# What and How does In-Context Learning Learn? Bayesian Model Averaging, Parameterization, and Generalization

arXiv: https://arxiv.org/abs/2305.19420 · HTML: https://mlsanity.com/paper/2305.19420/

## Key facts

- Cited by 118 papers in the map (data through 14 Oct 2026).
- Builds on 54 of its 76 references that are in the map.
- First posted on arXiv 30 May 2023.

## Builds on (most cited first, 30 of 54)

- [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)
- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Large Language Models are Zero-Shot Reasoners](https://mlsanity.com/paper/2205.11916/) (2022)
- [Finetuned Language Models Are Zero-Shot Learners](https://mlsanity.com/paper/2109.01652/) (2021)
- [Self-Instruct: Aligning Language Models with Self-Generated Instructions](https://mlsanity.com/paper/2212.10560/) (2022)
- [Emergent Abilities of Large Language Models](https://mlsanity.com/paper/2206.07682/) (2022)
- [Pre-train, Prompt, and Predict: A Systematic Survey of Prompting Methods in Natural Language Processing](https://mlsanity.com/paper/2107.13586/) (2021)
- [Rethinking the Role of Demonstrations: What Makes In-Context Learning Work?](https://mlsanity.com/paper/2202.12837/) (2022)
- [Deep Sets](https://mlsanity.com/paper/1703.06114/) (2017)
- [Least-to-Most Prompting Enables Complex Reasoning in Large Language Models](https://mlsanity.com/paper/2205.10625/) (2022)
- [What Makes Good In-Context Examples for GPT-3?](https://mlsanity.com/paper/2101.06804/) (2021)
- [TinyBERT: Distilling BERT for Natural Language Understanding](https://mlsanity.com/paper/1909.10351/) (2019)
- [Fantastically Ordered Prompts and Where to Find Them: Overcoming Few-Shot Prompt Order Sensitivity](https://mlsanity.com/paper/2104.08786/) (2021)
- [Large Language Models Are Human-Level Prompt Engineers](https://mlsanity.com/paper/2211.01910/) (2022)
- [An Explanation of In-context Learning as Implicit Bayesian Inference](https://mlsanity.com/paper/2111.02080/) (2021)
- [Are Sixteen Heads Really Better than One?](https://mlsanity.com/paper/1905.10650/) (2019)
- [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)
- [Automatic Chain of Thought Prompting in Large Language Models](https://mlsanity.com/paper/2210.03493/) (2022)
- [Spectrally-normalized margin bounds for neural networks](https://mlsanity.com/paper/1706.08498/) (2017)
- [What learning algorithm is in-context learning? Investigations with linear models](https://mlsanity.com/paper/2211.15661/) (2022)
- [MINE: Mutual Information Neural Estimation](https://mlsanity.com/paper/1801.04062/) (2018)
- [Unified Language Model Pre-training for Natural Language Understanding and Generation](https://mlsanity.com/paper/1905.03197/) (2019)
- [Learning To Retrieve Prompts for In-Context Learning](https://mlsanity.com/paper/2112.08633/) (2021)
- [Error bounds for approximations with deep ReLU networks](https://mlsanity.com/paper/1610.01145/) (2016)
- [MetaICL: Learning to Learn In Context](https://mlsanity.com/paper/2110.15943/) (2021)

