Related papers: The macroscopic dynamics in separable neural netwo…

To understand how rich dynamics emerge in neural populations, we require models exhibiting a wide range of activity patterns while remaining interpretable in terms of connectivity and single-neuron dynamics. However, it has been challenging…

In this work we study a Hebbian neural network, where neurons are arranged according to a hierarchical architecture such that their couplings scale with their reciprocal distance. As a full statistical mechanics solution is not yet…

Neural dynamics of energy-based models are governed by energy minimization and the patterns stored in the network are retrieved when the system reaches equilibrium. However, when the system is driven by time-varying external input, the…

Conditional Neural Processes (CNPs; Garnelo et al., 2018a) are meta-learning models which leverage the flexibility of deep learning to produce well-calibrated predictions and naturally handle off-the-grid and missing data. CNPs scale to…

We initiate the study of probabilistic parallel programs with dynamic process creation and synchronisation. To this end, we introduce probabilistic split-join systems (pSJSs), a model for parallel programs, generalising both probabilistic…

The emergence of collective dynamics in neural networks is a mechanism of the animal and human brain for information processing. In this paper, we develop a computational technique using distributed processing elements in a complex network,…

We study the dynamics of the processes in the small-world networks with a power-law degree distribution where every node is considered to be in one of the two available statuses. We present an algorithm for generation of such network and…

At functional scales, cortical behavior results from the complex interplay of a large number of excitable cells operating in noisy environments. Such systems resist to mathematical analysis, and computational neurosciences have largely…

This work presents a novel means for understanding learning dynamics and scaling relations in neural networks. We show that certain measures on the spectrum of the empirical neural tangent kernel, specifically entropy and trace, yield…

Massively parallel hardware (GPUs) and long sequence data have made parallel algorithms essential for machine learning at scale. Yet dynamical systems, like recurrent neural networks and Markov chain Monte Carlo, were thought to suffer from…

Continuous-Time Recurrent Neural Networks (CTRNNs) have been widely used for their capacity to model complex temporal behaviour. However, their internal dynamics often remain difficult to interpret. In this paper, we propose a new class of…

The macroscopic (population-level) dynamics of chemotactic cell movement -- arising from underlying microscopic (individual-based) models -- are often described by parabolic partial differential equations (PDEs) governing the…

We consider a class of stochastic dynamical systems, called piecewise deterministic Markov processes, with states $(x, \s)\in \O\times \G$, $\O$ being a region in $\bbR^d$ or the $d$--dimensional torus, $\G$ being a finite set. The…

Synchronization is a widespread phenomenon in the brain. Despite numerous studies, the specific parameter configurations of the synaptic network structure and learning rules needed to achieve robust and enduring synchronization in neurons…

A dynamical neural network consists of a set of interconnected neurons that interact over time continuously. It can exhibit computational properties in the sense that the dynamical system's evolution and/or limit points in the associated…

This paper aims at the study of controllability properties and induced controllability metrics on complex networks governed by a class of (discrete time) linear decision processes with mul-tiplicative noise. The dynamics are given by a…

We propose a scalable semiparametric Bayesian model to capture dependencies among multiple neurons by detecting their co-firing (possibly with some lag time) patterns over time. After discretizing time so there is at most one spike at each…

Machine learning simulations of open quantum dynamics often rely on recursive predictors that accumulate error. We develop a non-recursive convolutional neural networks (CNNs) that maps system parameters and a redundant time encoding…

We study the dynamics of multiparticle Carroll-Schr\"odinger (CS) quantum systems in $1{+}1$ dimensions, where $x$ acts as the evolution variable and $t$ as the configuration coordinate. We derive the $N$-body theory on equal-$x$ slices as…

Traditional mathematical approaches to studying analytically the dynamics of neural networks rely on the mean-field approximation, which is rigorously applicable only to networks of infinite size. However, all existing real biological…