Modular arithmetic induces cyclic rank-2 geometries via layerwise subspace locking and entropy-regularized phase alignment on S^1, prevailing over neural collapse simplices due to a Theta(K) advantage under weight-decay surrogates.
arXiv preprint arXiv:2408.00329 , year =
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Beyond Neural Collapse: Task-Intrinsic Geometry Governs Neural Representations in Modular Arithmetic
Modular arithmetic induces cyclic rank-2 geometries via layerwise subspace locking and entropy-regularized phase alignment on S^1, prevailing over neural collapse simplices due to a Theta(K) advantage under weight-decay surrogates.