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The Signal is in the Steps: Local Scoring for Reasoning Data Selection

ICML 2026 · Large language models › Reasoning and chain of thought · approach: Efficient and adaptive thinking · 0 citations (OpenAlex)

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Proposes Local Average Log Probability (LALP), a step-level student-likelihood score with short context windows, to select reasoning distillation data from multiple teachers, outperforming global average log probability (GRAPE/GALP).

Problem

Selecting which candidate long-form reasoning traces from multiple heterogeneous teachers to use for SFT distillation; global student likelihood (GALP) fails to rank teachers and responses correctly in this regime.

Approach

Score each reasoning step by its token-averaged student log probability conditioned only on a small window of preceding steps and the prompt, then average over steps, instead of scoring the full trajectory with full-context likelihood.

Key results

• Per-prompt selection from mixed-teacher pool: LALP reaches 0.726 average accuracy vs 0.632 for GALP on Qwen2.5-32B-Instruct (+9.4 points), and GALP underperforms random (0.651).
• LALP correctly ranks teachers (QwQ > DeepSeek-R1 > Qwen3) for 7B and 32B students, while GALP induces the opposite ordering; rankings from 200 prompts match the full set.
• LALP improves over GALP by +9.1 points on GPQA-Diamond and +2.9 points on LiveCodeBench-Hard when trained on LIMO-selected math data.

Surprising findings

• Global average log probability selection underperforms random selection for the 32B student in the mixed-teacher setting.
• Qwen3-32B traces receive the highest GALP yet yield the worst downstream student accuracy, attributed to self-conditioning on repeated content.

Limitations

• LALP cannot verify long-range consistency; errors in early steps may still score highly if later steps follow from them.
• Step segmentation depends on an external LLM (GLM-4.5-Air), adding cost and dependence on segmentation quality.
• Theoretical toy model is simplified (Markov chain, uniform background) and only a proxy for coverage.

Experimental setup

Datasets: LIMO MATH

Benchmarks: MATH500 AIME 2025 AMC 2023 MINERVA KAOYAN OlympiadBench CN_MATH_2024 GPQA-Diamond LiveCodeBench

Metrics: accuracy average accuracy

Baselines: GALP (GRAPE) Random selection Local Lowest

Builds on: GRAPE LIMO LLaMA-Factory

Closest papers by meaning

• Collaborative Reasoning Distillation via Cross-Feedback and Coherent Curation (NeurIPS 2026 · similarity 0.89)
• Beyond What Seems Necessary: Hidden Gains from Scaling Training-Time Reasoning Length under Outcome Supervision (NeurIPS 2026 · similarity 0.89)
• RLKD: Distilling LLMs’ Reasoning via Reinforcement Learning (AAAI 2026 · similarity 0.88)
• Characterizing, Evaluating, and Optimizing Complex Reasoning (ICML 2026 · similarity 0.88)
• LARK: Learnability-Grounded Trajectory Selection for Efficient Reasoning Distillation (NeurIPS 2026 · similarity 0.88)
• Teaching Models to Teach Themselves: Reasoning at the Edge of Learnability (ICML 2026 · similarity 0.88)