# Improving LLM Reasoning through Scaling Inference Computation with Collaborative Verification

arXiv: https://arxiv.org/abs/2410.05318 · HTML: https://mlsanity.com/paper/2410.05318/

## Key facts

- Cited by 40 papers in the map (data through 14 Oct 2026).
- Placed in Test-time compute and efficient thinking, one of 17 directions in LLM reasoning.
- Builds on 40 of its 62 references that are in the map.
- First posted on arXiv 5 Oct 2024.

## Placed in

- LLM reasoning / [Test-time compute and efficient thinking](https://mlsanity.com/lr/test-time-compute-and-efficient-thinking/)

## Builds on (most cited first, 30 of 40)

- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [Program Synthesis with Large Language Models](https://mlsanity.com/paper/2108.07732/) (2021)
- [Mistral 7B](https://mlsanity.com/paper/2310.06825/) (2023)
- [Qwen2 Technical Report](https://mlsanity.com/paper/2407.10671/) (2024)
- [Scaling LLM Test-Time Compute Optimally can be More Effective than Scaling Model Parameters](https://mlsanity.com/paper/2408.03314/) (2024)
- [Phi-3 Technical Report: A Highly Capable Language Model Locally on Your Phone](https://mlsanity.com/paper/2404.14219/) (2024)
- [Large Language Monkeys: Scaling Inference Compute with Repeated Sampling](https://mlsanity.com/paper/2407.21787/) (2024)
- [SimPO: Simple Preference Optimization with a Reference-Free Reward](https://mlsanity.com/paper/2405.14734/) (2024)
- [Math-Shepherd: Verify and Reinforce LLMs Step-by-step without Human Annotations](https://mlsanity.com/paper/2312.08935/) (2023)
- [Gemma: Open Models Based on Gemini Research and Technology](https://mlsanity.com/paper/2403.08295/) (2024)
- [Solving math word problems with process- and outcome-based feedback](https://mlsanity.com/paper/2211.14275/) (2022)
- [WizardMath: Empowering Mathematical Reasoning for Large Language Models via Reinforced Evol-Instruct](https://mlsanity.com/paper/2308.09583/) (2023)
- [ORPO: Monolithic Preference Optimization without Reference Model](https://mlsanity.com/paper/2403.07691/) (2024)
- [Generative Verifiers: Reward Modeling as Next-Token Prediction](https://mlsanity.com/paper/2408.15240/) (2024)
- [Improve Mathematical Reasoning in Language Models by Automated Process Supervision](https://mlsanity.com/paper/2406.06592/) (2024)
- [Contrastive Preference Optimization: Pushing the Boundaries of LLM Performance in Machine Translation](https://mlsanity.com/paper/2401.08417/) (2024)
- [DeepSeek-Coder-V2: Breaking the Barrier of Closed-Source Models in Code Intelligence](https://mlsanity.com/paper/2406.11931/) (2024)
- [KTO: Model Alignment as Prospect Theoretic Optimization](https://mlsanity.com/paper/2402.01306/) (2024)
- [V-STaR: Training Verifiers for Self-Taught Reasoners](https://mlsanity.com/paper/2402.06457/) (2024)
- [Accessing GPT-4 level Mathematical Olympiad Solutions via Monte Carlo Tree Self-refine with LLaMa-3 8B](https://mlsanity.com/paper/2406.07394/) (2024)
- [CodeGemma: Open Code Models Based on Gemma](https://mlsanity.com/paper/2406.11409/) (2024)
- [MAmmoTH2: Scaling Instructions from the Web](https://mlsanity.com/paper/2405.03548/) (2024)
- [MathScale: Scaling Instruction Tuning for Mathematical Reasoning](https://mlsanity.com/paper/2403.02884/) (2024)
- [OpenMathInstruct-1: A 1.8 Million Math Instruction Tuning Dataset](https://mlsanity.com/paper/2402.10176/) (2024)
- [InternLM-Math: Open Math Large Language Models Toward Verifiable Reasoning](https://mlsanity.com/paper/2402.06332/) (2024)

