Related papers: Solution of a large nonlinear recurrent neural net…

Training neural networks means solving a high-dimensional optimization problem. Normally the goal is to minimize a loss function that depends on what is called the network function, or in other words the function that gives the network…

We construct fast algorithms for evaluating transforms associated with families of functions which satisfy recurrence relations. These include algorithms both for computing the coefficients in linear combinations of the functions, given the…

A single neuron is known to generate almost identical spike trains when the same fluctuating input is repeatedly applied. Here, we study the reliability of spike firing in a pulse-coupled network of oscillator neurons receiving fluctuating…

We analyze the dynamics of networks of spiking neural oscillators. First, we present an exact linear stability theory of the synchronous state for networks of arbitrary connectivity. For general neuron rise functions, stability is…

We present an example of a highly connected closed network of servers, where the time correlations do not go to zero in the infinite volume limit. This phenomenon is similar to the continuous symmetry breaking at low temperatures in…

Sequence modeling tasks across domains such as natural language processing, time series forecasting, and control require learning complex input-output mappings. Nonlinear recurrence is theoretically required for universal approximation of…

This article presents a biological neural network model driven by inhomogeneous Poisson processes accounting for the intrinsic randomness of synapses. The main novelty is the introduction of local interactions: each firing neuron triggers…

It has been widely assumed that a neural network cannot be recovered from its outputs, as the network depends on its parameters in a highly nonlinear way. Here, we prove that in fact it is often possible to identify the architecture,…

The impressive performance of deep neural networks (DNNs) has immensely strengthened the line of research that aims at theoretically analyzing their effectiveness. This has incited research on the reaction of DNNs to noisy input, namely…

Using a generalized random recurrent neural network model, and by extending our recently developed mean-field approach [J. Aljadeff, M. Stern, T. Sharpee, Phys. Rev. Lett. 114, 088101 (2015)], we study the relationship between the network…

The problem of achieving consensus in a network of connected systems arises in many science and engineering applications. In contrast to previous works, we focus on the system reactivity, i.e., the initial amplification of the norm of the…

This paper is a review dealing with the study of large size random recurrent neural networks. The connection weights are selected according to a probability law and it is possible to predict the network dynamics at a macroscopic scale using…

In specific motifs of three recurrently connected neurons with probabilistic response, the spontaneous information flux, defined as the mutual information between subsequent states, has been shown to increase by adding ongoing white noise…

Exactly solvable neural network models with asymmetric weights are rare, and exact solutions are available only in some mean-field approaches. In this article we find exact analytical solutions of an asymmetric spin-glass-like model of…

The co-occurrence of action potentials of pairs of neurons within short time intervals is known since long. Such synchronous events can appear time-locked to the behavior of an animal and also theoretical considerations argue for a…

How do humans and animals perform trial-and-error learning when the space of possibilities is infinite? In a previous study, we used an interval timing production task and discovered an updating strategy in which the agent adjusted the…

We here unify the field theoretical approach to neuronal networks with large deviations theory. For a prototypical random recurrent network model with continuous-valued units, we show that the effective action is identical to the rate…

A mechanism for self-organization of the degree of connectivity in model neural networks is studied. Network connectivity is regulated locally on the basis of an order parameter of the global dynamics which is estimated from an observable…

We investigate the relationship of resting-state fMRI functional connectivity estimated over long periods of time with time-varying functional connectivity estimated over shorter time intervals. We show that using Pearson's correlation to…

Recommender systems objectives can be broadly characterized as modeling user preferences over short-or long-term time horizon. A large body of previous research studied long-term recommendation through dimensionality reduction techniques…