Does Reasoning Emerge? Examining the Probabilities of Causation in Large Language Models

Summary

This paper investigates the reasoning capabilities of large language models (LLMs) by examining the concepts of necessity and sufficiency, which are key elements of logical reasoning. To assess the LLMs' reasoning abilities, the authors introduce a framework that computes the probability of necessity (PN) and the probability of sufficiency (PS) by comparing the actual values derived from factual and counterfactual datasets with those simulated by the LLMs. The paper presents a reasoning test for assessing LLMs' reasoning abilities using a divisibility problem as an example. The authors create factual and counterfactual datasets based on a reasoning graph and compare the actual PN and PS values with those generated by the LLMs. The results show that the closer the estimated PN/PS values are to the actual PN/PS values, the better the LLM is at reasoning.

Strengths

The main strength of the paper is the introduction of a systematic method for evaluating the reasoning capabilities of large language models (LLMs) by examining the concepts of necessity and sufficiency. This novel framework can be beneficial for researchers and developers working on improving LLMs. The method tries to evaluate from two different angles: the accuracy with which an LLM solves a problem, and its capacity to understand and process the fundamental elements that lead to that solution. I think the authors tackles an important problem in LLM reasoning, which is an important and ongoing debate about the extent to which LLMs are capable of actual reasoning.

Weaknesses

- The paper uses a single example, the divisibility problem, to demonstrate the reasoning test. While this example helps illustrate the concepts, it may not be representative of the wide range of problems LLMs are expected to solve. Including additional examples from various domains would strengthen the paper's claims and generalizability. - The paper does experiments on specific LLMs (gpt series) but doesn't provide results on other models or comparisons between multiple models. Including a variety of LLMs with different architectures and training datasets would provide a more comprehensive evaluation of the proposed framework. And, as GPT series are not open-sourced, it's unclear how OpenAI's hidden prompts or value-alignment finetuning will influence the results. - The paper focuses on the probabilistic interpretations of necessity and sufficiency in a creatain math problem but does not explore a wider range forms of reasoning (I'm not seeing this point as a signifigant weaknesses though, but I think the word "reasoning" actually covers more complex scenarios). Also see the questions below.

Questions

- How do the authors distinguish the results from the influence of the LLMs' prior knowledge? The LLMs' performance in the reasoning test may be affected by the patterns and relationships they have learned from their training data, especially commonsense reasoning questions related to Math. Are there any steps taken to control or account for this influence when evaluating the LLMs' reasoning abilities? In the interpretation of results, how do you account for the potential influence of the prior knowledge and the LLM's understanding of reasoning capabilities? - Have the authors tried any prompt tuning or do they have some primary resuls? Although the authors have made this point clear in the limitations, I think the prompt actually greatly influence the output of the LLMs and may have a influence on the conclusions.

Rating

4

Confidence

3

Soundness

3

Presentation

3

Contribution

2

Limitations

N/A

Summary

To assess the reasoning abilities of large language models (LLMs) in complex tasks e.g., causation scenarios, this paper introduces a novel framework that utilizes probabilistic measures of necessity (PN) and sufficiency (PS). Through a series of mathematical examples, the study computes approximations of PN and PS using reasoning graphs and LLM that generate factual and counterfactual datasets. The generated results from the LLMs are then compared with true simulated PN and PS values from reasoning graphs. The experimental findings indicate an emerging trend towards improved reasoning capabilities within the GPT family of models, including GPT-2, GPT-3.5-turbo, and GPT-4.

Strengths

+ The paper provides a clear example case at the beginning, effectively illustrating the differences in reasoning abilities among various GPT models. + The examination of the concepts of necessity and sufficiency is well-founded, as these are crucial elements in causation and logical reasoning tasks, making them suitable for measuring LLMs' reasoning abilities. + The experimental design and results are easy to understand, facilitating comprehension of the study's findings.

Weaknesses

- Does four mathematic experiments representative in causal reasoning tasks? - Before presenting Sections 2 and 3 on the probabilities of causation in an LLM, the paper should first explain the method for computing true PS and PN values using reasoning graphs to provide better context for readers. - In Section 4.2 line 261: “Each density is labeled with the model that was used used to generate xxx”->typos

Questions

It would be clearer if the author(s) could explain: - What is the relationship between the experiment evaluation metrics, Factual Inconsistency Rate (FIR) and Counterfactual Inconsistency Rate (CIR), and the results of PN and PS? - Could you explain more about how the datasets (factual and counterfactual) were acquired from reasoning graphs? - What does the random noise introduced in the true counterfactuals mean, and how did you measure the noise level?

