# Boosting LLM Reasoning via Spontaneous Self-Correction

arXiv: https://arxiv.org/abs/2506.06923 · HTML: https://mlsanity.com/paper/2506.06923/

## Key facts

- Cited by 18 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 32 of its 44 references that are in the map.
- First posted on arXiv 7 Jun 2025.

## 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 32)

- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [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)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [Gemini 1.5: Unlocking multimodal understanding across millions of tokens of context](https://mlsanity.com/paper/2403.05530/) (2024)
- [AutoGen: Enabling Next-Gen LLM Applications via Multi-Agent Conversation](https://mlsanity.com/paper/2308.08155/) (2023)
- [Qwen2.5-Math Technical Report: Toward Mathematical Expert Model via Self-Improvement](https://mlsanity.com/paper/2409.12122/) (2024)
- [Large Language Models Cannot Self-Correct Reasoning Yet](https://mlsanity.com/paper/2310.01798/) (2023)
- [Encouraging Divergent Thinking in Large Language Models through Multi-Agent Debate](https://mlsanity.com/paper/2305.19118/) (2023)
- [Mastering Chess and Shogi by Self-Play with a General Reinforcement Learning Algorithm](https://mlsanity.com/paper/1712.01815/) (2017)
- [RAFT: Reward rAnked FineTuning for Generative Foundation Model Alignment](https://mlsanity.com/paper/2304.06767/) (2023)
- [Generative Verifiers: Reward Modeling as Next-Token Prediction](https://mlsanity.com/paper/2408.15240/) (2024)
- [Training Language Models to Self-Correct via Reinforcement Learning](https://mlsanity.com/paper/2409.12917/) (2024)
- [Self-critiquing models for assisting human evaluators](https://mlsanity.com/paper/2206.05802/) (2022)
- [Iterative Preference Learning from Human Feedback: Bridging Theory and Practice for RLHF under KL-Constraint](https://mlsanity.com/paper/2312.11456/) (2023)
- [Generating Sequences by Learning to Self-Correct](https://mlsanity.com/paper/2211.00053/) (2022)
- [REFINER: Reasoning Feedback on Intermediate Representations](https://mlsanity.com/paper/2304.01904/) (2023)
- [Recursive Introspection: Teaching Language Model Agents How to Self-Improve](https://mlsanity.com/paper/2407.18219/) (2024)
- [Orca-Math: Unlocking the potential of SLMs in Grade School Math](https://mlsanity.com/paper/2402.14830/) (2024)
- [Towards System 2 Reasoning in LLMs: Learning How to Think With Meta Chain-of-Thought](https://mlsanity.com/paper/2501.04682/) (2025)
- [Back to Basics: Revisiting REINFORCE Style Optimization for Learning from Human Feedback in LLMs](https://mlsanity.com/paper/2402.14740/) (2024)
- [RL4F: Generating Natural Language Feedback with Reinforcement Learning for Repairing Model Outputs](https://mlsanity.com/paper/2305.08844/) (2023)
- [GLoRe: When, Where, and How to Improve LLM Reasoning via Global and Local Refinements](https://mlsanity.com/paper/2402.10963/) (2024)
- [DeepSeek-R1 Thoughtology: Let's think about LLM Reasoning](https://mlsanity.com/paper/2504.07128/) (2025)
- [MALT: Improving Reasoning with Multi-Agent LLM Training](https://mlsanity.com/paper/2412.01928/) (2024)
- [Self-rewarding correction for mathematical reasoning](https://mlsanity.com/paper/2502.19613/) (2025)
- [Physics of Language Models: Part 2.2, How to Learn From Mistakes on Grade-School Math Problems](https://mlsanity.com/paper/2408.16293/) (2024)
- [The Perfect Blend: Redefining RLHF with Mixture of Judges](https://mlsanity.com/paper/2409.20370/) (2024)
- [S2R: Teaching LLMs to Self-verify and Self-correct via Reinforcement Learning](https://mlsanity.com/paper/2502.12853/) (2025)

