相关论文: Large deviations for randomly connected neural net…
The large deviation principle is proved for a class of $L^2$-valued processes that arise from the coarse-graining of a random field. Coarse-grained processes of this kind form the basis of the analysis of local mean-field models in…
We explore large populations of phase oscillators interacting via random coupling functions. Two types of coupling terms, the Kuramoto-Daido coupling and the Winfree coupling, are considered. Under the assumption of statistical independence…
Random features models play a distinguished role in the theory of deep learning, describing the behavior of neural networks close to their infinite-width limit. In this work, we present a thorough analysis of the generalization performance…
We consider the effects of long-range temporal correlations in many-particle systems, focusing particularly on fluctuations about the typical behaviour. For a specific class of memory dependence we discuss the modification of the large…
The inference of Markov models from data on stochastic dynamical trajectories over the large time-window $T$ is revisited via the Large Deviations at Level 2.5 for the time-empirical density and the time-empirical flows. The goal is to…
Coordination is ubiquitous in living systems. Existing theoretical models of coordination -- from bacteria to brains -- focus on either gross statistics in large-scale systems ($N\rightarrow\infty$) or detailed dynamics in small-scale…
We present large deviations estimates in the supremum norm for a system of independent random walks superposed with a birth-and-death dynamics evolving on the discrete torus with $N$ sites. The scaling limit considered is the so-called…
For any finite colored graph we define the empirical neighborhood measure, which counts the number of vertices of a given color connected to a given number of vertices of each color, and the empirical pair measure, which counts the number…
We consider a system of $N^{d}$ spins in random environment with a random local mean field type interaction. Each spin has a fixed spatial position on the torus $\mathbb{T}^{d}$, an attached random environment and a spin value in…
In various disordered systems or non-equilibrium dynamical models, the large deviations of some observables have been found to display different scalings for rare values bigger or smaller than the typical value. In the present paper, we…
The probability distribution of the maximum $M_t$ of a single resetting Brownian motion (RBM) of duration $t$ and resetting rate $r$, properly centred and scaled, is known to converge to the standard Gumbel distribution of the classical…
In this paper we analyze the second-order Kuramoto model presenting a positive correlation between the heterogeneity of the connections and the natural frequencies in scale-free networks. We numerically show that discontinuous transitions…
We use a neural network ansatz originally designed for the variational optimization of quantum systems to study dynamical large deviations in classical ones. We obtain the scaled cumulant-generating function for the dynamical activity of…
We study a Kuramoto model in which the oscillators are associated with the nodes of a complex network and the interactions include a phase frustration, thus preventing full synchronization. The system organizes into a regime of remote…
Consider a collection of particles whose state evolution is described through a system of interacting diffusions in which each particle is driven by an independent individual source of noise and also by a small amount of noise that is…
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…
The complexity of quantum many-body systems is manifested in the vast diversity of their correlations, making it challenging to distinguish the generic from the atypical features. This can be addressed by analyzing correlations through…
How condensed-matter simulations depend on the number of molecules being simulated ($N$) is sometimes itself a valuable piece of information. Liquid crystals provide a case in point. Light scattering and $2d$-IR experiments on…
Collective behaviors that emerge from interactions are fundamental to numerous biological systems. To learn such interacting forces from observations, we introduce a measure-valued neural network that infers measure-dependent interaction…
We investigate the dynamics of the adaptive Kuramoto model with slow adaptation in the continuum limit, $N\to\infty$. This model is distinguished by dense multistability, where multiple states coexist for the same system parameters. The…