Related papers: Propagation of Memory Parameter from Durations to …

The systematic development of Coarse-Grained (CG) models via the Mori-Zwanzig projector operator formalism requires the explicit description of several terms, including a deterministic drift term, a dissipative memory term and a random…

We present new estimators for the statistical analysis of the dependence of the mean gap time length between consecutive recurrent events, on a set of explanatory random variables and in the presence of right censoring. The dependence is…

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…

In systems which exhibit deterministic diffusion, the gross parameter dependence of the diffusion coefficient can often be understood in terms of random walk models. Provided the decay of correlations is fast enough, one can ignore memory…

Nonstationarity is ubiquitous in practical classification settings, leading deployed models to perform poorly even when they generalize well to holdout sets available at training time. We address this by reframing nonstationary…

The existing Neural ODE formulation relies on an explicit knowledge of the termination time. We extend Neural ODEs to implicitly defined termination criteria modeled by neural event functions, which can be chained together and…

Let $X_1, X_2,\dots$ be a short-memory linear process of random variables. For $1\leq q<2$, let $\cF$ be a bounded set of real-valued functions on $[0,1]$ with finite $q$-variation. It is proved that…

Continuous attractors offer a unique class of solutions for storing continuous-valued variables in recurrent system states for indefinitely long time intervals. Unfortunately, continuous attractors suffer from severe structural instability…

We study the existence and properties of stationary solution of ARCH-type equation $r_t= \zeta_t \sigma_t$, where $\zeta_t$ are standardized i.i.d. r.v.'s and the conditional variance satisfies an AR(1) equation $\sigma^2_t = Q^2\big(a +…

Bayesian inference allows machine learning models to express uncertainty. Current machine learning models use only a single learnable parameter combination when making predictions, and as a result are highly overconfident when their…

We address the problem of long-range memory in the financial markets. There are two conceptually different ways to reproduce power-law decay of auto-correlation function: using fractional Brownian motion as well as non-linear stochastic…

Chord recognition systems typically comprise an acoustic model that predicts chords for each audio frame, and a temporal model that casts these predictions into labelled chord segments. However, temporal models have been shown to only…

We examine a previouly introduced attractor neural network model that explains the persistent activities of neurons in the anterior ventral temporal cortex of the brain. In this model, the coexistence of several attractors including…

Localized persistent neural activity can encode delayed estimates of continuous variables. Common experiments require that subjects store and report the feature value (e.g., orientation) of a particular cue (e.g., oriented bar on a screen)…

Traditional studies of memory for meaningful narratives focus on specific stories and their semantic structures but do not address common quantitative features of recall across different narratives. We introduce a statistical ensemble of…

We extend Neural Processes (NPs) to sequential data through Recurrent NPs or RNPs, a family of conditional state space models. RNPs model the state space with Neural Processes. Given time series observed on fast real-world time scales but…

One of the defining traits of quantum mechanics is the uncertainty principle which was originally expressed in terms of the standard deviation of two observables. Alternatively, it can be formulated using entropic measures, and can also be…

A novel version of the Continuous-Time Random Walk (CTRW) model with memory is developed. This memory means the dependence between arbitrary number of successive jumps of the process, while waiting times between jumps are considered as…

Recurrent neural network is a powerful model that learns temporal patterns in sequential data. For a long time, it was believed that recurrent networks are difficult to train using simple optimizers, such as stochastic gradient descent, due…

We consider continuous-time models with a large panel of moment conditions, where the structural parameter depends on a set of characteristics, whose effects are of interest. The leading example is the linear factor model in financial…