# Distribution-Aligned Sequence Distillation for Superior Long-CoT Reasoning

arXiv: https://arxiv.org/abs/2601.09088 · HTML: https://mlsanity.com/paper/2601.09088/

## Key facts

- Cited by 17 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 41 of its 48 references that are in the map.
- First posted on arXiv 14 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 41)

- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [Emerging Properties in Self-Supervised Vision Transformers](https://mlsanity.com/paper/2104.14294/) (2021)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [The Curious Case of Neural Text Degeneration](https://mlsanity.com/paper/1904.09751/) (2019)
- [GPQA: A Graduate-Level Google-Proof Q&A Benchmark](https://mlsanity.com/paper/2311.12022/) (2023)
- [Categorical Reparameterization with Gumbel-Softmax](https://mlsanity.com/paper/1611.01144/) (2016)
- [LiveCodeBench: Holistic and Contamination Free Evaluation of Large Language Models for Code](https://mlsanity.com/paper/2403.07974/) (2024)
- [Gemma 3 Technical Report](https://mlsanity.com/paper/2503.19786/) (2025)
- [Competition-Level Code Generation with AlphaCode](https://mlsanity.com/paper/2203.07814/) (2022)
- [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)
- [ChatGLM: A Family of Large Language Models from GLM-130B to GLM-4 All Tools](https://mlsanity.com/paper/2406.12793/) (2024)
- [On-Policy Distillation of Language Models: Learning from Self-Generated Mistakes](https://mlsanity.com/paper/2306.13649/) (2023)
- [iBOT: Image BERT Pre-Training with Online Tokenizer](https://mlsanity.com/paper/2111.07832/) (2021)
- [Measuring Coding Challenge Competence With APPS](https://mlsanity.com/paper/2105.09938/) (2021)
- [Sequence-Level Knowledge Distillation](https://mlsanity.com/paper/1606.07947/) (2016)
- [Sequence Level Training with Recurrent Neural Networks](https://mlsanity.com/paper/1511.06732/) (2015)
- [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)
- [DeepMath-103K: A Large-Scale, Challenging, Decontaminated, and Verifiable Mathematical Dataset for Advancing Reasoning](https://mlsanity.com/paper/2504.11456/) (2025)
- [Light-R1: Curriculum SFT, DPO and RL for Long COT from Scratch and Beyond](https://mlsanity.com/paper/2503.10460/) (2025)
- [AIMO-2 Winning Solution: Building State-of-the-Art Mathematical Reasoning Models with OpenMathReasoning dataset](https://mlsanity.com/paper/2504.16891/) (2025)
- [TACO: Topics in Algorithmic COde generation dataset](https://mlsanity.com/paper/2312.14852/) (2023)
- [Llama-Nemotron: Efficient Reasoning Models](https://mlsanity.com/paper/2505.00949/) (2025)
- [OpenCodeReasoning: Advancing Data Distillation for Competitive Coding](https://mlsanity.com/paper/2504.01943/) (2025)
- [Curriculum Temperature for Knowledge Distillation](https://mlsanity.com/paper/2211.16231/) (2022)
- [Nemotron 3 Nano: Open, Efficient Mixture-of-Experts Hybrid Mamba-Transformer Model for Agentic Reasoning](https://mlsanity.com/paper/2512.20848/) (2025)
- [Retaining by Doing: The Role of On-Policy Data in Mitigating Forgetting](https://mlsanity.com/paper/2510.18874/) (2025)
- [AceReason-Nemotron: Advancing Math and Code Reasoning through Reinforcement Learning](https://mlsanity.com/paper/2505.16400/) (2025)

