Expressivity of congruence-based architectures for DNNs on positive-definite matrices
This work studies neural architectures for classifying symmetric positive-definite matrices, focusing on congruence-like layers, in which the input matrix is multiplied on the left and right by a (possibly rectangular) weight matrix $W$ and its transpose. Such layers lie at the core of the celebrated SPDNet and have also been employed independently for dimensionality reduction on positive-definite data. We show that the (semi)-orthogonality constraint commonly imposed on $W$ limits the expressivity of these layers: for certain activation functions, the resulting architecture collapses to a one-hidden-layer equivalent. This lack of expressivity follows from a loss of spectral diversity in ...
| Authors | Antonin Oswald, Estelle Massart |
|---|---|
| Primary category | cs.LG |
| Published | 1 June 2026 |
| Last updated at source | 1 June 2026 |
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