Research
Geodesics in the Deep Linear Network
arXiv:2510.07324v2 Announce Type: replace-cross Abstract: We derive a general system of ODEs and associated explicit solutions in a special case for geodesics between full rank matrices in the deep li
arXiv:2510.07324v2 Announce Type: replace-cross Abstract: We derive a general system of ODEs and associated explicit solutions in a special case for geodesics between full rank matrices in the deep linear network geometry. In the process, we find horizontal straight lines in the invariant balanced manifold that remain geodesics under Riemannian submersion.
Related
- Random Matrix Theory for Deep Learning: Beyond Eigenvalues of Linear Models
- The Linear Centroids Hypothesis: How Deep Network Features Represent Data
- Gaussian Equivalence for Self-Attention: Asymptotic Spectral Analysis of Attention Matrix
- Beyond ReLU: How Activations Affect Neural Kernels and Random Wide Networks
Source: arXiv cs.LG | 2026-04-28