Adaptive Learning of Tensor Network Structures

• URL: http://arxiv.org/abs/2008.05437v2
• Date: Tue, 22 Jun 2021 18:46:43 GMT
• Title: Adaptive Learning of Tensor Network Structures
• Authors: Meraj Hashemizadeh and Michelle Liu and Jacob Miller and Guillaume Rabusseau
• Abstract summary: We leverage the TN formalism to develop a generic and efficient adaptive algorithm to learn the structure and the parameters of a TN from data. Our algorithm can adaptively identify TN structures with small number of parameters that effectively optimize any differentiable objective function.
• Score: 6.407946291544721
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Tensor Networks (TN) offer a powerful framework to efficiently represent very high-dimensional objects. TN have recently shown their potential 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].

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