Related papers: On Macroscopic Complexity and Perceptual Coding
Data complexity is an important concept in the natural sciences and related areas, but lacks a rigorous and computable definition. In this paper, we focus on a particular sense of complexity that is high if the data is structured in a way…
We survey work on the paradigm called "computing by observing." Its central feature is that one considers the behavior of an evolving system as the result of a computation. To this end an observer records this behavior. It has turned out…
Complex systems are found in most branches of science. It is still argued how to best quantify their complexity and to what end. One prominent measure of complexity (the statistical complexity) has an operational meaning in terms of the…
Complexity of patterns is a key information for human brain to differ objects of about the same size and shape. Like other innate human senses, the complexity perception cannot be easily quantified. We propose a transparent and universal…
A general notion of information-related complexity applicable to both natural and man-made systems is proposed. The overall approach is to explicitly consider a rational agent performing a certain task with a quantifiable degree of success.…
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…
Sparse coding has been proposed as a theory of visual cortex and as an unsupervised algorithm for learning representations. We show empirically with the MNIST dataset that sparse codes can be very sensitive to image distortions, a behavior…
Depth is a complexity measure for natural systems of the kind studied in statistical physics and is defined in terms of computational complexity. Depth quantifies the length of the shortest parallel computation required to construct a…
Deep neural networks have recently advanced the state-of-the-art in image compression and surpassed many traditional compression algorithms. The training of such networks involves carefully trading off entropy of the latent representation…
How best to quantify the information of an object, whether natural or artifact, is a problem of wide interest. A related problem is the computability of an object. We present practical examples of a new way to address this problem. By…
In compressed sensing, we wish to reconstruct a sparse signal $x$ from observed data $y$. In sparse coding, on the other hand, we wish to find a representation of an observed signal $y$ as a sparse linear combination, with coefficients $x$,…
The concept of {\em complexity} (as a quantity) has been plagued by numerous contradictory and confusing definitions. By explicitly recognising a role for the observer of a system, an observer that attaches meaning to data about the system,…
There is no single definition of complexity (Edmonds 1999; Gershenson 2008; Mitchell 2009; De Domenico, et al., 2019), as it acquires different meanings in different contexts. A general notion is the amount of information required to…
The volume of data that will be produced by the next generation of astrophysical instruments represents a significant opportunity for making unplanned and unexpected discoveries. Conversely, finding unexpected objects or phenomena within…
We critically analyse the point of view for which laws of nature are just a mean to compress data. Discussing some basic notions of dynamical systems and information theory, we show that the idea that the analysis of large amount of data by…
This article extends the concept of compressed sensing to signals that are not sparse in an orthonormal basis but rather in a redundant dictionary. It is shown that a matrix, which is a composition of a random matrix of certain type and a…
Network or graph structures are ubiquitous in the study of complex systems. Often, we are interested in complexity trends of these system as it evolves under some dynamic. An example might be looking at the complexity of a food web as…
In complex environments, there are costs to both ignorance and perception. An organism needs to track fitness-relevant information about its world, but the more information it tracks, the more resources it must devote to memory and…
We study how macroscopic observational constraints restrict admissible microscopic explanatory structures when no intrinsic order or dynamics is assumed a priori. Starting from an unordered collection of measurement outcomes, we formulate…
In this letter we investigate the possibility of observing macroscopic entanglement, considering realistic factors such as decoherence, particle losses, and measurements of limited precision (coarse-grained collective measurements). This…