## Built on by (most cited first, 18 of 18)

- [Failure Makes the Agent Stronger: Enhancing Accuracy through Structured Reflection for Reliable Tool Interactions](https://mlsanity.com/paper/2509.18847/) (2025)
- [Token-Level LLM Collaboration via FusionRoute](https://mlsanity.com/paper/2601.05106/) (2026)
- [Population-Evolve: a Parallel Sampling and Evolutionary Method for LLM Math Reasoning](https://mlsanity.com/paper/2512.19081/) (2025)
- [Re2: Unlocking LLM Reasoning via Reinforcement Learning with Re-solving](https://mlsanity.com/paper/2603.07197/) (2026)
- [ThinkTwice: Jointly Optimizing Large Language Models for Reasoning and Self-Refinement](https://mlsanity.com/paper/2604.01591/) (2026)
- [Putting on the Thinking Hats: A Survey on Chain of Thought Fine-tuning from the Perspective of Human Reasoning Mechanism](https://mlsanity.com/paper/2510.13170/) (2025)
- [CoT-Seg: Rethinking Segmentation with Chain-of-Thought Reasoning and Self-Correction](https://mlsanity.com/paper/2601.17420/) (2026)
- [The Self-Correction Illusion: Role Relabeling Gates Explicit Error Flagging in Large Language Models](https://mlsanity.com/paper/2606.05976/) (2026)
- [Learning Deliberately, Acting Intuitively: Unlocking Test-Time Reasoning in Multimodal LLMs](https://mlsanity.com/paper/2507.06999/) (2025)
- [Beyond In-Domain Detection: SpikeScore for Cross-Domain Hallucination Detection](https://mlsanity.com/paper/2601.19245/) (2026)
- [VeryTrace: Verifying Reasoning Traces through Compilable Formalism and Structured Verification](https://mlsanity.com/paper/2606.24124/) (2026)
- [Mixture of Debaters: Learn to Debate at Architectural Level in Multi-Agent Reasoning](https://mlsanity.com/paper/2606.29425/) (2026)
- [SVR-R1: Bootstrapping Multi-modal Reasoning with Self-verification in Reinforcement Learning](https://mlsanity.com/paper/2607.10966/) (2026)
- [The Two-Stage Decision-Sampling Hypothesis: Understanding the Emergence of Self-Reflection in RL-Trained LLMs](https://mlsanity.com/paper/2601.01580/) (2026)
- [Learning When to Act: Interval-Aware Reinforcement Learning with Predictive Temporal Structure](https://mlsanity.com/paper/2603.22384/) (2026)
- [ReSum: Synergizing LLM Reasoning and Summarization with Reinforcement Learning](https://mlsanity.com/paper/2606.13316/) (2026)
- [AMTFV: Agentic Mathematical Tool-Flow Verification for LLM Self-Correction](https://mlsanity.com/paper/2607.29549/) (2026)
- [Reinforcing Step-level Reasoning for Effective Self-Correction in LLMs](https://mlsanity.com/paper/2608.11573/) (2026)

## Abstract (arXiv)

While large language models (LLMs) have demonstrated remarkable success on a broad range of tasks, math reasoning remains a challenging one. One of the approaches for improving math reasoning is self-correction, which designs self-improving loops to let the model correct its own mistakes. However, existing self-correction approaches treat corrections as standalone post-generation refinements, relying on extra prompt and system designs to elicit self-corrections, instead of performing real-time, spontaneous self-corrections in a single pass. To address this, we propose SPOC, a spontaneous self-correction approach that enables LLMs to generate interleaved solutions and verifications in a single inference pass, with generation dynamically terminated based on verification outcomes, thereby effectively scaling inference time compute. SPOC considers a multi-agent perspective by assigning dual roles -- solution proposer and verifier -- to the same model. We adopt a simple yet effective approach to generate synthetic data for fine-tuning, enabling the model to develop capabilities for self-verification and multi-agent collaboration. We further improve its solution proposal and verification accuracy through online reinforcement learning. Experiments on mathematical reasoning benchmarks show that SPOC significantly improves performance. Notably, SPOC boosts the accuracy of Llama-3.1-8B and 70B Instruct models, achieving gains of 8.8% and 11.6% on MATH500, 10.0% and 20.0% on AMC23, and 3.3% and 6.7% on AIME24, respectively.