Fast Differentiable SVD on GPU via Polar Decomposition

arXiv:2609.32505v1 Announce Type: cross Abstract: We present a fully GPU-oriented SVD pipeline based on polar decomposition, motivated by iterative methods that rely solely on matrix multiplications, such as the Newton-Schulz iteration. We show that this approach enables up to a 2imes speedup compared to standard implementations. Furthermore, we derive a numerically stable backward pass for the polar decomposition and leverage it to obtain a fully differentiable SVD. Our methods are released as open-source implementations in both PyTorch and JAX: https://github.com/fallnlove/cans_svd.

Source: arXiv cs.LG | 2026-09-29