Symmetry Reveals Layerwise Dynamics: How Transformers Perform In-Context Classification
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866911730498535424 |
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| author | Lutz, Patrick Haris, Themistoklis Chandra, Arjun Gangrade, Aditya Saligrama, Venkatesh |
| author_facet | Lutz, Patrick Haris, Themistoklis Chandra, Arjun Gangrade, Aditya Saligrama, Venkatesh |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_11613 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Symmetry Reveals Layerwise Dynamics: How Transformers Perform In-Context Classification Lutz, Patrick Haris, Themistoklis Chandra, Arjun Gangrade, Aditya Saligrama, Venkatesh Machine Learning Artificial Intelligence 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. |
| title | Symmetry Reveals Layerwise Dynamics: How Transformers Perform In-Context Classification |
| topic | Machine Learning Artificial Intelligence |
| url | https://arxiv.org/abs/2604.11613 |