相关论文: A multifractal phase-space analysis of perceptrons…
Boltzmann-Gibbs measures generated by logarithmically correlated random potentials are multifractal. We investigate the abrupt change ("pre-freezing") of multifractality exponents extracted from the averaged moments of the measure - the…
We present a theoretical study of a spectral filter, which consists of a diffraction grating, a coupling lens, and an optical fiber. As the diffracted beam is highly dispersed spatially, coupling into an optical fiber naturally creates a…
In photonic neural network a key building block is the perceptron. Here, we describe and demonstrate a complex-valued photonic perceptron that combines time and space multiplexing in a fully passive silicon photonics integrated circuit. An…
The normalized radial basis function neural network emerges in the statistical modeling of natural laws that relate components of multivariate data. The modeling is based on the kernel estimator of the joint probability density function…
Binary perceptron is a fundamental model of supervised learning for the non-convex optimization, which is a root of the popular deep learning. Binary perceptron is able to achieve a classification of random high-dimensional data by…
We show how phase-space simulations of Gaussian quantum states in a photonic network permit verification of measurable correlations of Gaussian boson sampling (GBS) quantum computers. Our results agree with experiments for up to 100-th…
An obstacle to artificial general intelligence is set by continual learning of multiple tasks of different nature. Recently, various heuristic tricks, both from machine learning and from neuroscience angles, were proposed, but they lack a…
In many signal processing problems arising in practical applications, we wish to reconstruct an unknown signal from its phaseless measurements with respect to a frame. This inverse problem is known as the phase retrieval problem. For each…
Network data are increasingly collected along with other variables of interest. Our motivation is drawn from neurophysiology studies measuring brain connectivity networks for a sample of individuals along with their membership to a low or…
We propose a novel approach to learning the generative neural fields represented by linear combinations of implicit basis networks. Our algorithm learns basis networks in the form of implicit neural representations and their coefficients in…
Several scenarios of interacting neural networks which are trained either in an identical or in a competitive way are solved analytically. In the case of identical training each perceptron receives the output of its neighbour. The symmetry…
We consider multi-antenna cooperative spectrum sensing in cognitive radio networks, when there may be multiple primary users. A detector based on the spherical test is analyzed in such a scenario. Based on the moments of the distributions…
Extracting the spectral representations of the neural processes that underlie spiking activity is key to understanding how the brain rhythms mediate cognitive functions. While spectral estimation of continuous time-series is well studied,…
Spectral network identification aims at inferring the eigenvalues of the Laplacian matrix of a network from measurement data. This allows to capture global information on the network structure from local measurements at a few number of…
Generalized dimensions of multifractal measures are usually seen as static objects, related to the scaling properties of suitable partition functions, or moments of measures of cells. When these measures are invariant for the flow of a…
We study the generalization ability of a simple perceptron which learns unlearnable rules. The rules are presented by a teacher perceptron with a non-monotonic transfer function. The student is trained in the on-line mode. The asymptotic…
In a mixed generalized linear model, the goal is to learn multiple signals from unlabeled observations: each sample comes from exactly one signal, but it is not known which one. We consider the prototypical problem of estimating two…
The cooperative behaviour of interacting neurons and synapses is studied using models and methods from statistical physics. The competition between training error and entropy may lead to discontinuous properties of the neural network. This…
The interpretability of neural networks (NNs) is a challenging but essential topic for transparency in the decision-making process using machine learning. One of the reasons for the lack of interpretability is random weight initialization,…
We study the task of agnostic learning of multiclass linear classifiers under the Gaussian distribution. Given labeled examples $(x, y)$ from a distribution over $\mathbb{R}^d \times [k]$, with Gaussian $x$-marginal, the goal is to output a…