Related papers: Thresholds in layered neural networks with variabl…

Important insights towards the explainability of neural networks reside in the characteristics of their decision boundaries. In this work, we borrow tools from the field of adversarial robustness, and propose a new perspective that relates…

For the retrieval dynamics of sparsely coded attractor associative memory models with synaptic noise the inclusion of a macroscopic time-dependent threshold is studied. It is shown that if the threshold is chosen appropriately as a function…

The ability to achieve coordinated behavior -- engineered or emergent -- on networked systems has attracted widespread interest over several fields. This interest has led to remarkable advances in developing a theoretical understanding of…

The identification of the limiting factors in the dynamical behavior of complex systems is an important interdisciplinary problem which often can be traced to the spectral properties of an underlying network. By deriving a general relation…

We consider a large-scale service system where incoming tasks have to be instantaneously dispatched to one out of many parallel server pools. The user-perceived performance degrades with the number of concurrent tasks and the dispatcher…

A person's decision to adopt an idea or product is often driven by the decisions of peers, mediated through a network of social ties. A common way of modeling adoption dynamics is to use threshold models, where a node may become an adopter…

In this paper, we investigate asymptotic properties of a consensus protocol taking place in a class of temporal (i.e., time-varying) networks called the activity driven network. We first show that a standard methodology provides us with an…

Graph attention networks learn neighbor importance through data-dependent coefficients, but standard layers lack explicit control over unreliable feature dimensions and use fixed sharpness of attention coefficient distributions. This paper…

Thresholding--the pruning of nodes or edges based on their properties or weights--is an essential preprocessing tool for extracting interpretable structure from complex network data, yet existing methods face several key limitations.…

Neural network models in neuroscience allow one to study how the connections between neurons shape the activity of neural circuits in the brain. In this chapter, we study Combinatorial Threshold-Linear Networks (CTLNs) in order to…

We study the diversity of complex spatio-temporal patterns in the behavior of random synchronous asymmetric neural networks (RSANNs). Special attention is given to the impact of disordered threshold values on limit-cycle diversity and…

On the basis of solutions of the master equation for networks with a small number of neurons it is shown that the conditional entropy and integrated information of neural networks depend on their average activity and inter-cluster…

Sequential learning in physical networks is hindered by catastrophic forgetting, where training a new task erases solutions to earlier ones. We show that we can significantly enhance memory of previous tasks by introducing a hard threshold…

In the context of attractor neural networks, we study how the equilibrium analog neural activities, reached by the network dynamics during memory retrieval, may improve storage performance by reducing the interferences between the recalled…

The connectivity of individual neurons of large neural networks determine both the steady state activity of the network and its answer to external stimulus. Highly diluted random networks have zero activity. We show that increasing the…

Linear thresholding systems have been used as a model of neural activation and more recently proposed as a model of gene regulation. Here we exhibit linear thresholding systems whose dynamics produce surprisingly long cycles.

The question of how clustering (non-zero density of triangles) in networks affects their bond percolation threshold has important applications in a variety of disciplines. Recent advances in modelling highly-clustered networks are employed…

The expressive power of artificial neural networks crucially depends on the nonlinearity of their activation functions. Though a wide variety of nonlinear activation functions have been proposed for use in artificial neural networks, a…

In this work we study the detection of weak stimuli by spiking neurons in the presence of certain level of noisy background neural activity. Our study has focused in the realistic assumption that the synapses in the network present…

In this paper we present a method which assigns to each layer of a multilayer neural network, whose network dynamics is governed by a noisy winner-take-all mechanism, a neural temperature. This neural temperature is obtained by a least mean…