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Here we demonstrate that tensor network techniques - originally devised for the analysis of quantum many-body problems - are well suited for the detailed study of rare event statistics in kinetically constrained models (KCMs). As concrete…
We determine the finite size corrections to the large deviation function of the activity in a kinetically constrained model (the Fredrickson-Andersen model in one dimension), in the regime of dynamical phase coexistence. Numerical results…
We analyze large deviations of the time-averaged activity in the one dimensional Fredrickson-Andersen model, both numerically and analytically. The model exhibits a dynamical phase transition, which appears as a singularity in the large…
We describe a simple form of importance sampling designed to bound and compute large-deviation rate functions for time-extensive dynamical observables in continuous-time Markov chains. We start with a model, defined by a set of rates, and a…
The use of artificial neural networks to represent quantum wave-functions has recently attracted interest as a way to solve complex many-body problems. The potential of these variational parameterizations has been supported by analytical…
Understanding the inductive bias and generalization properties of large overparametrized machine learning models requires to characterize the dynamics of the training algorithm. We study the learning dynamics of large two-layer neural…
Despite very promising results, capturing the dynamics of complex quantum systems with neural-network ans\"atze has been plagued by several problems, one of which being stochastic noise that makes the dynamics unstable and highly dependent…
Machine learning models often require large datasets and struggle to generalize beyond their training distribution. These limitations pose significant challenges in scientific and engineering contexts, where generating exhaustive datasets…
Nowadays, neural networks are widely used in many applications as artificial intelligence models for learning tasks. Since typically neural networks process a very large amount of data, it is convenient to formulate them within the…
We perform an average case analysis of the generalization dynamics of large neural networks trained using gradient descent. We study the practically-relevant "high-dimensional" regime where the number of free parameters in the network is on…
In this chapter, we utilize dynamical systems to analyze several aspects of machine learning algorithms. As an expository contribution we demonstrate how to re-formulate a wide variety of challenges from deep neural networks, (stochastic)…
We study large deviations in the context of stochastic gradient descent for one-hidden-layer neural networks with quadratic loss. We derive a quenched large deviation principle, where we condition on an initial weight measure, and an…
Artificial neural networks have been widely adopted as ansatzes to study classical and quantum systems. However, some notably hard systems such as those exhibiting glassiness and frustration have mainly achieved unsatisfactory results…
We study the dynamical large deviations (LD) of a class of one-dimensional kinetically constrained models whose (tilted) generators can be mapped into themselves via duality transformations. We consider four representative models in detail:…
In contrast to conventional artificial neural networks, which are structurally static, we present two approaches for evolving small networks into larger ones during training. The first method employs an auxiliary weight that directly…
In this paper we explore the performance of deep hidden physics model (M. Raissi 2018) for autonomous systems. These systems are described by set of ordinary differential equations which do not explicitly depend on time. Such systems can be…
We demonstrate the power of 2D tensor networks for obtaining large deviation functions of dynamical observables in a classical nonequilibrium setting. Using these methods, we analyze the previously unstudied dynamical phase behavior of the…
Recent work has shown the effectiveness of tensor network methods for computing large deviation functions in constrained stochastic models in the infinite time limit. Here we show that these methods can also be used to study the statistics…
Biological neural networks are notoriously hard to model due to their stochastic behavior and high dimensionality. We tackle this problem by constructing a dynamical model of both the expectations and covariances of the fractions of active…
Recurrent neural networks (RNNs) are a class of neural networks that have emerged from the paradigm of artificial intelligence and has enabled lots of interesting advances in the field of natural language processing. Interestingly, these…