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We establish a generalized work theorem for stochastic chemical reaction networks (CRNs). By using a compensated Poisson jump process, we identify a martingale structure in a generalized entropy defined relative to an auxiliary backward…
Understanding temporal processes and their correlations in time is of paramount importance for the development of near-term technologies that operate under realistic conditions. Capturing the complete multi-time statistics defining a…
Continual learning (CL) refers to a machine learning paradigm that learns continuously without forgetting previously acquired knowledge. Thereby, major difficulty in CL is catastrophic forgetting of preceding tasks, caused by shifts in data…
In reinforcement learning, an agent interacts sequentially with an environment to maximize a reward, receiving only partial, probabilistic feedback. This creates a fundamental exploration-exploitation trade-off: the agent must explore to…
This paper investigates the second order properties of a stationary process after random sampling. While a short memory process gives always rise to a short memory one, we prove that long-memory can disappear when the sampling law has heavy…
We consider simple random walks on Delaunay triangulations generated by point processes in $\mathbb{R}^d$. Under suitable assumptions on the point processes, we show that the random walk satisfies an almost sure (or quenched) invariance…
Quantum technologies offer a promising route to the efficient sampling and analysis of stochastic processes, with potential applications across the sciences. Such quantum advantages rely on the preparation of a quantum sample state of the…
Predictive coding (PC) is an influential theory of information processing in the brain, providing a biologically plausible alternative to backpropagation. It is motivated in terms of Bayesian inference, as hidden states and parameters are…
The notion of program sensitivity (aka Lipschitz continuity) specifies that changes in the program input result in proportional changes to the program output. For probabilistic programs the notion is naturally extended to expected…
Power law potentials dictate interactions across scales and matter, controlling the structure and dynamics of inanimate, and living systems. Though the equilibrium distributions of particles with a power law repulsion were extensively…
This article introduces the class of periodic trawl processes, which are continuous-time, infinitely divisible, stationary stochastic processes, that allow for periodicity and flexible forms of their serial correlation, including both…
We develop a martingale theory to describe fluctuations of entropy production for open quantum systems in nonequilbrium steady states. Using the formalism of quantum jump trajectories, we identify a decomposition of entropy production into…
The kicked Ising model with both a pulsed transverse and a continuous longitudinal field is studied numerically. Starting from a large transverse field and a state that is nearly an eigenstate, the pulsed transverse field is quenched with a…
In this paper, we consider a class of slow-fast systems of stochastic partial differential equations where the nonlinearity in the slow equation is not continuous and unbounded. We first provide conditions that ensure the existence of a…
Progressive Hedging is a popular decomposition algorithm for solving multi-stage stochastic optimization problems. A computational bottleneck of this algorithm is that all scenario subproblems have to be solved at each iteration. In this…
We investigate quantum information processing and manipulations in disordered systems of ultracold atoms and trapped ions. First, we demonstrate generation of entanglement and local realization of quantum gates in a quantum spin glass…
Quantum computing and neural networks show great promise for the future of information processing. In this paper we study a quantum reservoir computer (QRC), a framework harnessing quantum dynamics and designed for fast and efficient…
Reinforcement learning aims to learn optimal policies from interaction with environments whose dynamics are unknown. Many methods rely on the approximation of a value function to derive near-optimal policies. In partially observable…
We develop a general framework for extracting highly uniform bounds on local stability for stochastic processes in terms of information on fluctuations or crossings. This includes a large class of martingales: As a corollary of our main…
Works in quantum machine learning (QML) over the past few years indicate that QML algorithms can function just as well as their classical counterparts, and even outperform them in some cases. Among the corpus of recent work, many current…