Related papers: Latent Space Topology Evolution in Multilayer Perc…

When dealing with spreading processes on networks it can be of the utmost importance to test the reliability of data and identify potential unobserved spreading paths. In this paper we address these problems and propose methods for hidden…

A complex system comprises multiple interacting entities whose interdependencies form a unified whole, exhibiting emergent behaviours not present in individual components. Examples include the human brain, living cells, soft matter, Earth's…

This paper gives the definition of Transparent Neural Network "TNN" for the simulation of the globallocal vision and its application to the segmentation of administrative document image. We have developed and have adapted a recognition…

Modern deep learning architectures are ordinarily performed on high-performance computing facilities due to the large size of the input features and complexity of its model. This paper proposes traditional multilayer perceptrons (MLP) with…

We propose a modeling framework for growing multiplexes where a node can belong to different networks. We define new measures for multiplexes and we identify a number of relevant ingredients for modeling their evolution such as the coupling…

The increasing prevalence of multiplex networks has spurred a critical need to take into account potential dependencies across different layers, especially when the goal is community detection, which is a fundamental learning task in…

Living systems exhibit complex yet organized behavior on multiple spatiotemporal scales. To investigate the nature of multiscale coordination in living systems, one needs a meaningful and systematic way to quantify the complex dynamics, a…

Partial Differential Equations are infinite dimensional encoded representations of physical processes. However, imbibing multiple observation data towards a coupled representation presents significant challenges. We present a fully…

Over the last two decades, the Latent Position Model (LPM) has become a prominent tool to obtain model-based visualizations of networks. However, the geometric structure of the LPM is inherently symmetric, in the sense that outgoing and…

In this paper, we use topological data analysis techniques to construct a suitable neural network classifier for the task of learning sensor signals of entire power plants according to their reference designation system. We use…

The study of the interactions among different types of interconnected systems in complex networks has attracted significant interest across many research fields. However, effective signal processing over layered networks requires…

A topological shape analysis is proposed and utilized to learn concepts that reflect shape commonalities. Our approach is two-fold: i) a spatial topology analysis of point cloud segment constellations within objects. Therein constellations…

Two of the many trends in neural network research of the past few years have been (i) the learning of dynamical systems, especially with recurrent neural networks such as long short-term memory networks (LSTMs) and (ii) the introduction of…

We present a framework designed to learn the underlying dynamics between two images observed at consecutive time steps. The complex nature of image data and the lack of temporal information pose significant challenges in capturing the…

Persistent homology analysis provides means to capture the connectivity structure of data sets in various dimensions. On the mathematical level, by defining a metric between the objects that persistence attaches to data sets, we can…

Large Language Models (LLMs) perform internal computations in continuous vector spaces yet produce discrete tokens -- a fundamental mismatch whose geometric consequences remain poorly understood. We develop a mathematical framework that…

Feature maps in deep neural network generally contain different semantics. Existing methods often omit their characteristics that may lead to sub-optimal results. In this paper, we propose a novel end-to-end deep saliency network which…

Cognitive science suggests that spatial ability develops progressively-from perception to reasoning and interaction. Yet in multimodal LLMs (MLLMs), this hierarchy remains poorly understood, as most studies focus on a narrow set of tasks.…

We extend the recent latent recurrent modeling to sequential input streams. By interleaving fast, recurrent latent updates with self-organizational ability between slow observation updates, our method facilitates the learning of stable…

We introduce a framework to intertwine dynamical processes of different nature, each with its own distinct network topology, using a multilayer network approach. As an example of collective phenomena emerging from the interactions of…