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A major challenge in many machine learning tasks is that the model expressive power depends on model size. Low-rank tensor methods are an efficient tool for handling the curse of dimensionality in many large-scale machine learning models. The major challenges in training a tensor learning model include how to process the high-volume data, how to determine the tensor rank automatically, and how to estimate the uncertainty of the results. While existing tensor learning focuses on a specific task, this paper proposes a generic Bayesian framework that can be employed to solve a broad class of tensor learning problems such as tensor completion, tensor regression, and tensorized neural networks. We develop a low-rank tensor prior for automatic rank determination in nonlinear problems. Our method is implemented with both stochastic gradient Hamiltonian Monte Carlo (SGHMC) and Stein Variational Gradient Descent (SVGD). We compare the automatic rank determination and uncertainty quantification of these two solvers. We demonstrate that our proposed method can determine the tensor rank automatically and can quantify the uncertainty of the obtained results. We validate our framework on tensor completion tasks and tensorized neural network training tasks. 

Tensor decomposition is an effective approach to compress over-parameterized neural networks and to enable their deployment on resource-constrained hardware platforms. However, directly applying tensor compression in the training process is a challenging task due to the difficulty of choosing a proper tensor rank. In order to address this challenge, this paper proposes a low-rank Bayesian tensorized neural network. Our Bayesian method performs automatic model compression via an adaptive tensor rank determination. We also present approaches for posterior density calculation and maximum a posteriori (MAP) estimation for the end-to-end training of our tensorized neural network. We provide experimental validation on a two-layer fully connected neural network, a 6-layer CNN and a 110-layer residual neural network where our work produces 7.4X to 137X more compact neural networks directly from the training while achieving high prediction accuracy. 

Various hardware accelerators have been developed for energy-efficient and real-time inference of neural networks on edge devices. However, most training is done on high-performance GPUs or servers, and the huge memory and computing costs prevent training neural networks on edge devices. This paper proposes a novel tensor-based training framework, which offers orders-of-magnitude memory reduction in the training process. We propose a novel rank-adaptive tensorized neural network model, and design a hardware-friendly low-precision algorithm to train this model. We present an FPGA accelerator to demonstrate the benefits of this training method on edge devices. Our preliminary FPGA implementation achieves 59× speedup and 123× energy reduction compared to embedded CPU, and 292× memory reduction over a standard full-size training. 

Streaming tensor factorization is a powerful tool for processing high-volume and multi-way temporal data in Internet networks, recommender systems and image/video data analysis. Existing streaming tensor factorization algorithms rely on least-squares data fitting and they do not possess a mechanism for tensor rank determination. This leaves them susceptible to outliers and vulnerable to over-fitting. This paper presents a Bayesian robust streaming tensor factorization model to identify sparse outliers, automatically determine the underlying tensor rank and accurately fit low-rank structure. We implement our model in Matlab and compare it with existing algorithms on tensor datasets generated from dynamic MRI and Internet traffic.