Equiangular Tight Frame
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Related Articles from SNS
Neural Collapse Dynamics: Depth, Activation, Regularisation, and Feature Norm Threshold
arXiv:2604.00230v2 Announce Type: replace Abstract: Neural collapse (NC) -- the convergence of penultimate-layer features to a simplex equiangular tight frame -- is well understood at equilibrium, but the dynamics governing its onset remain poorly characterised. We identify a simple and predictive regularity: NC occurs when the mean feature norm reaches a model-dataset-specific critical value, fn*, that is largely invariant to training conditions. This value concentrates tightly within each...
When Tabular Foundation Models Transfer Across Modalities: A Systematic Evaluation Across 95 Datasets, 7 Modalities, and Two Regimes
arXiv:2606.02106v1 Announce Type: new Abstract: We present a single classification pipeline that combines an Equiangular Tight Frame (ETF) preprocessing stage with a tabular foundation model for in-context inference, applied identically across modalities once data is mapped to fixed vector representations. We evaluate it on 95 datasets spanning seven signal modalities -- vision, audio, speech, text, molecular, time-series, and tabular. The main methodological contribution is to fix the...
Beyond Neural Collapse: Task-Intrinsic Geometry Governs Neural Representations in Modular Arithmetic
arXiv:2606.08985v1 Announce Type: new Abstract: While neural collapse (NC) predicts that a $K$-class-balanced classifier should organize terminal representations as a $(K-1)$-dimensional simplex equiangular tight frame (ETF), modular addition consistently enters a different regime: networks compress to a two-dimensional cyclic geometry in which both classifier weights and token embeddings lie on circles. We refine the explanation of this phenomenon in three directions. First, we formalize a...