arXiv Artificial Intelligence

A Nonlinear Singular Value Theory for Neural Networks

1 hour ago 03.08.2026 07:00 👁 1 views
A Nonlinear Singular Value Theory for Neural Networks

Quick summary

arXiv:2605.06938v2 Announce Type: replace-cross Abstract: Recently Brown et al. [2025] established a singular value decomposition (SVD) for maps (especially nonlinear) satisfying certain norm conditions. We prove that most modern neural architectures admit this nonlinear SVD (NLSVD) representation---with no change in input--output behavior---and enumerate the classes covered. In this factorization the network is a left-invertible nonlinear map followed by a final linear layer. Moreover, the left-invertible factor is norm-preserving, so distances in the embedding (activations before the final l

Key takeaways

  • arXiv:2605.06938v2 Announce Type: replace-cross Abstract: Recently Brown et al.
  • [2025] established a singular value decomposition (SVD) for maps (especially nonlinear) satisfying certain norm conditions.
  • We prove that most modern neural architectures admit this nonlinear SVD (NLSVD) representation---with no change in input--output behavior---and enumerate the classes covered.

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The importance of “A Nonlinear Singular Value Theory for Neural Networks” will be measured by what changes in practice. User behavior, access conditions, verifiable performance and responsible-use outcomes are the signals worth following.

Kaynak sitede devamını oku: arXiv Artificial Intelligence ↗