><td>42</td><td>10</td><td>2</td><td>262</td></tr><tr><td>C4AI Command-R</td><td>75</td><td>216</td><td>26</td><td>71</td><td>9</td><td>11</td><td>265</td><td>76</td></tr><tr><td>Llama 3.1 70B-Instruct</td><td>75</td><td>101</td><td>220</td><td>34</td><td>22</td><td>9</td><td>59</td><td>232</td></tr><tr><td>Mixtral 8x22B</td><td>52</td><td>99</td><td>225</td><td>36</td><td>39</td><td>9</td><td>39</td><td>174</td></tr><tr><td>Bielik-11B-v2.3-Instruct</td><td>159</td><td>42</td><td>66</td><td>63</td><td>19</td><td>10</td><td>44</td><td>160</td></tr><tr><td>PLLuM-Mistral-12B</td><td>78</td><td>91</td><td>40</td><td>56</td><td>100</td><td>5</td><td>55</td><td>104</td></tr><tr><td>PLLuM-Mixtral-8x7B</td><td>116</td><td>44</td><td>62</td><td>39</td><td>43</td><td>9</td><td>26</td><td>112</td></tr><tr><td>Llama-3.1-8B-PLLuM</td><td>7</td><td>256</td><td>3</td><td>72</td><td>2</td><td>12</td><td>334</td><td>6</td></tr><tr><td>PLLuM-Mistral-12B (SFT)</td><td>31</td><td>47</td><td>68</td><td>12</td><td>16</td><td>12</td><td>42</td><td>37</td></tr><tr><td>Llama-3.1-8B-PLLuM (SFT)</td><td>58</td><td>24</td><td>73</td><td>36</td><td>10</td><td>12</td><td>28</td><td>49</td></tr><tr><td>1-shot</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>GPT-4o</td><td>117</td><td>28</td><td>241</td><td>37</td><td>44</td><td>10</td><td>1</td><td>293</td></tr><tr><td>C4AI Command-R</td><td>221</td><td>32</td><td>149</td><td>70</td><td>21</td><td>10</td><td>35</td><td>310</td></tr><tr><td>Llama 3.1 70B-Instruct</td><td>82</td><td>59</td><td>201</td><td>32</td><td>42</td><td>7</td><td>12</td><td>239</td></tr><tr><td>Mixtral 8x22B</td><td>87</td><td>66</td><td>166</td><td>43</td><td>80</td><td>7</td><td>27</td><td>185</td></tr><tr><td>Bielik-11B-v2.3-Instruct</td><td>194</td><td>27</td><td>95</td><td>64</td><td>35</td><td>9</td><td>6</td><td>213</td></tr><tr><td>PLLuM-Mistral-12B</td><td>56</td><td>105</td><td>39</td><td>65</td><td>56</td><td>5</td><td>93</td><td>55</td></tr><tr><td>PLLuM-Mixtral-8x7B</td><td>67</td><td>89</td><td>96</td><td>42</td><td>56</td><td>7</td><td>56</td><td>102</td></tr><tr><td>Llama-3.1-8B-PLLuM</td><td>60</td><td>208</td><td>65</td><td>71</td><td>32</td><td>11</td><td>255</td><td>120</td></tr><tr><td>PLLuM-Mistral-12B (SFT)</td><td>43</td><td>40</td><td>122</td><td>29</td><td>21</td><td>11</td><td>29</td><td>61</td></tr><tr><td>Llama-3.1-8B-PLLuM (SFT)</td><td>56</td><td>105</td><td>39</td><td>65</td><td>56</td><td>5</td><td>93</td><td>55</td></tr><tr><td>5-shot</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>GPT-4o</td><td>88</td><td>44</td><td>256</td><td>35</td><td>62</td><td>9</td><td>2</td><td>281</td></tr><tr><td>C4AI Command-R</td><td>193</td><td>110</td><td>70</td><td>33</td><td>20</td><td>8</td><td>136</td><td>225</td></tr><tr><td>Llama 3.1 70B-Instruct</td><td>85</td><td>52</td><td>272</td><td>31</td><td>48</td><td>7</td><td>8</td><td>258</td></tr><tr><td>Mixtral 8x22B</td><td>130</td><td>110</td><td>70</td><td>33</td><td>20</td><td>8</td><td>136</td><td>225</td></tr><tr><td>Bielik-11B-v2.3-Instruct</td><td>153</td><td>23</td><td>163</td><td>53</td><td>27</td><td>9</td><td>2</td><td>239</td></tr><tr><td>PLLuM-Mistral-12B</td><td>64</td><td>101</td><td>50</td><td>42</td><td>38</td><td>10</td><td>100</td><td>68</td></tr><tr><td>PLLuM-Mitral-8x7B</td><td>66</td><td>89</td><td>66</td><td>41</td><td>44</td><td>10</td><td>76</td><td>76</td></tr><tr><td>Llama-3.1-8B-PLLuM</td><td>19</td><td>237</td><td>24</td><td>68</td><td>25</td><td>10</td><td>296</td><td>36</td></tr><tr><td>PLLuM-Mistral-12B (SFT)</td><td>60</td><td>28</td><td>87</td><td>34</td><td>26</td><td>11</td><td>19</td><td>80</td></tr><tr><td>Llama-3.1-8B-PLLuM (SFT)</td><td>72</td><td>26</td><td>70</td><td>44</td><td>22</td><td>10</td><td>27</td><td>80</td></tr></table>
+
+Table 9: Detailed Type I and Type II error counts for various models for Extended dataset type.
+
+# D.3 Core
+
+<table><tr><td rowspan="2">Model</td><td colspan="2">Erotic</td><td colspan="2">Ambiguous</td><td colspan="2">Neutral</td></tr><tr><td>Type I</td><td>Type II</td><td>Type I</td><td>Type II</td><td>Type I</td><td>Type II</td></tr><tr><td>HerBERT Base</td><td>53</td><td>40</td><td>47</td><td>55</td><td>56</td><td>54</td></tr><tr><td>HerBERT Large</td><td>48</td><td>36</td><td>48</td><td>45</td><td>44</td><td>59</td></tr><tr><td>RoBERTa Base</td><td>37</td><td>46</td><td>46</td><td>46</td><td>62</td><td>51</td></tr><tr><td>RoBERTa Large</td><td>43</td><td>40</td><td>49</td><td>43</td><td>51</td><td>55</td></tr><tr><td>0-shot</td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>GPT-4o</td><td>74</td><td>25</td><td>301</td><td>23</td><td>1</td><td>279</td></tr><tr><td>C4AI Command-R</td><td>68</td><td>238</td><td>45</td><td>68</td><td>284</td><td>88</td></tr><tr><td>Llama 3.1 70B-Instruct</td><td>57</td><td>96</td><td>320</td><td>30</td><td>48</td><td>257</td></tr><tr><td>Mixtral 8x22B</td><td>58</td><td>90</td><td>241</td><td>30</td><td>35</td><td>172</td></tr><tr><td>Bielik-11B-v2.3-Instruct</td><td>142</td><td>21</td><td>109</td><td>59</td><td>20</td><td>178</td></tr><tr><td>PLLuM-Mistral-12B</td><td>87</td><td>39</td><td>98</td><td>52</td><td>36</td><td>110</td></tr><tr><td>PLLuM-Mixtral-8x7B</td><td>106</td><td>32</td><td>125</td><td>49</td><td>17</td><td>144</td></tr><tr><td>Llama-3.1-8B-PLLuM</td><td>10</td><td>239</td><td>8</td><td>72</td><td>305</td><td>12</td></tr><tr><td>PLLuM-Mistral-12B (SFT)</td><td>22</td><td>56</td><td>67</td><td>34</td><td>60</td><td>21</td></tr><tr><td>Llama-3.1-8B-PLLuM (SFT)</td><td>32</td><td>30</td><td>79</td><td>39</td><td>38</td><td>47</td></tr><tr><td>1-shot</td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>GPT-4o</td><td>95</td><td>21</td><td>327</td><td>28</td><td>0</td><td>329</td></tr><tr><td>C4AI Command-R</td><td>206</td><td>37</td><td>232</td><td>62</td><td>36</td><td>375</td></tr><tr><td>Llama 3.1 70B-Instruct</td><td>62</td><td>55</td><td>243</td><td>22</td><td>11</td><td>239</td></tr><tr><td>Mixtral 8x22B</td><td>79</td><td>61</td><td>229</td><td>31</td><td>18</td><td>193</td></tr><tr><td>Bielik-11B-v2.3-Instruct</td><td>140</td><td>19</td><td>181</td><td>52</td><td>2</td><td>232</td></tr><tr><td>PLLuM-Mistral-12B</td><td>89</td><td>57</td><td>86</td><td>60</td><td>67</td><td>113</td></tr><tr><td>PLLuM-Mixtral-8x7B</td><td>70</td><td>55</td><td>169</td><td>39</td><td>24</td><td>136</td></tr><tr><td>Llama-3.1-8B-PLLuM</td><td>72</td><td>197</td><td>92</td><td>69</td><td>232</td><td>127</td></tr><tr><td>PLLuM-Mistral-12B (SFT)</td><td>34</td><td>43</td><td>70</td><td>33</td><td>50</td><td>39</td></tr><tr><td>Llama-3.1-8B-PLLuM (SFT)</td><td>38</td><td>24</td><td>96</td><td>31</td><td>34</td><td>58</td></tr><tr><td>5-shot</td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>GPT-4o</td><td>88</td><td>29</td><td>303</td><td>29</td><td>0</td><td>290</td></tr><tr><td>C4AI Command-R</td><td>185</td><td>117</td><td>129</td><td>71</td><td>138</td><td>236</td></tr><tr><td>Llama 3.1 70B-Instruct</td><td>67</td><td>57</td><td>269</td><td>19</td><td>5</td><td>265</td></tr><tr><td>Mixtral 8x22B</td><td>105</td><td>37</td><td>253</td><td>41</td><td>16</td><td>243</td></tr><tr><td>Bielik-11B-v2.3-Instruct</td><td>106</td><td>31</td><td>240</td><td>44</td><td>1</td><td>244</td></tr><tr><td>PLLuM-Mistral-12B</td><td>102</td><td>54</td><td>62</td><td>62</td><td>67</td><td>97</td></tr><tr><td>PLLuM-Mixtral-8x7B</td><td>45</td><td>75</td><td>165</td><td>38</td><td>40</td><td>103</td></tr><tr><td>Llama-3.1-8B-PLLuM</td><td>24</td><td>247</td><td>43</td><td>69</td><td>290</td><td>38</td></tr><tr><td>PLLuM-Mistral-12B (SFT)</td><td>56</td><td>28</td><td>63</td><td>38</td><td>31</td><td>50</td></tr><tr><td>Llama-3.1-8B-PLLuM (SFT)</td><td>45</td><td>24</td><td>64</td><td>40</td><td>46</td><td>49</td></tr></table>
+
+Table 10: Detailed Type I and Type II error counts for various models for Core dataset type.
