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Recurrent Neural Networks (RNN) are a type of statistical model designed to handle sequential data. The model reads a sequence one symbol at a time. Each symbol is processed based on information collected from the previous symbols. With…
We present a general method for approximately contracting tensor networks with an arbitrary connectivity. This enables us to release the computational power of tensor networks to wide use in inference and learning problems defined on…
This work studies the problem of high-dimensional data (referred to as tensors) completion from partially observed samplings. We consider that a tensor is a superposition of multiple low-rank components. In particular, each component can be…
We present applications of the renormalization algorithm with graph enhancement (RAGE). This analysis extends the algorithms and applications given for approaches based on matrix product states introduced in [Phys. Rev. A 79, 022317 (2009)]…
Complex systems that consist of different kinds of entities that interact in different ways can be modeled by multilayer networks. This paper uses the tensor formalism with the Einstein tensor product to model this type of networks. Several…
Density based representations of atomic environments that are invariant under Euclidean symmetries have become a widely used tool in the machine learning of interatomic potentials, broader data-driven atomistic modelling and the…
We use an artificial neural network to analyze asymmetric noisy random telegraph signals (RTSs), and extract underlying transition rates. We demonstrate that a long short-term memory neural network can vastly outperform conventional…
We show how fermionic statistics can be naturally incorporated in tensor networks on arbitrary graphs through the use of graded Hilbert spaces. This formalism allows to use tensor network methods for fermionic lattice systems in a local…
The resemblance between the methods used in quantum-many body physics and in machine learning has drawn considerable attention. In particular, tensor networks (TNs) and deep learning architectures bear striking similarities to the extent…
We construct a tensor network representation of the partition function for the massless Schwinger model on a two dimensional lattice using staggered fermions. The tensor network representation allows us to include a topological term. Using…
Tensor networks are the main building blocks in a wide variety of computational sciences, ranging from many-body theory and quantum computing to probability and machine learning. Here we propose a parallel algorithm for the contraction of…
Despite the omnipresence of tensors and tensor operations in modern deep learning, the use of tensor mathematics to formally design and describe neural networks is still under-explored within the deep learning community. To this end, we…
Data in the form of images or higher-order tensors is ubiquitous in modern deep learning applications. Owing to their inherent high dimensionality, the need for subquadratic layers processing such data is even more pressing than for…
Deep neural networks (NNs) encounter scalability limitations when confronted with a vast array of neurons, thereby constraining their achievable network depth. To address this challenge, we propose an integration of tensor networks (TN)…
In a series of recent works, we have generalised the consistency results in the stochastic block model literature to the case of uniform and non-uniform hypergraphs. The present paper continues the same line of study, where we focus on…
Although tensor networks are powerful tools for simulating low-dimensional quantum physics, tensor network algorithms are very computationally costly in higher spatial dimensions. We introduce quantum gauge networks: a different kind of…
We introduce a method for extracting meaningful entanglement measures of tensor network states in general dimensions. Current methods require the explicit reconstruction of the density matrix, which is highly demanding, or the contraction…
The purpose of this paper is to outline a generalised model for representing hybrids of relational-categorical, symbolic, perceptual-sensory and perceptual-latent data, so as to embody, in the same architectural data layer, representations…
Higher-order tensor datasets arise commonly in recommendation systems, neuroimaging, and social networks. Here we develop probable methods for estimating a possibly high rank signal tensor from noisy observations. We consider a generative…
Tensor networks have been successfully applied in simulation of quantum physical systems for decades. Recently, they have also been employed in classical simulation of quantum computing, in particular, random quantum circuits. This paper…