# Why Can GPT Learn In-Context? Language Models Implicitly Perform Gradient Descent as Meta-Optimizers

arXiv: https://arxiv.org/abs/2212.10559 · HTML: https://mlsanity.com/paper/2212.10559/

## Key facts

- Cited by 204 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 29 references that are in the map.
- First posted on arXiv 20 Dec 2022.

## Builds on (most cited first, 14 of 14)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [PIQA: Reasoning about Physical Commonsense in Natural Language](https://mlsanity.com/paper/1911.11641/) (2019)
- [Character-level Convolutional Networks for Text Classification](https://mlsanity.com/paper/1509.01626/) (2015)
- [Train Short, Test Long: Attention with Linear Biases Enables Input Length Extrapolation](https://mlsanity.com/paper/2108.12409/) (2021)
- [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)
- [General-Purpose In-Context Learning by Meta-Learning Transformers](https://mlsanity.com/paper/2212.04458/) (2022)
- [Meta Learning Backpropagation And Improving It](https://mlsanity.com/paper/2012.14905/) (2020)
- [The Dual Form of Neural Networks Revisited: Connecting Test Time Predictions to Training Patterns via Spotlights of Attention](https://mlsanity.com/paper/2202.05798/) (2022)

## Built on by (most cited first, 30 of 204)

- [The Dawn of LMMs: Preliminary Explorations with GPT-4V(ision)](https://mlsanity.com/paper/2309.17421/) (2023)
- [Transformers as Statisticians: Provable In-Context Learning with In-Context Algorithm Selection](https://mlsanity.com/paper/2306.04637/) (2023)
- [Challenges and Applications of Large Language Models](https://mlsanity.com/paper/2307.10169/) (2023)
- [One Step of Gradient Descent is Provably the Optimal In-Context Learner with One Layer of Linear Self-Attention](https://mlsanity.com/paper/2307.03576/) (2023)
- [What In-Context Learning "Learns" In-Context: Disentangling Task Recognition and Task Learning](https://mlsanity.com/paper/2305.09731/) (2023)
- [Pretraining task diversity and the emergence of non-Bayesian in-context learning for regression](https://mlsanity.com/paper/2306.15063/) (2023)
- [Understanding Catastrophic Forgetting in Language Models via Implicit Inference](https://mlsanity.com/paper/2309.10105/) (2023)
- [In-Context Convergence of Transformers](https://mlsanity.com/paper/2310.05249/) (2023)
- [Are Emergent Abilities in Large Language Models just In-Context Learning?](https://mlsanity.com/paper/2309.01809/) (2023)
- [A Survey on LLM-Generated Text Detection: Necessity, Methods, and Future Directions](https://mlsanity.com/paper/2310.14724/) (2023)
- [How Many Pretraining Tasks Are Needed for In-Context Learning of Linear Regression?](https://mlsanity.com/paper/2310.08391/) (2023)
- [In-Context Learning with Iterative Demonstration Selection](https://mlsanity.com/paper/2310.09881/) (2023)
- [Generative Speech Recognition Error Correction with Large Language Models and Task-Activating Prompting](https://mlsanity.com/paper/2309.15649/) (2023)
- [Efficient Benchmarking of Language Models](https://mlsanity.com/paper/2308.11696/) (2023)
- [In-context Learning with Retrieved Demonstrations for Language Models: A Survey](https://mlsanity.com/paper/2401.11624/) (2024)
- [nGPT: Normalized Transformer with Representation Learning on the Hypersphere](https://mlsanity.com/paper/2410.01131/) (2024)
- [Evaluating the Zero-shot Robustness of Instruction-tuned Language Models](https://mlsanity.com/paper/2306.11270/) (2023)
- [Transformers Implement Functional Gradient Descent to Learn Non-Linear Functions In Context](https://mlsanity.com/paper/2312.06528/) (2023)
- [Towards Better Chain-of-Thought Prompting Strategies: A Survey](https://mlsanity.com/paper/2310.04959/) (2023)
- [LLM4Vuln: A Unified Evaluation Framework for Decoupling and Enhancing LLMs' Vulnerability Reasoning](https://mlsanity.com/paper/2401.16185/) (2024)
- [A Comprehensive Survey of Large Language Models and Multimodal Large Language Models in Medicine](https://mlsanity.com/paper/2405.08603/) (2024)
- [Revisiting VerilogEval: A Year of Improvements in Large-Language Models for Hardware Code Generation](https://mlsanity.com/paper/2408.11053/) (2024)
- [LLM as Dataset Analyst: Subpopulation Structure Discovery with Large Language Model](https://mlsanity.com/paper/2405.02363/) (2024)
- [Learning without training: The implicit dynamics of in-context learning](https://mlsanity.com/paper/2507.16003/) (2025)
- [In-Context Learning with Representations: Contextual Generalization of Trained Transformers](https://mlsanity.com/paper/2408.10147/) (2024)
- [Emergent Abilities in Large Language Models: A Survey](https://mlsanity.com/paper/2503.05788/) (2025)
- [M2IV: Towards Efficient and Fine-grained Multimodal In-Context Learning via Representation Engineering](https://mlsanity.com/paper/2504.04633/) (2025)
- [Can Multimodal Large Language Models Truly Perform Multimodal In-Context Learning?](https://mlsanity.com/paper/2311.18021/) (2023)
- [How to Configure Good In-Context Sequence for Visual Question Answering](https://mlsanity.com/paper/2312.01571/) (2023)
- [Safety Arithmetic: A Framework for Test-time Safety Alignment of Language Models by Steering Parameters and Activations](https://mlsanity.com/paper/2406.11801/) (2024)

## Abstract (arXiv)

Large pretrained language models have shown surprising in-context learning (ICL) ability. With a few demonstration input-label pairs, they can predict the label for an unseen input without parameter updates. Despite the great success in performance, its working mechanism still remains an open question. In this paper, we explain language models as meta-optimizers and understand in-context learning as implicit finetuning. Theoretically, we figure out that Transformer attention has a dual form of gradient descent. On top of it, we understand ICL as follows: GPT first produces meta-gradients according to the demonstration examples, and then these meta-gradients are applied to the original GPT to build an ICL model. We comprehensively compare the behaviors of in-context learning and explicit finetuning on real tasks to provide empirical evidence that supports our understanding. Experimental results show that in-context learning behaves similarly to explicit finetuning from multiple perspectives. Inspired by the dual form between Transformer attention and gradient descent, we design a momentum-based attention by analogy with gradient descent with momentum. The improved performance over vanilla attention further supports our understanding from another perspective, and more importantly, shows the potential to utilize our understanding for future model design. The code is available at urlhttps://aka.ms/icl.