# Self-Verifying Reflection Helps Transformers with CoT Reasoning

arXiv: https://arxiv.org/abs/2510.12157 · HTML: https://mlsanity.com/paper/2510.12157/

## Key facts

- Cited by 4 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 34 of its 42 references that are in the map.
- First posted on arXiv 14 Oct 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 34)

- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [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)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [GPT-4o System Card](https://mlsanity.com/paper/2410.21276/) (2024)
- [Large Language Models are Zero-Shot Reasoners](https://mlsanity.com/paper/2205.11916/) (2022)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [Self-Refine: Iterative Refinement with Self-Feedback](https://mlsanity.com/paper/2303.17651/) (2023)
- [Neural Machine Translation of Rare Words with Subword Units](https://mlsanity.com/paper/1508.07909/) (2015)
- [High-Dimensional Continuous Control Using Generalized Advantage Estimation](https://mlsanity.com/paper/1506.02438/) (2015)
- [Scaling LLM Test-Time Compute Optimally can be More Effective than Scaling Model Parameters](https://mlsanity.com/paper/2408.03314/) (2024)
- [Qwen2.5-Math Technical Report: Toward Mathematical Expert Model via Self-Improvement](https://mlsanity.com/paper/2409.12122/) (2024)
- [Tulu 3: Pushing Frontiers in Open Language Model Post-Training](https://mlsanity.com/paper/2411.15124/) (2024)
- [Does Reinforcement Learning Really Incentivize Reasoning Capacity in LLMs Beyond the Base Model?](https://mlsanity.com/paper/2504.13837/) (2025)
- [Faith and Fate: Limits of Transformers on Compositionality](https://mlsanity.com/paper/2305.18654/) (2023)
- [Improve Mathematical Reasoning in Language Models by Automated Process Supervision](https://mlsanity.com/paper/2406.06592/) (2024)
- [Training Language Models to Self-Correct via Reinforcement Learning](https://mlsanity.com/paper/2409.12917/) (2024)
- [DoReMi: Optimizing Data Mixtures Speeds Up Language Model Pretraining](https://mlsanity.com/paper/2305.10429/) (2023)
- [Towards Revealing the Mystery behind Chain of Thought: A Theoretical Perspective](https://mlsanity.com/paper/2305.15408/) (2023)
- [Physics of Language Models: Part 3.1, Knowledge Storage and Extraction](https://mlsanity.com/paper/2309.14316/) (2023)
- [Chain of Thought Empowers Transformers to Solve Inherently Serial Problems](https://mlsanity.com/paper/2402.12875/) (2024)
- [From Explicit CoT to Implicit CoT: Learning to Internalize CoT Step by Step](https://mlsanity.com/paper/2405.14838/) (2024)
- [Recursive Introspection: Teaching Language Model Agents How to Self-Improve](https://mlsanity.com/paper/2407.18219/) (2024)
- [O1 Replication Journey: A Strategic Progress Report -- Part 1](https://mlsanity.com/paper/2410.18982/) (2024)
- [Why think step by step? Reasoning emerges from the locality of experience](https://mlsanity.com/paper/2304.03843/) (2023)
- [GLoRe: When, Where, and How to Improve LLM Reasoning via Global and Local Refinements](https://mlsanity.com/paper/2402.10963/) (2024)
- [Beyond Answers: Transferring Reasoning Capabilities to Smaller LLMs Using Multi-Teacher Knowledge Distillation](https://mlsanity.com/paper/2402.04616/) (2024)
- [Can Large Language Models Detect Errors in Long Chain-of-Thought Reasoning?](https://mlsanity.com/paper/2502.19361/) (2025)

## Built on by (most cited first, 4 of 4)

- [Code as Agent Harness](https://mlsanity.com/paper/2605.18747/) (2026)
- [Memento 2: Learning by Stateful Reflective Memory](https://mlsanity.com/paper/2512.22716/) (2025)
- [Latent Thoughts Tuning: Bridging Context and Reasoning with Fused Information in Latent Tokens](https://mlsanity.com/paper/2602.10229/) (2026)
- [Position: Introspective Experience from Conversational Environments as a Path to Better Learning](https://mlsanity.com/paper/2602.14910/) (2026)

## Abstract (arXiv)

Advanced large language models (LLMs) frequently reflect in reasoning chain-of-thoughts (CoTs), where they self-verify the correctness of current solutions and explore alternatives. However, given recent findings that LLMs detect limited errors in CoTs, how reflection contributes to empirical improvements remains unclear. To analyze this issue, in this paper, we present a minimalistic reasoning framework to support basic self-verifying reflection for small transformers without natural language, which ensures analytic clarity and reduces the cost of comprehensive experiments. Theoretically, we prove that self-verifying reflection guarantees improvements if verification errors are properly bounded. Experimentally, we show that tiny transformers, with only a few million parameters, benefit from self-verification in both training and reflective execution, reaching remarkable LLM-level performance in integer multiplication and Sudoku. Similar to LLM results, we find that reinforcement learning (RL) improves in-distribution performance and incentivizes frequent reflection for tiny transformers, yet RL mainly optimizes shallow statistical patterns without faithfully reducing verification errors. In conclusion, integrating generative transformers with discriminative verification inherently facilitates CoT reasoning, regardless of scaling and natural language.