# Distillation Scaling Laws

arXiv: https://arxiv.org/abs/2502.08606 · HTML: https://mlsanity.com/paper/2502.08606/

## Key facts

- Cited by 67 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 65 of its 127 references that are in the map.
- First posted on arXiv 12 Feb 2025.

## Placed in

- LLM reasoning / [Prompting and chain-of-thought reasoning](https://mlsanity.com/lr/prompting-and-chain-of-thought-reasoning/)
- Knowledge distillation / [General knowledge distillation methods](https://mlsanity.com/distill/general-knowledge-distillation-methods/)

## Builds on (most cited first, 30 of 65)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [Outrageously Large Neural Networks: The Sparsely-Gated Mixture-of-Experts Layer](https://mlsanity.com/paper/1701.06538/) (2017)
- [Gemini 1.5: Unlocking multimodal understanding across millions of tokens of context](https://mlsanity.com/paper/2403.05530/) (2024)
- [Mistral 7B](https://mlsanity.com/paper/2310.06825/) (2023)
- [Training Compute-Optimal Large Language Models](https://mlsanity.com/paper/2203.15556/) (2022)
- [Gemma 2: Improving Open Language Models at a Practical Size](https://mlsanity.com/paper/2408.00118/) (2024)
- [Scaling LLM Test-Time Compute Optimally can be More Effective than Scaling Model Parameters](https://mlsanity.com/paper/2408.03314/) (2024)
- [Phi-3 Technical Report: A Highly Capable Language Model Locally on Your Phone](https://mlsanity.com/paper/2404.14219/) (2024)
- [Language Models (Mostly) Know What They Know](https://mlsanity.com/paper/2207.05221/) (2022)
- [GLU Variants Improve Transformer](https://mlsanity.com/paper/2002.05202/) (2020)
- [FitNets: Hints for Thin Deep Nets](https://mlsanity.com/paper/1412.6550/) (2014)
- [Large Language Monkeys: Scaling Inference Compute with Repeated Sampling](https://mlsanity.com/paper/2407.21787/) (2024)
- [Gemma: Open Models Based on Gemini Research and Technology](https://mlsanity.com/paper/2403.08295/) (2024)
- [DeepSeek-V3 Technical Report](https://mlsanity.com/paper/2412.19437/) (2024)
- [MiniCPM: Unveiling the Potential of Small Language Models with Scalable Training Strategies](https://mlsanity.com/paper/2404.06395/) (2024)
- [Phi-4 Technical Report](https://mlsanity.com/paper/2412.08905/) (2024)
- [DeepSeek LLM: Scaling Open-Source Language Models with Longtermism](https://mlsanity.com/paper/2401.02954/) (2024)
- [Deep Learning Scaling is Predictable, Empirically](https://mlsanity.com/paper/1712.00409/) (2017)
- [Textbooks Are All You Need II: phi-1.5 technical report](https://mlsanity.com/paper/2309.05463/) (2023)
- [Scaling Laws for Autoregressive Generative Modeling](https://mlsanity.com/paper/2010.14701/) (2020)
- [Scaling Data-Constrained Language Models](https://mlsanity.com/paper/2305.16264/) (2023)
- [Explaining Neural Scaling Laws](https://mlsanity.com/paper/2102.06701/) (2021)
- [Inference Scaling Laws: An Empirical Analysis of Compute-Optimal Inference for Problem-Solving with Language Models](https://mlsanity.com/paper/2408.00724/) (2024)

