mlsanityData to 14 Oct 2026

Which Tokens Should SFT Actually Learn? A Token-Trimming Perspective on Mathematical Reasoning

arXiv 2609.09707 ↗First posted 9 Sep 2026cs.AIcited by 0

On the map: LLM reasoning → Test-time compute and efficient thinking

Abstract (arXiv)

Supervised fine-tuning (SFT) applies a uniform cross-entropy loss to all target tokens, even though different tokens provide unequal learning signals for mathematical reasoning. This uniform treatment can over-sharpen already mastered tokens while amplifying learning pressure on uncertain, low-confidence tokens, leading to suboptimal training dynamics. We propose Trimmed Logit-Gap SFT (TrimSFT), a simple token-level reweighting method that scales the SFT loss according to the logit gap between the gold token and its strongest competitor. TrimSFT trims supervision away from both extremes: tokens already mastered (large logit gap) and tokens weakly supported by the current model (small or negative logit gap), concentrating learning within an intermediate logit-gap region between them. We instantiate this principle with a Gaussian weight centered at margin m with bandwidth τ, requiring no reference model or additional forward pass. We evaluate TrimSFT on six base models from the Llama, Qwen, and DeepMath families across five mathematical reasoning benchmarks. TrimSFT consistently improves over standard SFT, achieving the best average performance on five out of six models, with gains of up to +26.9 points over SFT on MATH500. Further analyses show that the bandwidth τ matters more than the exact margin location, and that half-trim variants that remove supervision pressure from only one side yield inferior trade-offs. A token-level logit-gap distribution analysis suggests that TrimSFT reshapes model confidence in a more balanced way than uniform SFT or monotonic reweighting methods. These results suggest that reasoning SFT can benefit from trimming both extremes rather than treating all tokens uniformly.

Key facts. No citing papers in the map yet (data through 14 Oct 2026). Placed in Test-time compute and efficient thinking, one of 17 directions in LLM reasoning. Builds on 33 of its 44 references that are in the map. First posted on arXiv 9 Sep 2026.

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33 of 44 references.

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Same direction, newest first

  1. 2025Enhancing Large Language Model Reasoning via Selective Critical Token Fine-Tuning13 Oct

Other references · 32

  1. 2022Training language models to follow instructions with human feedbackcited by 15,971
  2. 2024The Llama 3 Herd of Modelscited by 14,715
  3. 2022Chain-of-Thought Prompting Elicits Reasoning in Large Language Modelscited by 12,459
  4. 2021Training Verifiers to Solve Math Word Problemscited by 10,109
  5. 2024DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Modelscited by 9,379
  6. 2025Qwen3 Technical Reportcited by 8,820
  7. 2025DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learningcited by 6,330
  8. 2021Measuring Mathematical Problem Solving With the MATH Datasetcited by 5,371
  9. 2017On Calibration of Modern Neural Networkscited by 4,960
  10. 2022Training a Helpful and Harmless Assistant with Reinforcement Learning from Human Feedbackcited by 3,720
  11. 2024MMLU-Pro: A More Robust and Challenging Multi-Task Language Understanding Benchmarkcited by 1,848
  12. 2022Solving Quantitative Reasoning Problems with Language Modelscited by 1,392
20 more
  1. 2024Qwen2.5-Math Technical Report: Toward Mathematical Expert Model via Self-Improvementcited by 1,090
  2. 2018Co-teaching: Robust Training of Deep Neural Networks with Extremely Noisy Labelscited by 1,059
  3. 2019When Does Label Smoothing Help?cited by 988
  4. 2024SimPO: Simple Preference Optimization with a Reference-Free Rewardcited by 963
  5. 2017Focal Loss for Dense Object Detectioncited by 752
  6. 2023MetaMath: Bootstrap Your Own Mathematical Questions for Large Language Modelscited by 735
  7. 2023WizardMath: Empowering Mathematical Reasoning for Large Language Models via Reinforced Evol-Instructcited by 625
  8. 2025LIMO: Less is More for Reasoningcited by 498
  9. 2023MAmmoTH: Building Math Generalist Models through Hybrid Instruction Tuningcited by 487
  10. 2017Regularizing Neural Networks by Penalizing Confident Output Distributionscited by 464
  11. 2019Analysing Mathematical Reasoning Abilities of Neural Modelscited by 335
  12. 2022Mitigating Neural Network Overconfidence with Logit Normalizationcited by 252
  13. 2024OpenMathInstruct-1: A 1.8 Million Math Instruction Tuning Datasetcited by 143
  14. 2024Rho-1: Not All Tokens Are What You Needcited by 133
  15. 2025On the Generalization of SFT: A Reinforcement Learning Perspective with Reward Rectificationcited by 127
  16. 2024Taming Overconfidence in LLMs: Reward Calibration in RLHFcited by 112
  17. 2021The Devil is in the Margin: Margin-based Label Smoothing for Network Calibrationcited by 91
  18. 2025SFT Doesn't Always Hurt General Capabilities: Revisiting Domain-Specific Fine-Tuning in LLMscited by 24
  19. 2025What Makes a Good Curriculum? Disentangling the Effects of Data Ordering on LLM Mathematical Reasoningcited by 11
  20. 2026When Linguistic and Internal Confidence Diverge in Large Language Modelscited by 2

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