## Built on by (most cited first, 30 of 118)

- [Trained Transformers Learn Linear Models In-Context](https://mlsanity.com/paper/2306.09927/) (2023)
- [Function Vectors in Large Language Models](https://mlsanity.com/paper/2310.15213/) (2023)
- [In-Context Convergence of Transformers](https://mlsanity.com/paper/2310.05249/) (2023)
- [Should we be going MAD? A Look at Multi-Agent Debate Strategies for LLMs](https://mlsanity.com/paper/2311.17371/) (2023)
- [A Survey of Frontiers in LLM Reasoning: Inference Scaling, Learning to Reason, and Agentic Systems](https://mlsanity.com/paper/2504.09037/) (2025)
- [Are Emergent Abilities in Large Language Models just In-Context Learning?](https://mlsanity.com/paper/2309.01809/) (2023)
- [How Many Pretraining Tasks Are Needed for In-Context Learning of Linear Regression?](https://mlsanity.com/paper/2310.08391/) (2023)
- [Position: Graph Foundation Models are Already Here](https://mlsanity.com/paper/2402.02216/) (2024)
- [Can large language models explore in-context?](https://mlsanity.com/paper/2403.15371/) (2024)
- [How Do Transformers Learn In-Context Beyond Simple Functions? A Case Study on Learning with Representations](https://mlsanity.com/paper/2310.10616/) (2023)
- [Test-time regression: a unifying framework for designing sequence models with associative memory](https://mlsanity.com/paper/2501.12352/) (2025)
- [Is In-Context Learning in Large Language Models Bayesian? A Martingale Perspective](https://mlsanity.com/paper/2406.00793/) (2024)
- [In-Context Learning Learns Label Relationships but Is Not Conventional Learning](https://mlsanity.com/paper/2307.12375/) (2023)
- [Let Models Speak Ciphers: Multiagent Debate through Embeddings](https://mlsanity.com/paper/2310.06272/) (2023)
- [Reason for Future, Act for Now: A Principled Framework for Autonomous LLM Agents with Provable Sample Efficiency](https://mlsanity.com/paper/2309.17382/) (2023)
- [Transformers Learn Nonlinear Features In Context: Nonconvex Mean-field Dynamics on the Attention Landscape](https://mlsanity.com/paper/2402.01258/) (2024)
- [A Theoretical Understanding of Self-Correction through In-context Alignment](https://mlsanity.com/paper/2405.18634/) (2024)
- [An Information-Theoretic Analysis of In-Context Learning](https://mlsanity.com/paper/2401.15530/) (2024)
- [In-Context Learning with Representations: Contextual Generalization of Trained Transformers](https://mlsanity.com/paper/2408.10147/) (2024)
- [Do LLM Agents Have Regret? A Case Study in Online Learning and Games](https://mlsanity.com/paper/2403.16843/) (2024)
- [Large Language Models as Markov Chains](https://mlsanity.com/paper/2410.02724/) (2024)
- [The Mystery of In-Context Learning: A Comprehensive Survey on Interpretation and Analysis](https://mlsanity.com/paper/2311.00237/) (2023)
- [Pretrained transformer efficiently learns low-dimensional target functions in-context](https://mlsanity.com/paper/2411.02544/) (2024)
- [Unveiling the Statistical Foundations of Chain-of-Thought Prompting Methods](https://mlsanity.com/paper/2408.14511/) (2024)
- [Belief Dynamics Reveal the Dual Nature of In-Context Learning and Activation Steering](https://mlsanity.com/paper/2511.00617/) (2025)
- [Mind the Inconspicuous: Revealing the Hidden Weakness in Aligned LLMs' Refusal Boundaries](https://mlsanity.com/paper/2405.20653/) (2024)
- [Deciphering the Factors Influencing the Efficacy of Chain-of-Thought: Probability, Memorization, and Noisy Reasoning](https://mlsanity.com/paper/2407.01687/) (2024)
- [From Debate to Equilibrium: Belief-Driven Multi-Agent LLM Reasoning via Bayesian Nash Equilibrium](https://mlsanity.com/paper/2506.08292/) (2025)
- [Can In-context Learning Really Generalize to Out-of-distribution Tasks?](https://mlsanity.com/paper/2410.09695/) (2024)
- [AURORA:Automated Training Framework of Universal Process Reward Models via Ensemble Prompting and Reverse Verification](https://mlsanity.com/paper/2502.11520/) (2025)

## Abstract (arXiv)

In this paper, we conduct a comprehensive study of In-Context Learning (ICL) by addressing several open questions: (a) What type of ICL estimator is learned by large language models? (b) What is a proper performance metric for ICL and what is the error rate? (c) How does the transformer architecture enable ICL? To answer these questions, we adopt a Bayesian view and formulate ICL as a problem of predicting the response corresponding to the current covariate, given a number of examples drawn from a latent variable model. To answer (a), we show that, without updating the neural network parameters, ICL implicitly implements the Bayesian model averaging algorithm, which is proven to be approximately parameterized by the attention mechanism. For (b), we analyze the ICL performance from an online learning perspective and establish a O(1/T) regret bound for perfectly pretrained ICL, where T is the number of examples in the prompt. To answer (c), we show that, in addition to encoding Bayesian model averaging via attention, the transformer architecture also enables a fine-grained statistical analysis of pretraining under realistic assumptions. In particular, we prove that the error of pretrained model is bounded by a sum of an approximation error and a generalization error, where the former decays to zero exponentially as the depth grows, and the latter decays to zero sublinearly with the number of tokens in the pretraining dataset. Our results provide a unified understanding of the transformer and its ICL ability with bounds on ICL regret, approximation, and generalization, which deepens our knowledge of these essential aspects of modern language models.