Data symmetries generically do not induce conserved quantities in NN training for analytic non-polynomial losses, but can for MSE with tensorizable networks.
arXiv preprint arXiv:2501.18915 , year=
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Copositive matrices with nondecreasing off-diagonal entries admit a PSD plus nonnegative decomposition, which implies exactness of a natural relaxation for separable quadratic optimization over the simplex.
Counterexamples to the unimodal minimal filling architecture conjecture for PNNs, discovered via frontier search, dimension bounds on neurovarieties, and symbolic computation; some subarchitectures show large defect.
Introduces the Patnaik-Pearson intrinsic dimension estimator, proves some of its properties, relates it to HTSR/SETOL for Pareto spectra, and applies it to track embedding dimension evolution in BERT-base and DeepSeek-R1-Distill-Qwen-1.
Develops algebraic geometry tools for monomial neural networks and proves the singular locus of neurovarieties is contained in the architectural degeneracy locus for fully connected networks with non-increasing widths and scalar output under layerwise regularity assumptions.
citing papers explorer
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Conservation Laws from Data Symmetry in Neural Networks
Data symmetries generically do not induce conserved quantities in NN training for analytic non-polynomial losses, but can for MSE with tensorizable networks.
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Copositive Matrices with Ordered Off-Diagonal Entries
Copositive matrices with nondecreasing off-diagonal entries admit a PSD plus nonnegative decomposition, which implies exactness of a natural relaxation for separable quadratic optimization over the simplex.
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Minimal Filling Architectures of Polynomial Neural Networks: Counterexamples, Frontier Search, and Defects
Counterexamples to the unimodal minimal filling architecture conjecture for PNNs, discovered via frontier search, dimension bounds on neurovarieties, and symbolic computation; some subarchitectures show large defect.
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Patnaik-Pearson intrinsic dimension for internal representations of neural networks
Introduces the Patnaik-Pearson intrinsic dimension estimator, proves some of its properties, relates it to HTSR/SETOL for Pareto spectra, and applies it to track embedding dimension evolution in BERT-base and DeepSeek-R1-Distill-Qwen-1.
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Algebraic Networks and Architectural Degenerations
Develops algebraic geometry tools for monomial neural networks and proves the singular locus of neurovarieties is contained in the architectural degeneracy locus for fully connected networks with non-increasing widths and scalar output under layerwise regularity assumptions.