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Expanding Reasoning Potential in Foundation Model by Learning Diverse Chains of Thought Patterns

ICLR 2026 · Large language models › Reasoning and chain of thought · approach: Chain-of-thought training and analysis

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Defines foundation-model reasoning potential as inverse expected attempts and selects high-value long-CoT mid-training data (CoTP) via a Hungarian-matched weighted-DTW distance over reasoning-pattern chains and token-entropy chains.

Problem

Current mid-training with long chain-of-thought data uses CoT data indiscriminately, leaving unclear which CoT data most expands a foundation model's reasoning potential and RL upper bound.

Approach

Define reasoning potential as the inverse of expected first-passage attempts, build a core reference set of CoT samples enriched with TF-IDF-weighted atomic reasoning patterns, and select source CoT data by matching pattern chains (weighted DTW with n-gram cosine cost) and token-entropy chains via a Hungarian assignment.

Key results

• CoTP-selected 10B tokens improve the 85A6B MoE model by 9.58% on AIME 2024 and 2025 relative to LongCoTPool.
• CoTP raises downstream RL average accuracy to 51.44 vs 43.63 for LongCoTPool across AIME 2025, AIME 2024, HMMT 2025, BeyondAIME, MATH500.
• At 60B tokens, CoTP achieves a 4.72% average improvement on AIME 2025 and 2024 over its 30B-token results.

Surprising findings

• Mixing the LongCoTPool data pool yields lower average SFT performance than the constituent OpenR1-Math and AM-Distilled datasets alone.
• Chinese character-level n-gram pattern representations separate unrelated reasoning patterns much better than English (average similarity 0.035 vs 0.541).

Limitations

• Reasoning potential is evaluated via pass@k on a single proprietary 85A6B MoE model, limiting generality.
• Core set is partly built by manual selection of distinctive CoT samples.
• General-benchmark performance of CoTP is slightly below OpenR1-Math and AM-Distilled.

Experimental setup

Datasets: OpenR1-Math-220k AM-DeepSeek-R1-Distilled BoostQA KnowEdu

Benchmarks: AIME 2024 AIME 2025 HMMT 2025 BeyondAIME MATH500 MMLU CMMLU C-Eval WinoGrande HellaSwag ARC-C BBH

Metrics: pass@1 pass@k

Baselines: KnowEdu BoostQA JiuZhang3.0 MegaMathQA OpenMathInstruct-2 OpenR1-Math AM-DeepSeek-R1-Distilled LongCoTPool

Builds on: OctoThinker GSPO OpenR1-Math-220k

Closest papers by meaning

• Mind the Gap: Bridging Thought Leap for Improved Chain-of-Thought Tuning (NeurIPS 2025 · similarity 0.92)
• Demystifying Long Chain-of-Thought Reasoning (ICML 2025 · similarity 0.90)
• Facts Don't Speak Louder than Words: The Behavioral Essence of Long-CoT Distillation (NeurIPS 2026 · similarity 0.89)
• Unlocking the Capabilities of Thought: A Reasoning Boundary Framework to Quantify and Optimize Chain-of-Thought (NeurIPS 2024 · similarity 0.89)
• The CoT Encyclopedia: Analyzing, Predicting, and Controlling how a Reasoning Model will Think (ICLR 2026 · similarity 0.89)
• SCOUT: Teaching Pre-trained Language Models to Enhance Reasoning via Flow Chain-of-Thought (NeurIPS 2025 · similarity 0.89)