相关论文: Statistical Neurodynamics for sequence processing …

Symmetries are prevalent in deep learning and can significantly influence the learning dynamics of neural networks. In this paper, we examine how exponential symmetries -- a broad subclass of continuous symmetries present in the model…

Varied sensory systems use noise in order to enhance detection of weak signals. It has been conjectured in the literature that this effect, known as stochastic resonance, may take place in central cognitive processes such as the memory…

We perform network analysis of a system described by the master equation to estimate the lower bound of the steady-state current noise, starting from the level 2.5 large deviation function and using the graph theory approach. When the…

It has been proposed that neural noise in the cortex arises from chaotic dynamics in the balanced state: in this model of cortical dynamics, the excitatory and inhibitory inputs to each neuron approximately cancel, and activity is driven by…

We examine the full counting statistics of quantum dots, which display super-Poissonian shot noise. By an extension to a generic situation with many excited states we identify the underlying transport process. The statistics is a sum of…

One of the major challenges in neuroscience is to determine how noise that is present at the molecular and cellular levels affects dynamics and information processing at the macroscopic level of synaptically coupled neuronal populations.…

Statistical mechanics determines the abundance of different arrangements of matter depending on cost-benefit balances. Its formalism and phenomenology percolate throughout biological processes and set limits to effective computation. Under…

Machine learning models trained by different optimization algorithms under different data distributions can exhibit distinct generalization behaviors. In this paper, we analyze the generalization of models trained by noisy iterative…

This contribution reviews the parallel dynamics of Q-Ising neural networks for various architectures: extremely diluted asymmetric, layered feedforward, extremely diluted symmetric, and fully connected. Using a probabilistic signal-to-noise…

Latent dynamics discovery is challenging in extracting complex dynamics from high-dimensional noisy neural data. Many dimensionality reduction methods have been widely adopted to extract low-dimensional, smooth and time-evolving latent…

Neural network approaches for meta-learning distributions over functions have desirable properties such as increased flexibility and a reduced complexity of inference. Building on the successes of denoising diffusion models for generative…

Understanding the implicit bias of training algorithms is of crucial importance in order to explain the success of overparametrised neural networks. In this paper, we study the dynamics of stochastic gradient descent over diagonal linear…

Here we present a simple stochastic threshold model consisting of a deterministic slowly decaying term and a fast stochastic noise term. The process shows a pseudo-resonance, in the sense that for small and large intensities of the noise…

Temporal data such as time series can be viewed as discretized measurements of the underlying function. To build a generative model for such data we have to model the stochastic process that governs it. We propose a solution by defining the…

In this paper we present a novel quasi-Newton algorithm for use in stochastic optimisation. Quasi-Newton methods have had an enormous impact on deterministic optimisation problems because they afford rapid convergence and computationally…

Using a probabilistic approach we study the parallel dynamics of fully connected Q-Ising neural networks for arbitrary Q. A Lyapunov function is shown to exist at zero temperature. A recursive scheme is set up to determine the time…

In Score based Generative Modeling (SGMs), the state-of-the-art in generative modeling, stochastic reverse processes are known to perform better than their deterministic counterparts. This paper delves into the heart of this phenomenon,…

It is shown that an exact solution of the transient dynamics of an associative memory model storing an infinite number of limit cycles with l finite steps by means of the path-integral analysis. Assuming the Maxwell construction ansatz, we…

Diffusion models have attracted a lot of attention in recent years. These models view speech generation as a continuous-time process. For efficient training, this process is typically restricted to additive Gaussian noising, which is…

Microbial motion is typically analyzed by simplified models in which trajectories exhibit straight runs (perhaps with added Gaussian noise) followed by random, discrete tumbling events. We present the results of a statistical analysis of…