Symmetries in next-token prediction targets induce corresponding geometric symmetries such as circulant matrices and equiangular tight frames in the optimal weights and embeddings of a layer-peeled LLM surrogate model.
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The global empirical NTK for finite-width networks has a universal Kronecker-core form that makes it structurally low-rank and biases gradient descent toward dominant modes of joint input-hidden activity.
Spectral sparsification preserves GNN embedding geometry up to O(ε) perturbations in filters, representations, Gram matrices, and training trajectories.
Bifurcations cause sNTK to reduce to a dominant rank-one channel matching normal forms, collapsing effective rank and funneling gradient descent into critical dynamical directions.
citing papers explorer
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Uncovering Symmetry Transfer in Large Language Models via Layer-Peeled Optimization
Symmetries in next-token prediction targets induce corresponding geometric symmetries such as circulant matrices and equiangular tight frames in the optimal weights and embeddings of a layer-peeled LLM surrogate model.
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The Global Empirical NTK: Self-Referential Bias and Dimensionality of Gradient Descent Learning
The global empirical NTK for finite-width networks has a universal Kronecker-core form that makes it structurally low-rank and biases gradient descent toward dominant modes of joint input-hidden activity.
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Spectral Graph Sparsification Preserves Representation Geometry in Graph Neural Networks
Spectral sparsification preserves GNN embedding geometry up to O(ε) perturbations in filters, representations, Gram matrices, and training trajectories.
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State-Space NTK Collapse Near Bifurcations
Bifurcations cause sNTK to reduce to a dominant rank-one channel matching normal forms, collapsing effective rank and funneling gradient descent into critical dynamical directions.