A Nonlinear Singular Value Theory for Neural Networks
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 linear layer) calibrate directly to distances in input space. We introduce a flexible architecture that yields an explicit decomposition at training time, a...
| Authors | Brian Charles Brown, Mauricio Munoz, Robert Bridges et al. |
|---|---|
| Primary category | cs.LG |
| Published | 7 May 2026 |
| Last updated at source | 30 July 2026 |
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