Natural Riemannian gradient for learning functional tensor networks
We consider machine learning tasks with low-rank functional tree tensor networks (TTN) as the learning model. While in the case of least-squares regression, low-rank functional TTNs can be efficiently optimized using alternating optimization, this is not directly possible in other problems, such as multinomial logistic regression. We propose a natural Riemannian gradient descent type approach applicable to arbitrary losses which is based on the natural gradient by Amari. In particular, the search direction obtained by the natural gradient is independent of the choice of basis of the underlying functional tensor product space. Our framework applies to both the factorized and manifold-based...
| Authors | Nikolas Klug, Michael Ulbrich, André Uschmajew et al. |
|---|---|
| Primary category | math.OC |
| Published | 10 April 2026 |
| Last updated at source | 10 April 2026 |
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