Thanks for your insightful comments, the following is the detailed response:

1. More experiments (Weakness 1)

We have conducted experiments on LLaMA-3 which is shown in Table 5, our MeanLearn can improve the performance of LLaMA-3 on both vanilla accuracy and AbsAcc. We do not test GPT-4/4o is because: (1) our main focus is to improve small LLMs, which is also crucial and have a broader range of application. They are preferred for deployment on devices like cell phones due to their lower resource demands. (2) GPT-4o is released about a week before the deadline of NeurIPS 2024, leaving insufficient time to conduct experiments with GPT-4o. Furthermore, we are glad to offer more exploration in the future.

2. Some of the terminology used appears complex (Weakness 2)

Your understandings about K-example and R-example are correct. While for abstract reasoning, it is not a specific reasoning type. We can compute the performance of abstract reasoning for any task or benchmark, not just CommonsenseQA. For example, in math problems, abstract reasoning can help estimate the ability of LLMs to use the generic fact “x + y = y + x” to solve a series of problems in various scenarios that rely on this fact. While in commonsense problems, it can help estimate the ability of LLMs to use the generic fact “acid is corrosive” to solve a series of problems in various scenarios that rely on this fact.

We would like to clarify some critical misunderstandings in the preliminary review, which may have negative impacts on your assessment of our contributions.

1. The paper is rushed (Weakness 1)

Both sections 2 and 5 contain results, and this arrangement is intentional and not rushed. As in many prior works [1][2], the results in section 2 are preliminary and are used to demonstrate our motivations and introduce our following method. Meanwhile, the results in section 5 are related to our proposed methods and baselines. Thus, the results in sections 2 and 5 are independent and serve different purposes within our paper.

[1] Zhang et al., 2023: Automatic Chain of Thought Prompting in Large Language Models

[2] Jin et al., 2024: The Impact of Reasoning Step Length on Large Language Models

2. The methodology section is half a page (Weakness 2)

Due to the page limit, we are trying to put more important content in the main paper. To accommodate as much as experimental results, we describe our approach as concisely as possible (More details can refer to Appendix C and D). It is worth noting that our method has two sections, the construction method of AbsR dataset (section 3) and MeanLearn pipeline (section 4), a totally of 1.5 pages.

In Eq. (3), the first equation describes using input (X) to autoregressively model output (Y), the second is using X and generic fact r to autoregressively model Y, which is usually adopted by current LLMs posting-training works [3][4].

[3] Orca 2: Teaching Small Language Models How to Reason

[4] WizardLM: Empowering Large Language Models to Follow Complex Instructions

3. Insufficient related work on Abstract Reasoning (Weakness 3)

To the best of our knowledge, this is the first work to highlight the importance of abstract reasoning in the field of natural language processing. Thus, we include the most similar research directions: “Reasoning with LLMs” and “LLMs-as-annotators” in the related work section. Due to page limitations, we have condensed the related work. These sections will be expanded in the revised version.

4. Comparison to paper [5] (Weakness 4 and Question 1)

We believe there may be some critical misunderstandings concerning our paper and your referred paper. A comparison with this reference is unnecessary because: (1) it focuses on the reasoning on images or symbols, whereas our work is centered on abstract reasoning in natural language; (2) the paper does not propose a new method but merely presents an empirical study using ChatGPT and LLaMA on image tasks.

[5] LLMs and the Abstraction and Reasoning Corpus: Successes, Failures, and the Importance of Object-based Representations

5. The statement in our paper "Our findings reveal a substantial discrepancy between their general reasoning and abstract reasoning performances" and "LLMs know more than they can say" in [6] (Question 2)

These two statements indeed do not conflict. Most researches follow the conventional evaluation process to directly evaluate LLMs based on their outputs, quantifying their reasoning abilities. Our proposed abstract reasoning metric AbsAcc based on cognitive theory, and our results show a substantial disparity between general and abstract reasoning. On the other hand, the statement “LLMs know more than they can say” may be derived from the domain of interpretability. It concerns the LLMs’ inference processes on tasks, which may not be in a form understandable to humans, leading to performance loss when translating these processes into natural language. The focal points of our work and the work you referred to are distinct, each addressing different aspects of LLM capabilities and behaviors.

