Sven: Singular Value Descent as a Computationally Efficient Natural Gradient Method
We introduce Sven (Singular Value dEsceNt), a new optimization algorithm for neural networks that exploits the natural decomposition of loss functions into a sum over individual data points, rather than reducing the full loss to a single scalar before computing a parameter update. Sven treats each data point's residual as a separate condition to be satisfied simultaneously, using the Moore-Penrose pseudoinverse of the loss Jacobian to find the minimum-norm parameter update that best satisfies all conditions at once. In practice, this pseudoinverse is approximated via a truncated singular value decomposition, retaining only the $k$ most significant directions. We show that Sven can be unde...
| Authors | Samuel Bright-Thonney, Thomas R. Harvey, Andre Lukas et al. |
|---|---|
| Primary category | cs.LG |
| Published | 1 April 2026 |
| Last updated at source | 5 October 2026 |
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