相关论文: Mutual Information of Generalized Free Fields
These are a set of lecture notes on generalized global symmetries in quantum field theory. The focus is on invertible symmetries with a few comments regarding non-invertible symmetries. The main topics covered are the basics of higher-form…
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 $c$…
We study how information geometry is described by bulk geometry in the gauge/gravity correspondence. We consider a quantum information metric that measures the distance between the ground states of a CFT and a theory obtained by perturbing…
I study the mutual information between spatial subsystems in a variety of scale invariant quantum field theories. While it is derived from the bare entanglement entropy, the mutual information offers a more refined probe of the entanglement…
There is a vast body of recent literature on the reliability of communication through noisy channels, the recovery of community structures in the stochastic block model, the limiting behavior of the free entropy in spin glasses and the…
Sliced mutual information (SMI) is defined as an average of mutual information (MI) terms between one-dimensional random projections of the random variables. It serves as a surrogate measure of dependence to classic MI that preserves many…
The mutual information is bounded from above by a decreasing affine function of the square of the distance between the input distribution and the set of all capacity-achieving input distributions $\Pi_{\mathcal{A}}$, on small enough…
Federated Learning (FL) has attracted considerable interest due to growing privacy concerns and regulations like the General Data Protection Regulation (GDPR), which stresses the importance of privacy-preserving and fair machine learning…
We characterize the quantum states dual to entanglement wedges in arbitrary spacetimes, in settings where the matter entropy can be neglected compared to the geometric entropy. In AdS/CFT, such states obey special entropy inequalities known…
An information-theoretic upper bound on the generalization error of supervised learning algorithms is derived. The bound is constructed in terms of the mutual information between each individual training sample and the output of the…
Generalized mutual information (GMI) is used to compute achievable rates for fading channels with various types of channel state information at the transmitter (CSIT) and receiver (CSIR). The GMI is based on variations of auxiliary channel…
In the last decade, recent successes in deep clustering majorly involved the mutual information (MI) as an unsupervised objective for training neural networks with increasing regularisations. While the quality of the regularisations have…
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 develop the use of mutual information (MI), a well-established metric in information theory, to interpret the inner workings of deep learning models. To accurately estimate MI from a finite number of samples, we present GMM-MI…
This paper is devoted to the mathematical study of some divergences based on the mutual information well-suited to categorical random vectors. These divergences are generalizations of the "entropy distance" and "information distance". Their…
We compute the entanglement entropy and mutual information for two disjoint intervals in two-dimensional conformal field theories as a function of time after a local quench, using the replica trick and boundary conformal field theory. We…
Information-theoretic quantities reveal dependencies among variables in the structure of joint, marginal, and conditional entropies, but leave some fundamentally different systems indistinguishable. Furthermore, there is no consensus on how…
Post-data statistical inference concerns making probability statements about model parameters conditional on observed data. When a priori knowledge about parameters is available, post-data inference can be conveniently made from Bayesian…
It is well known that quantum mechanics admits a geometric formulation on the complex projective space as a Kahler manifold. In this paper we consider the notion of mutual information among continuous random variables in relation to the…
Relational data augmentation is a powerful technique for enhancing data analytics and improving machine learning models by incorporating columns from external datasets. However, it is challenging to efficiently discover relevant external…