# The mechanistic basis of data dependence and abrupt learning in an in-context classification task

arXiv: https://arxiv.org/abs/2312.03002 · HTML: https://mlsanity.com/paper/2312.03002/

## Key facts

- Cited by 118 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 24 references that are in the map.
- First posted on arXiv 3 Dec 2023.

## Builds on (most cited first, 18 of 18)

- [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)
- [Interpretability in the Wild: a Circuit for Indirect Object Identification in GPT-2 small](https://mlsanity.com/paper/2211.00593/) (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)
- [Data Distributional Properties Drive Emergent In-Context Learning in Transformers](https://mlsanity.com/paper/2205.05055/) (2022)
- [Transformers as Statisticians: Provable In-Context Learning with In-Context Algorithm Selection](https://mlsanity.com/paper/2306.04637/) (2023)
- [Transformers learn to implement preconditioned gradient descent for in-context learning](https://mlsanity.com/paper/2306.00297/) (2023)
- [Using the Output Embedding to Improve Language Models](https://mlsanity.com/paper/1608.05859/) (2016)
- [Human-Timescale Adaptation in an Open-Ended Task Space](https://mlsanity.com/paper/2301.07608/) (2023)
- [Are Emergent Abilities in Large Language Models just In-Context Learning?](https://mlsanity.com/paper/2309.01809/) (2023)
- [General-Purpose In-Context Learning by Meta-Learning Transformers](https://mlsanity.com/paper/2212.04458/) (2022)
- [Tying Word Vectors and Word Classifiers: A Loss Framework for Language Modeling](https://mlsanity.com/paper/1611.01462/) (2016)
- [In-Context Learning through the Bayesian Prism](https://mlsanity.com/paper/2306.04891/) (2023)
- [The Transient Nature of Emergent In-Context Learning in Transformers](https://mlsanity.com/paper/2311.08360/) (2023)
- [The Omniglot challenge: a 3-year progress report](https://mlsanity.com/paper/1902.03477/) (2019)

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

- [The Evolution of Statistical Induction Heads: In-Context Learning Markov Chains](https://mlsanity.com/paper/2402.11004/) (2024)
- [A Practical Review of Mechanistic Interpretability for Transformer-Based Language Models](https://mlsanity.com/paper/2407.02646/) (2024)
- [Attention Heads of Large Language Models: A Survey](https://mlsanity.com/paper/2409.03752/) (2024)
- [On the Emergence of Position Bias in Transformers](https://mlsanity.com/paper/2502.01951/) (2025)
- [Active-Dormant Attention Heads: Mechanistically Demystifying Extreme-Token Phenomena in LLMs](https://mlsanity.com/paper/2410.13835/) (2024)
- [Asymptotic theory of in-context learning by linear attention](https://mlsanity.com/paper/2405.11751/) (2024)
- [Training Dynamics of In-Context Learning in Linear Attention](https://mlsanity.com/paper/2501.16265/) (2025)
- [Is Mamba Capable of In-Context Learning?](https://mlsanity.com/paper/2402.03170/) (2024)
- [Why Larger Language Models Do In-context Learning Differently?](https://mlsanity.com/paper/2405.19592/) (2024)
- [Talking Heads: Understanding Inter-layer Communication in Transformer Language Models](https://mlsanity.com/paper/2406.09519/) (2024)
- [Language Models Are Capable of Metacognitive Monitoring and Control of Their Internal Activations](https://mlsanity.com/paper/2505.13763/) (2025)
- [How do language models learn facts? Dynamics, curricula and hallucinations](https://mlsanity.com/paper/2503.21676/) (2025)
- [Pixels Versus Priors: Controlling Knowledge Priors in Vision-Language Models through Visual Counterfacts](https://mlsanity.com/paper/2505.17127/) (2025)
- [Interpreting Key Mechanisms of Factual Recall in Transformer-Based Language Models](https://mlsanity.com/paper/2403.19521/) (2024)
- [Iteration Head: A Mechanistic Study of Chain-of-Thought](https://mlsanity.com/paper/2406.02128/) (2024)
- [A phase transition between positional and semantic learning in a solvable model of dot-product attention](https://mlsanity.com/paper/2402.03902/) (2024)
- [Belief Dynamics Reveal the Dual Nature of In-Context Learning and Activation Steering](https://mlsanity.com/paper/2511.00617/) (2025)
- [There Will Be a Scientific Theory of Deep Learning](https://mlsanity.com/paper/2604.21691/) (2026)
- [Out-of-distribution generalization via composition: a lens through induction heads in Transformers](https://mlsanity.com/paper/2408.09503/) (2024)
- [A Percolation Model of Emergence: Analyzing Transformers Trained on a Formal Language](https://mlsanity.com/paper/2408.12578/) (2024)
- [The emergence of sparse attention: impact of data distribution and benefits of repetition](https://mlsanity.com/paper/2505.17863/) (2025)
- [Attention Prompting on Image for Large Vision-Language Models](https://mlsanity.com/paper/2409.17143/) (2024)
- [Bypassing the Exponential Dependency: Looped Transformers Efficiently Learn In-context by Multi-step Gradient Descent](https://mlsanity.com/paper/2410.11268/) (2024)
- [Deeper Insights Without Updates: The Power of In-Context Learning Over Fine-Tuning](https://mlsanity.com/paper/2410.04691/) (2024)
- [Differential learning kinetics govern the transition from memorization to generalization during in-context learning](https://mlsanity.com/paper/2412.00104/) (2024)
- [How Do LLMs Perform Two-Hop Reasoning in Context?](https://mlsanity.com/paper/2502.13913/) (2025)
- [Toward Understanding In-context vs. In-weight Learning](https://mlsanity.com/paper/2410.23042/) (2024)
- [Context parroting: A simple but tough-to-beat baseline for foundation models in scientific machine learning](https://mlsanity.com/paper/2505.11349/) (2025)
- [Revisiting In-context Learning Inference Circuit in Large Language Models](https://mlsanity.com/paper/2410.04468/) (2024)
- [Strategy Coopetition Explains the Emergence and Transience of In-Context Learning](https://mlsanity.com/paper/2503.05631/) (2025)

## Abstract (arXiv)

Transformer models exhibit in-context learning: the ability to accurately predict the response to a novel query based on illustrative examples in the input sequence. In-context learning contrasts with traditional in-weights learning of query-output relationships. What aspects of the training data distribution and architecture favor in-context vs in-weights learning? Recent work has shown that specific distributional properties inherent in language, such as burstiness, large dictionaries and skewed rank-frequency distributions, control the trade-off or simultaneous appearance of these two forms of learning. We first show that these results are recapitulated in a minimal attention-only network trained on a simplified dataset. In-context learning (ICL) is driven by the abrupt emergence of an induction head, which subsequently competes with in-weights learning. By identifying progress measures that precede in-context learning and targeted experiments, we construct a two-parameter model of an induction head which emulates the full data distributional dependencies displayed by the attention-based network. A phenomenological model of induction head formation traces its abrupt emergence to the sequential learning of three nested logits enabled by an intrinsic curriculum. We propose that the sharp transitions in attention-based networks arise due to a specific chain of multi-layer operations necessary to achieve ICL, which is implemented by nested nonlinearities sequentially learned during training.