arXiv research

Quantum ML predicts data with improved speed and accuracy.

Quantum machine learning uses quantum cross entropy to minimize loss, but measurement loss affects this process.

Study quantifies information flow in neural networks using relative entropy and RG analogy.

Quantum channels' contraction under privacy constraints studied.

The density matrices are positively semi-definite Hermitian matrices of unit trace that describe the state of a quantum system. The goal of the paper is to develop minimax lower bounds on error rates of estimation of low rank density matrices in trace regression models used in quantum state tomography (in particular, i…

Improved MMWU algorithm achieves instance-optimal regret bound for matrix LEA.

Over the past three decades, black holes have played an important role in quantum gravity, mathematical physics, numerical relativity and gravitational wave phenomenology. However, conceptual settings and mathematical models used to discuss them have varied considerably from one area to another. Over the last five year…

The financial market entropy is modeled using open quantum systems.

Study on quantum state entanglement using Kaehler manifolds.

A quantum circuit designed for efficient statistical model preparation and training.

Study on relative entropy for hypersurfaces in hyperbolic space.

DO-EM framework for quantum models improves generative tasks.

Extends specific relative entropy to multidimensional continuous martingales.

Entropy asymmetry affects regularization in ERM, leading to biased solutions.

A measure called relative cluster entropy distinguishes between correlated and uncorrelated sequences.

We analyze the relationships between game theory and quantum mechanics and the extensions to statistical physics and information theory. We use certain quantization relationships to assign quantum states to the strategies of a player. These quantum states are contained in a density operator which describes the new quan…

We define a relative entropy for two expanding solutions to mean curvature flow of hypersurfaces, asymptotic to the same cone at infinity. Adapting work of White and using recent results of Bernstein and Bernstein-Wang, we show that expanders with vanishing relative entropy are unique in a generic sense. This also impl…

QNA uses quantum-inspired density operators to diagnose market dependence and structural risk.

New statistical test for change-point detection using relative entropy.

Inference for normal and Monte Carlo distributions using minimum relative entropy.

This essay quantifies convexities in incomplete markets using entropy, adjusting prices for risk and incompleteness.

The notion of utility maximising entropy (u-entropy) of a probability density, which was introduced and studied by Slomczynski and Zastawniak (Ann. Prob 32 (2004) 2261-2285, arXiv:math.PR/0410115 v1), is extended in two directions. First, the relative u-entropy of two probability measures in arbitrary probability space…

New regularization method reduces support of empirical risk minimization solutions.

Unique continuation result for expanding Ricci solitons.

We introduce a class of generalized relative entropies (inspired by the Bregman divergence in information theory) on the Wasserstein space over a weighted Riemannian or Finsler manifold. We prove that the convexity of all the entropies in this class is equivalent to the combination of the nonnegative weighted Ricci cur…

In this paper we consider the space of those probability distributions which maximize the $q$-Rényi entropy. These distributions have the same parameter space for every $q$, and in the $q=1$ case these are the normal distributions. Some methods to endow this parameter space with Riemannian metric is presented: the seco…

We investigate the $m$-relative entropy, which stems from the Bregman divergence, on weighted Riemannian and Finsler manifolds. We prove that the displacement $K$-convexity of the $m$-relative entropy is equivalent to the combination of the nonnegativity of the weighted Ricci curvature and the $K$-convexity of the weig…

New connections found for quantum flag manifolds modules.

A quantum state generation method that respects physical constraints.

Holomorphic structures on quantum flag manifolds uniquely defined.

A new method speeds up quantum state estimation.

Earlier studies have shown that stock market distributions can be well described by distributions derived from Tsallis entropy, which is a generalization of Shannon entropy to non-extensive systems. In this paper, Tsallis relative entropy (TRE), which is the generalization of Kullback-Leibler relative entropy (KLRE) to…

Entropy analysis via kernel methods for probabilistic inference.

Quantum memory limits set by relativity theory.

A $q$-Gaussian measure is a generalization of a Gaussian measure. This generalization is obtained by replacing the exponential function with the power function of exponent $1/(1-q)$ ($q\neq 1$). The limit case $q=1$ recovers a Gaussian measure. For $1\leq q <3$, the set of all $q$-Gaussian densities over the real line …

This paper optimizes trading strategies to minimize risk and maximize profit while accounting for market uncertainty.

Two entropy measures quantify suboptimal portfolio performance.

We analyze the Ricci flow of a noncompact metric that describes a two-dimensional black hole. We consider entanglement entropy of a 2d black hole which is due to the quantum correlations between two subsystems: one is inside and the other is outside the black hole horizon. It is demonstrated that the entanglement entro…

We study a notion of relative entropy motivated by self-expanders of mean curvature flow. In particular, we obtain the existence of this quantity for arbitrary hypersurfaces trapped between two disjoint self-expanders asymptotic to the same cone. This allows us to begin to develop the variational theory for the relativ…

The relative $α$-entropy is the Rényi analog of relative entropy and arises prominently in information-theoretic problems. Recent information geometric investigations on this quantity have enabled the generalization of the Cramér-Rao inequality, which provides a lower bound for the variance of an estimator of an escort…

We introduce a pathwise approach to analyze the relative performance of an equity portfolio with respect to a benchmark market portfolio. In this energy-entropy framework, the relative performance is decomposed into three components: a volatility term, a relative entropy term measuring the distance between the portfoli…

Paper proves Jeffrey's update rule minimizes relative entropy.

A new method, REC, compresses images by encoding their latent representations efficiently.

The paper proposes and proves asymptotic expansions for quantum invariants.

Abstract: Necessary and sufficient conditions for gradient flows of relative entropy in Lindblad equations.

We give a topological formula of the loop expansion of the colored Jones polynomials by using identification of generic quantum sl2 representation with homological representations. This gives a direct topological proof of the Melvin-Morton-Rozansky conjecture, and a connection between entropy of braids and quantum repr…

In this paper we focus on the uniqueness question for (expanding) solutions of the Harmonic map flow coming out of smooth 0-homogeneous maps with values into a closed Riemannian manifold. We introduce a relative entropy for two purposes. On the one hand, we prove the existence of two expanding solutions associated to a…

Constructs QFT on curved surfaces, proving axioms and calculating entropy.