相关论文: Range-Renewal Speed and Entropy for I.I.D Models

Entropy dimension is an entropy-type quantity which takes values in $[0,1]$ and classifies different levels of intermediate growth rate of complexity for dynamical systems. In this paper, we consider the complexity of skew products of…

An information-theoretic framework is introduced to analyze last-layer embedding, focusing on learned representations for regression tasks. We define representation-rate and derive limits on the reliability with which input-output…

Exemplar-based class-incremental learning is to recognize new classes while not forgetting old ones, whose samples can only be saved in limited memory. The ratio fluctuation of new samples to old exemplars, which is caused by the variation…

At the onset of an interaction between two initially independent systems, each system tends to experience an increase in its n-Renyi entropies, such as its von Neumann entropy (n = 1) and its mixedness (n = 2). We here ask which properties…

The growing study of time series, especially those related to nonlinear systems, has challenged the methodologies to characterize and classify dynamical structures of a signal. Here we conceive a new diagnostic tool for time series based on…

This work addresses challenges in evaluating adaptive artificial intelligence (AI) models for medical devices, where iterative updates to both models and evaluation datasets complicate performance assessment. We introduce a novel approach…

Self-replication is a capacity common to every species of living thing, and simple physical intuition dictates that such a process must invariably be fueled by the production of entropy. Here, we undertake to make this intuition rigorous…

In this work we introduce a method for estimating entropy rate and entropy production rate from finite symbolic time series. From the point of view of statistics, estimating entropy from a finite series can be interpreted as a problem of…

For deterministic continuous time nonlinear control systems, epsilon-practical stabilization entropy and practical stabilization entropy are introduced. Here the rate of attraction is specified by a KL-function. Upper and lower bounds for…

Entropy measures have become increasingly popular as an evaluation metric for complexity in the analysis of time series data, especially in physiology and medicine. Entropy measures the rate of information gain, or degree of regularity in a…

Entropy estimation, due in part to its connection with mutual information, has seen considerable use in the study of time series data including causality detection and information flow. In many cases, the entropy is estimated using…

Properties of scalar quantization with $r$th power distortion and constrained R\'enyi entropy of order $\alpha\in (0,1)$ are investigated. For an asymptotically (high-rate) optimal sequence of quantizers, the contribution to the R\'enyi…

When deployed in the wild, machine learning models are usually confronted with data and requirements that constantly vary, either because of changes in the generating distribution or because external constraints change the environment where…

Some bounds on the entropic informational quantities related to a quantum continual measurement are obtained and the time dependencies of these quantities are studied.

The range mode problem is a fundamental problem and there is a lot of work about it. There is also some work for the dynamic version of it and the enumerating version of it, but there is no previous research about the dynamic and…

We investigate the problem of synthesizing optimal control policies for Markov decision processes (MDPs) with both qualitative and quantitative objectives. Specifically, our goal is to achieve a given linear temporal logic (LTL) task with…

We introduce "Replicated Entanglement Entropy (REE)" as the entanglement entropy of a subspace in a replicated theory. We calculate this quantity by replicating the original theory in two steps along the same entangling region and taking…

Convergence to stable laws in relative entropy is established for sums of i.i.d. random variables.

We study the recurrence to mistake dynamical balls, that is, dynamical balls that admit some errors and whose proportion of errors decrease tends to zero with the length of the dynamical ball. We prove, under mild assumptions, that the…

Relative entropy is a measure of distinguishability for quantum states, and plays a central role in quantum information theory. The family of Renyi entropies generalizes to Renyi relative entropies that include as special cases most entropy…