Deep linear network theory derives logarithmic decay for cross-entropy loss under gap-growth conditions versus polynomial closure for Schatten-regularized structural energy under late-time KL tails, separating fitting from simplification; conditional reductions extend this to ReLU MLPs with fixed ac
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cs.LG 2years
2026 2verdicts
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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.
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Deciphering Two Training Clocks in Grokking via Deep Linear Network Theory with Conditional ReLU Reduction
Deep linear network theory derives logarithmic decay for cross-entropy loss under gap-growth conditions versus polynomial closure for Schatten-regularized structural energy under late-time KL tails, separating fitting from simplification; conditional reductions extend this to ReLU MLPs with fixed ac
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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.