Related papers: Approximating Tensor Network Contraction with Sket…
Tensor network contractions are widely used in statistical physics, quantum computing, and computer science. We introduce a method to efficiently approximate tensor network contractions using low-rank approximations, where each intermediate…
Tensor network contraction is central to problems ranging from many-body physics to computer science. We describe how to approximate tensor network contraction through bond compression on arbitrary graphs. In particular, we introduce a…
Deep neural networks are powerful learning models that achieve state-of-the-art performance on many computer vision, speech, and language processing tasks. In this paper, we study a fundamental question that arises when designing deep…
Low-rank approximation of tensors has been widely used in high-dimensional data analysis. It usually involves singular value decomposition (SVD) of large-scale matrices with high computational complexity. Sketching is an effective data…
Large tensors are frequently encountered in various fields such as computer vision, scientific simulations, sensor networks, and data mining. However, these tensors are often too large for convenient processing, transfer, or storage.…
Constrained least squares problems arise in many applications. Their memory and computation costs are expensive in practice involving high-dimensional input data. We employ the so-called "sketching" strategy to project the least squares…
Low-rank approximation in data streams is a fundamental and significant task in computing science, machine learning and statistics. Multiple streaming algorithms have emerged over years and most of them are inspired by randomized…
This work discusses tensor network embeddings, which are random matrices ($S$) with tensor network structure. These embeddings have been used to perform dimensionality reduction of tensor network structured inputs $x$ and accelerate…
Sketching is a randomized dimensionality-reduction method that aims to preserve relevant information in large-scale datasets. Count sketch is a simple popular sketch which uses a randomized hash function to achieve compression. In this…
Tensor network contraction is a powerful computational tool in quantum many-body physics, quantum information and quantum chemistry. The complexity of contracting a tensor network is thought to mainly depend on its entanglement properties,…
We propose a method for approximating the contraction of a tensor network by partitioning the network into a sum of computationally cheaper networks. This method, which we call a partitioned network expansion (PNE), builds upon recent work…
Tensor network methods are taking a central role in modern quantum physics and beyond. They can provide an efficient approximation to certain classes of quantum states, and the associated graphical language makes it easy to describe and…
Tensor network (TN), a young mathematical tool of high vitality and great potential, has been undergoing extremely rapid developments in the last two decades, gaining tremendous success in condensed matter physics, atomic physics, quantum…
For tensor linear systems with respect to the popular t-product, we first present the sketch-and-project method and its adaptive variants. Their Fourier domain versions are also investigated. Then, considering that the existing sketching…
Convolutional neural networks (CNNs) with deep architectures have substantially advanced the state-of-the-art in computer vision tasks. However, deep networks are typically resource-intensive and thus difficult to be deployed on mobile…
This paper develops the sketching (i.e., randomized dimension reduction) theory for real algebraic varieties and images of polynomial maps, including, e.g., the set of low rank tensors and tensor networks. Through the lens of norming sets,…
We present a general method for approximately contracting tensor networks with an arbitrary connectivity. This enables us to release the computational power of tensor networks to wide use in inference and learning problems defined on…
A tensor network is a type of decomposition used to express and approximate large arrays of data. A given data-set, quantum state or higher dimensional multi-linear map is factored and approximated by a composition of smaller multi-linear…
Tensor networks are the main building blocks in a wide variety of computational sciences, ranging from many-body theory and quantum computing to probability and machine learning. Here we propose a parallel algorithm for the contraction of…
There is a significant expansion in both volume and range of applications along with the concomitant increase in the variety of data sources. These ever-expanding trends have highlighted the necessity for more versatile analysis tools that…