Related papers: Quantifying information flow along a stochastic tr…

Information flow or information transfer is an important concept in dynamical systems which has applications in a wide variety of scientific disciplines. In this study, we show that a rigorous formalism can be established in the context of…

We introduce Statistical Flow Matching (SFM), a novel and mathematically rigorous flow-matching framework on the manifold of parameterized probability measures inspired by the results from information geometry. We demonstrate the…

In this paper, we present a new approach to interpret deep learning models. By coupling mutual information with network science, we explore how information flows through feedforward networks. We show that efficiently approximating mutual…

Semantic Information Theory (SIT) offers a new approach to evaluating the information architecture of complex systems. In this study we describe the steps required to {\it operationalize} SIT via its application to dynamical problems. Our…

Quantitative information flow (QIF) is traditionally defined as the expected value of information leakage over all feasible program runs and it fails to identify vulnerable programs where only limited number of runs leak large amount of…

We obtain a class of higher-degree stochastic integration filters (SIF) for nonlinear filtering applications. SIF are based on stochastic spherical-radial integration rules that achieve asymptotically exact evaluations of Gaussian weighted…

Generative models for sequential data often struggle with sparsely sampled and high-dimensional trajectories, typically reducing the learning of dynamics to pairwise transitions. We propose Interpolative Multi-Marginal Flow Matching…

In this paper, we investigate the stochastic mean curvature flow (SMCF) on networks, a niche area within stochastic processes and geometric analysis. By applying Ito calculus, we analyze the evolution of network structures influenced by…

In this paper, a network-based stochastic information propagation model is developed. The information flow is modeled by a probabilistic differential equation system. The numerical solution of these equations leads to the expected number of…

We derive a stochastic path integral representation of counting statistics in semi-classical systems. The formalism is introduced on the simple case of a single chaotic cavity with two quantum point contacts, and then further generalized to…

We present a new framework for analyzing the evolution of information in geophysical systems. Understanding how information, and its counterpart, uncertainty, propagates is central to predictability studies and has significant implications…

We propose a new measure to estimate the direction of information flux in multivariate time series from complex systems. This measure, based on the slope of the phase spectrum (Phase Slope Index) has invariance properties that are important…

We put forward a model of action-based randomization mechanisms to analyse quantitative information flow (QIF) under generic leakage functions, and under possibly adaptive adversaries. This model subsumes many of the QIF models proposed so…

Information theory provides a useful tool to understand the evolution of complex nonlinear systems and their sustainability. In particular, Fisher Information (FI) has been evoked as a useful measure of sustainability and the variability of…

We extend Stochastic Flow Models (SFMs), used for a large class of discrete event and hybrid systems, by including the delays which typically arise in flow movement. We apply this framework to the multi-intersection traffic light control…

Causal inference seeks to identify cause-and-effect interactions in coupled systems. A recently proposed method by Liang detects causal relations by quantifying the direction and magnitude of information flow between time series. The…

Standard quantum metrology relies on ensemble-averaged quantities, such as the Quantum Fisher Information (QFI), which often mask the fluctuations inherent to single-shot realizations. In this work, we bridge the gap between quantum…

Quantitative information flow (QIF) is concerned with assessing the leakage of information in computational systems. In QIF there are two main perspectives for the quantification of leakage. On one hand, the static perspective considers all…

Modeling transformations between arbitrary data distributions is a fundamental scientific challenge, arising in applications like drug discovery and evolutionary simulation. While flow matching offers a natural framework for this task, its…

Optical flow estimation is a fundamental and long-standing visual task. In this work, we present a novel method, dubbed HMAFlow, to improve optical flow estimation in challenging scenes, particularly those involving small objects. The…