Related papers: A tensor formalism for multilayer network centrali…

The non-trivial structure of such complex systems makes the analysis of their collective behavior a challenge. The problem is even more difficult when the information is distributed across networks (e.g., communication networks in different…

We investigate the potential of tensor network based machine learning methods to scale to large image and text data sets. For that, we study how the mutual information between a subregion and its complement scales with the subsystem size…

Tensor networks, which have been traditionally used to simulate many-body physics, have recently gained significant attention in the field of machine learning due to their powerful representation capabilities. In this work, we propose a…

Measures of complex network analysis, such as vertex centrality, have the potential to unveil existing network patterns and behaviors. They contribute to the understanding of networks and their components by analyzing their structural…

Dynamic multilayer networks are frequently used to describe the structure and temporal evolution of multiple relationships among common entities, with applications in fields such as sociology, economics, and neuroscience. However,…

This work introduces a tensor-based method to perform supervised classification on spatiotemporal data processed in an echo state network. Typically when performing supervised classification tasks on data processed in an echo state network,…

Centrality measures quantify the importance of a node in a network based on different geometric or diffusive properties, and focus on different scales. Here, we adopt a geometrical viewpoint to define a multi-scale centrality in networks.…

In this paper, we extend the analysis of random Kronecker graphs to multi-dimensional networks represented as tensors, enabling a more detailed and nuanced understanding of complex network structures. We decompose the adjacency tensor of…

We analyze the problem of high-order polynomial approximation from a many-body physics perspective, and demonstrate the descriptive power of entanglement entropy in capturing model capacity and task complexity. Instantiated with a…

Most network studies rely on an observed network that differs from the underlying network which is obfuscated by measurement errors. It is well known that such errors can have a severe impact on the reliability of network metrics,…

The general linear model is a universally accepted method to conduct and test multiple linear regression models. Using this model one has the ability to simultaneously regress covariates among different groups of data. Moreover, there are…

Tensor Network methods have been established as a powerful technique for simulating low dimensional strongly-correlated systems for over two decades. Employing the formalism of Matrix Product States, we investigate the phase diagram of the…

Multilayer network analysis is a useful approach for studying the structural properties of entities with diverse, multitudinous relations. Classifying the importance of nodes and node-layer tuples is an important aspect of the study of…

Tensor networks are efficient representations of high-dimensional tensors which have been very successful for physics and mathematics applications. We demonstrate how algorithms for optimizing such networks can be adapted to supervised…

Tensor networks have emerged as promising tools for machine learning, inspired by their widespread use as variational ansatze in quantum many-body physics. It is well known that the success of a given tensor network ansatz depends in part…

Tensor structured Markov chains are part of stochastic models of many practical applications, e.g., in the description of complex production or telephone networks. The most interesting question in Markov chain models is the determination of…

Tensor networks were developed in the context of many-body physics as compressed representations of multiparticle quantum states. These representations mitigate the exponential complexity of many-body systems by capturing only the most…

We present a high-accuracy procedure for electronic structure calculations of strongly correlated materials. To address limitations in current electronic structure methods, we employ density functional theory in combination with the…

We present a tensor-network-based method for simulating a weakly-measured quantum circuit. In particular, we use a Markov chain to efficiently sample measurements and contract the tensor network, propagating their effect forward along the…

In this thesis we extend the formalism of tensor network algorithms to incorporate global internal symmetries. We describe how to both numerically protect the symmetry and exploit it for computational gain in tensor network simulations. Our…