+
+# D.4 Basic
+
+<table><tr><td rowspan="2">Model</td><td colspan="2">Erotic</td><td colspan="2">Neutral</td></tr><tr><td>Type I</td><td>Type II</td><td>Type I</td><td>Type II</td></tr><tr><td>HerBERT Base</td><td>34</td><td>34</td><td>34</td><td>34</td></tr><tr><td>HerBERT Large</td><td>31</td><td>28</td><td>28</td><td>31</td></tr><tr><td>RoBERTa Base</td><td>31</td><td>23</td><td>23</td><td>31</td></tr><tr><td>RoBERTa Large</td><td>25</td><td>29</td><td>29</td><td>25</td></tr><tr><td>0-shot</td><td></td><td></td><td></td><td></td></tr><tr><td>GPT-4o</td><td>115</td><td>1</td><td>1</td><td>115</td></tr><tr><td>C4AI Command-R</td><td>76</td><td>191</td><td>191</td><td>76</td></tr><tr><td>Llama 3.1 70B-Instruct</td><td>152</td><td>19</td><td>19</td><td>152</td></tr><tr><td>Mixtral 8x22B</td><td>95</td><td>33</td><td>33</td><td>95</td></tr><tr><td>Bielik-11B-v2.3-Instruct</td><td>140</td><td>18</td><td>18</td><td>140</td></tr><tr><td>PLLuM-Mistral-12B</td><td>87</td><td>20</td><td>20</td><td>87</td></tr><tr><td>PLLuM-Mixtral-8x7B</td><td>127</td><td>4</td><td>4</td><td>127</td></tr><tr><td>Llama-3.1-8B-PLLuM</td><td>6</td><td>246</td><td>246</td><td>6</td></tr><tr><td>PLLuM-Mistral-12B (SFT)</td><td>17</td><td>34</td><td>34</td><td>17</td></tr><tr><td>Llama-3.1-8B-PLLuM (SFT)</td><td>31</td><td>20</td><td>20</td><td>31</td></tr><tr><td>1-shot</td><td></td><td></td><td></td><td></td></tr><tr><td>GPT-4o</td><td>132</td><td>1</td><td>1</td><td>132</td></tr><tr><td>C4AI Command-R</td><td>263</td><td>34</td><td>34</td><td>263</td></tr><tr><td>Llama 3.1 70B-Instruct</td><td>153</td><td>10</td><td>10</td><td>153</td></tr><tr><td>Mixtral 8x22B</td><td>134</td><td>18</td><td>18</td><td>134</td></tr><tr><td>Bielik-11B-v2.3-Instruct</td><td>149</td><td>1</td><td>1</td><td>149</td></tr><tr><td>PLLuM-Mistral-12B</td><td>127</td><td>35</td><td>35</td><td>127</td></tr><tr><td>PLLuM-Mixtral-8x7B</td><td>79</td><td>19</td><td>19</td><td>79</td></tr><tr><td>Llama-3.1-8B-PLLuM</td><td>76</td><td>156</td><td>156</td><td>76</td></tr><tr><td>PLLuM-Mistral-12B (SFT)</td><td>40</td><td>47</td><td>40</td><td></td></tr><tr><td>Llama-3.1-8B-PLLuM (SFT)</td><td>127</td><td>35</td><td>35</td><td>127</td></tr><tr><td>5-shot</td><td></td><td></td><td></td><td></td></tr><tr><td>GPT-4o</td><td>113</td><td>0</td><td>0</td><td>113</td></tr><tr><td>C4AI Command-R</td><td>199</td><td>96</td><td>96</td><td>199</td></tr><tr><td>Llama 3.1 70B-Instruct</td><td>159</td><td>4</td><td>4</td><td>159</td></tr><tr><td>Mixtral 8x22B</td><td>167</td><td>10</td><td>10</td><td>167</td></tr><tr><td>Bielik-11B-v2.3-Instruct</td><td>135</td><td>3</td><td>3</td><td>135</td></tr><tr><td>PLLuM-Mistral-12B</td><td>111</td><td>46</td><td>46</td><td>111</td></tr><tr><td>PLLuM-Mixtral-8x7B</td><td>44</td><td>32</td><td>32</td><td>44</td></tr><tr><td>Llama-3.1-8B-PLLuM</td><td>28</td><td>200</td><td>200</td><td>28</td></tr><tr><td>PLLuM-Mistral-12B (SFT)</td><td>73</td><td>15</td><td>15</td><td>73</td></tr><tr><td>Llama-3.1-8B-PLLuM (SFT)</td><td>43</td><td>17</td><td>17</td><td>43</td></tr></table>
+
+Table 11: Detailed Type I and Type II error counts for various models for Basic dataset type.
+
+# E Computational Details
+
+The details provided below correspond to the Full version of the dataset.
+
+The encoder-based models were trained for approximately 5 hours and 10 hours, respectively, for the Base and Large versions, using A100 (40GB) GPU with early stopping. The batch size was set to 8 for both model variants. Training of the PLLuM family models on our dataset took approximately 3 hours for the Llama-3.1-8B-PLLuM (SFT) model and 4 hours for the PLLuM-Mistral-12B (SFT) model. These models were trained on a distributed setup consisting of 2 nodes, each equipped with 4 H100 (96GB) GPUs, ensuring parallel processing across GPUs for enhanced training efficiency.

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ACL/2025/BelarusianGLUE_ Towards a Natural Language Understanding Benchmark for Belarusian/full.md

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+# BelarusianGLUE: Towards a Natural Language Understanding Benchmark for Belarusian
+
+Maksim Aparovich<sup>1</sup>, Volha Harytskaya<sup>2</sup>, Vladislav Poritski<sup>2</sup>, Oksana Volchek<sup>2</sup>, Pavel Smrz<sup>1</sup>
+
+<sup>1</sup> Brno University of Technology, Brno, Czech Republic
+
+$^{2}$  Independent researcher, Vilnius, Lithuania
+
+Correspondence: belarusianglue@gmail.com
+
+# Abstract
+
+In the epoch of multilingual large language models (LLMs), it is still challenging to evaluate the models' understanding of lower-resourced languages, which motivates further development of expert-crafted natural language understanding benchmarks. We introduce BelarusianGLUE — a natural language understanding benchmark for Belarusian, an East Slavic language, with  $\approx 15\mathrm{K}$  instances in five tasks: sentiment analysis, linguistic acceptability, word in context, Winograd schema challenge, textual entailment. A systematic evaluation of BERT models and LLMs against this novel benchmark reveals that both types of models approach human-level performance on easier tasks, such as sentiment analysis, but there is a significant gap in performance between machine and human on a harder task — Winograd schema challenge. We find the optimal choice of model type to be task-specific: e.g. BERT models underperform on textual entailment task but are competitive for linguistic acceptability. We release the datasets<sup>1</sup> and evaluation code.<sup>2</sup>
+
+# 1 Introduction
+
+Recent advances in NLP, such as large language models (LLMs) based on transformer architectures (Vaswani et al., 2017), have had groundbreaking impact on the field. LLMs are projected to bring significant economic effect in the future (Eloundou et al., 2023), however, in the first place it is anticipated to benefit the largest language communities, such as people speaking English or Chinese (Xie and Avila, 2024). For smaller language communities, especially those of vulnerable languages, state-of-the-art NLP tools may help preserve and promote the linguistic and cultural heritage (Mohanty et al., 2024), maybe even (under favorable
+
+circumstances) stimulate language revival, given that enough effort is put into improving the multilingual capabilities of LLMs. The case of Belarusian, an East Slavic language, illustrates this point.
+
+In the UNESCO World Atlas of Languages, Belarusian is characterized as "potentially vulnerable".<sup>3</sup> According to the 2019 population census data,  $54\%$  of the residents of Belarus consider Belarusian their native language but only  $26\%$  speak it at home.<sup>4</sup> Based on statistical analysis of the census data, it was argued that the true proportion of Belarusian-speaking residents of Belarus is in fact even lower (Sokolov, 2022). In an earlier study,  $4\%$  respondents in urban areas of Belarus claimed to be using standard Belarusian, possibly with some Russian words, as their primary language of communication, while  $41\%$  reported using substandard, mixed Belarusian-Russian varieties (Kittel et al., 2010). Despite its official status and symbolic importance, Belarusian is a de facto minority language in its home country (Zaprudski, 2007).
+
+To advance computational support of a particular language — such as Belarusian — in the epoch of LLMs, it is crucial to have (1) training data, (2) task-specific fine-tuning data, and (3) evaluation data for this language available in the open. In the case of Belarusian, as shown below, evaluation datasets are the most glaring omission; multilingual benchmarks that include tasks in Slavic languages, such as the recent EU-20 set of benchmarks (Thellmann et al., 2024), can only serve as a proxy indicator of the models' performance in Belarusian. To address this issue, we introduce BelarusianGLUE, the first natural language understanding benchmark for Belarusian, modeled after GLUE-type benchmarks for other languages. It includes five novel expert-crafted datasets.
+
+The rest of this paper is structured as follows. Section 2 is a review of existing datasets, containing Belarusian data, and natural language understanding benchmarks. Section 3 is a detailed description of BelarusianGLUE, its guiding principles and the datasets included. In section 4, we measure human performance on BelarusianGLUE and compare it with the performance of BERT models and LLMs. Discussion and conclusion follow.
+
+# 2 Related work
+
+# 2.1 Belarusian data in multilingual datasets
+
+Starting from (Buck et al., 2014), Belarusian texts are available in Common Crawl-based massively multilingual corpora: OSCAR (Ortiz Suárez et al., 2019), CC-100 (Conneau et al., 2020; Wenzek et al., 2020), mC4 (Xue et al., 2021), CulturaX (Nguyen et al., 2023), and HPLT (de Gibert et al., 2024) that also includes data from the Internet Archive's crawls. In each of the above, the amount of Belarusian texts ranges from several dozen million to several billion tokens, which is two-three orders of magnitude less than Russian, two orders less than Polish, one order less than Ukrainian, on par with e.g. Kazakh, Armenian, or Icelandic.
+
+Belarusian is not entirely lacking training data in other modalities than text: e.g. Common Voice (Ardila et al., 2020) includes 1873 hours of speech recordings in Belarusian, as of March 2025.
+
+The amount of task-specific data for Belarusian is smaller, and their quality is generally lower. As an example, consider machine translation. Among the parallel corpora available in OPUS (Tiedemann, 2012), the largest ones that include Belarusian data are NLLB (NLLB Team et al., 2022) derived from Common Crawl and ParaCrawl (Banon et al., 2020), bilingual HPLT and two other Common Crawl-based corpora: CCMatrix (Schwenk et al., 2021) and CCAIigned (El-Kishky et al., 2020). We labeled random samples of 100 Belarusian-English aligned sentence pairs from each corpus, following the taxonomy of Kreutzer et al. (2022), and found the ratios of natural, correctly translated sentences to be  $17\%$ ,  $41\%$ ,  $7\%$ , and  $31\%$  respectively in NLLB, HPLT, CCMatrix, and CCAIigned.
+
+Instruction tuning is another example. Upadhyay and Behzadan (2024) introduced a version of Alpaca-52K and Dolly-15K instruction tuning datasets machine-translated into 132 languages, in
+
+cluding Belarusian. Although the overall quality of the Belarusian translations is high, there is still some noise in translations of English-specific tasks, code snippets, rare words, etc.
+
+Evaluation datasets for Belarusian are scarce: available for some of the more traditional NLP tasks, such as POS tagging and dependency parsing, e.g. in Universal Dependencies (Shishkina and Lyashevskaya, 2022), but not available for most tasks related to natural language understanding, thus providing no guidance for future models supporting Belarusian. The situation has begun to improve only recently: e.g. the question-answering benchmark INCLUDE (Romanou et al., 2024) contains several hundred instances in Belarusian.
+
+# 2.2 GLUE-type benchmarks
+
+Language understanding benchmarks emerged as a way of assessing transformer models' capabilities to understand linguistic structure above the word level and apply this understanding in downstream tasks. The benchmarks are often based on pre-existing datasets and cover a wide range of tasks, from sentiment analysis to question answering and beyond. It is common to frame the tasks as classification, although other types of tasks, e.g. sequence tagging, may also be included in the benchmark.
