Related papers: Towards quantifying information flows: relative en…
This work presents a novel methodology for analysis and control of nonlinear fluid systems using neural networks. The approach is demonstrated on four different study cases being the Lorenz system, a modified version of the…
A central issue of the science of complex systems is the quantitative characterization of complexity. In the present work we address this issue by resorting to information geometry. Actually we propose a constructive way to associate to a -…
The quantum relative entropy is a fundamental quantity in quantum information science, characterizing the distinguishability between two quantum states. However, this quantity is not additive in general for correlated quantum states,…
Finding the dominant direction of flow of information in densely interconnected regulatory or signaling networks is required in many applications in computational biology and neuroscience. This is achieved by first identifying and removing…
The quantum field theory of two-dimensional sigma models with bulk and boundary couplings provides a natural framework to realize and unite different species of geometric flows that are of current interest in mathematics. In particular, the…
The study of quantum and classical correlations between subsystems is fundamental to understanding many-body physics. In quantum information theory, the quantum mutual information, $I(A;B)$, is a measure of correlation between the…
Information theory is a mathematical theory of learning with deep connections with topics as diverse as artificial intelligence, statistical physics, and biological evolution. Many primers on information theory paint a broad picture with…
We study the evolution of a metric of a two dimensional black hole under the second loop renormalization group fow, the RG-2 fow. Since the black hole metric is noncompact (we consider it asymptotically flat) we adapt some proofs for the…
We study the renormalization group flow in general quantum field theories with quenched disorder, focusing on random quantum critical points. We show that in disorder-averaged correlation functions the flow mixes local and non-local…
Despite the widespread empirical success of ResNet, the generalization properties of deep ResNet are rarely explored beyond the lazy training regime. In this work, we investigate \emph{scaled} ResNet in the limit of infinitely deep and wide…
Real-space renormalization-group techniques for quantum systems can be divided into two basic categories - those capable of representing correlations following a simple boundary (or area) law, and those which are not. I discuss the scaling…
We introduce two variants of the information spectrum relative entropy defined by Tomamichel and Hayashi which have the particular advantage of satisfying the data-processing inequality, i.e. monotonicity under quantum operations. This…
We consider the Hamiltonian renormalisation group flow of discretised one-dimensional physical theories. In particular, we investigate the influence the choice of different embedding maps has on the RG flow and the resulting continuum…
Different phenomenological RG transformations based on scaling relations for the derivatives of the inverse correlation length and singular part of the free-energy density are considered. These transformations are tested on the 2D square…
This work presents a novel means for understanding learning dynamics and scaling relations in neural networks. We show that certain measures on the spectrum of the empirical neural tangent kernel, specifically entropy and trace, yield…
Normalizing flows are powerful non-parametric statistical models that function as a hybrid between density estimators and generative models. Current learning algorithms for normalizing flows assume that data points are sampled…
The vacuum entanglement entropy in quantum field theory provides nonperturbative information about renormalization group flows. Most studies so far have focused on the universal terms, related to the Weyl anomaly in even space-time…
We propose an entropy measure for the analysis of chaotic attractors through recurrence networks which are un-weighted and un-directed complex networks constructed from time series of dynamical systems using specific criteria. We show that…
Complex networks have acquired a great popularity in recent years, since the graph representation of many natural, social and technological systems is often very helpful to characterize and model their phenomenology. Additionally, the…
We propose a theoretical understanding of neural networks in terms of Wilsonian effective field theory. The correspondence relies on the fact that many asymptotic neural networks are drawn from Gaussian processes, the analog of…