Abstract
Interest in machine learning with tensor networks has been growing rapidly in recent years. We show that tensor-based methods developed for learning the governing equations of dynamical systems from data can, in the same way, be used for supervised learning problems and propose two novel approaches for image classification. One is a kernel-based reformulation of the previously introduced multidimensional approximation of nonlinear dynamics (MANDy), the other an alternating ridge regression in the tensor train format. We apply both methods to the MNIST and fashion MNIST data set and show that the approaches are competitive with state-of-the-art neural network-based classifiers.
Highlights
Tensor-based methods have become a powerful tool for scientific computing over the last years.In addition to many application areas, such as quantum mechanics and computational dynamics, where low-rank tensor approximations have been successfully applied, using tensor networks for supervised learning has gained a lot of attention recently
The canonical format and the tensor train format have been considered for quantum machine learning (There are different research directions in the field of quantum machine learning, here we understand it as using quantum computing capabilities for machine learning problems.) problems, see, e.g., [1,2,3]
Our goal is to show that recently developed methods for recovering the governing equations of dynamical systems can be generalized in such a way that they can be used for supervised learning tasks, e.g., classification problems
Summary
Tensor-based methods have become a powerful tool for scientific computing over the last years.In addition to many application areas, such as quantum mechanics and computational dynamics, where low-rank tensor approximations have been successfully applied, using tensor networks for supervised learning has gained a lot of attention recently. Tensor-based methods have become a powerful tool for scientific computing over the last years. The canonical format and the tensor train format have been considered for quantum machine learning (There are different research directions in the field of quantum machine learning, here we understand it as using quantum computing capabilities for machine learning problems.) problems, see, e.g., [1,2,3]. A tensor-based algorithm for image classification using sweeping techniques inspired by the density matrix renormalization group (DMRG) [4] was proposed in [5,6] and further discussed in [7,8]. Researchers at Google are currently developing a tensor-based machine learning framework called “TensorNetwork (http://github.com/google/TensorNetwork)” [9,10]. The goal is to expedite the adoption of such methods by the machine learning community
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