## Built on by (most cited first, 30 of 40)

- [Evolving Deeper LLM Thinking](https://mlsanity.com/paper/2501.09891/) (2025)
- [A Survey of Mathematical Reasoning in the Era of Multimodal Large Language Model: Benchmark, Method & Challenges](https://mlsanity.com/paper/2412.11936/) (2024)
- [SETS: Leveraging Self-Verification and Self-Correction for Improved Test-Time Scaling](https://mlsanity.com/paper/2501.19306/) (2025)
- [The Limits of Inference Scaling Through Resampling](https://mlsanity.com/paper/2411.17501/) (2024)
- [Wider or Deeper? Scaling LLM Inference-Time Compute with Adaptive Branching Tree Search](https://mlsanity.com/paper/2503.04412/) (2025)
- [ReVISE: Learning to Refine at Test-Time via Intrinsic Self-Verification](https://mlsanity.com/paper/2502.14565/) (2025)
- [First SFT, Second RL, Third UPT: Continual Improving Multi-Modal LLM Reasoning via Unsupervised Post-Training](https://mlsanity.com/paper/2505.22453/) (2025)
- [Inference-Time Hyper-Scaling with KV Cache Compression](https://mlsanity.com/paper/2506.05345/) (2025)
- [From Passive to Active Reasoning: Can Large Language Models Ask the Right Questions under Incomplete Information?](https://mlsanity.com/paper/2506.08295/) (2025)
- [Entropy-Gated Branching for Efficient Test-Time Reasoning](https://mlsanity.com/paper/2503.21961/) (2025)
- [VeriPlan: Integrating Formal Verification and LLMs into End-User Planning](https://mlsanity.com/paper/2502.17898/) (2025)
- [GenEOL: Harnessing the Generative Power of LLMs for Training-Free Sentence Embeddings](https://mlsanity.com/paper/2410.14635/) (2024)
- [VerifyLLM: LLM-Based Pre-Execution Task Plan Verification for Robots](https://mlsanity.com/paper/2507.05118/) (2025)
- [Zero-Shot Verification-guided Chain of Thoughts](https://mlsanity.com/paper/2501.13122/) (2025)
- [VerifiAgent: a Unified Verification Agent in Language Model Reasoning](https://mlsanity.com/paper/2504.00406/) (2025)
- [Not All Votes Count! Programs as Verifiers Improve Self-Consistency of Language Models for Math Reasoning](https://mlsanity.com/paper/2410.12608/) (2024)
- [DISC: Dynamic Decomposition Improves LLM Inference Scaling](https://mlsanity.com/paper/2502.16706/) (2025)
- [RAG-KG-IL: A Multi-Agent Hybrid Framework for Reducing Hallucinations and Enhancing LLM Reasoning through RAG and Incremental Knowledge Graph Learning Integration](https://mlsanity.com/paper/2503.13514/) (2025)
- [Drowning in Documents: Consequences of Scaling Reranker Inference](https://mlsanity.com/paper/2411.11767/) (2024)
- [Enhancing Reasoning Abilities of Small LLMs with Cognitive Alignment](https://mlsanity.com/paper/2504.09802/) (2025)
- [LogicReward: Incentivizing LLM Reasoning via Step-Wise Logical Supervision](https://mlsanity.com/paper/2512.18196/) (2025)
- [LADs: Leveraging LLMs for AI-Driven DevOps](https://mlsanity.com/paper/2502.20825/) (2025)
- [UserCentrix: An Agentic Memory-augmented AI Framework for Smart Spaces](https://mlsanity.com/paper/2505.00472/) (2025)
- [VL-GenRM: Enhancing Vision-Language Verification via Vision Experts and Iterative Training](https://mlsanity.com/paper/2506.13888/) (2025)
- [Integrating Expert Knowledge into Logical Programs via LLMs](https://mlsanity.com/paper/2502.12275/) (2025)
- [OptScale: Probabilistic Optimality for Inference-time Scaling](https://mlsanity.com/paper/2506.22376/) (2025)
- [Fast, Slow, and Tool-augmented Thinking for LLMs: A Review](https://mlsanity.com/paper/2508.12265/) (2025)
- [The Thinking Therapist: Training Large Language Models to Deliver Acceptance and Commitment Therapy using Supervised Fine-Tuning and Odds Ratio Policy Optimization](https://mlsanity.com/paper/2509.09712/) (2025)
- [Instructional Text Across Disciplines: A Survey of Representations, Downstream Tasks, and Open Challenges Toward Capable AI Agents](https://mlsanity.com/paper/2410.18529/) (2024)
- [From Test-taking to Cognitive Scaffolding: A Pedagogical Diagnostic Benchmark for LLMs on English Standardized Tests](https://mlsanity.com/paper/2505.17056/) (2025)

## Abstract (arXiv)

Despite significant advancements in the general capability of large language models (LLMs), they continue to struggle with consistent and accurate reasoning, especially in complex tasks such as mathematical and code reasoning. One key limitation is that LLMs are trained primarily on correct solutions, reducing their ability to detect and learn from errors, which hampers their ability to reliably verify and rank outputs. To address this, we scale up the inference-time computation by generating multiple reasoning paths and employing verifiers to assess and rank the generated outputs by correctness. To facilitate this, we introduce a comprehensive dataset consisting of correct and incorrect solutions for math and code tasks, generated by multiple LLMs. This diverse set of solutions enables verifiers to more effectively distinguish and rank correct answers from erroneous outputs. The training methods for building verifiers were selected based on an extensive comparison of existing approaches. Moreover, to leverage the unique strengths of different reasoning strategies, we propose a novel collaborative method integrating Chain-of-Thought (CoT) and Program-of-Thought (PoT) solutions for verification. CoT provides a clear, step-by-step reasoning process that enhances interpretability, while PoT, being executable, offers a precise and error-sensitive validation mechanism. By taking both of their strengths, our approach significantly improves the accuracy and reliability of reasoning verification. Our verifiers, Math-Rev and Code-Rev, demonstrate substantial performance gains to existing LLMs, achieving state-of-the-art results on benchmarks such as GSM8k and MATH and even outperforming GPT-4o with Qwen-72B-Instruct as the reasoner.