Key Points

1. Robust Evaluation Framework: The research proposes a framework for robust evaluation of reasoning capabilities of language models using functional variants of benchmarks. Models that solve a reasoning test should exhibit no difference in performance over the static version of a problem compared to a snapshot of the functional variant.

2. Reasoning Gap: The study identifies a reasoning gap, which is the percentage difference between the static and functional accuracies. State-of-the-art models exhibit reasoning gaps ranging from 58.35% to 80.31%, suggesting that the current evaluation methods may overestimate the reasoning capabilities of these models.

3. Functional Variant of Benchmarks: The paper introduces the concept of functional variants of benchmarks, where each test in the functional variant cannot be directly used to evaluate, but instead needs to be instantiated.

4. Evaluation of Problem-Solving: The aim of testing generalized problem-solving is to assess whether the tested system can effectively answer questions it has not encountered before.

5. Contamination Testing: The study highlights the limitations of contamination testing by checking for k-contiguous token sequences and emphasizes the need to account for various other forms in which leakage might occur.

6. Accuracy Testing: The paper proposes rewriting each static reasoning into code, whose inputs can be varied to create infinite versions that follow the same reasoning pattern, but the steps needed in each would be different.

7. Coverage and Functional Accuracy: As of the study, 41.2% of the MATH benchmark has been functionalized, allowing for complete metrics over all MATH for current set of models. The paper also defines functional accuracy as the accuracy of solving a test in all k snapshots and the static variant.

8. Reasoning Gap in MATH Benchmark: The research presents the reasoning gap for the MATH benchmark across difficulty levels and subjects, showing that the reasoning gap increases with the difficulty levels and differs across subjects.

9. Future Work and Open Problems: The study suggests various avenues for future work, including the need for more sophisticated prompting strategies, tackling the open problem of training gap-0 models, and the ongoing effort to build reasoning metrics that are robust against contamination.

Summary

Reasoning Gap in Language Models
The paper proposes a framework for evaluating the reasoning capabilities of language models using functional variants of benchmarks. The authors have rewritten a portion of the MATH benchmark into its functional variant MATH(), and observed a reasoning gap among state-of-the-art models, ranging from 58.35% to 80.31%. The reasoning gap highlights the difference in performance between the static and functional variants. The study emphasizes the importance of accurately evaluating reasoning performance to improve large language models beyond their current capabilities.

Functional Variant of Benchmarks
The availability of evaluation code, new evaluation datasets, and three public snapshots of MATH() are presented to facilitate research in this area. The authors propose to convert static benchmarks into their functional variants, which allow for infinite snapshot instantiations to test against and assess whether the tested system can effectively answer questions it has not encountered before. This approach aims to improve on static QA evaluation and provide a more robust evaluation of reasoning capabilities.

Analysis of Model Performance
The paper also presents an analysis of problems solved across all snapshots by the top model, GPT4, and the OSS models. The study identifies reasoning subtypes and suggests alternative benchmarking techniques to address concerns of contamination and overoptimization in existing benchmarks.

Overall, the paper introduces the reasoning gap metric, highlights the need for more accurate assessment of reasoning capabilities in language models, and proposes a framework for the robust evaluation of reasoning performance. The study provides valuable insights into the evaluation and improvement of reasoning capabilities in large language models.

Reference: https://arxiv.org/abs/2402.194...