Related papers: Tensor Products and Hyperdimensional Computing
One way to study an hypergraph is to attach to it a tensor. Tensors are a generalization of matrices, and they are an efficient way to encode information in a compact form. In this paper we study how properties of weighted hypergraphs are…
We describe the image of the canonical tensor functor from Deligne's interpolating category $Rep(GL_{m-n})$ to $Rep(GL(m|n))$ attached to the standard representation. This implies explicit tensor product decompositions between any two…
Tensor classification has become increasingly crucial in statistics and machine learning, with applications spanning neuroimaging, computer vision, and recommendation systems. However, the high dimensionality of tensors presents significant…
A novel sequence architecture is introduced, Versor, which uses Conformal Geometric Algebra (CGA) in place of traditional linear operations to achieve structural generalization and significant performance improvements on a variety of tasks,…
The Hermitian decomposition of a linear operator is generalized to the case of two or more operations. An additive expansion of the product of three octonions into three parts is constructed, wherein each part either preserve or change the…
Human cognition excels at symbolic reasoning, deducing abstract rules from limited samples. This has been explained using symbolic and connectionist approaches, inspiring the development of a neuro-symbolic architecture that combines both…
Vector algebra is a powerful and needful tool for Physics but unfortunately, due to lack of mathematical skills, it becomes misleading for first undergraduate courses of science and engineering studies. Standard vector identities are…
Hyperdimensional computing (HDC) has emerged as a new light-weight learning algorithm with smaller computation and energy requirements compared to conventional techniques. In HDC, data points are represented by high-dimensional vectors…
A classical tensor product $A \,\otimes\, B$ of complete lattices $A$ and $B$, consisting of all down-sets in $A \times B$ that are join-closed in either coordinate, is isomorphic to the complete lattice $Gal(A,B)$ of Galois maps from $A$…
We describe the tensor products of two irreducible linear complex representations of the finite general linear group G = GL(3,q) in terms of induced representations by linear characters of maximal torii and also in terms of Gelfand-Graev…
The notion of non-abelian Hom-Leibniz tensor product is introduced and some properties are established. This tensor product is used in the description of the universal ($\alpha$-)central extensions of Hom-Leibniz algebras. We also give its…
Hyperdimensional computing (HDC) is an emerging computing paradigm that imitates the brain's structure to offer a powerful and efficient processing and learning model. In HDC, the data are encoded with long vectors, called hypervectors,…
Large transformers are powerful architectures used for self-supervised data analysis across various data types, including protein sequences, images, and text. In these models, the semantic structure of the dataset emerges from a sequence of…
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,…
Compressive sensing (CS) has triggered enormous research activity since its first appearance. CS exploits the signal's sparsity or compressibility in a particular domain and integrates data compression and acquisition, thus allowing exact…
Many data representations are vectors of continuous values. In particular, deep learning embeddings are data-driven representations, typically either unconstrained in Euclidean space, or constrained to a hypersphere. These may also be…
Classification of time series data is an important task for many application domains. One of the best existing methods for this task, in terms of accuracy and computation time, is MiniROCKET. In this work, we extend this approach to provide…
We show that general string-net condensed states have a natural representation in terms of tensor product states (TPS) . These TPS's are built from local tensors. They can describe both states with short-range entanglement (such as the…
A dot-product representation of a graph is a mapping of its vertices to vectors of length $k$ so that vertices are adjacent if and only if the inner product (a.k.a. dot product) of their corresponding vertices exceeds some threshold.…
A Hadamard-Hitchcock decomposition of a multidimensional array is a decomposition that expresses the latter as a Hadamard product of several tensor rank decompositions. Such decompositions can encode probability distributions that arise…