相关论文: Statistical Neurodynamics for sequence processing …

We study the noise of the cotunneling current through one or several tunnel-coupled quantum dots in the Coulomb blockade regime. The various regimes of weak and strong, elastic and inelastic cotunneling are analyzed for quantum-dot systems…

Generative models realized with machine learning techniques are powerful tools to infer complex and unknown data distributions from a finite number of training samples in order to produce new synthetic data. Diffusion models are an emerging…

We study the problem of learning general (i.e., not necessarily homogeneous) halfspaces with Random Classification Noise under the Gaussian distribution. We establish nearly-matching algorithmic and Statistical Query (SQ) lower bound…

We develop the general formalism for the study of neutrino propagation in presence of stochastic media. This formalism allows the systematic derivation of evolution equations for averaged quantities as survival probabilities and higher…

The inclusion of a macroscopic adaptive threshold is studied for the retrieval dynamics of both layered feedforward and fully connected neural network models with synaptic noise. These two types of architectures require a different method…

Many approaches to modelling reaction-diffusion systems with anomalous transport rely on deterministic equations and ignore fluctuations arising due to finite particle numbers. Starting from an individual-based model we use a…

We study the statistical physics of a surprising phenomenon arising in large networks of excitable elements in response to noise: while at low noise, solutions remain in the vicinity of the resting state and large-noise solutions show…

Biological systems are notoriously noisy. Noise, therefore, also plays an important role in many models of neural impulse generation. Noise is not only introduced for more realistic simulations but also to account for cooperative effects…

In this work we analyze the stochastic dynamics of the Kauffman model evolving under the influence of noise. By considering the average crossing time between two distinct trajectories, we show that different Kauffman models exhibit a…

This work is concerned with existence of weak solutions to discon- tinuous stochastic differential equations driven by multiplicative Gaus- sian noise and sliding mode control dynamics generated by stochastic differential equations with…

Networks of stochastic spiking neurons are interesting models in the area of Theoretical Neuroscience, presenting both continuous and discontinuous phase transitions. Here we study fully connected networks analytically, numerically and by…

The subject of study is a neural network with binary neurons, randomly diluted synapses and variable pattern activity. We look at the system with parallel updating using a probabilistic approach to solve the one step dynamics with one…

Stochastic systems feature, in general, both coherent dynamics and incoherent transitions between different states. We propose a method to identify the coherent part in the full counting statistics for the transitions. The proposal is…

We analyze the effect of synchronization on distributed stochastic gradient algorithms. By exploiting an analogy with dynamical models of biological quorum sensing - where synchronization between agents is induced through communication with…

We find that sensory noise delivered together with a weak periodic signal not only enhances nonlinear response of neuronal networks, but also improves the synchronization of the response to the signal. We reveal this phenomenon in neuronal…

Classical deep learning typically operates on individual cases. Despite its success, real-world usage often requires repeated inference to estimate statistical quantities for complex decision-making tasks involving uncertainty or…

Stochastic Gradient Descent (SGD) is the workhorse algorithm of deep learning technology. At each step of the training phase, a mini batch of samples is drawn from the training dataset and the weights of the neural network are adjusted…

We reinterpret multiplicative noise in neural networks as auxiliary random variables that augment the approximate posterior in a variational setting for Bayesian neural networks. We show that through this interpretation it is both efficient…

This chapter considers the computational and statistical aspects of learning linear thresholds in presence of noise. When there is no noise, several algorithms exist that efficiently learn near-optimal linear thresholds using a small amount…

We analyze the landscape and training dynamics of diagonal linear networks in a linear regression task, with the network parameters being perturbed by small isotropic normal noise. The addition of such noise may be interpreted as a…