Related papers: Mathematical Formulation of Multi-Layer Networks

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…

There is a significant expansion in both volume and range of applications along with the concomitant increase in the variety of data sources. These ever-expanding trends have highlighted the necessity for more versatile analysis tools that…

The field of neuroscience is facing an unprecedented expanse in the volume and diversity of available data. Traditionally, network models have provided key insights into the structure and function of the brain. With the advent of big data…

Tensor networks are a compressed format for multi-dimensional data. One-dimensional tensor networks -- often referred to as tensor trains (TT) or matrix product states (MPS) -- are increasingly being used as a numerical ansatz for continuum…

We study properties of multi-layered, interconnected networks from an ensemble perspective, i.e. we analyze ensembles of multi-layer networks that share similar aggregate characteristics. Using a diffusive process that evolves on a…

We propose a generalization of the concept of assortativity based on the tensorial representation of multilayer networks, covering the definitions given in terms of Pearson and Spearman coefficients. Our approach can also be applied to…

Complex networks are made up of vertices and edges. The edges, which may be directed or undirected, are equipped with positive weights. Modeling complex systems that consist of different types of objects leads to multilayer networks, in…

The mental lexicon is a complex cognitive system representing information about the words/concepts that one knows. Decades of psychological experiments have shown that conceptual associations across multiple, interactive cognitive levels…

The curse of dimensionality associated with the Hilbert space of spin systems provides a significant obstruction to the study of condensed matter systems. Tensor networks have proven an important tool in attempting to overcome this…

Interpreting the prediction mechanism of complex models is currently one of the most important tasks in the machine learning field, especially with layered neural networks, which have achieved high predictive performance with various…

A wide range of complex systems can be modeled as networks with corresponding constraints on the edges and nodes, which have been extensively studied in recent years. Nowadays, with the progress of information technology, systems that…

Complex systems are characterized by multiple spatial and temporal scales. A natural framework to capture their multiscale nature is that of multilayer networks, where different layers represent distinct physical processes that often…

We propose a novel framework that leverages large language models (LLMs) to guide the rank selection in tensor network models for higher-order data analysis. By utilising the intrinsic reasoning capabilities and domain knowledge of LLMs,…

Complex networks are characterized by latent geometries induced by their topology or by the dynamics on the top of them. In the latter case, different network-driven processes induce distinct geometric features that can be captured by…

Properties such as composability and automatic differentiation made artificial neural networks a pervasive tool in applications. Tackling more challenging problems caused neural networks to progressively become more complex and thus…

Many physical systems--from mechanical lattices and electrical circuits to biological tissues and architected metamaterials--can be understood as networks transmitting physical quantities. We present a unified mathematical framework for…

The use of complex networks as a modern approach to understanding the world and its dynamics is well-established in literature. The adjacency matrix, which provides a one-to-one representation of a complex network, can also yield several…

Many biological and man-made networked systems are characterized by the simultaneous presence of different sub-networks organized in separate layers, with links and nodes of qualitatively different types. While during the past few years…

Traditional network analysis focuses on single-layer networks, real-world systems often form multilayer networks with multiple relationship types. However, existing methods typically fail to capture complex inter-layer dependencies by…

Many real-world complex systems are well represented as multilayer networks; predicting interactions in those systems is one of the most pressing problems in predictive network science. To address this challenge, we introduce two stochastic…