# The Limits of Inference Scaling Through Resampling

arXiv: https://arxiv.org/abs/2411.17501 · HTML: https://mlsanity.com/paper/2411.17501/

## Key facts

- Cited by 53 papers in the map (data through 14 Oct 2026).
- Builds on 62 of its 70 references that are in the map.
- First posted on arXiv 26 Nov 2024.

## Builds on (most cited first, 30 of 62)

- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [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)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [Reflexion: Language Agents with Verbal Reinforcement Learning](https://mlsanity.com/paper/2303.11366/) (2023)
- [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)
- [Self-Refine: Iterative Refinement with Self-Feedback](https://mlsanity.com/paper/2303.17651/) (2023)
- [Tree of Thoughts: Deliberate Problem Solving with Large Language Models](https://mlsanity.com/paper/2305.10601/) (2023)
- [Scaling LLM Test-Time Compute Optimally can be More Effective than Scaling Model Parameters](https://mlsanity.com/paper/2408.03314/) (2024)
- [Concrete Problems in AI Safety](https://mlsanity.com/paper/1606.06565/) (2016)
- [τ-bench: A Benchmark for Tool-Agent-User Interaction in Real-World Domains](https://mlsanity.com/paper/2406.12045/) (2024)
- [Is Your Code Generated by ChatGPT Really Correct? Rigorous Evaluation of Large Language Models for Code Generation](https://mlsanity.com/paper/2305.01210/) (2023)
- [Scaling Laws for Reward Model Overoptimization](https://mlsanity.com/paper/2210.10760/) (2022)
- [Large Language Monkeys: Scaling Inference Compute with Repeated Sampling](https://mlsanity.com/paper/2407.21787/) (2024)
- [CodeGen: An Open Large Language Model for Code with Multi-Turn Program Synthesis](https://mlsanity.com/paper/2203.13474/) (2022)
- [Generative Verifiers: Reward Modeling as Next-Token Prediction](https://mlsanity.com/paper/2408.15240/) (2024)
- [WebVoyager: Building an End-to-End Web Agent with Large Multimodal Models](https://mlsanity.com/paper/2401.13919/) (2024)
- [LeanDojo: Theorem Proving with Retrieval-Augmented Language Models](https://mlsanity.com/paper/2306.15626/) (2023)
- [Llemma: An Open Language Model For Mathematics](https://mlsanity.com/paper/2310.10631/) (2023)
- [CodeT: Code Generation with Generated Tests](https://mlsanity.com/paper/2207.10397/) (2022)
- [Chain-of-Verification Reduces Hallucination in Large Language Models](https://mlsanity.com/paper/2309.11495/) (2023)
- [Large Language Models are Effective Text Rankers with Pairwise Ranking Prompting](https://mlsanity.com/paper/2306.17563/) (2023)
- [Rewarding Progress: Scaling Automated Process Verifiers for LLM Reasoning](https://mlsanity.com/paper/2410.08146/) (2024)
- [Agent-as-a-Judge: Evaluate Agents with Agents](https://mlsanity.com/paper/2410.10934/) (2024)
- [DeepSeek-Prover: Advancing Theorem Proving in LLMs through Large-Scale Synthetic Data](https://mlsanity.com/paper/2405.14333/) (2024)
- [AI Agents That Matter](https://mlsanity.com/paper/2407.01502/) (2024)
- [V-STaR: Training Verifiers for Self-Taught Reasoners](https://mlsanity.com/paper/2402.06457/) (2024)
- [DigiRL: Training In-The-Wild Device-Control Agents with Autonomous Reinforcement Learning](https://mlsanity.com/paper/2406.11896/) (2024)

