How Data Mixing Shapes In-Context Learning: Asymptotic Equivalence for Transformers with MLPs
This work provides theoretical foundations for in-context learning in realistic Transformer settings, addressing a gap for researchers in machine learning theory and practitioners using Transformers.
The paper tackles the theoretical understanding of in-context learning in Transformers with nonlinear MLPs on nonlinear tasks from multiple data sources, proving under high-dimensional asymptotics that such models are equivalent to structured polynomial predictors, which enhances performance on nonlinear tasks compared to linear baselines and reveals data mixing effects like the importance of low noise and structured covariances.
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), 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.