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Biological neural networks are notoriously hard to model due to their stochastic behavior and high dimensionality. We tackle this problem by constructing a dynamical model of both the expectations and covariances of the fractions of active…
We investigate anisotropy in Fourier-domain speckle correlations associated with the optical memory effect in disordered scattering media. Within a single scattering framework, we show that while the conventional memory effect constrains…
This article is concerned with the spectral behavior of $p$-dimensional linear processes in the moderately high-dimensional case when both dimensionality $p$ and sample size $n$ tend to infinity so that $p/n\to0$. It is shown that, under an…
In this work we investigate the generic properties of a stochastic linear model in the regime of high-dimensionality. We consider in particular the Vector AutoRegressive model (VAR) and the multivariate Hawkes process. We analyze both…
The use of covariance kernels is ubiquitous in the field of spatial statistics. Kernels allow data to be mapped into high-dimensional feature spaces and can thus extend simple linear additive methods to nonlinear methods with higher order…
It has been observed that neural networks perform poorly when the data or tasks are presented sequentially. Unlike humans, neural networks suffer greatly from catastrophic forgetting, making it impossible to perform life-long learning. To…
Deep neural networks can struggle to learn continually in the face of non-stationarity. This phenomenon is known as loss of plasticity. In this paper, we identify underlying principles that lead to plastic algorithms. In particular, we…
Time-series data with regular and/or seasonal long-memory are often aggregated before analysis. Often, the aggregation scale is large enough to remove any short-memory components of the underlying process but too short to eliminate seasonal…
We consider a continuous-space and continuous-time diffusion process under resetting with memory. A particle resets to a position chosen from its trajectory in the past according to a memory kernel. Depending on the form of the memory…
It is shown that due to memory effects the complex behaviour of components in a stochastic system can be transmitted to macroscopic evolution of the system as a whole. Within the Markov approximation widely using in ordinary statistical…
The long-term memory of most connectionist systems lies entirely in the weights of the system. Since the number of weights is typically fixed, this bounds the total amount of knowledge that can be learned and stored. Though this is not…
In this article, we propose a variational inference formulation of auto-associative memories, allowing us to combine perceptual inference and memory retrieval into the same mathematical framework. In this formulation, the prior probability…
This work brings together two powerful concepts in Gaussian processes: the variational approach to sparse approximation and the spectral representation of Gaussian processes. This gives rise to an approximation that inherits the benefits of…
.Stochastic models based on random diffusivities, such as the diffusing-diffusivity approach, are popular concepts for the description of non-Gaussian diffusion in heterogeneous media. Studies of these models typically focus on the moments…
We present computer simulations run with a stochastic cellular automaton which describes $d=1$ particle systems connected to reservoirs which keep two different densities at the endpoints. We fix the parameters so that there is a phase…
Tensor algebras give rise to one of the most powerful measures of similarity for sequences of arbitrary length called the signature kernel accompanied with attractive theoretical guarantees from stochastic analysis. Previous algorithms to…
Consider the empirical autocovariance matrix at a given non-zero time lag based on observations from a multivariate complex Gaussian stationary time series. The spectral analysis of these autocovariance matrices can be useful in certain…
We unify two paradigmatic mesoscopic mechanisms for the emergence of nonextensive statistics, namely the multiplicative noise mechanism leading to a {\it linear} Fokker-Planck (FP) equation with {\it inhomogenous} diffusion coefficient, and…
To describe longitudinal fine structure like microbunching within a particle beam, a classical approach is to define a bunching factor which is the Fourier transform of the particle longitudinal density distribution. Such a 1D definition of…
Temporal coherence-persistent alignment across time-can arise between agents with fundamentally distinct dynamics, a behavior that classical diffusion models (e.g., Brownian motion, fractional Brownian motion, generalized Langevin equation)…