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arXiv · 2604.11613

Symmetry Reveals Layerwise Dynamics: How Transformers Perform In-Context Classification

Patrick Lutz·Themistoklis Haris·Arjun Chandra·Aditya Gangrade·Venkatesh Saligrama
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Abstract

Transformers can perform in-context classification from a few labeled examples, yet the inference-time algorithm remains opaque. We study multi-class linear classification in the hard no-margin regime and make the computation identifiable by enforcing feature- and label-permutation equivariance at every layer. This enables interpretability while maintaining functional equivalence and yields highly structured weights. From these models we extract an explicit depth-indexed recursion: an end-to-end identified, emergent update rule inside a softmax transformer, to our knowledge the first of its kind. Attention matrices formed from mixed feature-label Gram structure drive coupled updates of training points, labels, and the test probe. The resulting dynamics implement a geometry-driven algorithmic motif, which can provably amplify class separation and yields robust expected class alignment.

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Patrick Lutz, Themistoklis Haris, Arjun Chandra, Aditya Gangrade, Venkatesh Saligrama. 2026-08-08. Symmetry Reveals Layerwise Dynamics: How Transformers Perform In-Context Classification. https://arxiv.org/abs/2604.11613

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