[6] Inference-time intervention: Eliciting truthful answers from a language model.

6. the effectiveness of MeanLearn (Question 3)

The benefits of our method MeanLearn do not diminish, but it is LLaMA-3 may need more data compared with other base models. The reason is because LLaMA-3 breaks conventional data scaling laws [7] by achieving a token-to-parameter (T/P) ratio of 1875:1, far surpassing the 286:1 ratio of LLaMA-2. This results in dense knowledge in the parametric memory of LLaMA-3. However, to ensure fair comparisons across different LLMs, we train MeanLearn based on LLaMA-3 with the same dataset size as the other LLMs. Furthermore, MeanLearn achieved satisfied improvements on LLaMA-2 and Orca-2.

[7] Pearce and Song, 2024. Reconciling Kaplan and Chinchilla Scaling Laws

Thanks for your reply. We want to clarify the critical misunderstandings in your response:

1. Q6 (the author should conduct experiments on LLaMA-3-13B) in the response

We do not incorporate LLaMA-3-13B because there is NO 13B version of LLaMA-3. (refer to https://huggingface.co/collections/meta-llama/meta-llama-3-66214712577ca38149ebb2b6) The second smallest LLaMA-3 is 70B. We indeed do not have the resources for training and inference. By the way, our MeanLearn method is effective on LLaMA-2-7B, LLaMA-2-13B, LLaMA-3-8B, Orca-2-7B, Orca-2-13B, and Mistral-7B (as mentioned in response to Reviewer XVL7, and you can refer to the table below).

About the performance on LLaMA-3-8B, we have offered some clarification in the rebuttal period, which is summarized as follows:

• We have improvements on LLAMA-3-8B;
• LLaMA-3 may need more data compared to other base models. The reason is that LLaMA-3 breaks conventional data scaling laws [1] by achieving a token-to-parameter (T/P) ratio of 1875:1, far surpassing the 286:1 ratio of LLaMA-2. This results in dense knowledge in the parametric memory of LLaMA-3. However, to ensure fair comparisons across different LLMs, we trained MeanLearn using LLaMA-3 with the same dataset size as the other LLMs.
• Although incorporating more data to train LLaMA-3 is unfair for the comparisons with other LLMs, we are interested in adopting more data to train LLaMA-3 in the future. Due to time limits and computational cost, we do not provide it in the rebuttal.

2. Q5 in the response

• For your referred paper[2], we do not incorporate it for comparison because: (1) it is a paper of abstraction AND reasoning on Visual Inputs and (2) it is an empirical study without proposing new methods or datasets. While we focus on abstracting reasoning on Natural Language.

• For the baseline proposed by Reviewer vYe8, we do not incorporate tree-of-thought (tot) for comparison because: tot focuses on the decoding stage, while we focus on the post-training stage to enhance the fundamental capabilities, they are complementary. We adhere to conventional standards by selecting baselines of similar types and scales to ensure a fair evaluation.

• Both Reviewers XVL7 and Fwhs think the soundness of our work is good.

[1] Pearce and Song, 2024. Reconciling Kaplan and Chinchilla Scaling Laws

[2] Xu, Yudong, et al. "LLMs and the Abstraction and Reasoning Corpus: Successes, Failures, and the Importance of Object-based Representations." Transactions on Machine Learning Research.

Thanks for your insightful comments, the following is the detailed response:

1. Limited scale (Weakness 1 and Question 4)

1.1 Limited scale

Due to limited computational resources, we conduct our experiments on small LLMs (7B-13B). It is worth noting that our main focus is also to improve small LLMs, which is also crucial, as evidenced by considerable research focus in this area [1][2]. Small LLMs have a broader range of applications and are preferred for deployment on devices like cell phones due to their lower resource demands. Despite their wider applicability, small LLMs are significantly weaker than their larger counterparts, underscoring the importance of prioritizing their improvement.

