Related papers: Tensor Products and Hyperdimensional Computing
Compressed sensing extends from the recovery of sparse vectors from undersampled measurements via efficient algorithms to the recovery of matrices of low rank from incomplete information. Here we consider a further extension to the…
Image and video descriptors are an omnipresent tool in computer vision and its application fields like mobile robotics. Many hand-crafted and in particular learned image descriptors are numerical vectors with a potentially (very) large…
The widespread use of multisensor technology and the emergence of big datasets have created the need to develop tools to reduce, approximate, and classify large and multimodal data such as higher-order tensors. While early approaches…
The tensor product algebra TA(n) for the complex general linear group GL(n), introduced by Howe et al., describes the decomposition of tensor products of irreducible polynomial representations of GL(n). Using the hive model for the…
The representation theory of tensor functions is a powerful mathematical tool for constitutive modeling of anisotropic materials. A major limitation of the traditional theory is that many point groups require fourth- or sixth-order…
Symbolic reasoning and neural networks are often considered incompatible approaches. Connectionist models known as Vector Symbolic Architectures (VSAs) can potentially bridge this gap. However, classical VSAs and neural networks are still…
Higher-order tensors have received increased attention across science and engineering. While most tensor decomposition methods are developed for a single tensor observation, scientific studies often collect side information, in the form of…
A non-trivial symbolic machinery is presented that can rephrase algorithmically a finite set of nested hypergeometric products in appropriately designed difference rings. As a consequence, one obtains an alternative representation in terms…
The tensor-tensor product (t-product) [M. E. Kilmer and C. D. Martin, 2011] is a natural generalization of matrix multiplication. Based on t-product, many operations on matrix can be extended to tensor cases, including tensor SVD, tensor…
We introduce an architecture, the Tensor Product Recurrent Network (TPRN). In our application of TPRN, internal representations learned by end-to-end optimization in a deep neural network performing a textual question-answering (QA) task…
Tensor products of ultrafilters have special combinatorial features closely related to Ramsey's Theorem, making them useful tools in applications. Here we first review their fundamental properties and isolate some new ones, including a…
We study embeddings and norm estimates for tensor products of weighted reproducing kernel Hilbert spaces. These results lead to a transfer principle that is directly applicable to tractability studies of multivariate problems as integration…
We derive integral formulas that simplify the Vector Spherical Tensor Product recently introduced by Xie et al., which generalizes the Gaunt tensor product to antisymmetric couplings. In particular, we obtain explicit closed-form…
We introduce both the notions of tensor product of convex bodies that contain zero in the interior, and of tensor product of $0$-symmetric convex bodies in Euclidean spaces. We prove that there is a bijection between tensor products of…
The purpose of this paper is to outline a generalised model for representing hybrids of relational-categorical, symbolic, perceptual-sensory and perceptual-latent data, so as to embody, in the same architectural data layer, representations…
Vector space models for symbolic processing that encode symbols by random vectors have been proposed in cognitive science and connectionist communities under the names Vector Symbolic Architecture (VSA), and, synonymously, Hyperdimensional…
Vision Transformers have achieved state-of-the-art performance in a wide range of computer vision tasks, but their practical deployment is limited by high computational and memory costs. In this paper, we introduce a novel tensor-based…
We study when a tensor product of irreducible representations of the symmetric group $S_n$ contains all irreducibles as subrepresentations; we say such a tensor product covers $\mathsf{Irrep}(S_n)$. Our results show that this behavior is…
This paper introduces matrix product state (MPS) decomposition as a computational tool for extracting features of multidimensional data represented by higher-order tensors. Regardless of tensor order, MPS extracts its relevant features to…
Tensor networks have in recent years emerged as the powerful tools for solving the large-scale optimization problems. One of the most popular tensor network is tensor train (TT) decomposition that acts as the building blocks for the…