EconProver: Towards More Economical Test-Time Scaling for Automated
  Theorem Proving
Authors: name: Mukai Li, name: Linfeng Song, name: Zhenwen Liang, name: Jiahao Xu, name: Shansan Gong, name: Qi Liu, name: Haitao Mi, name: Dong Yu

Large Language Models (LLMs) have recently advanced the field of Automated
Theorem Proving (ATP), attaining substantial performance gains through widely
adopted test-time scaling strategies, notably reflective Chain-of-Thought (CoT)
reasoning and increased sampling passes. However, they both introduce
significant computational overhead for inference. Moreover, existing cost
analyses typically regulate only the number of sampling passes, while
neglecting the substantial disparities in sampling costs introduced by
different scaling strategies. In this paper, we systematically compare the
efficiency of different test-time scaling strategies for ATP models and
demonstrate the inefficiency of the current state-of-the-art (SOTA) open-source
approaches. We then investigate approaches to significantly reduce token usage
and sample passes while maintaining the original performance. Specifically, we
propose two complementary methods that can be integrated into a unified EconRL
pipeline for amplified benefits: (1) a dynamic Chain-of-Thought (CoT) switching
mechanism designed to mitigate unnecessary token consumption, and (2) Diverse
parallel-scaled reinforcement learning (RL) with trainable prefixes to enhance
pass rates under constrained sampling passes. Experiments on miniF2F and
ProofNet demonstrate that our EconProver achieves comparable performance to
baseline methods with only 12% of the computational cost. This work provides
actionable insights for deploying lightweight ATP models without sacrificing
performance.