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Tensor Networks (TN) offer a powerful framework to efficiently represent very high-dimensional objects. TN have recently shown their potenti… (voir plus)al for machine learning applications and offer a unifying view of common tensor decomposition models such as Tucker, tensor train (TT) and tensor ring (TR). However, identifying the best tensor network structure from data for a given task is challenging. In this work, we leverage the TN formalism to develop a generic and efficient adaptive algorithm to jointly learn the structure and the parameters of a TN from data. Our method is based on a simple greedy approach starting from a rank one tensor and successively identifying the most promising tensor network edges for small rank increments. Our algorithm can adaptively identify TN structures with small number of parameters that effectively optimize any differentiable objective function. Experiments on tensor decomposition, tensor completion and model compression tasks demonstrate the effectiveness of the proposed algorithm. In particular, our method outperforms the state-of-the-art evolutionary topology search [Li and Sun, 2020] for tensor decomposition of images (while being orders of magnitude faster) and finds efficient tensor network structures to compress neural networks outperforming popular TT based approaches [Novikov et al., 2015].
We approach the problem of implicit regularization in deep learning from a geometrical viewpoint. We highlight a possible regularization eff… (voir plus)ect induced by a dynamical alignment of the neural tangent features introduced by Jacot et al, along a small number of task-relevant directions. By extrapolating a new analysis of Rademacher complexity bounds in linear models, we propose and study a new heuristic complexity measure for neural networks which captures this phenomenon, in terms of sequences of tangent kernel classes along in the learning trajectories.
