# Continually Post-training Small Models via Synthetic Self-distillation

arXiv: https://arxiv.org/abs/2610.13113 · HTML: https://mlsanity.com/paper/2610.13113/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Distillation for continual learning, one of 12 directions in Knowledge distillation.
- Builds on 32 of its 40 references that are in the map.
- First posted on arXiv 9 Oct 2026.

## Placed in

- Knowledge distillation / [Distillation for continual learning](https://mlsanity.com/distill/distillation-for-continual-learning/)

## Builds on (most cited first, 30 of 32)

- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [Overcoming catastrophic forgetting in neural networks](https://mlsanity.com/paper/1612.00796/) (2016)
- [Program Synthesis with Large Language Models](https://mlsanity.com/paper/2108.07732/) (2021)
- [GPQA: A Graduate-Level Google-Proof Q&A Benchmark](https://mlsanity.com/paper/2311.12022/) (2023)
- [Phi-3 Technical Report: A Highly Capable Language Model Locally on Your Phone](https://mlsanity.com/paper/2404.14219/) (2024)
- [MMLU-Pro: A More Robust and Challenging Multi-Task Language Understanding Benchmark](https://mlsanity.com/paper/2406.01574/) (2024)
- [Accelerating Large Language Model Decoding with Speculative Sampling](https://mlsanity.com/paper/2302.01318/) (2023)
- [On-Policy Distillation of Language Models: Learning from Self-Generated Mistakes](https://mlsanity.com/paper/2306.13649/) (2023)
- [An Empirical Study of Catastrophic Forgetting in Large Language Models During Continual Fine-tuning](https://mlsanity.com/paper/2308.08747/) (2023)
- [MedMCQA : A Large-scale Multi-Subject Multi-Choice Dataset for Medical domain Question Answering](https://mlsanity.com/paper/2203.14371/) (2022)
- [ToolAlpaca: Generalized Tool Learning for Language Models with 3000 Simulated Cases](https://mlsanity.com/paper/2306.05301/) (2023)
- [Beyond Human Data: Scaling Self-Training for Problem-Solving with Language Models](https://mlsanity.com/paper/2312.06585/) (2023)
- [Small Language Models are the Future of Agentic AI](https://mlsanity.com/paper/2506.02153/) (2025)
- [Self-Distillation Enables Continual Learning](https://mlsanity.com/paper/2601.19897/) (2026)
- [Continual Learning of Large Language Models: A Comprehensive Survey](https://mlsanity.com/paper/2404.16789/) (2024)
- [MobileLLM: Optimizing Sub-billion Parameter Language Models for On-Device Use Cases](https://mlsanity.com/paper/2402.14905/) (2024)
- [RL's Razor: Why Online Reinforcement Learning Forgets Less](https://mlsanity.com/paper/2509.04259/) (2025)
- [On the Generalization of SFT: A Reinforcement Learning Perspective with Reward Rectification](https://mlsanity.com/paper/2508.05629/) (2025)
- [Retaining by Doing: The Role of On-Policy Data in Mitigating Forgetting](https://mlsanity.com/paper/2510.18874/) (2025)
- [Towards Lifelong Learning of Large Language Models: A Survey](https://mlsanity.com/paper/2406.06391/) (2024)
- [InsCL: A Data-efficient Continual Learning Paradigm for Fine-tuning Large Language Models with Instructions](https://mlsanity.com/paper/2403.11435/) (2024)
- [Spurious Forgetting in Continual Learning of Language Models](https://mlsanity.com/paper/2501.13453/) (2025)
- [Reinforcement Fine-Tuning Naturally Mitigates Forgetting in Continual Post-Training](https://mlsanity.com/paper/2507.05386/) (2025)
- [Scaling Laws for Forgetting When Fine-Tuning Large Language Models](https://mlsanity.com/paper/2401.05605/) (2024)
- [Anchored Supervised Fine-Tuning](https://mlsanity.com/paper/2509.23753/) (2025)
- [Mapping Post-Training Forgetting in Language Models at Scale](https://mlsanity.com/paper/2510.17776/) (2025)
- [How to Fine-Tune a Reasoning Model? A Teacher-Student Cooperation Framework to Synthesize Student-Consistent SFT Data](https://mlsanity.com/paper/2604.14164/) (2026)
- [Beyond Static Models: An Evolving Framework for Continual Learning in Large Language Models across Training Stages](https://mlsanity.com/paper/2603.12658/) (2026)

## Abstract (arXiv)

Continual post-training faces a dual challenge of acquisition and retention: models must learn new capabilities while preserving prior knowledge. While Self-Distillation Fine-Tuning (SDFT) mitigates this using self-supervision with in-context demonstrations, it relies on strong in-context learning and instruction-following abilities. Consequently, SDFT fails on smaller models critical for low-latency, on-device use. To enable continual learning at smaller scales, we first identify the root cause of failure. We show that poor acquisition and forgetting correlate linearly with the post-trained model's distribution shift, revealing the necessity of in-distribution learning. We thus introduce Synthetic Self-Distillation (SynthSelf), imitating SDFT's in-distribution rewrite by outsourcing the task to a minimally larger, same-family aligner. Coupled with off-policy supervision and rejection sampling, this provides the high-quality supervision small models require without breaking their original distribution. Evaluations spanning 4 acquisition datasets (including a mixture) and 14 retention benchmarks show SynthSelf consistently outperforms 6 methods (including off- and on-policy distillation) across 3 small model scales. Extensive further analyses confirm SynthSelf paves the way toward effective small-model continual learning.