Related papers: Tensor Network Rewriting Strategies for Satisfiabi…
We introduce tensor network contraction algorithms for counting satisfying assignments of constraint satisfaction problems (#CSPs). We represent each arbitrary #CSP formula as a tensor network, whose full contraction yields the number of…
The computational cost of counting the number of solutions satisfying a Boolean formula, which is a problem instance of #SAT, has proven subtle to quantify. Even when finding individual satisfying solutions is computationally easy (e.g.…
We construct a tensor network that delivers an unnormalized quantum state whose coefficients are the solutions to a given instance of 3SAT, an NP-complete problem. The tensor network contraction that corresponds to the norm of the state…
The ZX-calculus is a graphical language for suitably represented tensor networks, called ZX-diagrams. Calculations are performed by transforming ZX-diagrams with rewrite rules. The ZX-calculus has found applications in reasoning about…
Counting the solutions to Boolean formulae defines the problem #SAT, which is complete for the complexity class #P. We use the ZH-calculus, a universal and complete graphical language for linear maps which naturally encodes counting…
We study tensor networks as a model of arithmetic computation for evaluating multilinear maps. These capture any algorithm based on low border rank tensor decompositions, such as $O(n^{\omega+\epsilon})$ time matrix multiplication, and in…
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 study the counting version of the Boolean satisfiability problem #SAT using the ZH-calculus, a graphical language originally introduced to reason about quantum circuits. Using this, we generalize #SAT to a weighted variant we call…
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…
Many datasets in scientific and engineering applications are comprised of objects which have specific geometric structure. A common example is data which inhabits a representation of the group SO$(3)$ of 3D rotations: scalars, vectors,…
Part 2 of this monograph builds on the introduction to tensor networks and their operations presented in Part 1. It focuses on tensor network models for super-compressed higher-order representation of data/parameters and related cost…
In this paper we review basic and emerging models and associated algorithms for large-scale tensor networks, especially Tensor Train (TT) decompositions using novel mathematical and graphical representations. We discus the concept of…
Recent findings indicate that over-parametrization, while crucial for successfully training deep neural networks, also introduces large amounts of redundancy. Tensor methods have the potential to efficiently parametrize over-complete…
Anticipating audience reaction towards a certain text is integral to several facets of society ranging from politics, research, and commercial industries. Sentiment analysis (SA) is a useful natural language processing (NLP) technique that…
In CS literature, the efforts can be divided into two groups: finding a measurement matrix that preserves the compressed information at the maximum level, and finding a reconstruction algorithm for the compressed information. In the…
Despite their simple intuition, convolutions are more tedious to analyze than dense layers, which complicates the transfer of theoretical and algorithmic ideas to convolutions. We simplify convolutions by viewing them as tensor networks…
Recurrent neural networks (RNNs) are powerful tools for sequential modeling, but typically require significant overparameterization and regularization to achieve optimal performance. This leads to difficulties in the deployment of large…
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…
A tensor network is a diagram that specifies a way to "multiply" a collection of tensors together to produce another tensor (or matrix). Many existing algorithms for tensor problems (such as tensor decomposition and tensor PCA), although…
Synthetic aperture radar tomography (TomoSAR) has been extensively employed in 3-D reconstruction in dense urban areas using high-resolution SAR acquisitions. Compressive sensing (CS)-based algorithms are generally considered as the state…