Rating

6

Confidence

3

Soundness

3

Presentation

3

Contribution

3

Limitations

The limitations and broader impact of the study are clearly outlined in the paper.

Summary

The paper introduces a systematic method for assessing the reasoning capabilities of large language models (LLMs) by focusing on the concepts of necessity and sufficiency in logical reasoning. It leverages a probabilistic interpretation of these concepts and uses a reasoning graph based on boolean conditions to test the models.

Strengths

1. The paper introduces a novel method for evaluating the reasoning capabilities of LLMs, which which is a critical issue in the field of LLMs. 2.The paper includes numerous diagrams, effectively illustrating the background and contributions of the study.

Weaknesses

1. The workload and the introduction of related work in the main body of the article appears somewhat insufficient. It is recommended to incorporate the more significant content from the appendix into the main text. 2. Due to the lack of more rigorous and in-depth theoretical analysis, the results may not have sufficient theoretical persuasiveness. Thus, the paper would be more valuable if it provided some conclusive summaries or proposed improvement methods for the assessment results.

Questions

1. Is subsection 3.2 of the paper complete? 2. The paper treats large language models (LLMs) as black boxes to measure the probabilities of causation. Does this approach have deeper significance and value? Additionally, is this evaluation method applicable to recurrent neural networks (RNNs) or large vision models (LVMs)?

Rating

4

Confidence

3

Soundness

2

Presentation

2

Contribution

2

Limitations

The limitations are mentioned by the author in Section 5.

Summary

This paper evaluates the reasoning capabilities of LLMs within the framework of Judea Pearl's hierarchy of causality, focusing particularly on the ability to perform counterfactual reasoning. LLMs are perceived as (non-deterministic) abstract machines within the HEX framework. The study assesses these models by comparing their performance on factual versus counterfactual problems, which are structured as reasoning graphs of boolean conditions. The necessity (PN) and sufficiency (PS) probabilities are estimated for 4 reasoning tasks: Divisibility by 6, Even Sum, Candy Party, and ConPref, ranging in complexity. The paper investigates whether the actual PN and PS align with those estimated from both factual and counterfactual data, using models from the GPT family (GPT-2, GPT-3.5, and GPT-4). Findings show limited reasoning capabilities for the evaluated model family, with GPT-4 performing the best on the divisibility task.

Strengths

- Applies probabilistic measures of necessity and sufficiency to asses specifically the reasoning capabilities of LLMs, offering a nuanced evaluation that extends beyond the accuracy metric. - Evaluates and compares LLMs performance on both factual and counterfactual problems.

Weaknesses

- From the introduction "...reasoning is typically understood to be the ability of these models to demonstrate emergent capabilities that surpass mere statistical pattern recognition in the training set.". Without knowledge of or control on pre-training/post-training data for the GPT model family, it is difficult to infer that a measured reasoning capability via the introduced framework is due to "emergence" and not pattern recognition in the training data. - The framework's applicability is reduced to reasoning tasks that can be represented as graphs of boolean variables, which may limit its broader adoption. - Line 84-85: "The closer the estimated PN/PS values to the actual PN/PS values, the better it is at reasoning. " needs further elaboration. Specifically, an explanation of how these metrics correlate with enhanced reasoning capabilities would help in understanding the effectiveness of the framework. - The framework imposes that LMs are abstract machines, suggesting deterministic behavior. Yet estimating probabilities of necessity (PN) and sufficiency (PS) inherently relies on variability in model responses. - Statistical significance of observed results could further support the validity of the framework.

Questions

- I assume all findings are based on temperature > 0 to fulfill the variability criterion. Did you generate multiple completions for each prompt (factual and counterfactual), and if so, how were these incorporated into the final analysis? "10 replicated tests" is mentioned under Figure 5, How these 10 contribute to the final findings? - Was prompt optimization attempted for smaller models as well, or just for GPT-4? Given the sensitivity of LMs to prompts, could there be a bias towards GPT-4 because it handles more complex prompts better? -While the paper discusses PN and PS as measures of reasoning, there is less focus on how these measures help in interpreting the decisions making process. What are the main benefits in comparison to just using accuracy?

Rating

6

Confidence

3

Soundness

3

Presentation

3

Contribution

2

Limitations

yes. See Weaknesses and Questions.