Related papers: Geometric framework to predict structure from func…

Recent experimental advances are producing an avalanche of data on both neural connectivity and neural activity. To take full advantage of these two emerging datasets we need a framework that links them, revealing how collective neural…

Control is essential to the functioning of any neural system. Indeed, under healthy conditions the brain must be able to continuously maintain a tight functional control between the system's inputs and outputs. One may therefore hypothesise…

Hyperbolic networks are supposed to be congruent with their underlying latent geometry and following geodesics in the hyperbolic space is believed equivalent to navigate through topological shortest paths (TSP). This assumption of…

The current understanding of deep neural networks can only partially explain how input structure, network parameters and optimization algorithms jointly contribute to achieve the strong generalization power that is typically observed in…

Understanding network functionality requires integrating structure and dynamics, and emergent latent geometry induced by network-driven processes captures the low-dimensional spaces governing this interplay. Here, we focus on…

Even when neural networks are widely used in a large number of applications, they are still considered as black boxes and present some difficulties for dimensioning or evaluating their prediction error. This has led to an increasing…

Building on evidence of structural parallels between brain networks and the cosmic web [1], we apply AI-based geometric analysis to cultured neuronal networks. Isolated neurons self-organize into dendritic lattices shaped by reproducible…

Understanding the relation between cortical neuronal network structure and neuronal activity is a fundamental unresolved question in neuroscience, with implications to our understanding of the mechanism by which neuronal networks evolve…

The emergence of detailed maps of physical networks, like the brain connectome, vascular networks, or composite networks in metamaterials, whose nodes and links are physical entities, have demonstrated the limits of the current network…

An essential step toward understanding neural circuits is linking their structure and their dynamics. In general, this relationship can be almost arbitrarily complex. Recent theoretical work has, however, begun to identify some broad…

Understanding the deep representations of complex networks is an important step of building interpretable and trustworthy machine learning applications in the age of internet. Global surrogate models that approximate the predictions of a…

A neural network with fixed topology can be regarded as a parametrization of functions, which decides on the correlations between functional variations when parameters are adapted. We propose an analysis, based on a differential geometry…

The representations of neural networks are often compared to those of biological systems by performing regression between the neural network responses and those measured from biological systems. Many different state-of-the-art deep neural…

Geometry is a ubiquitous tool in computer graphics, design, and engineering. However, the lack of large shape datasets limits the application of state-of-the-art supervised learning methods and motivates the exploration of alternative…

Turing patterns, arising from the interplay between competing species of diffusive particles, has long been an important concept for describing non-equilibrium self-organization in nature, and has been extensively investigated in many…

Motivated by the potential similarities between the underlying mechanisms of the enhanced memory storage capacity in black holes and in brain networks, we construct an artificial quantum neural network based on gravity-like synaptic…

The dynamics of neural networks is often characterized by collective behavior and quasi-synchronous events, where a large fraction of neurons fire in short time intervals, separated by uncorrelated firing activity. These global temporal…

Networks are useful for describing systems of interacting objects, where the nodes represent the objects and the edges represent the interactions between them. The applications include chemical and metabolic systems, food webs as well as…

The inclusion of a macroscopic adaptive threshold is studied for the retrieval dynamics of both layered feedforward and fully connected neural network models with synaptic noise. These two types of architectures require a different method…

Interactions and relations between objects may be pairwise or higher-order in nature, and so network-valued data are ubiquitous in the real world. The "space of networks", however, has a complex structure that cannot be adequately described…