## Built on by (most cited first, 30 of 53)

- [A Survey of Frontiers in LLM Reasoning: Inference Scaling, Learning to Reason, and Agentic Systems](https://mlsanity.com/paper/2504.09037/) (2025)
- [Establishing Best Practices for Building Rigorous Agentic Benchmarks](https://mlsanity.com/paper/2507.02825/) (2025)
- [S*: Test Time Scaling for Code Generation](https://mlsanity.com/paper/2502.14382/) (2025)
- [Is Best-of-N the Best of Them? Coverage, Scaling, and Optimality in Inference-Time Alignment](https://mlsanity.com/paper/2503.21878/) (2025)
- [Best-of-N Jailbreaking](https://mlsanity.com/paper/2412.03556/) (2024)
- [Scaling of Search and Learning: A Roadmap to Reproduce o1 from Reinforcement Learning Perspective](https://mlsanity.com/paper/2412.14135/) (2024)
- [PonderLM: Pretraining Language Models to Ponder in Continuous Space](https://mlsanity.com/paper/2505.20674/) (2025)
- [From Passive to Active Reasoning: Can Large Language Models Ask the Right Questions under Incomplete Information?](https://mlsanity.com/paper/2506.08295/) (2025)
- [Think Deep, Not Just Long: Measuring LLM Reasoning Effort via Deep-Thinking Tokens](https://mlsanity.com/paper/2602.13517/) (2026)
- [Incentivizing LLMs to Self-Verify Their Answers](https://mlsanity.com/paper/2506.01369/) (2025)
- [AgentTTS: Large Language Model Agent for Test-time Compute-optimal Scaling Strategy in Complex Tasks](https://mlsanity.com/paper/2508.00890/) (2025)
- [PonderLM-2: Pretraining LLM with Latent Thoughts in Continuous Space](https://mlsanity.com/paper/2509.23184/) (2025)
- [Generative AI Act II: Test Time Scaling Drives Cognition Engineering](https://mlsanity.com/paper/2504.13828/) (2025)
- [Generating Symbolic World Models via Test-time Scaling of Large Language Models](https://mlsanity.com/paper/2502.04728/) (2025)
- [Multi2: Multi-Agent Test-Time Scalable Framework for Multi-Document Processing](https://mlsanity.com/paper/2502.20592/) (2025)
- [Better Process Supervision with Bi-directional Rewarding Signals](https://mlsanity.com/paper/2503.04618/) (2025)
- [Examining False Positives under Inference Scaling for Mathematical Reasoning](https://mlsanity.com/paper/2502.06217/) (2025)
- [VerifiAgent: a Unified Verification Agent in Language Model Reasoning](https://mlsanity.com/paper/2504.00406/) (2025)
- [Revisiting Test-Time Scaling: A Survey and a Diversity-Aware Method for Efficient Reasoning](https://mlsanity.com/paper/2506.04611/) (2025)
- [When Life Gives You Samples: The Benefits of Scaling up Inference Compute for Multilingual LLMs](https://mlsanity.com/paper/2506.20544/) (2025)
- [Trust but Verify! A Survey on Verification Design for Test-time Scaling](https://mlsanity.com/paper/2508.16665/) (2025)
- [Helpful Agent Meets Deceptive Judge: Understanding Vulnerabilities in Agentic Workflows](https://mlsanity.com/paper/2506.03332/) (2025)
- [Scaling Agentic Verifier for Competitive Coding](https://mlsanity.com/paper/2602.04254/) (2026)
- [Diverse Inference and Verification for Advanced Reasoning](https://mlsanity.com/paper/2502.09955/) (2025)
- [Making, not Taking, the Best of N](https://mlsanity.com/paper/2510.00931/) (2025)
- [Toward a Safe Internet of Agents](https://mlsanity.com/paper/2512.00520/) (2025)
- [Think in Parallel, Answer as One: Logit Averaging for Open-Ended Reasoning](https://mlsanity.com/paper/2512.02874/) (2025)
- [On the Limits of Test-Time Compute: Sequential Reward Filtering for Better Inference](https://mlsanity.com/paper/2512.04558/) (2025)
- [When the Reward Suite Is Leaky: A Preregistered Causal Contrast of Natural Verifier False Positives in RLVR](https://mlsanity.com/paper/2607.11022/) (2026)
- [Feedback That Backfires: Why Small Language Model Agents Repeat the Call They Just Watched Fail](https://mlsanity.com/paper/2608.23651/) (2026)

## Abstract (arXiv)

Recent research has generated hope that inference scaling, such as resampling solutions until they pass verifiers like unit tests, could allow weaker models to match stronger ones. Beyond inference, this approach also enables training reasoning models, where data is curated using rejection sampling against a verifier. However, we show that this approach is fundamentally limited when verifiers are imperfect and have a non-zero probability of producing false positives. Resampling cannot decrease this probability, so it imposes an upper bound to the accuracy of resampling-based inference scaling, regardless of compute budget. Our analysis shows that there is a strong correlation between the model's single-sample accuracy and its false positive rate on HumanEval and MBPP, whose unit tests have limited coverage. Therefore, no amount of inference scaling of weaker models can enable them to match the single-sample accuracy of a sufficiently strong model. Empirical results show that optimal sampling attempts are often fewer than 10, as the negative utility of false positives outweighs benefits, bending inference scaling curves downward. Finally, false positives may have other undesirable qualities, like poor adherence to coding style conventions.