Escaping the Cognitive Well: Efficient Competition Math with Off-the-Shelf Models

TL;DR

This paper introduces an efficient inference pipeline using off-the-shelf models that achieves state-of-the-art performance on IMO-style math problems at a fraction of the cost of previous methods.

Contribution

The work presents a novel pipeline that overcomes grader failure modes through conjecture extraction and context detachment, enabling high performance with general-purpose models.

Findings

Achieves 67.1% accuracy on IMO-ProofBench Advanced

Reduces inference cost to approximately 31 USD per question

Doubles success rate compared to previous public pipelines

Abstract

In the past year, custom and unreleased math reasoning models reached gold medal performance on the International Mathematical Olympiad (IMO). Similar performance was then reported using large-scale inference on publicly available models but at prohibitive costs (e.g., 3000 USD per problem). In this work, we present an inference pipeline that attains best-in-class performance on IMO-style math problems at an average inference cost orders of magnitude below competing methods while using only general-purpose off-the-shelf models. Our method relies on insights about grader failure in solver-grader pipelines, which we call the Cognitive Well (iterative refinement converging to a wrong solution that the solver as well as the pipeline's internal grader consider to be basically correct). Our pipeline addresses these failure modes through conjecture extraction, wherein candidate lemmas are isolated from generated solutions and independently verified alongside their negations in a fresh environment (context detachment). On IMO-ProofBench Advanced (PB-Adv), our pipeline achieves 67.1 percent performance using Gemini 3.0 Pro with an average cost per question of approximately 31 USD. At the time of evaluation, this represented the state-of-the-art on PB-Adv among both public and unreleased models, and more than doubles the success rate of the next best publicly accessible pipeline, all at a fraction of the cost.