+
+Most of the GLUE-type benchmarks created to date are monolingual. While the original GLUE and SuperGLUE focused on English (Wang et al., 2019a,b), their influence has since expanded through the development of benchmarks for many genetically and typologically diverse languages, such as Chinese (Xu et al., 2020), Arabic (Elmadany et al., 2022), or Hungarian (Ligeti-Nagy et al., 2024). Russian and Ukrainian, the two East Slavic languages most closely related to Belarusian, are covered by RussianSuperGLUE (Shavrina et al., 2020) and Eval-UA-tion (Hamotskyi et al., 2024) respectively; one more benchmark, MERA (Fenogenova et al., 2024), specifically targeting LLMs, has recently been proposed for Russian. Another neighboring and related language, Polish, has two comprehensive benchmarks: KLEJ (Rybak et al., 2020) and LEPISZCZE (Augustniak et al., 2022). Language understanding datasets have also been created for smaller Slavic languages, such as Bulgarian (Hardalov et al., 2023) or Slovene (Žagar and Robnik-Šikonja, 2022). Multilingual benchmarks XGLUE (Liang et al., 2020) and XTREMER (Ruder et al., 2021) include tasks for Slavic languages, however, Belarusian is missing from both.
+
+<table><tr><td rowspan="2">Dataset ID</td><td rowspan="2">Task</td><td rowspan="2">Instance type</td><td colspan="3">No. instances</td></tr><tr><td>train</td><td>dev</td><td>test</td></tr><tr><td>BeSLS</td><td>sentiment analysis</td><td>sentence</td><td>1500</td><td>250</td><td>250</td></tr><tr><td>BelaCoLA</td><td>acceptability prediction</td><td>sentence</td><td>1992</td><td>800</td><td>800</td></tr><tr><td>BeWiC</td><td>word sense disambiguation</td><td>word + sentence pair</td><td>5626</td><td>400</td><td>400</td></tr><tr><td>BeWSC</td><td>coreference resolution</td><td>sentence / sentence pair</td><td>570</td><td>200</td><td>200</td></tr><tr><td>BeRTE-WD</td><td>textual entailment</td><td>sentence pair</td><td>1080</td><td>360</td><td>360</td></tr></table>
+
+Table 1: Datasets summary.
+
+# 3 BelarusianGLUE
+
+BelarusianGLUE is a natural language understanding benchmark that includes five novel expert-crafted datasets (summarized in Table 1), with all tasks formulated as binary classification. Sample instances from each dataset are shown in Table 4 in Appendix A. All Belarusian examples below are given in romanized spelling.
+
+# 3.1 Guiding principles
+
+During the benchmark development we adhered to the following principles:
+
+- Prefer quality over size. The material was selected from representative sources for each dataset (see the descriptions below). When necessary to construct or label linguistic data in Belarusian, this was done by at least two fluent speakers of Belarusian with a background in linguistics (M.A. or Ph.D. degree). Each dataset was thoroughly reviewed.  
+- When possible, leverage existing resources. For example, Wikidata properties and labels in Belarusian were leveraged to build a textual entailment dataset, with careful attention given to gender and cultural balance (representation of women, Belarusian objects, etc.). Some of our datasets are modeled after similar resources in other languages: e.g., to construct the train set of a Belarusian Winograd schema challenge (WSC), English instances were translated, incorporating insights from the corresponding Russian dataset and adapting examples where needed. This approach minimized effort and maximized the quality and consistency of new datasets while respecting the unique characteristics of the target language.  
+- Take into account the specifics of Belarusian. While sampling linguistic data from various sources, we tried to reflect the variability of modern Belarusian language. E.g., the distribution of orthographic variants in the sentiment analysis dataset reflects the real-world diversity of written Belarusian: most sentences follow the official modern orthography (narkamaäka), some — less than  $10\%$  — use the classical orthography (taraskievica), and
+
+a tiny minority is written in Latin script (lacinka).
+
+- Embrace open licensing. While the sources are variously (and not always permissively) licensed, we made sure that none of the passages borrowed or derived from copyrighted work are longer than one sentence. We believe such use of copyrighted material for scholarly purposes to qualify under fair use or similar provisions in most legislations, thus allowing us to publish the novel datasets under an open license.
+
+# 3.2 Tasks
+
+# 3.2.1 Sentiment analysis
+
+BeSLS is a small dataset of sentiment-labeled Belarusian sentences, partially inspired by a similar English dataset from (Kotzias et al., 2015).
+
+Data sources: The sentences were sampled from newspaper articles, reviews posted by the users of online shopping and booking platforms, messages in thematic Telegram channels and other social media, such as Mastodon. Five domains are covered: movie reviews, book reviews, hotel and travel reviews, consumer product reviews, social media posts.
+
+Methodology of data selection and processing: In multilingual sources, non-Belarusian sentences were filtered out using Lingua. Following Petrović et al. (2010), we anonymized user mentions in Mastodon posts. The sentences were manually tagged for sentiment polarity using a two-stage approach: initial labeling by one expert followed by comprehensive review and refinement by another. This results in  $100\%$  agreement, as either both labelers agree on the label, or the instance is not included in the dataset.
+
+Dataset structure: The dataset contains 2000 sentences with positive or negative polarity. The classes are balanced:  $50\%$  positive and  $50\%$  negative, none of the sentences are neutral. Sentences are equally distributed over domains: 300 per domain in the train set, 50 in the dev and test sets.
+
+# 3.2.2 Linguistic acceptability
+
+BelaCoLA is a small-scale Belarusian corpus of linguistic acceptability, similar to CoLA (Warstadt et al., 2019) and RuCoLA (Mikhailov et al., 2022), with some inspiration also taken from BLiMP (Warstadt et al., 2020).
+
+Data sources: We used five major sources of data to create the corpus:
+
+1) sentences from Russian linguistic publications included in RuCoLA, manually translated into Belarusian and reviewed (we made sure to keep only instances with acceptability judgments transferable from the original Russian sentences to their Belarusian translations, due to deep similarities between Russian and Belarusian grammar);  
+2) contexts from Belarusian language textbooks and other normative sources;  
+3) sentences from the Belarusian section of Common Voice project, evaluated as unacceptable by speakers of Belarusian participating in the project;  
+4) passages produced by lightweight, non-state-of-the-art language models, i.e. hallucinations;  
+5) outputs of machine translation models.
+
+Methodology of data selection and processing: All unacceptable sentences in the corpus were taken from the sources "as is" or with minor simplifications. Unlike the original CoLA, they exemplify not only morphological, syntactic, and semantic violations, but also certain pragmatical anomalies, prescriptive rule violations, and errors produced by language models, such as hallucinations and machine translation errors, which don't always fall neatly into a single category. Their corresponding acceptable sentences were extracted from the sources (if available) or, more typically, constructed by the experts — three of the paper's authors. For example, a hallucinated sentence Jana navat zlohku zachvalavausia i vyjsaui 'She even got.3SG.M a little excited and left.3SG.M' is transformed to Jon navat zlohku zachvalavausia i vyjsaui 'He even got.3SG.M a little excited and left.3SG.M' by correcting the gender agreement.
+
+Dataset structure: The dataset contains 3592 sentences tagged as acceptable or unacceptable. The class balance is close to  $50:50$ . The sentences have been randomly shuffled. Sentences translated from Russian, extracted from Belarusian textbooks and Common Voice data constitute the in-domain set, split into train/dev/test sets. Hallucinations and machine translations constitute the out-of-domain set, split into dev/test sets.
+
+# 3.2.3 Word in context
+
+BeWiC is a Word-in-Context dataset for Belarusian, similar to the original WiC (Pilehvar and Camacho-Collados, 2019) and RUSSE (Shavrina et al., 2020, section 3.1.2). It can be viewed as a version of word sense disambiguation task.
+
+Data sources: The dataset is based on the Explanatory Dictionary of Belarusian (Thumačalny stoünik bietaruskaj movy, 1977-1984, vol. 1-5). While a newer dictionary exists (Thumačalny stoünik bietaruskaj litaraturnaj movy, 1996, revised 2022), our choice of the older source was deliberate based on several advantages: broader lexical coverage, machine-readable accessibility and, crucially, availability of illustrative contexts.
+
+Methodology of data selection and processing: For most words and word senses, the dictionary provides usage examples — phrases or sentences. To make each context one sentence long, we expanded phrases to full sentences by finding suitable contexts on the web or constructing them from scratch. E.g., the phrase abarvac spietyja jahady 'to pick ripe berries' was expanded to My abarvali spietyja jahady 'We've picked the ripe berries', and hruntouny adkaz 'a profound answer' to Hruntouny adkaz vučnia šciieszynastainika 'The student's profound answer made the teacher happy'.
+
+Each instance in the dataset is a pair of contexts  $c_1, c_2$  containing the target word  $w$ . The contexts refer either to the same word sense of  $w$  or to two different homonyms of  $w$ . An instance is positive if both  $c_1$  and  $c_2$  refer to the same word sense of  $w$ , and negative if  $c_1$  and  $c_2$  refer to two different homonyms of  $w$  (possibly belonging to different parts of speech), which are listed separately in the dictionary with their respective word senses. This is a stronger distinction than in WiC, so that less instances can be constructed from the dictionary data but they are easier to solve for humans and therefore don't require pruning.
+
+Dataset structure: The dataset contains 6426 instances. The dev and test sets contain 400 instances each, half of them positive and half negative. None of the sentences repeat across instances in the dev and test sets, and each target word is represented by  $\leq 3$  instances. The training set contains all positive and negative instances that can be constructed from the remaining sentences.
+
+# 3.2.4 Winograd schema challenge
+
+BeWSC is a Belarusian version of the Winograd schema challenge, WSC (Levesque et al., 2012).
+
+The dataset is available in two flavors: WSC proper, formatted as in SuperGLUE, and WNLI, formatted as in GLUE, i.e. converted into an NLI task. The number of instances and their (randomized) ordering are the same in both variants.
+
+Data sources: Most of the training instances have been manually translated into Belarusian from the standard English dataset, WSC-285<sup>8</sup>; when adaptation was not possible, we translated those items from the similar Russian dataset RWSD (Shavrina et al., 2020, section 3.1.4) that were created specifically to replace unsuitable English sentences. The dev and test instances are based on or inspired by contexts from fiction books in Belarusian, available on the web.
+
+Methodology of data selection and processing: Issues in English  $\rightarrow$  Belarusian translation of the training instances are typically caused by differences in grammar, such as the grammaticalization of gender in Belarusian, or the reflexive pronoun svoj, which is equivalent to English possessive pronouns in certain contexts but doesn't have ambiguous reference. In such cases, the sentences were adapted to maintain the overall meaning of the original while altering its grammatical structure and wording.
+
+The dev and test sentences were sampled (with modifications) from a corpus of Belarusian fiction books: we split the texts into sentences using sentence-splitter, added morphological tags using beltagger, extracted all sentences with a personal pronoun and at least two distinct nouns that precede it and have matching gender/number, then processed the output manually. These instances are intended to be hard to solve by selectional restrictions. Not all of them are Googleproof, as some sentences follow the source contexts rather closely.
+
+Dataset structure: The training set has 570 instances, the dev and test sets have 200 instances each. Half of the instances are positive (the antecedent is correct), and half negative.
+
+# 3.2.5 Textual entailment
+
+BeRTE-WD is a small-scale textual entailment dataset for Belarusian, derived from Wikidata.11
+
+Data sources: To produce the sentences, we
+
+extracted all statements from a June 2024 dump of Wikidata such that: (1) the property relates an entity to a timestamp, a number, or another entity; and (2) all entities in the statement, i.e. one or both, have Belarusian labels available.
+
+Methodology of data selection and processing: Each instance in the dataset is a pair of sentences in Belarusian, denoted "text"  $(t)$  and "hypothesis"  $(h)$ ;  $t$  is said to entail  $h$  if, typically, a human reading  $t$  would infer that  $h$  is most likely true (Dagan et al., 2006). Unlike many of the standard benchmarks, such as SNLI (Bowman et al., 2015), MNLI (Williams et al., 2018), or XNLI (Conneau et al., 2018), we don't distinguish between contradictory and neutral pairs, so the labels are binary: entailment or non-entailment.