## Built on by (most cited first, 17 of 17)

- [A Survey of On-Policy Distillation for Large Language Models](https://mlsanity.com/paper/2604.00626/) (2026)
- [Purified OPSD: On-Policy Self-Distillation Without Losing How to Think](https://mlsanity.com/paper/2607.02234/) (2026)
- [PACED: Distillation and On-Policy Self-Distillation at the Frontier of Student Competence](https://mlsanity.com/paper/2603.11178/) (2026)
- [Prefix Teach, Suffix Fade: Local Teachability Collapse in Strong-to-Weak On-Policy Distillation](https://mlsanity.com/paper/2605.13643/) (2026)
- [Adaptive Teacher Exposure for Self-Distillation in LLM Reasoning](https://mlsanity.com/paper/2605.11458/) (2026)
- [Backtracking When It Strays: Mitigating Dual Exposure Biases in LLM Reasoning Distillation](https://mlsanity.com/paper/2605.19433/) (2026)
- [Nanbeige4.1-3B: A Small General Model that Reasons, Aligns, and Acts](https://mlsanity.com/paper/2602.13367/) (2026)
- [From Chatbot to Digital Colleague: The Paradigm Shift Toward Persistent Autonomous AI](https://mlsanity.com/paper/2606.14502/) (2026)
- [ReasonXL: Shifting LLM Reasoning Language Without Sacrificing Performance](https://mlsanity.com/paper/2604.12378/) (2026)
- [Decomposing the Basic Abilities of Large Language Models: Mitigating Cross-Task Interference in Multi-Task Instruct-Tuning](https://mlsanity.com/paper/2605.05676/) (2026)
- [Path-Lock Expert: Separating Reasoning Mode in Hybrid Thinking via Architecture-Level Separation](https://mlsanity.com/paper/2604.27201/) (2026)
- [Medmarks: A Comprehensive Open-Source LLM Benchmark Suite for Medical Tasks](https://mlsanity.com/paper/2605.01417/) (2026)
- [ResearchMath-14K: Scaling Research-Level Mathematics via Agents](https://mlsanity.com/paper/2605.28003/) (2026)
- [Capacity-Dependent Effects of Data Selection for Reasoning](https://mlsanity.com/paper/2608.13721/) (2026)
- [Estimating and Orthogonalizing Unknown Pre-training Gradients for Continual Fine-tuning of Large Language Models](https://mlsanity.com/paper/2609.30935/) (2026)
- [Rufus-Air: An Open LLM Post-Training Recipe](https://mlsanity.com/paper/2609.29421/) (2026)
- [BoundaryEvo: Data-Model Co-Evolution at the Capability Boundary for Long-Chain Reasoning Distillation](https://mlsanity.com/paper/2610.13285/) (2026)

## Abstract (arXiv)

In this report, we introduce DASD-4B-Thinking, a lightweight yet highly capable, fully open-source reasoning model. It achieves SOTA performance among open-source models of comparable scale across challenging benchmarks in mathematics, scientific reasoning, and code generation -- even outperforming several larger models. We begin by critically reexamining a widely adopted distillation paradigm in the community: SFT on teacher-generated responses, also known as sequence-level distillation. Although a series of recent works following this scheme have demonstrated remarkable efficiency and strong empirical performance, they are primarily grounded in the SFT perspective. Consequently, these approaches focus predominantly on designing heuristic rules for SFT data filtering, while largely overlooking the core principle of distillation itself -- enabling the student model to learn the teacher's full output distribution so as to inherit its generalization capability. Specifically, we identify three critical limitations in current practice: i) Inadequate representation of the teacher's sequence-level distribution; ii) Misalignment between the teacher's output distribution and the student's learning capacity; and iii) Exposure bias arising from teacher-forced training versus autoregressive inference. In summary, these shortcomings reflect a systemic absence of explicit teacher-student interaction throughout the distillation process, leaving the essence of distillation underexploited. To address these issues, we propose several methodological innovations that collectively form an enhanced sequence-level distillation training pipeline. Remarkably, DASD-4B-Thinking obtains competitive results using only 448K training samples -- an order of magnitude fewer than those employed by most existing open-source efforts. To support community research, we publicly release our models and the training dataset.