相关论文: Central and Non-central Limit Theorems arising fro…

The highly irregular spiking activity of cortical neurons and behavioral variability suggest that the brain could operate in a fundamentally probabilistic way. Mimicking how the brain implements and learns probabilistic computation could be…

Scattering Networks were initially designed to elucidate the behavior of early layers in Convolutional Neural Networks (CNNs) over Euclidean spaces and are grounded in wavelets. In this work, we introduce a scattering transform on an…

We analyse the scattering operator associated with the defocusing nonlinear Schr{\"o}dinger equation which captures the evolution of solutions over an infinite time-interval under the nonlinear flow of this equation. The asymptotic nature…

The works of Gatys et al. demonstrated the capability of Convolutional Neural Networks (CNNs) in creating artistic style images. This process of transferring content images in different styles is called Neural Style Transfer (NST). In this…

The statistics of correlations are central quantities characterizing the collective dynamics of recurrent neural networks. We derive exact expressions for the statistics of correlations of nonlinear recurrent networks in the limit of a…

Metastable brain dynamics are characterized by abrupt, jump-like modulations so that the neural activity in single trials appears to unfold as a sequence of discrete, quasi-stationary states. Evidence that cortical neural activity unfolds…

Recent studies using four-point correlations suggest a parity violation in the galaxy distribution, though the significance of these detections is sensitive to the choice of simulation used to model the noise properties of the galaxy…

We present a cosmology analysis of simulated weak lensing convergence maps using the Neural Field Scattering Transform (NFST) to constrain cosmological parameters. The NFST extends the Wavelet Scattering Transform (WST) by incorporating…

Under the high-dimensional setting that data dimension and sample size tend to infinity proportionally, we derive the central limit theorem (CLT) for linear spectral statistics (LSS) of large-dimensional sample covariance matrix. Different…

Studying particle-laden flows is essential to understand diverse physical processes such as rain formation in clouds, pathogen transmission, and pollutant dispersal. Distinct clustering patterns are formed in such flows with particles of…

In this manuscript we show that a noise-activated escape phenomenon occurs in closed Hamiltonian systems. Due to the energy fluctuations generated by the noise, the isopotential curves open up and the particles can eventually escape in…

In this article, we study the properties of the nonlinear Fourier spectrum in order to gain better control of the temporal support of the signals synthesized using the inverse nonlinear Fourier transform (NFT). In particular, we provide…

The Central Limit Theorem (CLT) establishes that sufficiently large sequences of independent and identically distributed random variables converge in probability to a normal distribution. This makes the CLT a fundamental building block of…

Reliable quantification of uncertainty estimates in continuous-time (CT) representation learning remains nascent, particularly within CT attention architectures. We introduce the Neuronal Stochastic Attention Circuit (NSAC), a novel…

We consider linear two-time-scale stochastic approximation algorithms driven by martingale noise. Recent applications in machine learning motivate the need to understand finite-time error rates, but conventional stochastic approximation…

Spiking Neural Networks (SNNs) can do inference with low power consumption due to their spike sparsity. ANN-SNN conversion is an efficient way to achieve deep SNNs by converting well-trained Artificial Neural Networks (ANNs). However, the…

This article presents the consensus of a saturated second order multi-agent system with non-switching dynamics that can be represented by a directed graph. The system is affected by data processing (input delay) and communication…

The time evolution of the thermally activated decay rates is considered. This evolution is of particular importance for the recent nanoscale experiments discussed in the literature, where the potential barrier is relatively low (or the…

This paper develops an adaptive version of Mallat's scattering transform for signals on graphs. The main results are norm bounds for the layers of the transform, obtained from a version of a Beurling-Deny inequality that permits to remove…

Activation functions play a key role in neural networks so it becomes fundamental to understand their advantages and disadvantages in order to achieve better performances. This paper will first introduce common types of non linear…