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Memory, as the basis of learning, determines the storage, update and forgetting of knowledge and further determines the efficiency of learning. Featured with the mechanism of memory, a radial basis function neural network based learning…
Probabilistic graphical models (PGMs) provide a compact representation of knowledge that can be queried in a flexible way: after learning the parameters of a graphical model once, new probabilistic queries can be answered at test time…
This paper introduces a periodic multivariate Poisson autoregression with potentially infinite memory, with a special focus on the network setting. Using contraction techniques, we study the stability of such a process and provide upper…
We prove regenerative properties for the linear Hawkes process under minimal assumptions on the transfer function, which may have unbounded support. These results are applicable to sliding window statistical estimators. We exploit…
If a given aggregate process $S$ is a compound mixed Poisson process under a probability measure $P$, a characterization of all probability measures $Q$ on the domain of $P$, such that $P$ and $Q$ are progressively equivalent and $S$…
The mechanical behavior of disordered materials such as dense suspensions, glasses or granular materials depends on their thermal and mechanical past. Here we report the memory behavior of a quenched mesoscopic elasto-plastic (QMEP) model.…
We study general properties for the family of stochastic processes with polynomial regression property, that is that every conditional moment of the process is a polynomial. It turns out that then there exists a family of polynomial…
This paper introduces a new parsimonious structure for mixture of autoregressive models. the weighting coefficients are determined through latent random variables, following a hidden Markov model. We propose a dynamic programming algorithm…
In a recent article we described a new type of deep neural network - a Perpetual Learning Machine (PLM) - which is capable of learning 'on the fly' like a brain by existing in a state of Perpetual Stochastic Gradient Descent (PSGD). Here,…
Typical address-oriented computer memories cannot recognize incomplete or noisy information. Associative (content-addressable) memories solve this problem but suffer from severe capacity shortages. I propose a model of a quantum memory that…
Probabilistic Quantum Memory (PQM) is a data structure that computes the distance from a binary input to all binary patterns stored in superposition on the memory. This data structure allows the development of heuristics to speed up…
Arguably, the largest class of stochastic processes generated by means of a finite memory consists of those that are sequences of observations produced by sequential measurements in a suitable generalized probabilistic theory (GPT). These…
Non-Markovian quantum processes exhibit different memory effects when measured in different ways; an unambiguous characterization of memory length requires accounting for the sequence of instruments applied to probe the system dynamics.…
In this paper, we obtain stability results for martingale representations in a very general framework. More specifically, we consider a sequence of martingales each adapted to its own filtration, and a sequence of random variables…
We investigate congestion-aware control of quantum repeater nodes operating under stochastic traffic and finite memory coherence. Entanglement generation is modeled as a probabilistic process producing Werner states subject to depolarizing…
The orientational memory of particles can serve as an effective measure of diffusivity, spreading, and search efficiency in complex stochastic processes. We develop a theoretical framework to describe the decay of directional correlations…
Hidden Markov chains are widely applied statistical models of stochastic processes, from fundamental physics and chemistry to finance, health, and artificial intelligence. The hidden Markov processes they generate are notoriously…
We consider a stochastic process which is (a) described by a continuous-time Markov chain on only short time-scales and (b) constrained to conserve a number of hidden quantities on long time-scales. We assume that the transition matrix of…
We establish a continuous-time framework for analyzing Deep Q-Networks (DQNs) via stochastic control and Forward-Backward Stochastic Differential Equations (FBSDEs). Considering a continuous-time Markov Decision Process (MDP) driven by a…
To make progress in understanding the issue of memory loss and history dependence in evolving complex systems, we consider the mixing rate that specifies how fast the future states become independent of the initial condition. We propose a…