# Brewing Knowledge in Context: Distillation Perspectives on In-Context Learning

arXiv: https://arxiv.org/abs/2506.11516 · HTML: https://mlsanity.com/paper/2506.11516/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 39 of its 52 references that are in the map.
- First posted on arXiv 13 Jun 2025.

## Builds on (most cited first, 30 of 39)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer](https://mlsanity.com/paper/1910.10683/) (2019)
- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [PaLM: Scaling Language Modeling with Pathways](https://mlsanity.com/paper/2204.02311/) (2022)
- [On the Opportunities and Risks of Foundation Models](https://mlsanity.com/paper/2108.07258/) (2021)
- [Pre-train, Prompt, and Predict: A Systematic Survey of Prompting Methods in Natural Language Processing](https://mlsanity.com/paper/2107.13586/) (2021)
- [FitNets: Hints for Thin Deep Nets](https://mlsanity.com/paper/1412.6550/) (2014)
- [Root Mean Square Layer Normalization](https://mlsanity.com/paper/1910.07467/) (2019)
- [Rethinking the Role of Demonstrations: What Makes In-Context Learning Work?](https://mlsanity.com/paper/2202.12837/) (2022)
- [In-context Learning and Induction Heads](https://mlsanity.com/paper/2209.11895/) (2022)
- [An Explanation of In-context Learning as Implicit Bayesian Inference](https://mlsanity.com/paper/2111.02080/) (2021)
- [Transformers learn in-context by gradient descent](https://mlsanity.com/paper/2212.07677/) (2022)
- [What Can Transformers Learn In-Context? A Case Study of Simple Function Classes](https://mlsanity.com/paper/2208.01066/) (2022)
- [What learning algorithm is in-context learning? Investigations with linear models](https://mlsanity.com/paper/2211.15661/) (2022)
- [Prompt Programming for Large Language Models: Beyond the Few-Shot Paradigm](https://mlsanity.com/paper/2102.07350/) (2021)
- [MetaICL: Learning to Learn In Context](https://mlsanity.com/paper/2110.15943/) (2021)
- [Function Vectors in Large Language Models](https://mlsanity.com/paper/2310.15213/) (2023)
- [Transformers as Statisticians: Provable In-Context Learning with In-Context Algorithm Selection](https://mlsanity.com/paper/2306.04637/) (2023)
- [Can We Edit Factual Knowledge by In-Context Learning?](https://mlsanity.com/paper/2305.12740/) (2023)
- [Transformers as Algorithms: Generalization and Stability in In-context Learning](https://mlsanity.com/paper/2301.07067/) (2023)
- [The Learnability of In-Context Learning](https://mlsanity.com/paper/2303.07895/) (2023)
- [What and How does In-Context Learning Learn? Bayesian Model Averaging, Parameterization, and Generalization](https://mlsanity.com/paper/2305.19420/) (2023)
- [Uncovering mesa-optimization algorithms in Transformers](https://mlsanity.com/paper/2309.05858/) (2023)
- [A Theory of Emergent In-Context Learning as Implicit Structure Induction](https://mlsanity.com/paper/2303.07971/) (2023)
- [In-Context Learning through the Bayesian Prism](https://mlsanity.com/paper/2306.04891/) (2023)

## Built on by (most cited first, 1 of 1)

- [GUIDE: Guided Updates for In-context Decision Evolution in LLM-Driven Spacecraft Operations](https://mlsanity.com/paper/2603.27306/) (2026)

## Abstract (arXiv)

In-context learning (ICL) allows large language models (LLMs) to solve novel tasks without weight updates. Despite its empirical success, the mechanism behind ICL remains poorly understood, limiting our ability to interpret, improve, and reliably apply it. In this paper, we propose a new theoretical perspective that interprets ICL as an implicit form of knowledge distillation (KD), where prompt demonstrations guide the model to form a task-specific reference model during inference. Under this view, we derive a Rademacher complexity-based generalization bound and prove that the bias of the distilled weights grows linearly with the Maximum Mean Discrepancy (MMD) between the prompt and target distributions. This theoretical framework explains several empirical phenomena and unifies prior gradient-based and distributional analyses. To the best of our knowledge, this is the first to formalize inference-time attention as a distillation process, which provides theoretical insights for future prompt engineering and automated demonstration selection.