Diverse Inference and Verification for Advanced Reasoning

TL;DR

This paper introduces a diverse inference approach that combines multiple models and verification methods to significantly improve reasoning accuracy on complex mathematical, coding, and puzzle tasks, surpassing previous benchmarks.

Contribution

The paper presents a novel diverse inference framework that integrates multiple models and verification techniques, enhancing reasoning performance on challenging tasks like IMO, ARC, and HLE.

Findings

Increased IMO combinatorics accuracy from 33.3% to 77.8%.

Improved HLE question accuracy from 8% to 37%.

Solved 80% of ARC puzzles that humans failed and 26.5% that high compute models do not.

Abstract

Reasoning LLMs such as OpenAI o1, o3 and DeepSeek R1 have made significant progress in mathematics and coding, yet find challenging advanced tasks such as International Mathematical Olympiad (IMO) combinatorics problems, Abstraction and Reasoning Corpus (ARC) puzzles, and Humanity's Last Exam (HLE) questions. We use a diverse inference approach that combines multiple models and methods at test time. We find that verifying mathematics and code problems, and rejection sampling on other problems is simple and effective. We automatically verify correctness of solutions to IMO problems by Lean, and ARC puzzles by code, and find that best-of-N effectively answers HLE questions. Our approach increases answer accuracy on IMO combinatorics problems from 33.3% to 77.8%, accuracy on HLE questions from 8% to 37%, and solves 80% of ARC puzzles that 948 humans could not and 26.5% of ARC puzzles that o3 high compute does not. Test-time simulations, reinforcement learning, and meta-learning with inference feedback improve generalization by adapting agent graph representations and varying prompts, code, and datasets. Our approach is reliable, robust, and scalable, and in the spirit of reproducible research, we will make it publicly available upon publication.