Related papers: Three Perspectives on Complexity $-$ Entropy, Comp…
A two-parameter family of complexity measures $\tilde{C}^{(\alpha,\beta)}$ based on the R\'enyi entropies is introduced and characterized by a detailed study of its mathematical properties. This family is the generalization of a continuous…
We define the notion of localizable property for a dynamical system. Then we survey three properties of complexity and relate how they are known to be typical among differentiable dynamical systems. These notions are the fast growth of the…
The unreduced, universally nonperturbative analysis of arbitrary interaction process, described by a quite general equation, provides the truly complete, "dynamically multivalued" general solution that leads to dynamically derived,…
A powerful tool is developed for the characterization of chaotic signals. The approach is based on the symbolic encoding of time series (according to their ordinal patterns) combined with the ensuing characterization of the corresponding…
Partly motivated by entropy-estimation problems in neuroscience, we present a detailed and extensive comparison between some of the most popular and effective entropy estimation methods used in practice: The plug-in method, four different…
This paper explores the concept of "entropy of knowledge" (EoN) as a framework for understanding the challenges and complexities of scientific discovery. Drawing from principles in thermodynamics and information theory, I propose that the…
The defining property of an artificial physical self-replicating system, such as a self-replicating robot, is that it has the ability to make copies of itself from basic parts. Three questions that immediately arises in the study of such…
Entropy measures are effective features for time series classification problems. Traditional entropy measures, such as Shannon entropy, use probability distribution function. However, for the effective separation of time series, new entropy…
Several well-known statistical measures similar to \emph{LMC} and \emph{Fisher-Shannon} complexity have been computed for confined hydrogen atom in both position ($r$) and momentum ($p$) spaces. Further, a more generalized form of these…
Estimating entropies from limited data series is known to be a non-trivial task. Naive estimations are plagued with both systematic (bias) and statistical errors. Here, we present a new 'balanced estimator' for entropy functionals Shannon,…
In the nonlinear timeseries analysis literature, countless quantities have been presented as new ``entropy'' or ``complexity'' measures, often with similar roles. The ever-increasing pool of such measures makes creating a sustainable and…
While various complexity measures for deep neural networks exist, specifying an appropriate measure capable of predicting and explaining generalization in deep networks has proven challenging. We propose Neural Complexity (NC), a…
The universal concept of complexity by the dynamic redundance paradigm and the ensuing concept of extended dynamic fractality (physics/9806002) are applied here to higher levels of complexity corresponding to living systems. After recalling…
Code complexity metrics such as cyclomatic complexity have long been used to assess software quality and maintainability. With the rapid advancement of large language models (LLMs) on coding tasks, an important yet underexplored question…
Some established and also novel techniques in the field of applications of algorithmic (Kolmogorov) complexity currently co-exist for the first time and are here reviewed, ranging from dominant ones such as statistical lossless compression…
We extend the definitions of complexity measures of functions to domains such as the symmetric group. The complexity measures we consider include degree, approximate degree, decision tree complexity, sensitivity, block sensitivity, and a…
Entropy is a measure of heterogeneity widely used in applied sciences, often when data are collected over space. Recently, a number of approaches has been proposed to include spatial information in entropy. The aim of entropy is to…
We define a notion of complexity, which quantifies the nonlinearity of the computation of a neural network, as well as a complementary measure of the effective dimension of feature representations. We investigate these observables both for…
We discuss algorithms for estimating the Shannon entropy h of finite symbol sequences with long range correlations. In particular, we consider algorithms which estimate h from the code lengths produced by some compression algorithm. Our…
Considering the difficulty of interpreting generative model output, there is significant current research focused on determining meaningful evaluation metrics. Several recent approaches utilize "precision" and "recall," borrowed from the…