mlsanityData to 14 Oct 2026

LARK: Learnability-Grounded Trajectory Selection for Efficient Reasoning Distillation

arXiv 2605.30651 ↗First posted 28 May 2026cs.LG cs.AIcited by 1

On the map: LLM reasoning → Prompting and chain-of-thought reasoning

also in 1 more
Abstract (arXiv)

We study trajectory selection for reasoning distillation, where teacher-generated reasoning trajectories are selectively used as supervision for a student model. Existing methods rely on heuristics such as trajectory quality or model confidence, but they often overlook whether a trajectory is learnable by the student. In this paper, we present LARK, a learnability-grounded method for reasoning trajectory selection. LARK selects trajectories that the student can learn efficiently while preserving the generalization of the full training distribution. At the core of LARK is a learnability factor ρ, which characterizes the rate at which the student's training loss decreases. To estimate this rate efficiently and maintain generalization, we introduce a learnability proxy and a chi2-regularized selection policy that balances learnability and distributional coverage, both with strong theoretical guarantees on their estimation error. Empirically, LARK consistently outperforms data selection baselines across multiple base models and reasoning tasks. Diagnostic analyses show that the LARK score predicts downstream training utility and that LARK-selected trajectories induce faster supervised fine-tuning loss reduction. Our code is available at https://github.com/Tianrun-Yu/LARK.

Key facts. Cited by 1 paper 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 31 of its 35 references that are in the map. First posted on arXiv 28 May 2026.

Builds on

31 of 35 references.

Closest ancestors · 1

Same direction, newest first

  1. 2026Which Reasoning Trajectories Teach Students to Reason Better? A Simple Metric of Informative Alignment20 Jan

Other references · 30

  1. 2024The Llama 3 Herd of Modelscited by 14,715
  2. 2021Training Verifiers to Solve Math Word Problemscited by 10,109
  3. 2025Qwen3 Technical Reportcited by 8,820
  4. 2023Judging LLM-as-a-Judge with MT-Bench and Chatbot Arenacited by 8,626
  5. 2023Direct Preference Optimization: Your Language Model is Secretly a Reward Modelcited by 8,065
  6. 2021Measuring Mathematical Problem Solving With the MATH Datasetcited by 5,371
  7. 2023GPQA: A Graduate-Level Google-Proof Q&A Benchmarkcited by 2,879
  8. 2018Neural Tangent Kernel: Convergence and Generalization in Neural Networkscited by 2,621
  9. 2019Root Mean Square Layer Normalizationcited by 1,480
  10. 2025s1: Simple test-time scalingcited by 1,341
  11. 2024Qwen2.5-Math Technical Report: Toward Mathematical Expert Model via Self-Improvementcited by 1,090
  12. 2019Wide Neural Networks of Any Depth Evolve as Linear Models Under Gradient Descentcited by 738
18 more
  1. 2023Distilling Step-by-Step! Outperforming Larger Language Models with Less Training Data and Smaller Model Sizescited by 737
  2. 2023MetaMath: Bootstrap Your Own Mathematical Questions for Large Language Modelscited by 735
  3. 2018On Lazy Training in Differentiable Programmingcited by 675
  4. 2018Gradient Descent Provably Optimizes Over-parameterized Neural Networkscited by 659
  5. 2016Linear Convergence of Gradient and Proximal-Gradient Methods Under the Polyak-Lojasiewicz Conditioncited by 539
  6. 2024LESS: Selecting Influential Data for Targeted Instruction Tuningcited by 532
  7. 2025LIMO: Less is More for Reasoningcited by 498
  8. 2023Scaling Relationship on Learning Mathematical Reasoning with Large Language Modelscited by 427
  9. 2020Loss landscapes and optimization in over-parameterized non-linear systems and neural networkscited by 233
  10. 2025LIMR: Less is More for RL Scalingcited by 139
  11. 2022A Kernel-Based View of Language Model Fine-Tuningcited by 121
  12. 2022The Role of Coverage in Online Reinforcement Learningcited by 83
  13. 2024Correcting the Mythos of KL-Regularization: Direct Alignment without Overoptimization via Chi-Squared Preference Optimizationcited by 78
  14. 2025The Best Instruction-Tuning Data are Those That Fitcited by 52
  15. 2018On exponential convergence of SGD in non-convex over-parametrized learningcited by 33
  16. 2022Convergence of gradient descent for deep neural networkscited by 24
  17. 2025D3: Diversity, Difficulty, and Dependability-Aware Data Selection for Sample-Efficient LLM Instruction Tuningcited by 21
  18. 2025Bilevel Data Curation for LLM Fine-tuning: Offline Selection and Online Self-Refining Generationcited by 2

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2026: 1.

1 paper.

  1. 2026Self-Correction Can Amplify Hallucinations: Fact-Level Repair with Graph-Based Evidence Routing in Multimodal Generationcited by 0

Similar, not cited

Close in wording, no citation either way

  1. 2026Beyond Rejection Sampling: Trajectory Fusion for Scaling Mathematical Reasoning
  2. 2026Student-in-the-Loop Chain-of-Thought Distillation via Generation-Time Selection
  3. 2025TrajSelector: Harnessing Latent Representations for Efficient and Effective Best-of-N in Large Reasoning Model
  4. 2026Validity-Calibrated Reasoning Distillation
  5. 2025The Signal is in the Steps: Local Scoring for Reasoning Data Selection
  6. 2025Distilling the Essence: Efficient Reasoning Distillation via Sequence Truncation
  7. 2026Backtracking When It Strays: Mitigating Dual Exposure Biases in LLM Reasoning Distillation
  8. 2025Beyond Templates: Dynamic Adaptation of Reasoning Demonstrations via Feasibility-Aware Exploration