[1] Orca 2: Teaching Small Language Models How to Reason

[2] WizardLM: Empowering Large Language Models to Follow Complex Instructions

1.2 Applying MeanLearn to 100B+ LLMs

We are attempting to discuss to apply our method to 100B+ LLMs, but it is out of the scope of this paper. Applying MeanLearn to 100B+ LLMs would presents both challenges and benefits: Challenges: (1) Resource Requirements: the post-training of such large LLMs demands additional and more stable computational resources to manage the high costs associated with their scale; (2) Data Demands: according to the data scaling law [3], there is a significant need for extensive training data to achieve adequate coverage and ensure the generalization capabilities of these large models. Acquiring such large datasets is often costly. Benefits: (1) Enhanced Learning Abilities: larger LLMs possess stronger learning capacities, enabling them to more effectively comprehend and assimilate the knowledge presented to them; (2) Superior Performance: these models typically outperform smaller LLMs, offering better overall performance in tasks due to their advanced capabilities.

[3] Pearce and Song, 2024. Reconciling Kaplan and Chinchilla Scaling Laws

2. Human evaluation scale (Weakness 2)

We mainly follow previous works [4] [5], which conduct human evaluation on 100-200 instances. We choose 200 instances for evaluation, which is a balance between maintaining evaluation quality and managing labor costs.

[4] Du et al., e-CARE: a New Dataset for Exploring Explainable Causal Reasoning

[5] Ying et al., Intuitive or Dependent? Investigating LLMs' Robustness to Conflicting Prompts

3. Lack of comparison to more recent reasoning techniques (Weakness 3 and Question 2)

We adhere to conventional standards by selecting baselines of similar types and scales to ensure a fair evaluation. Our focus is on enhancing the fundamental capabilities of LLMs through post-training techniques. In contrast, methods like Tree-of-Thought (ToT) primarily target improvements during the decoding stage, which complements our proposed method.

4. Perplexity-based evaluation (Weakness 4 and Question1)

We align with the evaluation criteria established by prior research [6][7] and leaderboards [8][9], adopting perplexity as our evaluation metric. The advantages of employing perplexity are twofold:

• Clarity in Evaluation: evaluation with perplexity can extract an answer for each example, while generation-based evaluation is hard to do this, since LLMs might either refuse to provide an answer or treat any option as valid;
• Efficiency: Calculating perplexity requires only a single forward pass through the LLMs, making it more cost-efficient compared to generation-based methods, which require text to be generated in an autoregressive manner. This streamlined process enhances both the speed and the resource efficiency of the evaluation.

[6] Sun et al., 2024: A Simple and Effective Pruning Approach for Large Language Models

[7] Zhao et al., 2024: Deciphering the lmpact of Pretraining Data on Large Language Models through Machine Unlearning

[8] OpenCompass, 2023: OpenCompass: A Universal Evaluation Platform for Foundation Models

[9] Huggingface 2024: Open LLM Leaderboard

5. About AbsAcc (Weakness 4 and Question 5)

Theoretically, AbsAcc offers a more reliable measurement of abstract reasoning. For each generic fact, we have multiple examples to test LLMs, effectively reducing the influences of memorization and pattern matching. Ideally, increasing the number of examples for each generic fact would enhance the reliability of AbsAcc. We do not incorporate more examples per generic fact for the balance between cost and effectiveness. Please note that, our method is scalable with respect to the number of examples for each generic fact.

6. Examples or analysis of of the implicit learning process (Question 3)

Humans can apply the grasped generic fact to solve problems in different scenarios. For example, in Figure 1 of our paper, if humans grasp “acid is corrosive”, they can deduce “rock dissolved” and “the skin suffers pain” when respectively given “adding rock into hydrochloric acid” and “acid touches human skin”. MeanLearn is designed to imitate the above meaningful learning process of humans.

As for analysis, this question is indeed interesting and merits exploration. However, it falls outside the scope of the main contributions of our work. Our focus is not on demonstrating the implicit learning processes within a black-box LLM, as that pertains more to the field of interpretability. Addressing this would require a significantly different research approach and substantial additional effort.

Dear Reviewer vYe8:

We appreciate your thoughtful review. As the rebuttal deadline approaches, we kindly ask if our responses have sufficiently addressed your concerns. If you require further clarification, we are prepared to provide additional information.

