# Training-Trajectory-Aware Token Selection

arXiv: https://arxiv.org/abs/2601.10348 · HTML: https://mlsanity.com/paper/2601.10348/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Placed in Test-time compute and efficient thinking, one of 17 directions in LLM reasoning.
- Builds on 41 of its 56 references that are in the map.
- First posted on arXiv 15 Jan 2026.

## Placed in

- LLM reasoning / [Test-time compute and efficient thinking](https://mlsanity.com/lr/test-time-compute-and-efficient-thinking/)

## Builds on (most cited first, 30 of 41)

- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [GPQA: A Graduate-Level Google-Proof Q&A Benchmark](https://mlsanity.com/paper/2311.12022/) (2023)
- [Self-Instruct: Aligning Language Models with Self-Generated Instructions](https://mlsanity.com/paper/2212.10560/) (2022)
- [LiveCodeBench: Holistic and Contamination Free Evaluation of Large Language Models for Code](https://mlsanity.com/paper/2403.07974/) (2024)
- [MMLU-Pro: A More Robust and Challenging Multi-Task Language Understanding Benchmark](https://mlsanity.com/paper/2406.01574/) (2024)
- [Instruction-Following Evaluation for Large Language Models](https://mlsanity.com/paper/2311.07911/) (2023)
- [Diffusion-LM Improves Controllable Text Generation](https://mlsanity.com/paper/2205.14217/) (2022)
- [On-Policy Distillation of Language Models: Learning from Self-Generated Mistakes](https://mlsanity.com/paper/2306.13649/) (2023)
- [Large Language Diffusion Models](https://mlsanity.com/paper/2502.09992/) (2025)
- [Simple and Effective Masked Diffusion Language Models](https://mlsanity.com/paper/2406.07524/) (2024)
- [Discrete Diffusion Modeling by Estimating the Ratios of the Data Distribution](https://mlsanity.com/paper/2310.16834/) (2023)
- [Beyond the 80/20 Rule: High-Entropy Minority Tokens Drive Effective Reinforcement Learning for LLM Reasoning](https://mlsanity.com/paper/2506.01939/) (2025)
- [Dream 7B: Diffusion Large Language Models](https://mlsanity.com/paper/2508.15487/) (2025)
- [Zephyr: Direct Distillation of LM Alignment](https://mlsanity.com/paper/2310.16944/) (2023)
- [LIMO: Less is More for Reasoning](https://mlsanity.com/paper/2502.03387/) (2025)
- [OpenThoughts: Data Recipes for Reasoning Models](https://mlsanity.com/paper/2506.04178/) (2025)
- [Seed Diffusion: A Large-Scale Diffusion Language Model with High-Speed Inference](https://mlsanity.com/paper/2508.02193/) (2025)
- [Light-R1: Curriculum SFT, DPO and RL for Long COT from Scratch and Beyond](https://mlsanity.com/paper/2503.10460/) (2025)
- [LLaDA2.0: Scaling Up Diffusion Language Models to 100B](https://mlsanity.com/paper/2512.15745/) (2025)
- [Rho-1: Not All Tokens Are What You Need](https://mlsanity.com/paper/2404.07965/) (2024)
- [DPO Meets PPO: Reinforced Token Optimization for RLHF](https://mlsanity.com/paper/2404.18922/) (2024)
- [Small Models Struggle to Learn from Strong Reasoners](https://mlsanity.com/paper/2502.12143/) (2025)
- [Long Is More for Alignment: A Simple but Tough-to-Beat Baseline for Instruction Fine-Tuning](https://mlsanity.com/paper/2402.04833/) (2024)
- [Critical Tokens Matter: Token-Level Contrastive Estimation Enhances LLM's Reasoning Capability](https://mlsanity.com/paper/2411.19943/) (2024)
- [Maybe Only 0.5% Data is Needed: A Preliminary Exploration of Low Training Data Instruction Tuning](https://mlsanity.com/paper/2305.09246/) (2023)
- [LLaDA-MoE: A Sparse MoE Diffusion Language Model](https://mlsanity.com/paper/2509.24389/) (2025)
- [Diffusion Language Models are Super Data Learners](https://mlsanity.com/paper/2511.03276/) (2025)
- [Scaling Laws of Synthetic Data for Language Models](https://mlsanity.com/paper/2503.19551/) (2025)
- [Deconstructing Long Chain-of-Thought: A Structured Reasoning Optimization Framework for Long CoT Distillation](https://mlsanity.com/paper/2503.16385/) (2025)
- [PhyBench: A Physical Commonsense Benchmark for Evaluating Text-to-Image Models](https://mlsanity.com/paper/2406.11802/) (2024)

## Built on by (most cited first, 4 of 4)

- [Supervised Fine-Tuning Needs to Unlock the Potential of Token Priority](https://mlsanity.com/paper/2602.01227/) (2026)
- [FedSDR: Federated Self-Distillation with Rectification](https://mlsanity.com/paper/2605.18028/) (2026)
- [Momentum for Reasoning: Dense Intrinsic Signals in Policy Optimization](https://mlsanity.com/paper/2606.08815/) (2026)
- [Training LLM Judges from Language Feedback via Position-Selective Self-Distillation](https://mlsanity.com/paper/2609.38792/) (2026)

## Abstract (arXiv)

Efficient distillation is a key pathway for converting expensive reasoning capability into deployable efficiency, yet in the frontier regime where the student already has strong reasoning ability, naive continual distillation often yields limited gains or even degradation. We observe a characteristic training phenomenon: even as loss decreases monotonically, all performance metrics can drop sharply at almost the same bottleneck, before gradually recovering. We further uncover a token-level mechanism: confidence bifurcates into steadily increasing Imitation-Anchor Tokens that quickly anchor optimization and other yet-to-learn tokens whose confidence is suppressed until after the bottleneck. And the characteristic that these two types of tokens cannot coexist is the root cause of the failure in continual distillation. To this end, we propose Training-Trajectory-Aware Token Selection (T3S) to reconstruct the training objective at the token level, clearing the optimization path for yet-to-learn tokens. T3S yields consistent gains in both AR and dLLM settings: with only hundreds of examples, Qwen3-8B surpasses DeepSeek-R1 on competitive reasoning benchmarks, Qwen3-32B approaches Qwen3-235B, and T3-trained LLaDA-2.0-Mini exceeds its AR baseline, achieving state-of-the-art performance among all of 16B-scale no-think models.