相关论文: What is the Relationship between Tensor Factorizat…
We discuss the variational optimization of a unitary tensor-network circuit with different network structures. The ansatz is performed based on a generalization of well-developed multi-scale entanglement renormalization algorithm and also…
Embedding learning, a.k.a. representation learning, has been shown to be able to model large-scale semantic knowledge graphs. A key concept is a mapping of the knowledge graph to a tensor representation whose entries are predicted by models…
Factorization algebras are local-to-global objects living on manifolds, and they arise naturally in mathematics and physics. Their local structure encompasses examples like associative algebras and vertex algebras; in these examples, their…
Tensors are multidimensional arrays of numerical values and therefore generalize matrices to multiple dimensions. While tensors first emerged in the psychometrics community in the $20^{\text{th}}$ century, they have since then spread to…
In the last decades, tensors have emerged as the right tool to represent multidimensional data in a compact yet informative manner. Moreover, it is well-known that by performing low-rank factorizations of such tensors one is often able to…
The increasing availability of temporal network data is calling for more research on extracting and characterizing mesoscopic structures in temporal networks and on relating such structure to specific functions or properties of the system.…
We study glued tensor and free products of compact matrix quantum groups with cyclic groups -- so-called tensor and free complexifications. We characterize them by studying their representation categories and algebraic relations. In…
Self-attentive transformer models have recently been shown to solve the next item recommendation task very efficiently. The learned attention weights capture sequential dynamics in user behavior and generalize well. Motivated by the special…
Low rank matrix and tensor completion problems are to recover the incomplete two and higher order data by using their low rank structures. The essential problem in the matrix and tensor completion problems is how to improve the efficiency.…
We shall discuss how the notions of multicategories and their linear representations are related with tensor categories. When one focuses on the ones arizing from planar diagrams, it particularly implies that there is a natural one-to-one…
We present a fit-for-purpose introduction to tensors and their operations. It is envisaged to help the reader become acquainted with its underpinning concepts for the study of path signatures. The text includes exercises, solutions and many…
The quality of learned features by representation learning determines the performance of learning algorithms and the related application tasks (such as high-dimensional data clustering). As a relatively new paradigm for representation…
Constraint answer set programming is a promising research direction that integrates answer set programming with constraint processing. It is often informally related to the field of satisfiability modulo theories. Yet, the exact formal link…
We introduce extriangulated factorization systems in extriangulated categories and show that there exists a bijection between $s$-torsion pairs and extriangulated factorization systems. We also consider the gluing of $s$-torsion pairs and…
Hypergraphs allow one to encode higher-order relationships in data and are thus a very flexible modeling tool. Current learning methods are either based on approximations of the hypergraphs via graphs or on tensor methods which are only…
The key to high-level cognition is believed to be the ability to systematically manipulate and compose knowledge pieces. While token-like structured knowledge representations are naturally provided in text, it is elusive how to obtain them…
We introduce a neural network architecture and a learning algorithm to produce factorized symbolic representations. We propose to learn these concepts by observing consecutive frames, letting all the components of the hidden representation…
We investigate the relationship between the algebra of tensor categories and the topology of framed 3-manifolds. On the one hand, tensor categories with certain algebraic properties determine topological invariants. We prove that fusion…
We define and study a certain relative tensor product of subfactors over a modular tensor category. This gives a relative tensor product of two completely rational heterotic full local conformal nets with trivial superselection structures…
We study in detail the algebraic structures underlying quantum circuits generated by CNOT gates. Our results allow us to propose polynomial-time heuristics to reduce the number of gates used in a given CNOT circuit and we also give…