Escaping the Cognitive Well: Efficient Competition Math with Off-the-Shelf Models
This work addresses the problem of prohibitive computational costs for advanced math reasoning in AI, making high-performance solutions more accessible, though it is incremental as it builds on existing solver-grader pipelines.
The authors tackled the high cost of achieving top performance on International Mathematical Olympiad (IMO)-style math problems with off-the-shelf models by developing an inference pipeline that reduces average cost to $31 per question while achieving 67.1% performance on IMO-ProofBench Advanced, more than doubling the success rate of the next best public pipeline.
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.