+
+For each of the three value types, as described above, we manually sampled 200 diverse statements. Three fluent speakers of Belarusian then transformed the statements into texts and wrote two hypotheses per text: one entailed, one non-entailed. Additional texts and hypotheses were produced from the same statements grouped into pairs.
+
+The entailed hypotheses have at their core a wide range of phenomena, including but not limited to timestamp or numeric comparison, reasoning about time intervals, conversion of units, domain-specific or world knowledge, logical consequence, paraphrasing, etc. A non-entailed hypothesis is typically produced by modifying the entailed one to make its claim contrary or neutral w.r.t. the text.
+
+Dataset structure: The dataset contains 1800 instances. Train/dev/test split was obtained by grouping the statement pairs belonging to each value type into  $60:20:20$ , so that none of the source statements would overlap between the samples. The dataset is balanced by class (half of the instances entailed, half non-entailed) and by value type (equal counts of timestamps, numbers, and entities).
+
+# 3.3 Evaluation
+
+For BeSLS, BeWiC, BeWSC and BeRTE-WD, accuracy is reported. For BelaCoLA, Matthews correlation and accuracy are reported. Although there have been attempts to evaluate model performance on various datasets with a single metric, such as Krippendorff's alpha (Berdicevskis et al., 2023), or a unified set of metrics, such as accuracy, precision, recall, and F1 (Augustyniak et al., 2022), these choices are still not very popular, so we use the most common evaluation metric(s) for each dataset type, to ensure compatibility of our results with
+
+related work for other languages.
+
+# 4 Experiments
+
+# 4.1 Human baseline
+
+We evaluated human performance on each dataset for comparison with the performance of NLP models. The usual procedure, outlined e.g. in (Wang et al., 2019a, §5.2), involves recruiting paid crowdworkers, who are first provided with task-specific instructions, then asked to label a few dozen dev set instances as a pre-screening, and then proceed to annotate a sample of test set instances. Due to the low availability of crowdworkers fluent in Belarusian, we recruited unpaid volunteers from the language community and followed a simplified version of the above procedure. We wrote task-specific instructions including labeled examples from the train set (3 positive + 3 negative) and 5 self-check instances from the dev set. A random sample of 100 instances, balanced by class and certain other parameters (such as in-domain / out-of-domain in BelaCoLA, PoS of the target word in BeWiC, etc.), was then extracted from the test set and split into 5 groups of 20 instances with approximately the same balance of classes in each group. 5 volunteers, all of them competent and fluent speakers of Belarusian, were invited to tag the samples. Each volunteer tagged 20 instances per dataset, i.e. 100 instances in total, without overlaps (a single label obtained per instance). A balanced Latin square (Bradley, 1958) was used to reduce order effects while presenting the samples to volunteers.
+
+Human baseline scores are shown in Table 2. BeSLS gold labels are in near-perfect agreement with speaker judgments, while in all other datasets the agreement is around  $90\%$ . The human baseline in BelaCoLA is lower than in other tasks but this difference in scores isn't statistically significant, given the sample size. It might reflect the unique linguistic situation of Belarusian with two codified standards (narkamauka and taraškievica), so that even competent speakers show variation in grammatical form usage.
+
+<table><tr><td>Dataset</td><td>Metric</td><td>Score</td></tr><tr><td>BeSLS</td><td>acc</td><td>0.99</td></tr><tr><td>BelaCoLA</td><td>acc / MCC</td><td>0.87 / 0.754</td></tr><tr><td>BeWiC</td><td>acc</td><td>0.91</td></tr><tr><td>BeWSC</td><td>acc</td><td>0.91</td></tr><tr><td>BeRTE-WD</td><td>acc</td><td>0.89</td></tr></table>
+
+Table 2: Human baseline scores.
+
+# 4.2 BERT baselines
+
+We fine-tuned mBERT (Devlin et al., 2019), XLM-R base (Conneau et al., 2020), mDeBERTa-v3 (He et al., 2023) and a recent monolingual model — Belarusian HPLT BERT (Samuel et al., 2023; de Gibert et al., 2024) on each of the five training sets separately. All tasks were formulated as binary classification: in particular, BeWSC was presented in WNLI format, i.e. as a sentence pair classification task. Evaluation scores for BelaCoLA indomain and out-of-domain instances were calculated separately. The models were fine-tuned for 5 epochs with learning rate 2e-5, batch size 16 on a single GeForce RTX 4090 GPU. Snapshots were saved once per epoch, and the best snapshot for evaluation was selected by the dev set accuracy.
+
+The results are shown in Table 3. Since mDeBERTa-v3 has the strongest overall performance, we experimented with additional pretraining of this model on Belarusian texts from HPLT 1.2 (deduplicated version<sup>12</sup> with custom filtering applied), adjusting the script published by the model authors.<sup>13</sup> This brought some more performance gains. Further experiments are targeting this enhanced version of mDeBERTa-v3.
+
+With the size of our training datasets ranging between several hundred and a few thousand instances, it may be beneficial to freeze a subset of the model's layers while training the classifier on top of it (Grießhaber et al., 2020). We tried progressively freezing the layers of mDeBERTa-v3 during fine-tuning: only the embeddings or 3, 6, 9, 12 layers in addition to the embeddings. As shown in Table 3, the model's performance on BelaCoLA and BeWiC goes up but is sensitive to the number of layers frozen: in particular, prediction quality drops abruptly when all layers are frozen and only the classification head is trained. Also, freezing layers doesn't help to beat the trivial baseline on BeWSC and BeRTE-WD.
+
+We also tried transfer learning by mixing our training data with instances from larger datasets:
+
+- Sentiment analysis: all positive and negative instances no longer than 500 characters with self-confidence score at least 0.7 were taken from the train folds of MMS (Augustniak et al., 2023) for all languages in it. The classes were balanced per
+
+<table><tr><td>Model</td><td>Dataset: Metric:</td><td>BeSLS acc</td><td>BelaCoLA i.d. acc / MCC</td><td>BelaCoLA o.o.d. acc / MCC</td><td>BeWiC acc</td><td>BeWSC acc</td><td>BeRTE-WD acc</td></tr><tr><td>mBERT</td><td></td><td>0.712</td><td>0.490 / -0.029</td><td>0.510 / 0.029</td><td>0.515</td><td>0.500</td><td>0.517</td></tr><tr><td>XLM-R</td><td></td><td>0.816</td><td>0.510 / 0.033</td><td>0.506 / 0.019</td><td>0.500</td><td>0.500</td><td>0.503</td></tr><tr><td>HPLT BERT be mDeBERTa-v3:</td><td></td><td>0.912</td><td>0.480 / -0.048</td><td>0.576 / 0.167</td><td>0.575</td><td>0.495</td><td>0.506</td></tr><tr><td rowspan="2">Original With pre-train</td><td>no layers</td><td>0.892</td><td>0.623 / 0.260</td><td>0.742 / 0.488</td><td>0.613</td><td>0.500</td><td>0.511</td></tr><tr><td>only emb.</td><td>0.928</td><td>0.610 / 0.234</td><td>0.826 / 0.666</td><td>0.678</td><td>0.500</td><td>0.522</td></tr><tr><td rowspan="4">Frozen:</td><td>emb. + 3</td><td>0.916</td><td>0.640 / 0.297</td><td>0.828 / 0.666</td><td>0.685</td><td>0.500</td><td>0.514</td></tr><tr><td>emb. + 6</td><td>0.924</td><td>0.633 / 0.322</td><td>0.772 / 0.570</td><td>0.690</td><td>0.500</td><td>0.517</td></tr><tr><td>emb. + 9</td><td>0.916</td><td>0.657 / 0.362</td><td>0.788 / 0.590</td><td>0.710</td><td>0.490</td><td>0.494</td></tr><tr><td>emb. + 12</td><td>0.508</td><td>0.547 / 0.221</td><td>0.628 / 0.369</td><td>0.510</td><td>0.500</td><td>0.500</td></tr><tr><td rowspan="3">With pre-train &amp; transfer</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>no layers</td><td>0.904</td><td>0.693 / 0.425</td><td>0.802 / 0.622</td><td>0.745</td><td>0.650</td><td>0.633</td></tr><tr><td>only emb.</td><td>0.896</td><td>0.717 / 0.461</td><td>0.822 / 0.661</td><td>0.760</td><td>0.500</td><td>0.661</td></tr><tr><td rowspan="4">Frozen:</td><td>emb. + 3</td><td>0.916</td><td>0.720 / 0.449</td><td>0.830 / 0.677</td><td>0.768</td><td>0.500</td><td>0.664</td></tr><tr><td>emb. + 6</td><td>0.896</td><td>0.743 / 0.502</td><td>0.838 / 0.688</td><td>0.773</td><td>0.500</td><td>0.619</td></tr><tr><td>emb. + 9</td><td>0.920</td><td>0.707 / 0.454</td><td>0.826 / 0.671</td><td>0.748</td><td>0.600</td><td>0.600</td></tr><tr><td>emb. + 12</td><td>0.848</td><td>0.637 / 0.348</td><td>0.730 / 0.480</td><td>0.510</td><td>0.515</td><td>0.494</td></tr></table>
+
+Table 3: Results of BERT model fine-tuning.
+
+language by subsampling the larger class. Together with the BeSLS data, there are  $\approx 970\mathrm{K}$  instances.
+
+- Linguistic acceptability: all train and dev instances were taken from MELA v1.0 (Zhang et al., 2024), as well as Dutch  $\mathrm{COLA}^{14}$  and HuCOLA (Ligeti-Nagy et al., 2024). Positive instances were subsampled to maintain the class balance. Together with the BelaCoLA data, there are  $\approx 42\mathrm{K}$  instances.  
+- Word in context: all train and dev instances were taken from XL-WiC (Raganato et al., 2020) and RUSSE (Shavrina et al., 2020, section 3.1.2). Negative instances in RUSSE were subsampled to maintain the class balance. Together with the BeWiC data, there are  $\approx 145\mathrm{K}$  instances.  
+- Winograd schema challenge: all training instances were taken from WinoGrande (Sakaguchi et al., 2021) and XWINO (Tikhonov and Ryabinin, 2021), and all German, French, Russian instances — from the folder lm_wino_x of Wino-X (Emelin and Sennrich, 2021). To deal with three different formats in the data, we brought all instances to WNLI structure by constructing the hypotheses automatically from the original sentences: the pronoun or the _ sign is replaced with one of the two coreference candidate spans, and the label is 1 with the correct candidate and 0 otherwise. Note this is a very crude procedure, so that in morphologically richer languages it often produces ungrammatical (although comprehensible) sentences. Together with the BeWSC data, there are  $\approx 110\mathrm{K}$  instances.  
+- Textual entailment: all instances in the folds
+
+dev_MATCHed and dev_mismatched were taken from MNLI (Williams et al., 2018), and all dev instances — from XNLI (Conneau et al., 2018). Since there are three balanced classes (entailment / neutral / contradiction), we subsampled half of the neutral / contradictory instances to represent non-entailment. Together with the BeRTE-WD data, there are  $\approx 40\mathrm{K}$  instances.
+
+Transfer learning allows to beat the trivial baseline on BeWSC and BeRTE-WD (see Table 3). Improvement is also observed in other datasets.
+
+# 4.3 LLM baselines
+
+We added configurations for BelarusianGLUE tasks to a fork of lm-evaluation-harness (Gao et al., 2024). Four types of prompts are examined:
+
+- instructions in Belarusian, zero-shot or few-shot (11 instances, the same as those provided to humans to establish their baseline performance);  
+- instructions in English, zero-shot or few-shot (first 10 instances in the dev set of each dataset).