## Built on by (most cited first, 30 of 67)

- [Towards Reasoning Era: A Survey of Long Chain-of-Thought for Reasoning Large Language Models](https://mlsanity.com/paper/2503.09567/) (2025)
- [Rethinking On-Policy Distillation of Large Language Models: Phenomenology, Mechanism, and Recipe](https://mlsanity.com/paper/2604.13016/) (2026)
- [A Survey of On-Policy Distillation for Large Language Models](https://mlsanity.com/paper/2604.00626/) (2026)
- [Ministral 3](https://mlsanity.com/paper/2601.08584/) (2026)
- [Scaling Laws for Optimal Data Mixtures](https://mlsanity.com/paper/2507.09404/) (2025)
- [Scaling Laws of Synthetic Data for Language Models](https://mlsanity.com/paper/2503.19551/) (2025)
- [Universal Cross-Tokenizer Distillation via Approximate Likelihood Matching](https://mlsanity.com/paper/2503.20083/) (2025)
- [Prune-OPD: Efficient and Reliable On-Policy Distillation for Long-Horizon Reasoning](https://mlsanity.com/paper/2605.07804/) (2026)
- [Unmasking On-Policy Distillation: Where It Helps, Where It Hurts, and Why](https://mlsanity.com/paper/2605.10889/) (2026)
- [Hyperparameter Transfer Enables Consistent Gains of Matrix-Preconditioned Optimizers Across Scales](https://mlsanity.com/paper/2512.05620/) (2025)
- [Language Models Improve When Pretraining Data Matches Target Tasks](https://mlsanity.com/paper/2507.12466/) (2025)
- [DOPD: Dual On-policy Distillation](https://mlsanity.com/paper/2606.30626/) (2026)
- [Improved Scaling Laws in Linear Regression via Data Reuse](https://mlsanity.com/paper/2506.08415/) (2025)
- [Multi-Rollout On-Policy Distillation via Peer Successes and Failures](https://mlsanity.com/paper/2605.12652/) (2026)
- [Scaling with Collapse: Efficient and Predictable Training of LLM Families](https://mlsanity.com/paper/2509.25087/) (2025)
- [Towards Efficient CoT Distillation: Self-Guided Rationale Selector for Better Performance with Fewer Rationales](https://mlsanity.com/paper/2509.23574/) (2025)
- [Enhancing Reasoning Abilities of Small LLMs with Cognitive Alignment](https://mlsanity.com/paper/2504.09802/) (2025)
- [SCOUT: Teaching Pre-trained Language Models to Enhance Reasoning via Flow Chain-of-Thought](https://mlsanity.com/paper/2505.24181/) (2025)
- [Distilled Pretraining: A modern lens of Data, In-Context Learning and Test-Time Scaling](https://mlsanity.com/paper/2509.01649/) (2025)
- [Synthetic bootstrapped pretraining](https://mlsanity.com/paper/2509.15248/) (2025)
- [The Design Space of Tri-Modal Masked Diffusion Models](https://mlsanity.com/paper/2602.21472/) (2026)
- [A Theory of Inference Compute Scaling: Reasoning through Directed Stochastic Skill Search](https://mlsanity.com/paper/2507.00004/) (2025)
- [Compressibility Measures Complexity: Minimum Description Length Meets Singular Learning Theory](https://mlsanity.com/paper/2510.12077/) (2025)
- [In Good GRACEs: Principled Teacher Selection for Knowledge Distillation](https://mlsanity.com/paper/2511.02833/) (2025)
- [Balancing the Budget: Understanding Trade-offs Between Supervised and Preference-Based Finetuning](https://mlsanity.com/paper/2502.11284/) (2025)
- [Scalable Strategies for Continual Learning with Replay](https://mlsanity.com/paper/2505.12512/) (2025)
- [Realizing Scaling Laws in Recommender Systems: A Foundation-Expert Paradigm for Hyperscale Model Deployment](https://mlsanity.com/paper/2508.02929/) (2025)
- [Self-Distillation for Multi-Token Prediction](https://mlsanity.com/paper/2603.23911/) (2026)
- [Scaling Laws for Data-Efficient Visual Transfer Learning](https://mlsanity.com/paper/2504.13219/) (2025)
- [Improving Respiratory Sound Classification with Architecture-Agnostic Knowledge Distillation from Ensembles](https://mlsanity.com/paper/2505.22027/) (2025)

## Abstract (arXiv)

We propose a distillation scaling law that estimates distilled model performance based on a compute budget and its allocation between the student and teacher. Our findings mitigate the risks associated with large-scale distillation by enabling compute-optimal allocation for both the teacher and student to maximize student performance. We provide compute-optimal distillation recipes for two key scenarios: when a teacher already exists, and when a teacher needs training. In settings involving many students or an existing teacher, distillation outperforms supervised learning up to a compute level that scales predictably with student size. Conversely, if only one student is to be distilled and a teacher also requires training, supervised learning is generally preferable. Additionally, our large-scale study of distillation increases our understanding of the process and helps inform experimental design.