Related papers: Tensor Network Rewriting Strategies for Satisfiabi…
We introduce a method for transforming low-order tensors into higher-order tensors and apply it to tensors defined by graphs and hypergraphs. The transformation proceeds according to a surgery-like procedure that splits vertices, creates…
Sparse tensor networks are commonly used to represent contractions over sparse tensors. Tensor contractions are higher-order analogs of matrix multiplication. Tensor networks arise commonly in many domains of scientific computing and data…
High-dimensional data arise naturally in many areas of science and engineering, including machine learning, signal processing, computational physics, and statistics. Such data are often represented as tensors, multi-dimensional…
We investigate how the computational difficulty of contracting tensor networks depends on the sign structure of the tensor entries. Using results from computational complexity, we observe that the approximate contraction of tensor networks…
Tensor Network (TN) decompositions have emerged as an indispensable tool in Big Data analytics owing to their ability to provide compact low-rank representations, thus alleviating the ``Curse of Dimensionality'' inherent in handling…
Sorting networks are oblivious sorting algorithms with many practical applications and rich theoretical properties. Propositional encodings of sorting networks are a key tool for proving concrete bounds on the minimum number of comparators…
The ZX calculus is a mathematical tool to represent and analyse quantum operations by manipulating diagrams which in effect represent tensor networks. Two families of nodes of these networks are ones which commute with either Z rotations or…
Graph representation learning methods have mostly been limited to the modelling of node-wise interactions. Recently, there has been an increased interest in understanding how higher-order structures can be utilised to further enhance the…
We propose tensorial neural networks (TNNs), a generalization of existing neural networks by extending tensor operations on low order operands to those on high order ones. The problem of parameter learning is challenging, as it corresponds…
The tensor network, as a facterization of tensors, aims at performing the operations that are common for normal tensors, such as addition, contraction and stacking. However, due to its non-unique network structure, only the tensor network…
Tensor compilers, essential for generating efficient code for deep learning models across various applications, employ tensor graph rewrites as one of the key optimizations. These rewrites optimize tensor computational graphs with the…
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…
The ZX calculus and ZH calculus use diagrams to denote and compute properties of quantum operations, using `rewrite rules' to transform between diagrams which denote the same operator through a functorial semantic map. Different semantic…
Parallel tensor network contraction algorithms have emerged as the pivotal benchmarks for assessing the classical limits of computation, exemplified by Google's demonstration of quantum supremacy through random circuit sampling. However,…
A tensor network is a product of tensors associated with vertices of some graph $G$ such that every edge of $G$ represents a summation (contraction) over a matching pair of indexes. It was shown recently by Valiant, Cai, and Choudhary that…
Tensor network contraction is a fundamental mathematical operation that generalizes the dot product and matrix multiplication. It finds applications in numerous domains, such as database systems, graph theory, machine learning, probability…
In this contribution, we provide a comprehensive evaluation of graph neural networks applied to Boolean satisfiability problems, accompanied by an intuitive explanation of the mechanisms enabling the model to generalize to different…
It has long been conjectured that hypotheses spaces suitable for data that is compositional in nature, such as text or images, may be more efficiently represented with deep hierarchical networks than with shallow ones. Despite the vast…
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…
This paper introduces the tensor representation of a network, here tensors are the primitive structures of the network. In view of tensor chains, two binary operations on tensor sets are defined: chain addition and reducing. Based on the…