+
+Predictions are estimated from log probabilities of the tokens  $0 / 1$  to follow the target instance.
+
+We measured the performance of local LLMs below 15B parameters on BelarusianGLUE. Among recent (as of December 2024) models and model families with multilingual capabilities, we evaluated Llama 3.1 and 3.2 (Dubey et al., 2024), Phi 3 and 3.5 (Abdin et al., 2024), Gemma 2 (Riviere et al., 2024), Qwen 2 and 2.5 (Yang et al., 2024), Mistral Nemo and Ministral (Jiang et al., 2023), Aya 23 8B (Aryabumi et al., 2024). Additionally we tested several models that demonstrate state
+
+![](images/3e5671f868255bb0c6453c5cd9a707a86c8025a2170833e4a9b8b95123190abc.jpg)  
+Figure 1: Local LLM size vs. accuracy on BelarusianGLUE. Each point represents a single evaluation run against a local LLM with prompt in Belarusian (blue) or English (red), zero-shot (circle marks) or few-shot (triangle marks). Scores  $\leq 0.5$  are not shown. Dotted lines are human scores and the best BERT model scores on each dataset respectively. Dashed line is the Pareto front of optimal LLM performance at given size.
+
+of-the-art performance for Ukrainian and Russian: Sherlock (Boros et al., 2024) and Vikhr (Nikolich et al., 2024), based on various versions of Llama and Mistral, — as well as several older multilingual models: XGLM-7.5B (Lin et al., 2022), mGPT-13B (Shliazhko et al., 2023), BLOOM (Scao et al., 2023) and BLOOMZ (Muennighoff et al., 2023) up to 7B parameters.
+
+Our evaluation of state-of-the-art commercial models was less systematic: we tested GPT-4o and Claude 3.5 Sonnet, but, since their APIs don't support sampling log probabilities for the tokens specified in advance (such as  $\emptyset / 1$ ), we only checked for exact match. This may understate the true performance of these models in comparison with the local models. Due to Claude's tendency to include reasoning in its outputs, an additional post-processing step was required to extract predictions.
+
+Full evaluation results are available in the Tables 6-9 in Appendix B. Among the local LLMs below 15B parameters, Gemma 2 9B is the top competitor, in line with the findings of Thellmann et al. (2024). When a model beats the trivial baseline of  $50\%$  accuracy, its few-shot scores tend to be better than zero-shot ones, while the impact of prompting language, Belarusian or English, isn't as clear and varies between datasets.
+
+Figure 1 visualizes the dependency between model size and its scores. Larger models gener
+
+ally perform better, although the Pareto fronts show that the relation isn't linear. Both in zero-shot and in few-shot setting, LLMs outperform supervised BERT baselines on BeSLS and, most impressively, BeRTE-WD, which may be a sign of inherently stronger reasoning capabilities. In other tasks, the supervised baselines are closer to the human level.
+
+Additionally, we tried fine-tuning Gemma 2 9B with  $\mathrm{PEFT^{15}}$  on each of the five training sets separately. LoRA adapters were trained in 4-bit precision for 10 epochs with learning rate 2e-4, batch size 64 on a single GPU. Snapshots were saved once per epoch, and the best snapshot was selected by the dev set loss. As shown in Table 5 in Appendix B, this brings some improvements, especially in BeWiC and BeRTE-WD, although there doesn't seem to be any consistent pattern.
+
+Overall, the highest scores were observed for commercial models with Belarusian prompts. While both GPT-4o and Claude perform well with Belarusian prompts in the zero-shot setting, their behavior diverges with in-context examples. GPT-4o maintains consistent performance with Belarusian prompts and shows improvements in certain tasks with the English ones. Claude 3.5 Sonnet tends to provide reasoning, when prompted in Belarusian, and shows weaker performance on BeWSC with in-context examples.
+
+# 5 Discussion
+
+Our findings indicate that a traditional GLUE-type benchmark for a lower-resourced language (Belarusian) may still be challenging for the current generation of LLMs. This offers a complementary perspective to Fenogenova et al. (2024) who assess the benchmarks existing for a related high-resource language (Russian) to be not challenging enough.
+
+Unlike Rybak et al. (2020), we find that a multilingual pretrained BERT model, such as mDeBERTa-v3, is able to outperform a more narrowly focused, monolingual model, such as Belarusian HPLT BERT, possibly due to more advanced architecture or larger scale of the pre-training data.
+
+Our results support the conventional wisdom that the model size is not the only factor that affects the down-stream performance (Hardalov et al., 2023).
+
+# 6 Conclusion
+
+We have introduced BelarusianGLUE and measured how BERT models and LLMs perform on this novel benchmark, as compared with human performance. The easiest dataset, BeSLS, is mostly solved, although some of the instances in it are challenging even for state-of-the-art commercial LLMs: they are struggling to correctly classify instances with implied positivity that relies on domain knowledge or complex pragmatics. For the hardest dataset, BeWSC, there is still a significant gap in performance between human and machine. To obtain higher scores from the LLMs, further prompting tweaks may be required.
+
+We release the datasets<sup>16</sup> and evaluation code.<sup>17</sup>
+
+In the future, we may want to expand the benchmark by adding a diagnostic dataset (present in many of the GLUE-type benchmarks); a perplexity dataset for evaluating generative capabilities of multilingual LLMs, applied to Belarusian; a culture-specific QA dataset that would be hard for the current generation of LLMs but reasonably easy for the native speakers, etc. Converting all datasets to the alternative Belarusian orthographies, taraskievica and lacinka, may help understand how the model performance on Belarusian language tasks depends on the choice of orthography. Following the common practice, we may want to create a leaderboard to automate evaluation of new models on BelarusianGLUE. For the cutting-edge reasoning models, not covered in our evaluation, it
+
+remains to be investigated how the token budget (Wang et al., 2024) affects performance. Finally, the analysis of model errors is also a promising direction of further research.
+
+# Acknowledgments
+
+This work was supported by the Technology Agency of the Czech Republic under the project FactDeMice - Fact Verification Based on Textual Evidence Using Fact-Consistent Translation, Fake Review Detection, and Automatic Extraction of Misleading Claims (Project Code: TQ16000028).
+
+# Limitations and ethical considerations
+
+As of yet, we haven't been able to train strong baseline models based on mT5 architecture (Xue et al., 2021) for our datasets, although state-of-the-art performance was reported for similar English datasets, such as WinoGrande (Sakaguchi et al., 2021).
+
+Dataset usage is affected by the political situation in Belarus. Due to sheer amount of sources officially recognized as "extremist materials" by Belarusian courts,[18] we cannot guarantee that BelarusianGLUE is legally safe to use in Belarus — or will be safe in the future, as the list of "extremist materials" is being regularly updated.
+
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+
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+
+# A Sample instances
+
+<table><tr><td>Dataset ID</td><td>Instance</td><td>Label</td></tr><tr><td>BeSLS</td><td>Nie razumieju, Čamu niedaku niè spadabalasia kniha.‘I don’t understand why someone didn’t like the book.’Stolki pafasu, a na vychadzie adzin pšyk.‘So much pathos, and nothing at the end.’</td><td>10</td></tr><tr><td>BelaCoLA</td><td>Aleš zaúvažyǔ na drevie niedvycjajnych ptušak.‘Aleš noticed unusual birds on the tree.’Jany lčyli jaho talenavitymi.‘They considered him talented.PL.’</td><td>10</td></tr><tr><td>BeWiC</td><td>U spravazdačnym dakladzie starvjynia zviarnuš uvahu na šerah važnych momantaš. | Uviečary š klobie, pašla daklada, byla mastackaja Častka.‘In the status report, the chairman drew attention to a number of important points. | In the evening in the club, after the report, there was a performance.’Hordaja hatava alenia, uprhyozhanaja raskidzistymi rahami, byla krychu pryuzniata, vušy našciarovžany. | Prypynišysia na rahu vulicy, Natala Maksimäuna pačakala, pakul projdzie kalona audamašyn z vajskošcami.‘The deer’s proud head, decorated with spreading antlers, was slightly raised, the ears were alert. | Having stopped at the corner of the street, Natala Maksimaùna waited for a column of cars with soldiers to pass.’</td><td>10</td></tr><tr><td>BeWSC</td><td>Navat smiety voin byu biansilny suprac lutaha lva, i navat vostry mieč nie moh dapamahčy jamu.(⇒ Navat vostry mieč nie moh dapamahčy voinu.)‘Even a brave warrior was powerless against the fierce lion, and even a sharp sword could not help him.’(⇒ ‘Even a sharp sword could not help the warrior.’)Ja apušciū haracuju dalón u vadu, ijana astyla.(⇒ Vada astyla.)‘I dipped my hot palm into water, and it cooled down.’(⇒ ‘The water cooled down.’)</td><td>10</td></tr><tr><td>BeRTE-WD</td><td>Natalka Babina pieraklala kulinarnuju knihu «Litoškaja kucharka». ⇒ Natalka Babina maje dośvied u halinie pierakladiu.Natalka Babina translated the cookbook “Lithuanian Cook”. ⇒ Natalka Babina has experience in the field of translation.Kamianieckaja vieža byla pabudavana š 1288 hodzie, a Novy zamak u Hrodnie byš pabudavany š 1751 hodzie. ⇒ Kamianieckaja vieža byla pabudavana bolš jak na Čatyry stahodždi za Novy zamak u Hrodnie.The Kamianiec Tower was built in 1288, and the New Castle in Hrodna was built in 1751. ⇒ The Kamianiec Tower was built more than four centuries later than the New Castle in Hrodna.’</td><td>10</td></tr></table>
+
+# B Detailed results of LLM evaluation
+
+Table 4: Sample instances (in romanized spelling) with English translations.  
+
+<table><tr><td>Prompt language and type</td><td>Dataset: Metric:</td><td>BeSLS acc</td><td>BelaCoLA i.d. acc / MCC</td><td>BelaCoLA o.o.d. acc / MCC</td><td>BeWiC acc</td><td>BeWSC acc</td><td>BeRTE-WD acc</td></tr><tr><td rowspan="3">Belarusian</td><td>zero-shot</td><td>0.944</td><td>0.620 / 0.247</td><td>0.698 / 0.397</td><td>0.585</td><td>0.585</td><td>0.664</td></tr><tr><td>few-shot</td><td>0.960</td><td>0.663 / 0.327</td><td>0.698 / 0.396</td><td>0.585</td><td>0.605</td><td>0.772</td></tr><tr><td>zero-shot w. fine-tuning</td><td>0.936</td><td>0.620 / 0.255</td><td>0.678 / 0.356</td><td>0.685</td><td>0.585</td><td>0.792</td></tr><tr><td rowspan="3">English</td><td>zero-shot</td><td>0.928</td><td>0.550 / 0.124</td><td>0.592 / 0.202</td><td>0.600</td><td>0.575</td><td>0.764</td></tr><tr><td>few-shot</td><td>0.952</td><td>0.580 / 0.235</td><td>0.708 / 0.443</td><td>0.633</td><td>0.605</td><td>0.781</td></tr><tr><td>zero-shot w. fine-tuning</td><td>0.956</td><td>0.643 / 0.287</td><td>0.686 / 0.379</td><td>0.635</td><td>0.605</td><td>0.814</td></tr></table>
+
+Table 5: Results of Gemma 2 9B fine-tuning.
