Related papers: TensorGRaD: Tensor Gradient Robust Decomposition f…
Tensors, which provide a powerful and flexible model for representing multi-attribute data and multi-way interactions, play an indispensable role in modern data science across various fields in science and engineering. A fundamental task is…
Tensor decompositions, which represent an $N$-order tensor using approximately $N$ factors of much smaller dimensions, can significantly reduce the number of parameters. This is particularly beneficial for high-order tensors, as the number…
Training neural networks is a challenging non-convex optimization problem, and backpropagation or gradient descent can get stuck in spurious local optima. We propose a novel algorithm based on tensor decomposition for guaranteed training of…
Tensor decomposition, a collection of factorization techniques for multidimensional arrays, are among the most general and powerful tools for scientific analysis. However, because of their increasing size, today's data sets require more…
Tensors, which give a faithful and effective representation to deliver the intrinsic structure of multi-dimensional data, play a crucial role in an increasing number of signal processing and machine learning problems. However, tensor data…
Many real-world datasets are represented as tensors, i.e., multi-dimensional arrays of numerical values. Storing them without compression often requires substantial space, which grows exponentially with the order. While many tensor…
Tensors provide a robust framework for managing high-dimensional data. Consequently, tensor analysis has emerged as an active research area in various domains, including machine learning, signal processing, computer vision, graph analysis,…
Tensor methods have become a promising tool to solve high-dimensional problems in the big data era. By exploiting possible low-rank tensor factorization, many high-dimensional model-based or data-driven problems can be solved to facilitate…
In tensor completion tasks, the traditional low-rank tensor decomposition models suffer from the laborious model selection problem due to their high model sensitivity. In particular, for tensor ring (TR) decomposition, the number of model…
Tensor decomposition has been widely used in machine learning and high-volume data analysis. However, large-scale tensor factorization often consumes huge memory and computing cost. Meanwhile, modernized computing hardware such as tensor…
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…
Deep neural networks (NNs) encounter scalability limitations when confronted with a vast array of neurons, thereby constraining their achievable network depth. To address this challenge, we propose an integration of tensor networks (TN)…
Unsupervised learning aims at the discovery of hidden structure that drives the observations in the real world. It is essential for success in modern machine learning. Latent variable models are versatile in unsupervised learning and have…
State-of-the-art models are now trained with billions of parameters, reaching hardware limits in terms of memory consumption. This has created a recent demand for memory-efficient optimizers. To this end, we investigate the limits and…
Memory complexity and data scarcity have so far prohibited learning solution operators of partial differential equations (PDEs) at high resolutions. We address these limitations by introducing a new data efficient and highly parallelizable…
Decompositions of tensors into factor matrices, which interact through a core tensor, have found numerous applications in signal processing and machine learning. A more general tensor model which represents data as an ordered network of…
Low rank tensor decompositions are a powerful tool for learning generative models, and uniqueness results give them a significant advantage over matrix decomposition methods. However, tensors pose significant algorithmic challenges and…
The Recurrent Neural Networks and their variants have shown promising performances in sequence modeling tasks such as Natural Language Processing. These models, however, turn out to be impractical and difficult to train when exposed to very…
We present Tensor4D, an efficient yet effective approach to dynamic scene modeling. The key of our solution is an efficient 4D tensor decomposition method so that the dynamic scene can be directly represented as a 4D spatio-temporal tensor.…
High-order tensor decomposition has been widely adopted to obtain compact deep neural networks for edge deployment. However, existing studies focus primarily on its algorithmic advantages such as accuracy and compression ratio-while…