# Diverse Inference and Verification for Advanced Reasoning

arXiv: https://arxiv.org/abs/2502.09955 · HTML: https://mlsanity.com/paper/2502.09955/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Placed in Mathematical reasoning, one of 17 directions in LLM reasoning.
- Builds on 47 of its 117 references that are in the map.
- First posted on arXiv 14 Feb 2025.

## Placed in

- LLM reasoning / [Mathematical reasoning](https://mlsanity.com/lr/mathematical-reasoning/)

## Builds on (most cited first, 30 of 47)

- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [Training Compute-Optimal Large Language Models](https://mlsanity.com/paper/2203.15556/) (2022)
- [Mixtral of Experts](https://mlsanity.com/paper/2401.04088/) (2024)
- [Improving Factuality and Reasoning in Language Models through Multiagent Debate](https://mlsanity.com/paper/2305.14325/) (2023)
- [GShard: Scaling Giant Models with Conditional Computation and Automatic Sharding](https://mlsanity.com/paper/2006.16668/) (2020)
- [Large Language Monkeys: Scaling Inference Compute with Repeated Sampling](https://mlsanity.com/paper/2407.21787/) (2024)
- [LLM-Blender: Ensembling Large Language Models with Pairwise Ranking and Generative Fusion](https://mlsanity.com/paper/2306.02561/) (2023)
- [Humanity's Last Exam](https://mlsanity.com/paper/2501.14249/) (2025)
- [Mixture-of-Agents Enhances Large Language Model Capabilities](https://mlsanity.com/paper/2406.04692/) (2024)
- [MiniF2F: a cross-system benchmark for formal Olympiad-level mathematics](https://mlsanity.com/paper/2109.00110/) (2021)
- [Generative Language Modeling for Automated Theorem Proving](https://mlsanity.com/paper/2009.03393/) (2020)
- [Quiet-STaR: Language Models Can Teach Themselves to Think Before Speaking](https://mlsanity.com/paper/2403.09629/) (2024)
- [FrontierMath: A Benchmark for Evaluating Advanced Mathematical Reasoning in AI](https://mlsanity.com/paper/2411.04872/) (2024)
- [Monte Carlo Tree Search Boosts Reasoning via Iterative Preference Learning](https://mlsanity.com/paper/2405.00451/) (2024)
- [DeepSeek-Prover: Advancing Theorem Proving in LLMs through Large-Scale Synthetic Data](https://mlsanity.com/paper/2405.14333/) (2024)
- [When Scaling Meets LLM Finetuning: The Effect of Data, Model and Finetuning Method](https://mlsanity.com/paper/2402.17193/) (2024)
- [PutnamBench: Evaluating Neural Theorem-Provers on the Putnam Mathematical Competition](https://mlsanity.com/paper/2407.11214/) (2024)
- [Beyond Chinchilla-Optimal: Accounting for Inference in Language Model Scaling Laws](https://mlsanity.com/paper/2401.00448/) (2023)
- [On the Measure of Intelligence](https://mlsanity.com/paper/1911.01547/) (2019)
- [Formal Mathematics Statement Curriculum Learning](https://mlsanity.com/paper/2202.01344/) (2022)
- [Competitive Programming with Large Reasoning Models](https://mlsanity.com/paper/2502.06807/) (2025)
- [Broken Neural Scaling Laws](https://mlsanity.com/paper/2210.14891/) (2022)
- [Gold-medalist Performance in Solving Olympiad Geometry with AlphaGeometry2](https://mlsanity.com/paper/2502.03544/) (2025)
- [The Surprising Effectiveness of Test-Time Training for Few-Shot Learning](https://mlsanity.com/paper/2411.07279/) (2024)
- [Prover-Verifier Games improve legibility of LLM outputs](https://mlsanity.com/paper/2407.13692/) (2024)
- [Scaling Scaling Laws with Board Games](https://mlsanity.com/paper/2104.03113/) (2021)
- [TheoremLlama: Transforming General-Purpose LLMs into Lean4 Experts](https://mlsanity.com/paper/2407.03203/) (2024)

## Built on by (most cited first, 6 of 6)

- [Towards Reasoning Era: A Survey of Long Chain-of-Thought for Reasoning Large Language Models](https://mlsanity.com/paper/2503.09567/) (2025)
- [HybridProver: Augmenting Theorem Proving with LLM-Driven Proof Synthesis and Refinement](https://mlsanity.com/paper/2505.15740/) (2025)
- [CSR-RAG: An Efficient Retrieval System for Text-to-SQL on the Enterprise Scale](https://mlsanity.com/paper/2601.06564/) (2026)
- [STAR-P'olyaMath: Multi-Agent Reasoning under Persistent Meta-Strategic Supervision](https://mlsanity.com/paper/2605.19338/) (2026)
- [The Periodic Table of LLM Reasoning: A Structured Survey of Reasoning Paradigms, Methods, and Failure Modes](https://mlsanity.com/paper/2606.11470/) (2026)
- [On Understanding, Identifying, and Mitigating Vulnerabilities in Agentic Large Language Models](https://mlsanity.com/paper/2608.10530/) (2026)

## Abstract (arXiv)

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.