# Which Reasoning Trajectories Teach Students to Reason Better? A Simple Metric of Informative Alignment

arXiv: https://arxiv.org/abs/2601.14249 · HTML: https://mlsanity.com/paper/2601.14249/

## Key facts

- Cited by 13 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 48 of its 70 references that are in the map.
- First posted on arXiv 20 Jan 2026.

## Placed in

- LLM reasoning / [Prompting and chain-of-thought reasoning](https://mlsanity.com/lr/prompting-and-chain-of-thought-reasoning/)
- Knowledge distillation / [Knowledge distillation for LLMs](https://mlsanity.com/distill/knowledge-distillation-for-llms/)

## Builds on (most cited first, 30 of 48)

- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [Efficient Memory Management for Large Language Model Serving with PagedAttention](https://mlsanity.com/paper/2309.06180/) (2023)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [GPQA: A Graduate-Level Google-Proof Q&A Benchmark](https://mlsanity.com/paper/2311.12022/) (2023)
- [FlashAttention-2: Faster Attention with Better Parallelism and Work Partitioning](https://mlsanity.com/paper/2307.08691/) (2023)
- [LlamaFactory: Unified Efficient Fine-Tuning of 100+ Language Models](https://mlsanity.com/paper/2403.13372/) (2024)
- [gpt-oss-120b & gpt-oss-20b Model Card](https://mlsanity.com/paper/2508.10925/) (2025)
- [s1: Simple test-time scaling](https://mlsanity.com/paper/2501.19393/) (2025)
- [LIMA: Less Is More for Alignment](https://mlsanity.com/paper/2305.11206/) (2023)
- [STaR: Bootstrapping Reasoning With Reasoning](https://mlsanity.com/paper/2203.14465/) (2022)
- [On-Policy Distillation of Language Models: Learning from Self-Generated Mistakes](https://mlsanity.com/paper/2306.13649/) (2023)
- [Instruction Tuning with GPT-4](https://mlsanity.com/paper/2304.03277/) (2023)
- [Improved Knowledge Distillation via Teacher Assistant](https://mlsanity.com/paper/1902.03393/) (2019)
- [LIMO: Less is More for Reasoning](https://mlsanity.com/paper/2502.03387/) (2025)
- [Studying Large Language Model Generalization with Influence Functions](https://mlsanity.com/paper/2308.03296/) (2023)
- [From Quantity to Quality: Boosting LLM Performance with Self-Guided Data Selection for Instruction Tuning](https://mlsanity.com/paper/2308.12032/) (2023)
- [OpenThoughts: Data Recipes for Reasoning Models](https://mlsanity.com/paper/2506.04178/) (2025)
- [Llama-Nemotron: Efficient Reasoning Models](https://mlsanity.com/paper/2505.00949/) (2025)
- [Phi-4-reasoning Technical Report](https://mlsanity.com/paper/2504.21318/) (2025)
- [LLMs Can Easily Learn to Reason from Demonstrations Structure, not content, is what matters!](https://mlsanity.com/paper/2502.07374/) (2025)
- [On the Generalization of SFT: A Reinforcement Learning Perspective with Reward Rectification](https://mlsanity.com/paper/2508.05629/) (2025)
- [Small Models Struggle to Learn from Strong Reasoners](https://mlsanity.com/paper/2502.12143/) (2025)
- [Learning What Reinforcement Learning Can't: Interleaved Online Fine-Tuning for Hardest Questions](https://mlsanity.com/paper/2506.07527/) (2025)
- [Retaining by Doing: The Role of On-Policy Data in Mitigating Forgetting](https://mlsanity.com/paper/2510.18874/) (2025)
- [Speculative Knowledge Distillation: Bridging the Teacher-Student Gap Through Interleaved Sampling](https://mlsanity.com/paper/2410.11325/) (2024)
- [BREAD: Branched Rollouts from Expert Anchors Bridge SFT & RL for Reasoning](https://mlsanity.com/paper/2506.17211/) (2025)
- [Selective Reflection-Tuning: Student-Selected Data Recycling for LLM Instruction-Tuning](https://mlsanity.com/paper/2402.10110/) (2024)
- [The Best Instruction-Tuning Data are Those That Fit](https://mlsanity.com/paper/2502.04194/) (2025)

## Built on by (most cited first, 13 of 13)

- [Towards Understanding On-Policy Distillation through the Lens of Test-Time Scaling](https://mlsanity.com/paper/2608.11829/) (2026)
- [On the Role of Reasoning Patterns in the Generalization Discrepancy of Long Chain-of-Thought Supervised Fine-Tuning](https://mlsanity.com/paper/2604.01702/) (2026)
- [Execution-First Synthetic Tool-Use Trace Generation for LLM Agents](https://mlsanity.com/paper/2607.29175/) (2026)
- [DeltaPrompts: Escaping the Zero-Delta Trap in Multimodal Distillation](https://mlsanity.com/paper/2605.15532/) (2026)
- [When the Strongest Teacher Is Not the Best Teacher: Student-Centric Answer Selection](https://mlsanity.com/paper/2605.26872/) (2026)
- [LARK: Learnability-Grounded Trajectory Selection for Efficient Reasoning Distillation](https://mlsanity.com/paper/2605.30651/) (2026)
- [Diagnosing Harmful Continuation in Answer-Correct Long-CoT Training Traces](https://mlsanity.com/paper/2605.29288/) (2026)
- [MI-Distillation: Selecting from Model-Interpolated Instruct-Reasoning Data Spectrum for Chain-of-Thought Distillation](https://mlsanity.com/paper/2608.29623/) (2026)
- [Which Medical Questions Deserve Rationales? Perturbation-Sensitive Selection for Robust QA](https://mlsanity.com/paper/2609.09684/) (2026)
- [On-Policy Parameter Update Direction Underlies Generalization in LLM Post-Training](https://mlsanity.com/paper/2609.36659/) (2026)
- [Learning More by Training Less: Uncertainty-Guided Progressive Contraction for Efficient Reasoning Post-Training](https://mlsanity.com/paper/2610.12933/) (2026)
- [Audit Before You Distill: A Controlled Workflow for Reasoning Transfer into Compact Medical Language Models](https://mlsanity.com/paper/2610.16713/) (2026)
- [Cowork-Gym: Synthesizing Interactive Work Environments at Scale](https://mlsanity.com/paper/2610.17670/) (2026)

## Abstract (arXiv)

Long chain-of-thought (CoT) trajectories provide rich supervision signals for distilling reasoning from teacher to student LLMs. However, both prior work and our experiments show that trajectories from stronger teachers do not necessarily yield better students, highlighting the importance of data-student suitability in distillation. Existing methods assess suitability primarily through student likelihood, favoring trajectories that align closely with the student model's current behavior but overlooking more informative ones. Addressing this, we propose Rank-Surprisal Ratio (RSR), a simple metric that captures both alignment and informativeness to assess the suitability of a reasoning trajectory. RSR is motivated by the observation that effective trajectories typically balance learning signal strength and behavioral alignment by combining low absolute probability with relatively high-ranked tokens under the student model. Concretely, RSR is defined as the ratio of a trajectory's average token-wise rank to its average negative log-likelihood, and is straightforward to compute and interpret. Across five student models and reasoning trajectories from 11 diverse teachers, RSR strongly correlates with post-training reasoning performance (average Spearman 0.86), consistently outperforming existing metrics. We further demonstrate its practical utility in both trajectory selection and teacher selection.