Related papers: Statistical Neurodynamics for sequence processing …
To accommodate structured approaches of neural computation, we propose a class of recurrent neural networks for indexing and storing sequences of symbols or analog data vectors. These networks with randomized input weights and orthogonal…
Despite the prevalent view that quantum mechanics is irrelevant to macroscopic biological systems because of inherent noise and decoherence, this paper demonstrates that the electrical noise (Brownian motion) in neuron membranes gives rise…
Denoising diffusion models have proven to be a flexible and effective paradigm for generative modelling. Their recent extension to infinite dimensional Euclidean spaces has allowed for the modelling of stochastic processes. However, many…
For optimizing a non-convex function in finite dimension, a method is to add Brownian noise to a gradient descent, allowing for transitions between basins of attractions of different minimizers. To adapt this for optimization over a space…
Some systems cannot be predicted by classical theories and it is required the development of combined deterministic and stochastic theories that make used of noise for dynamical prediction. Noise is not always an interfering signal which…
The retrieval behavior and thermodynamic properties of symmetrically diluted Q-Ising neural networks are derived and studied in replica-symmetric mean-field theory generalizing earlier works on either the fully connected or the symmetrical…
In the cerebral cortex, neurons are subject to a continuous bombardment of synaptic inputs originating from the network's background activity. This leads to ongoing, mostly subthreshold membrane dynamics that depends on the statistics of…
We apply Bayesian statistics to the estimation of correlation functions. We give the probability distributions of auto- and cross-correlations as functions of the data. Our procedure uses the measured data optimally and informs about the…
Stochastic systems with memory naturally appear in life science, economy, and finance. We take the modelling point of view of stochastic functional delay equations and we study these structures when the driving noises admit jumps. Our…
Training recurrent neural networks (RNNs) is a hard problem due to degeneracies in the optimization landscape, a problem also known as vanishing/exploding gradients. Short of designing new RNN architectures, previous methods for dealing…
Random label noises (or observational noises) widely exist in practical machine learning settings. While previous studies primarily focus on the affects of label noises to the performance of learning, our work intends to investigate the…
We study a class of stochastic evolution equations with a dissipative forcing nonlinearity and additive noise. The noise is assumed to satisfy rather general assumptions about the form of the covariance function; our framework covers…
In the last three decades, Numerical Stochastic Perturbation Theory (NSPT) has proven to be an excellent tool for calculating perturbative expansions in theories such as Lattice QCD, for which standard, diagrammatic perturbation theory is…
We construct Langevin equations describing the fluctuations of the tensor order parameter $Q_{\alpha\beta}$ in nematic liquid crystals by adding noise terms to time-dependent variational equations that follow from the Ginzburg-Landau-de…
We consider a generalization of the Hopfield model, where the entries of patterns are Gaussian and diluted. We focus on the high-storage regime and we investigate analytically the topological properties of the emergent network, as well as…
Injecting gaussian noise into training features is well known to have regularization properties. This paper considers noise injections to numeric or categoric tabular features as passed to inference, which translates inference to a…
We introduce a signal processing model for signals in non-white noise, where the exact noise spectrum is a priori unknown. The model is based on a Student's t distribution and constitutes a natural generalization of the widely used normal…
We study macroscopic behavior of populations of quadratic integrate-and-fire neurons subject to non-Gaussian noises; we argue that these noises must be alpha-stable whenever they are delta-correlated (white). For the case of…
We analyse how the sampling dynamics of distributions evolve in score-based diffusion models using cross-fluctuations, a centered-moment statistic from statistical physics. Specifically, we show that starting from an unbiased isotropic…
Gaussian processes are a powerful framework for quantifying uncertainty and for sequential decision-making but are limited by the requirement of solving linear systems. In general, this has a cubic cost in dataset size and is sensitive to…