Related papers: Mutual Information from Modular Flow in General CF…
Exponential models of distributions are widely used in machine learning for classiffication and modelling. It is well known that they can be interpreted as maximum entropy models under empirical expectation constraints. In this work, we…
In this note we compute mutual information between two intervals in CFTs dual to extremal BTZ (UV CFT) and near horizon limit of extremal BTZ (IR CFT) using the replica technique in some limiting regimes, which can be compared with…
Confluence in abstract parallel category systems is established for net class-rewriting in iterative closed multilevel quotient graph structures with uncountable node arities by multi-dimensional transducer operations in topological metrics…
We derive a well-defined renormalized version of mutual information that allows to estimate the dependence between continuous random variables in the important case when one is deterministically dependent on the other. This is the situation…
Thermal fluctuations of a critical system induce long-ranged Casimir forces between objects that couple to the underlying field. For two dimensional (2D) conformal field theories (CFT) we derive an exact result for the Casimir interaction…
Long ago, Argyres and Douglas discovered a particularly simple interacting 4D $\mathcal{N}=2$ superconformal field theory (SCFT) on the Coulomb branch of $SU(3)$ $\mathcal{N}=2$ super Yang-Mills. Further hints of the theory's simplicity…
Symmetric alpha-stable (S alpha S) distributions with alpha<2 lack finite classical Fisher information. Building on Johnson's framework, we define Mixed Fractional Information (MFI) via the initial rate of relative entropy dissipation…
Variational inference often struggles with the posterior geometry exhibited by complex hierarchical Bayesian models. Recent advances in flow-based variational families and Variationally Inferred Parameters (VIP) each address aspects of this…
We aim to discover manipulation concepts embedded in the unannotated demonstrations, which are recognized as key physical states. The discovered concepts can facilitate training manipulation policies and promote generalization. Current…
In the past few decades, researchers have proposed many discriminant analysis (DA) algorithms for the study of high-dimensional data in a variety of problems. Most DA algorithms for feature extraction are based on transformations that…
Mutual information (MI) is an information-theoretic measure of dependency between two random variables. Several methods to estimate MI, from samples of two random variables with unknown underlying probability distributions have been…
A practical use of the entanglement entropy in a 1d quantum system is to identify the conformal field theory describing its critical behavior. It is exactly $(c/3)\ln \ell$ for an interval of length $\ell$ in an infinite system, where $c$…
Learning from expert demonstrations is a promising approach for training robotic manipulation policies from limited data. However, imitation learning algorithms require a number of design choices ranging from the input modality, training…
We present several new results for the $N$-partite information, $I_N$, of spatial regions in the ground state of $d$-dimensional conformal field theories. First, we show that $I_N$ can be written in terms of a single $N$-point function of…
We derive the closed-form expression of the maximum mutual information - the maximum value of $I(X;Z)$ obtainable via training - for a broad family of neural network architectures. The quantity is essential to several branches of machine…
Mutual information (MI) is a fundamental measure of statistical dependence, with a myriad of applications to information theory, statistics, and machine learning. While it possesses many desirable structural properties, the estimation of…
We study formal properties of smooth max-information, a generalization of von Neumann mutual information derived from the max-relative entropy. Recent work suggests that it is a useful quantity in one-shot channel coding, quantum rate…
In two-dimensional conformal field theories (CFT) in Minkowski spacetime, we study the spacetime distance between two events along two distinct modular trajectories. When the spatial line is bipartite by a single interval, we consider both…
Mutual information is one of the essential building blocks of information theory. Yet, it is only finitely defined for distributions with fast decaying tails on a countable joint alphabet of two random elements. The unboundedness of mutual…
The maximal information coefficient (MIC) is a tool for finding the strongest pairwise relationships in a data set with many variables (Reshef et al., 2011). MIC is useful because it gives similar scores to equally noisy relationships of…