# On Learning Verifiers and Implications to Chain-of-Thought Reasoning

arXiv: https://arxiv.org/abs/2505.22650 · HTML: https://mlsanity.com/paper/2505.22650/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Placed in Prompting and chain-of-thought reasoning, one of 17 directions in LLM reasoning.
- Builds on 63 of its 104 references that are in the map.
- First posted on arXiv 28 May 2025.

## Placed in

- LLM reasoning / [Prompting and chain-of-thought reasoning](https://mlsanity.com/lr/prompting-and-chain-of-thought-reasoning/)

## Builds on (most cited first, 30 of 63)

- [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)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [Tree of Thoughts: Deliberate Problem Solving with Large Language Models](https://mlsanity.com/paper/2305.10601/) (2023)
- [WebGPT: Browser-assisted question-answering with human feedback](https://mlsanity.com/paper/2112.09332/) (2021)
- [Reasoning with Language Model is Planning with World Model](https://mlsanity.com/paper/2305.14992/) (2023)
- [Automatic Chain of Thought Prompting in Large Language Models](https://mlsanity.com/paper/2210.03493/) (2022)
- [On Exact Computation with an Infinitely Wide Neural Net](https://mlsanity.com/paper/1904.11955/) (2019)
- [Fine-Grained Analysis of Optimization and Generalization for Overparameterized Two-Layer Neural Networks](https://mlsanity.com/paper/1901.08584/) (2019)
- [Sophia: A Scalable Stochastic Second-order Optimizer for Language Model Pre-training](https://mlsanity.com/paper/2305.14342/) (2023)
- [Chain of Thought Empowers Transformers to Solve Inherently Serial Problems](https://mlsanity.com/paper/2402.12875/) (2024)
- [Reasoning with Latent Thoughts: On the Power of Looped Transformers](https://mlsanity.com/paper/2502.17416/) (2025)
- [Towards Resolving the Implicit Bias of Gradient Descent for Matrix Factorization: Greedy Low-Rank Learning](https://mlsanity.com/paper/2012.09839/) (2020)
- [Towards Understanding the Role of Over-Parametrization in Generalization of Neural Networks](https://mlsanity.com/paper/1805.12076/) (2018)
- [Understanding Gradient Descent on Edge of Stability in Deep Learning](https://mlsanity.com/paper/2205.09745/) (2022)
- [Deductive Verification of Chain-of-Thought Reasoning](https://mlsanity.com/paper/2306.03872/) (2023)
- [An Exponential Learning Rate Schedule for Deep Learning](https://mlsanity.com/paper/1910.07454/) (2019)
- [What Happens after SGD Reaches Zero Loss? --A Mathematical Framework](https://mlsanity.com/paper/2110.06914/) (2021)
- [Chain of Thoughtlessness? An Analysis of CoT in Planning](https://mlsanity.com/paper/2405.04776/) (2024)
- [Harnessing the Power of Infinitely Wide Deep Nets on Small-data Tasks](https://mlsanity.com/paper/1910.01663/) (2019)
- [Understanding the Generalization Benefit of Normalization Layers: Sharpness Reduction](https://mlsanity.com/paper/2206.07085/) (2022)
- [Same Pre-training Loss, Better Downstream: Implicit Bias Matters for Language Models](https://mlsanity.com/paper/2210.14199/) (2022)
- [Gradient Descent on Two-layer Nets: Margin Maximization and Simplicity Bias](https://mlsanity.com/paper/2110.13905/) (2021)
- [Understanding Warmup-Stable-Decay Learning Rates: A River Valley Loss Landscape Perspective](https://mlsanity.com/paper/2410.05192/) (2024)
- [Dichotomy of Early and Late Phase Implicit Biases Can Provably Induce Grokking](https://mlsanity.com/paper/2311.18817/) (2023)
- [Enhanced Convolutional Neural Tangent Kernels](https://mlsanity.com/paper/1911.00809/) (2019)
- [On the Validity of Modeling SGD with Stochastic Differential Equations (SDEs)](https://mlsanity.com/paper/2102.12470/) (2021)
- [The Optimal Sample Complexity of PAC Learning](https://mlsanity.com/paper/1507.00473/) (2015)
- [A Characterization of Multiclass Learnability](https://mlsanity.com/paper/2203.01550/) (2022)

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

- [Unlocking the Power of Multi-Agent LLM for Reasoning: From Lazy Agents to Deliberation](https://mlsanity.com/paper/2511.02303/) (2025)
- [Sample Complexity of Autoregressive Reasoning: Chain-of-Thought vs. End-to-End](https://mlsanity.com/paper/2604.12013/) (2026)
- [Adaptive Generate-Rank-Verify: Inference-Time Search with Costly Verification](https://mlsanity.com/paper/2605.17609/) (2026)
- [A Theoretical Framework for Self-Play Theorem Proving Algorithms](https://mlsanity.com/paper/2606.01861/) (2026)
- [If generative AI is the answer, what is the question?](https://mlsanity.com/paper/2509.06120/) (2025)
- [Prior Knowledge Makes It Possible: From Sublinear Graph Algorithms to LLM Test-Time Methods](https://mlsanity.com/paper/2510.16609/) (2025)

## Abstract (arXiv)

Chain-of-Thought reasoning has emerged as a powerful approach for solving complex mathematical and logical problems. However, it can often veer off track through incorrect or unsubstantiated inferences. Formal mathematical reasoning, which can be checked with a formal verifier, is one approach to addressing this issue. However, currently LLMs are simply not good enough to solve complex problems in a formal way, and even just formalizing an informal problem statement can be challenging. Motivated by this fact, in this work we consider the problem of learning reliable verifiers for natural language Chain-of-Thought reasoning. That is, given a problem statement and step-by-step solution in natural language, the aim of the verifier is to output [Yes] if the reasoning steps in the solution are all valid, and [No] otherwise. In this work we give a formal PAC-learning framework for studying this problem. We propose and analyze several natural verification goals, at different levels of strength, in this framework. We provide sample complexity upper-bounds for learning verifiers satisfying these goals, as well as lower-bound and impossibility results for learning other natural verification objectives without additional assumptions.