+
+<table><tr><td>Model ID on HuggingFace</td><td>Size</td><td>Dataset: Metric: Prec.</td><td>BeSLS acc</td><td>BelaCoLA i.d. acc / MCC</td><td>BelaCoLA o.o.d. acc / MCC</td><td>BeWiC acc</td><td>BeWSC acc</td><td>BeRTE-WD acc</td></tr><tr><td>ai-forever/mGPT-13B</td><td>13,0</td><td>8bit</td><td>0.500</td><td>0.500 / 0.000</td><td>0.500 / 0.000</td><td>0.500</td><td>0.500</td><td>0.503</td></tr><tr><td>bigscience/bloom-1b1</td><td>1,1</td><td>full</td><td>0.504</td><td>0.500 / 0.000</td><td>0.500 / 0.000</td><td>0.500</td><td>0.500</td><td>0.503</td></tr><tr><td>bigscience/bloom-3b</td><td>3,0</td><td>full</td><td>0.488</td><td>0.497 / -0.014</td><td>0.502 / 0.010</td><td>0.500</td><td>0.505</td><td>0.500</td></tr><tr><td>bigscience/bloom-7b1</td><td>7,1</td><td>full</td><td>0.500</td><td>0.500 / 0.000</td><td>0.500 / 0.000</td><td>0.500</td><td>0.500</td><td>0.500</td></tr><tr><td>bigscience/bloomz-1b1</td><td>1,1</td><td>full</td><td>0.520</td><td>0.510 / 0.023</td><td>0.492 / -0.019</td><td>0.498</td><td>0.500</td><td>0.500</td></tr><tr><td>bigscience/bloomz-3b</td><td>3,0</td><td>full</td><td>0.500</td><td>0.500 / 0.000</td><td>0.498 / -0.026</td><td>0.500</td><td>0.500</td><td>0.500</td></tr><tr><td>bigscience/bloomz-7b1</td><td>7,1</td><td>full</td><td>0.500</td><td>0.500 / 0.000</td><td>0.500 / 0.000</td><td>0.500</td><td>0.500</td><td>0.500</td></tr><tr><td>CohereForAI/aya-23-8B</td><td>8,0</td><td>full</td><td>0.520</td><td>0.510 / 0.078</td><td>0.508 / 0.074</td><td>0.500</td><td>0.490</td><td>0.503</td></tr><tr><td>facebook/xglm-7.5B</td><td>7,5</td><td>full</td><td>0.456</td><td>0.497 / -0.007</td><td>0.516 / 0.033</td><td>0.495</td><td>0.505</td><td>0.497</td></tr><tr><td>google/gemma-2-2b-it</td><td>2,6</td><td>full</td><td>0.596</td><td>0.497 / -0.034</td><td>0.506 / 0.060</td><td>0.508</td><td>0.500</td><td>0.519</td></tr><tr><td>google/gemma-2-9b-it</td><td>9,2</td><td>full</td><td>0.944</td><td>0.620 / 0.247</td><td>0.698 / 0.397</td><td>0.585</td><td>0.585</td><td>0.664</td></tr><tr><td>meta-IIlama/Llama-3.1-8B-Instruct</td><td>8,0</td><td>full</td><td>0.884</td><td>0.530 / 0.063</td><td>0.598 / 0.198</td><td>0.508</td><td>0.530</td><td>0.636</td></tr><tr><td>meta-IIlama/Llama-3.2-1B-Instruct</td><td>1,2</td><td>full</td><td>0.556</td><td>0.500 / 0.000</td><td>0.520 / 0.040</td><td>0.493</td><td>0.495</td><td>0.492</td></tr><tr><td>meta-IIlama/Llama-3.2-3B-Instruct</td><td>3,2</td><td>full</td><td>0.544</td><td>0.533 / 0.069</td><td>0.502 / 0.004</td><td>0.518</td><td>0.500</td><td>0.539</td></tr><tr><td>microsoft/Phi-3-medium-4k-instruct</td><td>14,0</td><td>8bit</td><td>0.496</td><td>0.493 / -0.019</td><td>0.494 / -0.020</td><td>0.528</td><td>0.495</td><td>0.578</td></tr><tr><td>microsoft/Phi-3-small-8k-instruct</td><td>7,4</td><td>full</td><td>0.540</td><td>0.537 / 0.091</td><td>0.492 / -0.021</td><td>0.538</td><td>0.510</td><td>0.572</td></tr><tr><td>microsoft/Phi-3.5-mini-instruct</td><td>3,8</td><td>full</td><td>0.552</td><td>0.537 / 0.133</td><td>0.498 / -0.009</td><td>0.495</td><td>0.500</td><td>0.506</td></tr><tr><td>mistralai/Ministral-8B-Instruct-2410</td><td>8,0</td><td>full</td><td>0.900</td><td>0.563 / 0.171</td><td>0.574 / 0.186</td><td>0.553</td><td>0.535</td><td>0.614</td></tr><tr><td>mistralai/Mistral-Nemo-Instruct-2407</td><td>12,2</td><td>8bit</td><td>0.880</td><td>0.550 / 0.164</td><td>0.606 / 0.297</td><td>0.503</td><td>0.520</td><td>0.658</td></tr><tr><td>Qwen/Qwen2-0.5B-Instruct</td><td>0,5</td><td>full</td><td>0.504</td><td>0.523 / 0.084</td><td>0.504 / 0.014</td><td>0.498</td><td>0.505</td><td>0.500</td></tr><tr><td>Qwen/Qwen2-1.5B-Instruct</td><td>1,5</td><td>full</td><td>0.512</td><td>0.503 / 0.058</td><td>0.498 / -0.045</td><td>0.500</td><td>0.480</td><td>0.533</td></tr><tr><td>Qwen/Qwen2-7B-Instruct</td><td>7,6</td><td>full</td><td>0.516</td><td>0.507 / 0.082</td><td>0.522 / 0.129</td><td>0.498</td><td>0.530</td><td>0.644</td></tr><tr><td>Qwen/Qwen2.5-0.5B-Instruct</td><td>0,5</td><td>full</td><td>0.536</td><td>0.490 / -0.046</td><td>0.502 / 0.009</td><td>0.498</td><td>0.500</td><td>0.497</td></tr><tr><td>Qwen/Qwen2.5-1.5B-Instruct</td><td>1,5</td><td>full</td><td>0.616</td><td>0.440 / -0.120</td><td>0.484 / -0.032</td><td>0.523</td><td>0.500</td><td>0.539</td></tr><tr><td>Qwen/Qwen2.5-3B-Instruct</td><td>3,1</td><td>full</td><td>0.528</td><td>0.507 / 0.034</td><td>0.488 / -0.036</td><td>0.610</td><td>0.505</td><td>0.600</td></tr><tr><td>Qwen/Qwen2.5-7B-Instruct</td><td>7,6</td><td>full</td><td>0.400</td><td>0.550 / 0.115</td><td>0.548 / 0.123</td><td>0.550</td><td>0.520</td><td>0.697</td></tr><tr><td>Qwen/Qwen2.5-14B-Instruct</td><td>14,8</td><td>8bit</td><td>0.436</td><td>0.520 / 0.065</td><td>0.522 / 0.091</td><td>0.590</td><td>0.580</td><td>0.719</td></tr><tr><td>SherlockAssistant/Mistral-7B-Instruct-Ukrainian</td><td>7,2</td><td>full</td><td>0.536</td><td>0.513 / 0.038</td><td>0.550 / 0.116</td><td>0.490</td><td>0.500</td><td>0.550</td></tr><tr><td>Vikhrmodels/Vikhr-7B-instruct_0.4</td><td>7,6</td><td>full</td><td>0.612</td><td>0.497 / -0.018</td><td>0.506 / 0.041</td><td>0.503</td><td>0.490</td><td>0.519</td></tr><tr><td>Vikhrmodels/Vikhr-Llama3.1-8B-Instruct-R-21-09-24</td><td>8,0</td><td>full</td><td>0.840</td><td>0.580 / 0.169</td><td>0.608 / 0.218</td><td>0.508</td><td>0.560</td><td>0.639</td></tr><tr><td>Vikhrmodels/Vikhr-Nemo-12B-Instruct-R-21-09-24</td><td>12,2</td><td>8bit</td><td>0.904</td><td>0.543 / 0.087</td><td>0.622 / 0.245</td><td>0.513</td><td>0.560</td><td>0.675</td></tr><tr><td>claude-3-5-sonnet-20241022</td><td>—</td><td>—</td><td>0.956</td><td>0.747 / 0.523</td><td>0.882 / 0.767</td><td>0.878</td><td>0.775</td><td>0.778</td></tr><tr><td>gpt-4o-2024-11-20</td><td>—</td><td>—</td><td>0.976</td><td>0.700 / 0.473</td><td>0.860 / 0.739</td><td>0.850</td><td>0.710</td><td>0.889</td></tr></table>
+
+Table 6: Results of LLM evaluation with zero-shot prompts in Belarusian.  
