Related papers: Notes on the Causal Structure in a Tensor Network

This review explains in a self-contained way the properties of random Boolean networks and their attractors, with a special focus on critical networks. Using small example networks, analytical calculations, phenomenological arguments, and…

Tensor Network States are ans\"atze for the efficient description of quantum many-body systems. Their success for one dimensional problems, together with the fact that they do not suffer from the sign problem and can address the simulation…

We develop some foundations of commutative algebra, with a view towards algebraic geometry, in symmetric tensor categories. Most results establish analogues of classical theorems, in tensor categories which admit a tensor functor to some…

We consider the interpretation of tetrad fields as reference frames in spacetime. Reference frames may be characterized by an antisymmetric acceleration tensor, whose components are identified as the inertial accelerations of the frame (the…

We examine the use of string diagrams and the mathematics of category theory in the description of quantum states by tensor networks. This approach lead to a unification of several ideas, as well as several results and methods that have not…

In this paper we propose a space-time random tensor network approach for understanding holographic duality. Using tensor networks with random link projections, we define boundary theories with interesting holographic properties, such as the…

The unification of neural and symbolic approaches to artificial intelligence remains a central open challenge. In this work, we introduce a tensor network formalism, which captures sparsity principles originating in the different approaches…

Graphical tensor notation is a simple way of denoting linear operations on tensors, originating from physics. Modern deep learning consists almost entirely of operations on or between tensors, so easily understanding tensor operations is…

Neural networks have been able to achieve groundbreaking accuracy at tasks conventionally considered only doable by humans. Using stochastic gradient descent, optimization in many dimensions is made possible, albeit at a relatively high…

We take causality and uniqueness of events observation as our driving forces. They are built in in the way we define distinct observers, which then require a finite time to communicate between each other. This unavoidably leads to the…

This is the second paper of a series of two about the structural properties that influence the asymptotic dynamics of Random Boolean Networks. Here we study the functionally independent clusters in which the relevant elements, introduced…

Understanding the equilibrium properties and out of equilibrium dynamics of quantum field theories are key aspects of fundamental problems in theoretical particle physics and cosmology. However, their classical simulation is highly…

Observability is a fundamental concept in system inference and estimation. This paper is focused on structural observability analysis of Cartesian product networks. Cartesian product networks emerge in variety of applications including in…

Tensor networks (TNs) and neural networks (NNs) are two fundamental data modeling approaches. TNs were introduced to solve the curse of dimensionality in large-scale tensors by converting an exponential number of dimensions to polynomial…

Tensor network methods are a class of numerical tools and algorithms to study many-body quantum systems in and out of equilibrium, based on tailored variational wave functions. They have found significant applications in simulating lattice…

Phylogenetic networks model reticulate evolutionary histories. The last two decades have seen an increased interest in establishing mathematical results and developing computational methods for inferring and analyzing these networks. A…

Scalar-Tensor theories of gravity can be formulated in different frames, most notably, the Einstein and the Jordan one. While some debate still persists in the literature on the physical status of the different frames, a frame…

Factorization machines and polynomial networks are supervised polynomial models based on an efficient low-rank decomposition. We extend these models to the multi-output setting, i.e., for learning vector-valued functions, with application…

Tensor network decompositions offer an efficient description of certain many-body states of a lattice system and are the basis of a wealth of numerical simulation algorithms. In a recent paper [arXiv:0907.2994v1] we discussed how to…

Tensor networks are a popular and computationally efficient approach to simulate general quantum systems on classical computers and, in a broader sense, a framework for dealing with high-dimensional numerical problems. This paper presents a…