Research map / Large language models / Reasoning and chain of thought
S^3cMath: Spontaneous Step-Level Self-Correction Makes Large Language Models Better Mathematical Reasoners
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Proposes S^3c-Math, LLMs trained via SFT on step-level self-correction data (S^3c-MathQA, 532K samples built from MetaMathQA by sampling wrong steps and annotating reflections with loss masking) to spontaneously detect and fix errors mid-reasoning.
Problem
LLM self-correction is usually post-hoc, multi-model, or externally guided rather than an intrinsic, spontaneous capability during step-by-step mathematical reasoning.
Approach
Build step-level self-correction SFT data from existing CoT data by sampling erroneous steps from a model trained on other folds, verifying them with pass@16 answer matching, inserting them with correction markers, annotating reflection and improvement with Llama-3-70B-Instruct, and masking loss on the wrong steps.
Key results
- On Meta-Llama-3-8B, S^3c-MathQA raised GSM8K Pass@1 from 81.12 to 82.94 and MATH Pass@1 from 30.58 to 33.14.
- On DeepSeek-Math-base, GSM8K Pass@1 rose from 79.30 to 82.49 and MATH Pass@1 from 38.22 to 41.40.
- Instance-level correction and MCTS-based correction data gave smaller gains than step-level S^3c-MathQA in ablations (e.g., GSM8K P@1 79.98 and 79.98 vs 81.65).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| add S3c-MathQA self-correction data with reflection and improvement (mixed into MetaMathQA) | Meta-Llama-3-8B · GSM8K | P@1: +1.82 (81.12 to 82.94) | Helped |
| add S3c-MathQA self-correction data with reflection and improvement | Deepseek-math-base · MATH | P@1: +3.18 (38.22 to 41.40) | Helped |
| add S3c-MathQA self-correction data with reflection and improvement | Meta-Llama-3-70B · Mathematics | P@1: +5.09 (29.08 to 34.17) | Helped |
| add S3c-MathQA self-correction data with reflection and improvement | Qwen2-Math-7B · MATH | P@1: -0.00 to -0.4 (51.32 to 51.76 P@1 is up, but M@32 62.64 to 62.40 down) | No clear effect |
| add S3c-MathQA self-correction data with reflection and improvement | Mistral-7B-v0.3 · Mathematics | P@1: 16.07 vs 17.35 P@1 (down); 28.10 vs 27.98 M@32 (up) | Mixed |
| remove reflection and improvement annotations from self-correction data (ablation) | Meta-Llama-3-8B · GSM8K | P@1: -1.29 (82.94 to 81.65) | Hurt |
| add reflection and improvement annotations to self-correction data (ablation) | Meta-Llama-3-8B · MATH | P@1: +0.82 (32.32 to 33.14) | Helped |
| over-sample MetaMathQA queries to match self-correction query distribution (no self-correction data) (ablation) | Meta-Llama-3-8B · GSM8K | P@1: -2.58 vs MetaMathQA baseline (81.12 to 78.54) | Hurt |
| replace step-level correction with instance-level correction data (ablation) | Meta-Llama-3-8B · GSM8K | P@1: -1.67 vs step-level w/o R&I (81.65 to 79.98) | Hurt |
| replace existing-path step sampling with MCTS-generated correction steps (ablation) | Meta-Llama-3-8B · GSM8K | P@1: -1.67 vs S3c-MathQA w/o R&I (81.65 to 79.98) | Hurt |
Surprising findings
- Changing query distribution to match S^3c-MathQA without self-correction content reduced GSM8K Pass@1 (78.54 vs 81.12), indicating the gains are not from distribution shift alone.
Limitations
- Sampled erroneous steps lack diversity; authors note need for diverse step generation.
- Quality of reflection and improvement annotations is not examined.
- Gains on some benchmarks are small or mixed (e.g., Mathematics for Llama-3-8B drops in w/o R&I setting).
Experimental setup
Datasets: MetaMathQA GSM8K MATH SVAMP Mathematics
Benchmarks: GSM8K MATH SVAMP Mathematics
Metrics: Pass@1 Majority@32
Baselines: MetaMathQA SFT baseline instance-level correction MCTS corrections
Builds on: MetaMathQA self-consistency Megatron-LM vLLM
Closest papers by meaning
- Can LLMs Correct Themselves? A Benchmark of Self-Correction in LLMs (NeurIPS 2025 · similarity 0.93)
- Large Language Models Cannot Self-Correct Reasoning Yet (ICLR 2024 · similarity 0.90)
- SuperCorrect: Advancing Small LLM Reasoning with Thought Template Distillation and Self-Correction (ICLR 2025 · similarity 0.90)
- Putnam-AXIOM: A Functional & Static Benchmark for Measuring Higher Level Mathematical Reasoning in LLMs (ICML 2025 · similarity 0.89)
- Toward Self-Improvement of LLMs via Imagination, Searching, and Criticizing (NeurIPS 2024 · similarity 0.89)
- Physics of Language Models: Part 2.2, How to Learn From Mistakes on Grade-School Math Problems (ICLR 2025 · similarity 0.89)
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