+
+<table><tr><td>Model ID on HuggingFace</td><td>Size</td><td>Dataset: Metric: Prec.</td><td>BeSLS acc</td><td>BelaCoLA i.d. acc / MCC</td><td>BelaCoLA o.o.d. acc / MCC</td><td>BeWiC acc</td><td>BeWSC acc</td><td>BeRTE-WD acc</td></tr><tr><td>ai-forever/mGPT-13B</td><td>13,0</td><td>8bit</td><td>0.500</td><td>0.500 / 0.000</td><td>0.500 / 0.000</td><td>0.505</td><td>0.500</td><td>0.500</td></tr><tr><td>bigscience/bloom-1b1</td><td>1,1</td><td>full</td><td>0.508</td><td>0.490 / -0.101</td><td>0.500 / 0.000</td><td>0.495</td><td>0.500</td><td>0.497</td></tr><tr><td>bigscience/bloom-3b</td><td>3,0</td><td>full</td><td>0.552</td><td>0.490 / -0.038</td><td>0.498 / -0.007</td><td>0.483</td><td>0.500</td><td>0.494</td></tr><tr><td>bigscience/bloom-7b1</td><td>7,1</td><td>full</td><td>0.504</td><td>0.500 / 0.000</td><td>0.500 / 0.000</td><td>0.500</td><td>0.500</td><td>0.497</td></tr><tr><td>bigscience/bloomz-1b1</td><td>1,1</td><td>full</td><td>0.500</td><td>0.500 / 0.000</td><td>0.500 / 0.000</td><td>0.500</td><td>0.500</td><td>0.500</td></tr><tr><td>bigscience/bloomz-3b</td><td>3,0</td><td>full</td><td>0.500</td><td>0.500 / 0.000</td><td>0.500 / 0.000</td><td>0.500</td><td>0.500</td><td>0.500</td></tr><tr><td>bigscience/bloomz-7b1</td><td>7,1</td><td>full</td><td>0.504</td><td>0.500 / 0.000</td><td>0.500 / 0.000</td><td>0.460</td><td>0.500</td><td>0.500</td></tr><tr><td>CohereForAI/aya-23-8B</td><td>8,0</td><td>full</td><td>0.636</td><td>0.510 / 0.028</td><td>0.520 / 0.051</td><td>0.500</td><td>0.500</td><td>0.528</td></tr><tr><td>facebook/xglm-7.5B</td><td>7,5</td><td>full</td><td>0.568</td><td>0.533 / 0.077</td><td>0.510 / 0.025</td><td>0.500</td><td>0.500</td><td>0.511</td></tr><tr><td>google/gemma-2-2b-it</td><td>2,6</td><td>full</td><td>0.712</td><td>0.503 / 0.010</td><td>0.534 / 0.105</td><td>0.600</td><td>0.515</td><td>0.539</td></tr><tr><td>google/gemma-2-9b-it</td><td>9,2</td><td>full</td><td>0.960</td><td>0.663 / 0.327</td><td>0.698 / 0.396</td><td>0.585</td><td>0.605</td><td>0.772</td></tr><tr><td>meta-IIlama/Llama-3.1-8B-Instruct</td><td>8,0</td><td>full</td><td>0.912</td><td>0.520 / 0.067</td><td>0.550 / 0.133</td><td>0.580</td><td>0.580</td><td>0.672</td></tr><tr><td>meta-IIlama/Llama-3.2-1B-Instruct</td><td>1,2</td><td>full</td><td>0.572</td><td>0.490 / -0.046</td><td>0.506 / 0.038</td><td>0.535</td><td>0.500</td><td>0.531</td></tr><tr><td>meta-IIlama/Llama-3.2-3B-Instruct</td><td>3,2</td><td>full</td><td>0.784</td><td>0.497 / -0.008</td><td>0.504 / 0.009</td><td>0.525</td><td>0.515</td><td>0.583</td></tr><tr><td>microsoft/Phi-3-medium-4k-instruct</td><td>14,0</td><td>8bit</td><td>0.740</td><td>0.530 / 0.065</td><td>0.526 / 0.058</td><td>0.555</td><td>0.550</td><td>0.611</td></tr><tr><td>microsoft/Phi-3-small-8k-instruct</td><td>7,4</td><td>full</td><td>0.668</td><td>0.507 / 0.019</td><td>0.502 / 0.006</td><td>0.530</td><td>0.495</td><td>0.617</td></tr><tr><td>microsoft/Phi-3.5-mini-instruct</td><td>3,8</td><td>full</td><td>0.608</td><td>0.483 / -0.035</td><td>0.490 / -0.022</td><td>0.503</td><td>0.530</td><td>0.525</td></tr><tr><td>mistralai/Ministral-8B-Instruct-2410</td><td>8,0</td><td>full</td><td>0.872</td><td>0.587 / 0.201</td><td>0.612 / 0.249</td><td>0.585</td><td>0.560</td><td>0.694</td></tr><tr><td>mistralai/Mistral-Nemo-Instruct-2407</td><td>12,2</td><td>8bit</td><td>0.908</td><td>0.607 / 0.213</td><td>0.666 / 0.334</td><td>0.615</td><td>0.600</td><td>0.719</td></tr><tr><td>Qwen/Qwen2-0.5B-Instruct</td><td>0,5</td><td>full</td><td>0.568</td><td>0.470 / -0.065</td><td>0.492 / -0.017</td><td>0.435</td><td>0.505</td><td>0.514</td></tr><tr><td>Qwen/Qwen2-1.5B-Instruct</td><td>1,5</td><td>full</td><td>0.692</td><td>0.503 / 0.034</td><td>0.500 / 0.000</td><td>0.508</td><td>0.510</td><td>0.544</td></tr><tr><td>Qwen/Qwen2-7B-Instruct</td><td>7,6</td><td>full</td><td>0.864</td><td>0.530 / 0.071</td><td>0.560 / 0.138</td><td>0.558</td><td>0.535</td><td>0.664</td></tr><tr><td>Qwen/Qwen2.5-0.5B-Instruct</td><td>0,5</td><td>full</td><td>0.592</td><td>0.500 / 0.000</td><td>0.472 / -0.060</td><td>0.443</td><td>0.515</td><td>0.500</td></tr><tr><td>Qwen/Qwen2.5-1.5B-Instruct</td><td>1,5</td><td>full</td><td>0.584</td><td>0.513 / 0.028</td><td>0.522 / 0.046</td><td>0.468</td><td>0.510</td><td>0.544</td></tr><tr><td>Qwen/Qwen2.5-3B-Instruct</td><td>3,1</td><td>full</td><td>0.536</td><td>0.517 / 0.033</td><td>0.550 / 0.105</td><td>0.505</td><td>0.480</td><td>0.597</td></tr><tr><td>Qwen/Qwen2.5-7B-Instruct</td><td>7,6</td><td>full</td><td>0.788</td><td>0.573 / 0.148</td><td>0.610 / 0.220</td><td>0.590</td><td>0.580</td><td>0.697</td></tr><tr><td>Qwen/Qwen2.5-14B-Instruct</td><td>14,8</td><td>8bit</td><td>0.888</td><td>0.577 / 0.201</td><td>0.620 / 0.286</td><td>0.693</td><td>0.610</td><td>0.750</td></tr><tr><td>SherlockAssistant/Mistral-7B-Instruct-Ukrainian</td><td>7,2</td><td>full</td><td>0.748</td><td>0.510 / 0.024</td><td>0.534 / 0.087</td><td>0.528</td><td>0.505</td><td>0.622</td></tr><tr><td>Vikhrmodels/Vikhr-7B-instruct_0.4</td><td>7,6</td><td>full</td><td>0.764</td><td>0.510 / 0.026</td><td>0.494 / -0.014</td><td>0.548</td><td>0.510</td><td>0.594</td></tr><tr><td>Vikhrmodels/Vikhr-Llama3.1-8B-Instruct-R-21-09-24</td><td>8,0</td><td>full</td><td>0.920</td><td>0.557 / 0.136</td><td>0.600 / 0.227</td><td>0.590</td><td>0.610</td><td>0.686</td></tr><tr><td>Vikhrmodels/Vikhr-Nemo-12B-Instruct-R-21-09-24</td><td>12,2</td><td>8bit</td><td>0.920</td><td>0.510 / 0.039</td><td>0.526 / 0.136</td><td>0.593</td><td>0.610</td><td>0.739</td></tr><tr><td>claude-3-5-sonnet-20241022</td><td>—</td><td>—</td><td>0.964</td><td>0.773 / 0.565</td><td>0.874 / 0.748</td><td>0.755</td><td>0.570</td><td>0.806</td></tr><tr><td>gpt-4o-2024-11-20</td><td>—</td><td>—</td><td>0.980</td><td>0.733 / 0.513</td><td>0.864 / 0.733</td><td>0.843</td><td>0.740</td><td>0.883</td></tr></table>
+
+Table 7: Results of LLM evaluation with few-shot prompts in Belarusian.
+
+<table><tr><td>Model ID on HuggingFace</td><td>Size</td><td>Dataset: Metric: Prec.</td><td>BeSLS acc</td><td>BelaCoLA i.d. acc / MCC</td><td>BelaCoLA o.o.d. acc / MCC</td><td>BeWiC acc</td><td>BeWSC acc</td><td>BeRTE-WD acc</td></tr><tr><td>ai-forever/mGPT-13B</td><td>13,0</td><td>8bit</td><td>0.500</td><td>0.500 / 0.000</td><td>0.500 / 0.000</td><td>0.500</td><td>0.500</td><td>0.500</td></tr><tr><td>bigscience/bloom-1b1</td><td>1,1</td><td>full</td><td>0.500</td><td>0.500 / 0.000</td><td>0.500 / 0.000</td><td>0.500</td><td>0.500</td><td>0.500</td></tr><tr><td>bigscience/bloom-3b</td><td>3,0</td><td>full</td><td>0.500</td><td>0.500 / 0.000</td><td>0.500 / 0.000</td><td>0.500</td><td>0.500</td><td>0.500</td></tr><tr><td>bigscience/bloom-7b1</td><td>7,1</td><td>full</td><td>0.500</td><td>0.500 / 0.000</td><td>0.500 / 0.000</td><td>0.500</td><td>0.500</td><td>0.500</td></tr><tr><td>bigscience/bloomz-1b1</td><td>1,1</td><td>full</td><td>0.500</td><td>0.500 / 0.000</td><td>0.500 / 0.000</td><td>0.500</td><td>0.510</td><td>0.500</td></tr><tr><td>bigscience/bloomz-3b</td><td>3,0</td><td>full</td><td>0.500</td><td>0.500 / 0.000</td><td>0.500 / 0.000</td><td>0.500</td><td>0.500</td><td>0.500</td></tr><tr><td>bigscience/bloomz-7b1</td><td>7,1</td><td>full</td><td>0.500</td><td>0.500 / 0.000</td><td>0.500 / 0.000</td><td>0.500</td><td>0.500</td><td>0.503</td></tr><tr><td>CohereForAI/aya-23-8B</td><td>8,0</td><td>full</td><td>0.656</td><td>0.503 / 0.034</td><td>0.488 / -0.064</td><td>0.498</td><td>0.500</td><td>0.542</td></tr><tr><td>facebook/xglm-7.5B</td><td>7,5</td><td>full</td><td>0.500</td><td>0.500 / 0.000</td><td>0.500 / 0.000</td><td>0.500</td><td>0.500</td><td>0.500</td></tr><tr><td>google/gemma-2-2b-it</td><td>2,6</td><td>full</td><td>0.852</td><td>0.533 / 0.083</td><td>0.520 / 0.057</td><td>0.515</td><td>0.510</td><td>0.575</td></tr><tr><td>google/gemma-2-9b-it</td><td>9,2</td><td>full</td><td>0.928</td><td>0.550 / 0.124</td><td>0.592 / 0.202</td><td>0.600</td><td>0.575</td><td>0.764</td></tr><tr><td>meta-IIlama/Llama-3.1-8B-Instruct</td><td>8,0</td><td>full</td><td>0.840</td><td>0.497 / -0.026</td><td>0.498 / -0.014</td><td>0.493</td><td>0.520</td><td>0.642</td></tr><tr><td>meta-IIlama/Llama-3.2-1B-Instruct</td><td>1,2</td><td>full</td><td>0.532</td><td>0.500 / 0.000</td><td>0.500 / 0.000</td><td>0.505</td><td>0.500</td><td>0.506</td></tr><tr><td>meta-IIlama/Llama-3.2-3B-Instruct</td><td>3,2</td><td>full</td><td>0.688</td><td>0.500 / 0.000</td><td>0.504 / 0.037</td><td>0.483</td><td>0.500</td><td>0.553</td></tr><tr><td>microsoft/Phi-3-medium-4k-instruct</td><td>14,0</td><td>8bit</td><td>0.708</td><td>0.493 / -0.041</td><td>0.502 / 0.020</td><td>0.520</td><td>0.515</td><td>0.606</td></tr><tr><td>microsoft/Phi-3-small-8k-instruct</td><td>7,4</td><td>full</td><td>0.756</td><td>0.530 / 0.070</td><td>0.522 / 0.045</td><td>0.473</td><td>0.480</td><td>0.625</td></tr><tr><td>microsoft/Phi-3.5-mini-instruct</td><td>3,8</td><td>full</td><td>0.700</td><td>0.517 / 0.041</td><td>0.518 / 0.049</td><td>0.498</td><td>0.490</td><td>0.517</td></tr><tr><td>mistralai/Ministral-8B-Instruct-2410</td><td>8,0</td><td>full</td><td>0.840</td><td>0.487 / -0.074</td><td>0.500 / 0.000</td><td>0.513</td><td>0.510</td><td>0.658</td></tr><tr><td>mistralai/Mistral-Nemo-Instruct-2407</td><td>12,2</td><td>8bit</td><td>0.892</td><td>0.477 / -0.063</td><td>0.520 / 0.048</td><td>0.553</td><td>0.540</td><td>0.700</td></tr><tr><td>Qwen/Qwen2-0.5B-Instruct</td><td>0,5</td><td>full</td><td>0.504</td><td>0.500 / 0.000</td><td>0.500 / 0.000</td><td>0.498</td><td>0.500</td><td>0.514</td></tr><tr><td>Qwen/Qwen2-1.5B-Instruct</td><td>1,5</td><td>full</td><td>0.556</td><td>0.503 / 0.018</td><td>0.490 / -0.052</td><td>0.500</td><td>0.505</td><td>0.578</td></tr><tr><td>Qwen/Qwen2-7B-Instruct</td><td>7,6</td><td>full</td><td>0.744</td><td>0.543 / 0.096</td><td>0.522 / 0.044</td><td>0.575</td><td>0.515</td><td>0.661</td></tr><tr><td>Qwen/Qwen2.5-0.5B-Instruct</td><td>0,5</td><td>full</td><td>0.500</td><td>0.500 / 0.000</td><td>0.502 / 0.045</td><td>0.500</td><td>0.505</td><td>0.508</td></tr><tr><td>Qwen/Qwen2.5-1.5B-Instruct</td><td>1,5</td><td>full</td><td>0.704</td><td>0.500 / 0.000</td><td>0.502 / 0.045</td><td>0.495</td><td>0.500</td><td>0.572</td></tr><tr><td>Qwen/Qwen2.5-3B-Instruct</td><td>3,1</td><td>full</td><td>0.776</td><td>0.530 / 0.064</td><td>0.542 / 0.090</td><td>0.500</td><td>0.525</td><td>0.625</td></tr><tr><td>Qwen/Qwen2.5-7B-Instruct</td><td>7,6</td><td>full</td><td>0.756</td><td>0.500 / 0.000</td><td>0.508 / 0.037</td><td>0.505</td><td>0.540</td><td>0.697</td></tr><tr><td>Qwen/Qwen2.5-14B-Instruct</td><td>14,8</td><td>8bit</td><td>0.848</td><td>0.533 / 0.067</td><td>0.552 / 0.105</td><td>0.508</td><td>0.560</td><td>0.692</td></tr><tr><td>SherlockAssistant/Mistral-7B-Instruct-Ukrainian</td><td>7,2</td><td>full</td><td>0.764</td><td>0.560 / 0.121</td><td>0.504 / 0.008</td><td>0.533</td><td>0.505</td><td>0.606</td></tr><tr><td>Vikhrmodels/Vikhr-7B-instruct_0.4</td><td>7,6</td><td>full</td><td>0.508</td><td>0.510 / 0.027</td><td>0.516 / 0.045</td><td>0.538</td><td>0.505</td><td>0.625</td></tr><tr><td>Vikhrmodels/Vikhr-Llama3.1-8B-Instruct-R-21-09-24</td><td>8,0</td><td>full</td><td>0.780</td><td>0.497 / -0.034</td><td>0.504 / 0.023</td><td>0.543</td><td>0.545</td><td>0.644</td></tr><tr><td>Vikhrmodels/Vikhr-Nemo-12B-Instruct-R-21-09-24</td><td>12,2</td><td>8bit</td><td>0.876</td><td>0.533 / 0.068</td><td>0.540 / 0.087</td><td>0.495</td><td>0.520</td><td>0.594</td></tr><tr><td>claude-3-5-sonnet-20241022</td><td>—</td><td>—</td><td>0.828</td><td>0.670 / 0.389</td><td>0.808 / 0.632</td><td>0.585</td><td>0.710</td><td>0.506</td></tr><tr><td>gpt-4o-2024-11-20</td><td>—</td><td>—</td><td>0.964</td><td>0.680 / 0.450</td><td>0.814 / 0.674</td><td>0.845</td><td>0.685</td><td>0.911</td></tr></table>
+
+Table 8: Results of LLM evaluation with zero-shot prompts in English.  
