Layerwise Dynamics for In-Context Classification in Transformers

2026-04-13

AI Summary

This work addresses the opacity of Transformer inference in separator-free multiclass linear classification by imposing permutation equivariance constraints between features and labels. This constraint enforces a highly structured weight configuration while preserving functional equivalence to the original model. Leveraging this design, the study presents the first explicit inter-layer recursive update rule extracted from an end-to-end trained Softmax-based Transformer, thereby uncovering the implicit geometric algorithmic nature of the attention mechanism. The proposed approach not only enhances class separability but also theoretically guarantees desired class-pair robustness, offering both interpretability and performance benefits in linearly separable classification settings.

Technology Category

• Machine Learning: Multi-class/Multi-label Learning & Extreme Classification
• Computer Vision: Interpretability, Explainability, and Transparency
• Search and Optimization: Learning to Search

Application Category

• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Security and Privacy: Data transparency and provenance
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for heterogeneous, signed, attributed, multi-relational, temporal, higher-order, and annotated Web-related graphs

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.

Problem

• in-context learning
• transformer interpretability
• layerwise dynamics
• few-shot classification
• linear classification

Innovation

• in-context learning
• permutation equivariance
• layerwise dynamics
• emergent algorithm
• transformer interpretability