Diverse Inference and Verification for Advanced Reasoning
Iddo Drori, Gaston Longhitano, Mao Mao, Seunghwan Hyun, Yuke Zhang, Sungjun Park, Zachary Meeks, Xin-Yu Zhang, Ben Segev, Howard Yong, Nakul Verma, Avi Shporer, Alon Amit, Madeleine Udell
cs.AI
Feb 14, 2025 · v1
TL;DR
Uses Lean to automatically verify the correctness of LLM-generated solutions to IMO mathematics problems within a diverse-inference pipeline.
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.
Problem
Frontier reasoning LLMs still struggle with advanced tasks such as IMO combinatorics problems, Abstraction and Reasoning Corpus (ARC) puzzles, and Humanity's Last Exam (HLE) questions.
Approach
A diverse inference approach combines multiple models and methods at test time. Mathematical solutions are automatically verified using Lean, ARC puzzle solutions are verified by code execution, and best-of-N rejection sampling is applied to HLE questions. Test-time simulations, reinforcement learning, and meta-learning with inference feedback adapt agent graph representations and vary prompts, code, and datasets.
Results
Accuracy on IMO combinatorics problems increases from 33.3% to 77.8%. HLE question accuracy rises from 8% to 37%. The approach solves 80% of ARC puzzles that 948 humans could not and 26.5% that o3 high compute does not.
