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Steering LLMs for Formal Theorem Proving (2502.15507v4)

Published 21 Feb 2025 in cs.LG, cs.AI, and cs.CL

Abstract: LLMs have shown promise in proving formal theorems using proof assistants like Lean. However, current state of the art LLMs struggles to predict next step in proofs leading practitioners to use different sampling techniques to improve LLMs capabilities. We observe that the LLM is capable of predicting the correct tactic; however, it faces challenges in ranking it appropriately within the set of candidate tactics, affecting the overall selection process. To overcome this hurdle, we use activation steering to guide LLMs responses to improve the generations at the time of inference. Our results suggest that activation steering offers a promising lightweight alternative to specialized fine-tuning for enhancing theorem proving capabilities in LLMs, particularly valuable in resource-constrained environments.

Summary

  • The paper demonstrates that activation steering significantly improves LLM tactic prediction and theorem proving success rates.
  • Learned steering vectors modify LLM activations during inference, substantially improving theorem proving success rates on the MiniF2F benchmark.
  • Activation steering is a lightweight alternative to extensive fine-tuning, offering a promising method for enhancing automated reasoning in resource-constrained environments.
  • Activation steering significantly improves theorem proving success rates by modifying LLM internal representations during inference.
  • Learned steering vectors modify LLM activations during inference, substantially boosting theorem proving success rates on the MiniF2F benchmark.
  • Activation steering offers a lightweight alternative to fine-tuning, enhancing automated reasoning in resource-constrained environments.
  • The paper presents activation steering as a method to significantly improve LLM tactic prediction and theorem proving success rates.
  • Learned steering vectors modify LLM activations during inference, substantially boosting theorem proving success rates on the MiniF2F benchmark.
  • Activation steering provides a lightweight alternative to extensive fine-tuning for enhancing automated reasoning.

Activation Steering in Neural Theorem Provers

The paper "Activation Steering in Neural Theorem Provers" offers an in-depth exploration of advancing tactic prediction capabilities in LLMs when applied to theorem proving. It specifically focuses on leveraging activation steering techniques to enhance the performance of these models within interactive theorem proving environments.

Overview

In the domain of formal theorem proving, LLMs have shown potential in tasks such as tactic prediction by interfacing with proof assistants like Lean. Despite advances, one significant challenge remains: these models often falter in ranking the correct tactics, which undermines their overall selection process. This research meticulously addresses this challenge by employing activation steering — a method that modifies internal representations within the model during inference to guide its responses more effectively.

The paper predominantly uses Llemma and InternLM2, both being state-of-the-art LLMs tailored for theorem proving. The principal innovation lies in steering the LLM’s activation vectors during proof generation, which enhances the logical coherence and effectiveness of tactic predictions.

Methodology

The methodology revolves around creating steering datasets and calculating steering vectors to modulate the model’s behavior. The authors initiate their experiment by constructing steering datasets from a subset of Lean-STaR data, incorporating both natural and synthetically enhanced prompt pairs. This is followed by evaluating the effectiveness of these steering vectors through inference-time modifications in the models.

The process utilizes a combination of reasoning abstraction from Lean states and employs GPT-4 for generating structured reasoning prompts. These structured prompts are integral to guiding LLMs towards accurate tactic prediction.

Empirical Results

The evaluation, conducted on the MiniF2F benchmark, leverages Best First Search technique to assess model performance. The results reveal that activation steering substantially improves theorem prover success rates. Key observations include enhanced pass rates when steering is applied in conjunction with sampling strategies, significantly outperforming base models without steering intervention.

A notable part of the evaluation also included a comparison using random activation vectors, which underscored the effectiveness of systematic steering over random perturbations, attributed to meaningful directional adjustments within the model activations.

Implications and Future Directions

This research underscores the utility of activation steering as a lightweight alternative to extensive fine-tuning, especially in resource-constrained environments where computational efforts and dataset availability may limit model refinement. Steering techniques can bypass extensive training phases and adapt LLMs towards specific reasoning pathways, which is paramount in domains requiring precision, such as formal theorem proving.

Looking forward, the paper suggests several avenues for exploration, including deeper investigations into the representational geometry of steering vectors within LLMs and extending these techniques across various mathematical domains. Integrating adaptive steering methods dynamically and extending them to interactively guide proof search heuristics can further optimize computational overheads during inference.

The methods and conclusions drawn in this paper offer promising directions for enhancing automated reasoning tasks, providing a bridge between generic LLMs and the specialized domain requirements of automated theorem proving. As theorem proving continues to evolve, methods like activation steering will undoubtedly play a crucial role in scaling and refining the capabilities of AI systems in mathematical reasoning.

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