Related papers: Large deviations for randomly connected neural net…
We study the asymptotics of large, moderate and normal deviations for the connected components of the sparse random graph by the method of stochastic processes. We obtain the logarithmic asymptotics of large deviations of the joint…
The theory of stochastic approximations form the theoretical foundation for studying convergence properties of many popular recursive learning algorithms in statistics, machine learning and statistical physics. Large deviations for…
Let $\Delta^o$ be a finite set and, for each probability measure $m$ on $\Delta^o$, let $G(m)$ be a transition probability kernel on $\Delta^o$. Fix $x_0 \in \Delta^o$ and consider the chain $\{X_n, \; n \in \mathbb{N}_0\}$ of…
In modern deep learning, there is a recent and growing literature on the interplay between large-width asymptotic properties of deep Gaussian neural networks (NNs), i.e. deep NNs with Gaussian-distributed weights, and Gaussian stochastic…
We propose a general framework to extract microscopic interactions from raw configurations with deep neural networks. The approach replaces the modeling Hamiltonian by the neural networks, in which the interaction is encoded. It can be…
We study two problems. First, we consider the large deviation behavior of empirical measures of certain diffusion processes as, simultaneously, the time horizon becomes large and noise becomes vanishingly small. The law of large numbers…
We establish the large deviations asymptotic performance (error exponent) of consensus+innovations distributed detection over random networks with generic (non-Gaussian) sensor observations. At each time instant, sensors 1) combine theirs…
A distributed average consensus algorithm in which every sensor transmits with bounded peak power is proposed. In the presence of communication noise, it is shown that the nodes reach consensus asymptotically to a finite random variable…
This paper considers the consensus problem for a network of nodes with random interactions and sampled-data control actions. We first show that consensus in expectation, in mean square, and almost surely are equivalent for a general random…
The cortex is a very large network characterized by a complex connectivity including at least two scales: a microscopic scale at which the interconnections are non-specific and very dense, while macroscopic connectivity patterns connecting…
Many mathematical models of interacting agents assume that individual interactions scale down in proportion to the network size, ensuring that the combined input received from the network does not diverge. In theoretical neuroscience,…
We continue the development, started in of the asymptotic description of certain stochastic neural networks. We use the Large Deviation Principle (LDP) and the good rate function H announced there to prove that H has a unique minimum mu_e,…
We study binary state dynamics on a network where each node acts in response to the average state of its neighborhood. Allowing varying amounts of stochasticity in both the network and node responses, we find different outcomes in random…
Machine learning, and in particular neural network models, have revolutionized fields such as image, text, and speech recognition. Today, many important real-world applications in these areas are driven by neural networks. There are also…
Understanding the dynamics of spatially extended systems represents a challenge in diverse scientific disciplines, ranging from physics and mathematics to the earth and climate sciences or the neurosciences. This challenge has stimulated…
We investigate two asymptotic properties of a spatial preferential-attachment model introduced by E. Jacob and P. M\"orters (2013). First, in a regime of strong linear reinforcement, we show that typical distances are at most of…
We consider the quasi-deterministic behavior of systems with a large number, $n$, of deterministically interacting constituents. This work extends the results of a previous paper [J. Stat. Phys. 99:1225-1249 (2000)] to include vector-valued…
We study the large-volume asymptotics of the sum of power-weighted edge lengths $\sum_{e \in E}|e|^\alpha$ in Poisson-based spatial random networks. In the regime $\alpha > d$, we provide a set of sufficient conditions under which the upper…
A basic result of large deviations theory is Sanov's theorem, which states that the sequence of empirical measures of independent and identically distributed samples satisfies the large deviation principle with rate function given by…
We show that under certain simple assumptions on the topology (structure) of networks of strongly interacting chaotic elements a phenomenon of long range action takes place, namely that the asymptotic (as time goes to infinity) dynamics of…