Natural gradient descent with momentum
We consider the problem of approximating a function by an element of a nonlinear manifold which admits a differentiable parametrization, typical examples being neural networks with differentiable activation functions or tensor networks. Natural gradient descent (NGD) for the optimization of a loss function can be seen as a preconditioned gradient descent where updates in the parameter space are driven by a functional perspective. In a spirit similar to Newton's method, a NGD step uses, instead of the Hessian, the Gram matrix of the generating system of the tangent space to the approximation manifold at the current iterate, with respect to a suitable metric. This corresponds to a locally o...
| Authors | Anthony Nouy, Agustín Somacal |
|---|---|
| Primary category | cs.LG |
| Published | 16 April 2026 |
| Last updated at source | 16 April 2026 |
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