+
+<table><tr><td>Model ID on HuggingFace</td><td>Size</td><td>Dataset: Metric: Prec.</td><td>BeSLS acc</td><td>BelaCoLA i.d. acc / MCC</td><td>BelaCoLA o.o.d. acc / MCC</td><td>BeWiC acc</td><td>BeWSC acc</td><td>BeRTE-WD acc</td></tr><tr><td>ai-forever/mGPT-13B</td><td>13,0</td><td>8bit</td><td>0.500</td><td>0.497 / -0.058</td><td>0.470 / -0.070</td><td>0.483</td><td>0.500</td><td>0.514</td></tr><tr><td>bigscience/bloom-1b1</td><td>1,1</td><td>full</td><td>0.496</td><td>0.497 / -0.034</td><td>0.470 / -0.070</td><td>0.490</td><td>0.500</td><td>0.514</td></tr><tr><td>bigscience/bloom-3b</td><td>3,0</td><td>full</td><td>0.576</td><td>0.510 / 0.025</td><td>0.462 / -0.076</td><td>0.478</td><td>0.505</td><td>0.494</td></tr><tr><td>bigscience/bloom-7b1</td><td>7,1</td><td>full</td><td>0.616</td><td>0.497 / -0.058</td><td>0.496 / -0.014</td><td>0.525</td><td>0.500</td><td>0.500</td></tr><tr><td>bigscience/bloomz-1b1</td><td>1,1</td><td>full</td><td>0.500</td><td>0.500 / 0.000</td><td>0.496 / -0.063</td><td>0.500</td><td>0.500</td><td>0.500</td></tr><tr><td>bigscience/bloomz-3b</td><td>3,0</td><td>full</td><td>0.500</td><td>0.500 / 0.000</td><td>0.480 / -0.094</td><td>0.500</td><td>0.500</td><td>0.500</td></tr><tr><td>bigscience/bloomz-7b1</td><td>7,1</td><td>full</td><td>0.496</td><td>0.500 / 0.000</td><td>0.498 / -0.045</td><td>0.500</td><td>0.500</td><td>0.503</td></tr><tr><td>CohereForAI/aya-23-8B</td><td>8,0</td><td>full</td><td>0.820</td><td>0.513 / 0.033</td><td>0.560 / 0.120</td><td>0.528</td><td>0.500</td><td>0.622</td></tr><tr><td>facebook/xglm-7.5B</td><td>7,5</td><td>full</td><td>0.504</td><td>0.473 / -0.056</td><td>0.488 / -0.030</td><td>0.508</td><td>0.505</td><td>0.494</td></tr><tr><td>google/gemma-2-2b-it</td><td>2,6</td><td>full</td><td>0.884</td><td>0.543 / 0.157</td><td>0.594 / 0.205</td><td>0.530</td><td>0.475</td><td>0.631</td></tr><tr><td>google/gemma-2-9b-it</td><td>9,2</td><td>full</td><td>0.952</td><td>0.580 / 0.235</td><td>0.708 / 0.443</td><td>0.633</td><td>0.605</td><td>0.781</td></tr><tr><td>meta-IIlama/Llama-3.1-8B-Instruct</td><td>8,0</td><td>full</td><td>0.912</td><td>0.540 / 0.160</td><td>0.596 / 0.215</td><td>0.558</td><td>0.525</td><td>0.706</td></tr><tr><td>meta-IIlama/Llama-3.2-1B-Instruct</td><td>1,2</td><td>full</td><td>0.692</td><td>0.513 / 0.031</td><td>0.510 / 0.020</td><td>0.500</td><td>0.510</td><td>0.514</td></tr><tr><td>meta-IIlama/Llama-3.2-3B-Instruct</td><td>3,2</td><td>full</td><td>0.820</td><td>0.533 / 0.096</td><td>0.556 / 0.112</td><td>0.515</td><td>0.495</td><td>0.625</td></tr><tr><td>microsoft/Phi-3-medium-4k-instruct</td><td>14,0</td><td>8bit</td><td>0.808</td><td>0.487 / -0.068</td><td>0.548 / 0.096</td><td>0.558</td><td>0.525</td><td>0.647</td></tr><tr><td>microsoft/Phi-3-small-8k-instruct</td><td>7,4</td><td>full</td><td>0.784</td><td>0.523 / 0.084</td><td>0.520 / 0.058</td><td>0.523</td><td>0.495</td><td>0.608</td></tr><tr><td>microsoft/Phi-3.5-mini-instruct</td><td>3,8</td><td>full</td><td>0.720</td><td>0.490 / -0.028</td><td>0.520 / 0.040</td><td>0.533</td><td>0.490</td><td>0.536</td></tr><tr><td>mistralai/Ministral-8B-Instruct-2410</td><td>8,0</td><td>full</td><td>0.932</td><td>0.517 / 0.068</td><td>0.624 / 0.297</td><td>0.515</td><td>0.520</td><td>0.764</td></tr><tr><td>mistralai/Mistral-Nemo-Instruct-2407</td><td>12,2</td><td>8bit</td><td>0.940</td><td>0.553 / 0.154</td><td>0.648 / 0.343</td><td>0.595</td><td>0.540</td><td>0.769</td></tr><tr><td>Qwen/Qwen2-0.5B-Instruct</td><td>0,5</td><td>full</td><td>0.632</td><td>0.500 / 0.000</td><td>0.494 / -0.018</td><td>0.500</td><td>0.500</td><td>0.500</td></tr><tr><td>Qwen/Qwen2-1.5B-Instruct</td><td>1,5</td><td>full</td><td>0.664</td><td>0.503 / 0.009</td><td>0.496 / -0.023</td><td>0.505</td><td>0.505</td><td>0.569</td></tr><tr><td>Qwen/Qwen2-7B-Instruct</td><td>7,6</td><td>full</td><td>0.888</td><td>0.510 / 0.046</td><td>0.564 / 0.171</td><td>0.608</td><td>0.505</td><td>0.692</td></tr><tr><td>Qwen/Qwen2.5-0.5B-Instruct</td><td>0,5</td><td>full</td><td>0.500</td><td>0.503 / 0.008</td><td>0.496 / -0.045</td><td>0.500</td><td>0.500</td><td>0.508</td></tr><tr><td>Qwen/Qwen2.5-1.5B-Instruct</td><td>1,5</td><td>full</td><td>0.752</td><td>0.487 / -0.028</td><td>0.540 / 0.094</td><td>0.503</td><td>0.510</td><td>0.533</td></tr><tr><td>Qwen/Qwen2.5-3B-Instruct</td><td>3,1</td><td>full</td><td>0.772</td><td>0.540 / 0.082</td><td>0.584 / 0.190</td><td>0.500</td><td>0.515</td><td>0.650</td></tr><tr><td>Qwen/Qwen2.5-7B-Instruct</td><td>7,6</td><td>full</td><td>0.904</td><td>0.567 / 0.179</td><td>0.642 / 0.285</td><td>0.575</td><td>0.490</td><td>0.731</td></tr><tr><td>Qwen/Qwen2.5-14B-Instruct</td><td>14,8</td><td>8bit</td><td>0.924</td><td>0.587 / 0.174</td><td>0.658 / 0.339</td><td>0.600</td><td>0.525</td><td>0.758</td></tr><tr><td>SherlockAssistant/Mistral-7B-Instruct-Ukrainian</td><td>7,2</td><td>full</td><td>0.836</td><td>0.557 / 0.114</td><td>0.560 / 0.122</td><td>0.510</td><td>0.535</td><td>0.639</td></tr><tr><td>Vikhrmodels/Vikhr-7B-instruct_0.4</td><td>7,6</td><td>full</td><td>0.752</td><td>0.500 / 0.000</td><td>0.536 / 0.098</td><td>0.550</td><td>0.510</td><td>0.642</td></tr><tr><td>Vikhrmodels/Vikhr-Llama3.1-8B-Instruct-R-21-09-24</td><td>8,0</td><td>full</td><td>0.936</td><td>0.590 / 0.233</td><td>0.614 / 0.256</td><td>0.548</td><td>0.550</td><td>0.714</td></tr><tr><td>Vikhrmodels/Vikhr-Nemo-12B-Instruct-R-21-09-24</td><td>12,2</td><td>8bit</td><td>0.932</td><td>0.590 / 0.186</td><td>0.606 / 0.246</td><td>0.585</td><td>0.570</td><td>0.761</td></tr><tr><td>claude-3-5-sonnet-20241022</td><td>—</td><td>—</td><td>0.888</td><td>0.667 / 0.383</td><td>0.754 / 0.540</td><td>0.585</td><td>0.515</td><td>0.656</td></tr><tr><td>gpt-4o-2024-11-20</td><td>—</td><td>—</td><td>0.976</td><td>0.720 / 0.506</td><td>0.864 / 0.742</td><td>0.848</td><td>0.740</td><td>0.914</td></tr></table>
+
+Table 9: Results of LLM evaluation with few-shot prompts in English.

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