Functional Benchmarks for Robust Evaluation of Reasoning Performance, and the Reasoning Gap (2402.19450v1)

Abstract: We propose a framework for robust evaluation of reasoning capabilities of LLMs, 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. We have rewritten the relevant fragment of the MATH benchmark into its functional variant MATH(), with functionalization of other benchmarks to follow. When evaluating current state-of-the-art models over snapshots of MATH(), we find a reasoning gap -- the percentage difference between the static and functional accuracies. We find reasoning gaps from 58.35% to 80.31% among the state-of-the-art closed and open weights models that perform well on static benchmarks, with the caveat that the gaps are likely to be smaller with more sophisticated prompting strategies. Here we show that models which anecdotally have good reasoning performance over real-world tasks, have quantifiable lower gaps, motivating the open problem of building "gap 0" models. Code for evaluation and new evaluation datasets, three MATH() snapshots, are publicly available at https://github.com/consequentai/fneval/.

• The paper presents a novel methodology that transforms static QA benchmarks into dynamic, functional variants for deeper reasoning evaluation.
• It evidences a reasoning gap of 58.35% to 80.31% between traditional static testing and dynamic functional assessments.
• The findings underline the need for improved LLM designs that reason from first principles rather than relying solely on memorization.

A Comprehensive Framework for Evaluating Reasoning in LLMs through Functional Benchmarks

Introduction

Evaluating the reasoning abilities of LLMs has emerged as a pivotal challenge, necessitating robust benchmarks that can accurately measure these capabilities beyond mere language comprehension or recall. The introduced framework takes a significant step toward addressing this challenge by presenting a novel methodology for evaluating reasoning through functional variants of benchmarks. This approach, specifically its application to a segment of the MATH benchmark to create MATH(), demonstrates a nuanced strategy to identify and quantify the "reasoning gap" between performances on static problem sets versus their functional, or dynamically variable, counterparts.

Framework and Methodology

The core of the proposed framework lies in transforming static question-answer (QA) benchmarks into their functional variants, denoted as QA(rngs), wherein each problem is reimagined as a piece of code that generates an infinite array of similar problem instances with varying inputs but requiring the same underlying reasoning. This transformation is methodologically significant as it moves beyond testing models for rote memorization, guiding towards an evaluation that measures genuine reasoning capability.

To achieve an unbiased assessment, the authors undertook a one-time, albeit intensive, task of manual functionalization for a significant portion of the MATH benchmark. This effort resulted in the creation of MATH() - a dynamic, functional version of the benchmark conceived to challenge models with tasks they have not seen before, thus pushing the limits of their reasoning faculties.

Findings and Reasoning Gap

Upon comparing state-of-the-art models' performances on static versus functional versions of selected MATH problems, a pronounced "reasoning gap" emerged, varying from 58.35% to 80.31% across different models. This gap starkly highlights the discrepancy between models' abilities to solve previously encountered problems versus their capacity for genuine reasoning on novel instances generated by the functional benchmarks.

Furthermore, the results underscored that even advanced models, although seemingly adept at reasoning tasks in real-world applications, demonstrate a substantial gap when rigorously tested. Models exhibited measurable, albeit varied, reasoning performance, directly correlated to the complexity and novelty presented by the functional tasks.

Implications and Future Directions

The profound implications of this research for the development of LLMs are twofold. Practically, it provides a tool for more accurately gauging models' reasoning capabilities, essential for fine-tuning and improving these complex systems. Theoretically, it poses an open challenge to the AI research community to develop models capable of closing the reasoning gap, ushering in a new direction aimed at fostering models that can reason from first principles rather than rely on memorization.

The groundwork laid by this paper, and the subsequent release of functionalized benchmark snapshots, set the stage for an ongoing quest towards improving and truly understanding the reasoning capabilities of LLMs. As this is an evolving field, the promise of refining these benchmarks and exploring sophisticated prompting strategies or model augmentations offers a glimpse into a future where LLMs can genuinely understand and reason with the nuance and depth akin to human cognition.

Concluding Remarks

By introducing functional benchmarks as a robust tool for evaluating the reasoning performance of LLMs, this research steers the conversation towards recognizing and bridging the reasoning gap. It lays a foundation for future investigations and model development aimed at achieving not just higher accuracy on benchmarks but a deeper, more genuine form of computational reasoning. The pursuit of models with minimized reasoning gaps represents not only a technical challenge but a philosophical one, prompting us to reconsider what it means for a machine to "understand" and "reason" in a world where those capabilities are increasingly indispensable.