Sincerely,

Authors

Thanks for your response, we are glad to have addressed your concerns in your preliminary review, and we want to kindly remind that:

Actually, in Table 5 of our paper, we have provided the post-training baselines (Vicuna [1], WizardLM [2], Orca-2 [3]) , and you can refer to the table below (the average performance on 7B models), we have varying advantages over these methods on both vanilla accuracy and AbsAcc.

If you have any further concerns, feel free to leave comments.

[1] https://lmsys.org/blog/2023-03-30-vicuna/

[2] WizardLM: Empowering Large Language Models to Follow Complex Instructions

[3] Orca 2: Teaching Small Language Models How to Reason

Thanks for your insightful comments, the following is the detailed response:

1. Evaluation on Advanced LLMs (Weakness 1)

The benefits of our method MeanLearn do not diminish, but it is LLaMA-3 may need more data compared with other base models. The reason is because LLaMA-3 breaks conventional data scaling laws [1] by achieving a token-to-parameter (T/P) ratio of 1875:1, far surpassing the 286:1 ratio of LLaMA-2. This results in dense knowledge in the parametric memory of LLaMA-3. However, to ensure fair comparisons across different LLMs, we trained MeanLearn using LLaMA-3 with the same dataset size as the other LLMs.

Due to limited time, we train MeanLearn based on Mistral-7B-Instruct-v0.2, and evaluate them on Com., MMLU, RACE and AbsR, the results are shown in the following table:

On average, our proposed MeanLearn can outperform Mistral by 3.03% in vanilla accuracy and 3.70% in AbsAcc, which demonstrates the superiority of MeanLearn. The main reason is that Mistral does not have a dense knowledge in parameters as LLaMA-3.

[1] Pearce and Song, 2024. Reconciling Kaplan and Chinchilla Scaling Laws

2. Data Augmentation and Training Dynamics (Weakness 2)

GPT-4o was released about a week before the NeurIPS 2024 deadline, making it too late to use for synthesizing AbsR. Indeed, leveraging cost-effective models like GPT-4o or open-source LLMs for data generation is crucial for future performance improvements. We are enthusiastic about exploring this and the training dynamics in the future to achieve continual performance gains.

3. Expanding Reasoning Benchmarks (Weakness 3)

There are mathematical tasks in MMLU, following [2], we select five mathematical reasoning datasets (abstract algebra, college mathematics, elementary mathematics, high school statistics, and high school mathematics) from MMLU to demonstrate the superiority of MeanLearn. The results are shown in the following table:

On average, MeanLearn outperforms baselines on both vanilla accuracy and AbsAcc. It is interesting to note that we do not synthesize math questions to train MeanLearn, improvements on math reasoning are largely due to the enhancement of abstract reasoning.

Meaningful Learning is one of the main contributions of our work, and we are excited about the improvements brought by MeanLearn. Building on this foundation, we are now conducting a new work to expand our investigations with additional tasks such as mathematical and logical reasoning.

[2] MMLU-Pro: A More Robust and Challenging Multi-Task Language Understanding Benchmark

4. Presentation Clarity and Improvements (Weakness 4)

Abstract reasoning is not a specific type of reasoning; rather, it measures the ability of employing generic facts to solve problems. For each reasoning type, an abstract reasoning performance metric can be derived. For example, in math problems, abstract reasoning can help estimate the ability of LLMs to use the generic fact “x + y = y + x” to solve a series of problems in various scenarios that rely on this fact. While in commonsense problems, it can help estimate the ability of LLMs to use the generic fact “acid is corrosive” to solve a series of problems in various scenarios that rely on this fact.

The pilot investigation results presented in introduction serve to intuitively highlight the disparity (Table 1) between general and abstract reasoning, which is used to demonstrate our motivation that LLMs have a substantial discrepancy between their general reasoning and abstract reasoning performances. Detailed discussions of this investigation are available in sections 2.1 and 2.3.

Furthermore, Figure 2 illustrates the calculations for vanilla accuracy and AbsAcc, employing the same symbols and formulas outlined in section 2.1 and equation (1).

5. Updated Related Work (Weakness 5)

Due to page limitations and to place more experimental results, we have condensed some sections of the related work. We will expand the related work in the revised version.

Thanks for the clarification. I would like to mention that MATH also has a fine-grained classification for analysis. I will keep my rating positive for this paper.