Related papers: Memory equations as reduced Markov processes
We develop a resource-theoretic framework that allows one to bridge the gap between two approaches to quantum thermodynamics based on Markovian thermal processes (which model memoryless dynamics) and thermal operations (which model…
Lying on the heart of intelligent decision-making systems, how policy is represented and optimized is a fundamental problem. The root challenge in this problem is the large scale and the high complexity of policy space, which exacerbates…
Diffusive approximations of Markov jump processes often fail to accurately capture large fluctuations. This is confounding, as the rare events triggered by these large fluctuations, such as the failure of electronic memories, are often the…
It has recently been shown that if feedback effects of decisions are ignored, then imposing fairness constraints such as demographic parity or equality of opportunity can actually exacerbate unfairness. We propose to address this challenge…
It is shown that a convex combination of two non-Markovian evolutions may lead to Markovian semigroup. This shows that convex combination of quantum evolutions displaying nontrivial memory effects may result in a perfectly memoryless…
Semi-Markov processes are a generalization of Markov processes since the exponential distribution of time intervals is replaced with an arbitrary distribution. This paper provides an integro-differential form of the Kolmogorov's backward…
Ever since the last two decades of the past century pioneering studies in the field of statistical physics had focused their efforts on developing models of neural networks that could display memory storage and retrieval. Though many…
Consider first a memoryless population model described by the usual branching process with a given mean reproduction matrix on a finite space of types. Motivated by the consequences of atavism in Evolutionary Biology, we are interested in a…
Inference in hidden Markov model has been challenging in terms of scalability due to dependencies in the observation data. In this paper, we utilize the inherent memory decay in hidden Markov models, such that the forward and backward…
Memory effects can be studied through a conditional past-future correlation, which measures departure with respect to a conditional past-future independence valid in a memoryless Markovian regime. In a quantum regime this property leads to…
Real-world sequential decision making problems commonly involve partial observability, which requires the agent to maintain a memory of history in order to infer the latent states, plan and make good decisions. Coping with partial…
We describe a neural-based method for generating exact or approximate solutions to differential equations in the form of mathematical expressions. Unlike other neural methods, our system returns symbolic expressions that can be interpreted…
Euclidean Markov decision processes are a powerful tool for modeling control problems under uncertainty over continuous domains. Finite state imprecise, Markov decision processes can be used to approximate the behavior of these infinite…
We develop the thermodynamics of non-Markovian generalized Langevin equations by embedding them in a high-dimensional Markovian representation involving auxiliary degrees of freedom. If the memory is linear and satisfies detailed balance…
We introduce a new method to accurately and efficiently estimate the effective dynamics of collective variables in molecular simulations. Such reduced dynamics play an essential role in the study of a broad class of processes, ranging from…
The idea that memory behavior relies on a gradually-changing internal state has a long history in mathematical psychology. This chapter traces this line of thought from statistical learning theory in the 1950s, through distributed memory…
This note provides several recent progresses in the study of long time behavior of Markov processes. The examples presented below are related to other scientific fields as PDE's, physics or biology. The involved mathematical tools as…
Stochastic processes abound in nature and accurately modeling them is essential across the quantitative sciences. They can be described by hidden Markov models (HMMs) or by their quantum extensions (QHMMs). These models explain and give…
Based on information theory, we present a method to determine an optimal Markov approximation for modelling and prediction from time series data. The method finds a balance between minimal modelling errors by taking as much as possible…
Intelligence necessitates memory. Without memory, humans fail to perform various nontrivial tasks such as reading novels, playing games or solving maths. As the ultimate goal of machine learning is to derive intelligent systems that learn…