Riemannian Structure and Optimization for a Class of Low-Parametric Orthogonal Matrices
In this paper, we are concerned with matrices formed by block-diagonal factors interleaved with fixed permutations -- a flexible family of structured matrices. This class has recently drawn interest in deep learning architectures for its balanced expressivity-efficiency trade-off, yet efficient computational strategies for working with it remain to be found. We approach this problem through Riemannian geometry and examine under what conditions this class admits a smooth manifold structure. For the practically important case of orthogonal two-factor matrices, we derive the essential Riemannian tools and propose efficient algorithms for their implementation. The algorithms leverage automati...
| Authors | Ali Aliev, Maxim Rakhuba |
|---|---|
| Primary category | cs.LG |
| Published | 23 September 2026 |
| Last updated at source | 23 September 2026 |
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