# How Data Mixing Shapes In-Context Learning: Asymptotic Equivalence for Transformers with MLPs

arXiv: https://arxiv.org/abs/2510.25753 · HTML: https://mlsanity.com/paper/2510.25753/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 37 of its 49 references that are in the map.
- First posted on arXiv 29 Oct 2025.

## Builds on (most cited first, 30 of 37)

- [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)
- [Emergent Abilities of Large Language Models](https://mlsanity.com/paper/2206.07682/) (2022)
- [In-context Learning and Induction Heads](https://mlsanity.com/paper/2209.11895/) (2022)
- [Reconciling modern machine learning practice and the bias-variance trade-off](https://mlsanity.com/paper/1812.11118/) (2018)
- [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)
- [Are Emergent Abilities of Large Language Models a Mirage?](https://mlsanity.com/paper/2304.15004/) (2023)
- [Multilingual E5 Text Embeddings: A Technical Report](https://mlsanity.com/paper/2402.05672/) (2024)
- [Trained Transformers Learn Linear Models In-Context](https://mlsanity.com/paper/2306.09927/) (2023)
- [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)
- [Transformers as Algorithms: Generalization and Stability in In-context Learning](https://mlsanity.com/paper/2301.07067/) (2023)
- [Data Mixing Laws: Optimizing Data Mixtures by Predicting Language Modeling Performance](https://mlsanity.com/paper/2403.16952/) (2024)
- [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)
- [Neural Networks can Learn Representations with Gradient Descent](https://mlsanity.com/paper/2206.15144/) (2022)
- [High-dimensional Asymptotics of Feature Learning: How One Gradient Step Improves the Representation](https://mlsanity.com/paper/2205.01445/) (2022)
- [Pretraining task diversity and the emergence of non-Bayesian in-context learning for regression](https://mlsanity.com/paper/2306.15063/) (2023)
- [The Multilingual Amazon Reviews Corpus](https://mlsanity.com/paper/2010.02573/) (2020)
- [The Gaussian equivalence of generative models for learning with shallow neural networks](https://mlsanity.com/paper/2006.14709/) (2020)
- [How Many Pretraining Tasks Are Needed for In-Context Learning of Linear Regression?](https://mlsanity.com/paper/2310.08391/) (2023)
- [Universality of empirical risk minimization](https://mlsanity.com/paper/2202.08832/) (2022)
- [How Two-Layer Neural Networks Learn, One (Giant) Step at a Time](https://mlsanity.com/paper/2305.18270/) (2023)
- [Asymptotic theory of in-context learning by linear attention](https://mlsanity.com/paper/2405.11751/) (2024)
- [Competition Dynamics Shape Algorithmic Phases of In-Context Learning](https://mlsanity.com/paper/2412.01003/) (2024)
- [A Theory of Non-Linear Feature Learning with One Gradient Step in Two-Layer Neural Networks](https://mlsanity.com/paper/2310.07891/) (2023)
- [Transformers Learn to Achieve Second-Order Convergence Rates for In-Context Linear Regression](https://mlsanity.com/paper/2310.17086/) (2023)
- [Bridging the Divide: Reconsidering Softmax and Linear Attention](https://mlsanity.com/paper/2412.06590/) (2024)
- [Transformers Learn Nonlinear Features In Context: Nonconvex Mean-field Dynamics on the Attention Landscape](https://mlsanity.com/paper/2402.01258/) (2024)

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

- [Sequential Correlations Change In-Context Learning: Effective Context Length and Architectural Mismatch](https://mlsanity.com/paper/2607.03660/) (2026)

## Abstract (arXiv)

Pretrained Transformers demonstrate remarkable in-context learning (ICL) capabilities, enabling them to adapt to new tasks from demonstrations without parameter updates. However, theoretical studies often rely on simplified architectures (e.g., omitting MLPs), plain data models (e.g., linear regression with isotropic inputs), and single-source training, limiting their relevance to realistic settings. In this work, we study ICL in pretrained Transformers with nonlinear MLP heads on nonlinear tasks drawn from multiple data sources with heterogeneous input, task, and noise distributions. We analyze a model where the MLP comprises two layers, with the first layer trained via a single gradient step and the second layer fully optimized. Under high-dimensional asymptotics, we prove that such models are equivalent in ICL error to structured polynomial predictors, leveraging results from the theory of Gaussian universality and orthogonal polynomials. This equivalence reveals that nonlinear MLPs meaningfully enhance ICL performance, particularly on nonlinear tasks, compared to linear baselines. It also enables a precise analysis of data mixing effects: we identify key properties of high-quality data sources (low noise, structured covariances) and show that feature learning emerges only when the task covariance exhibits sufficient structure. These results are validated empirically across various activation functions, model sizes, and data distributions. Finally, we experiment with a real-world scenario involving multilingual sentiment analysis where each language is treated as a different source. Our experimental results for this case exemplify how our findings extend to real-world cases. Overall, our work advances the theoretical foundations of ICL in Transformers and provides actionable insight into the role of architecture and data in ICL.