arXiv research

Unified entropy formula for real, complex, and quaternionic DLNs.

The entropy of geodesic currents on hyperbolic surfaces is bounded by their self-intersection number.

Entropy of critical points generalizes Morse theory.

Finite entropy translating solitons in slabs have quantized entropy and unique structure.

Behavior of the entropy numbers of classes of multivariate functions with mixed smoothness is studied here. This problem has a long history and some fundamental problems in the area are still open. The main goal of this paper is to develop a new method of proving the upper bounds for the entropy numbers. This method is…

Develops correlation number for specific potentials and Hitchin representations.

This is full length article (draft version) where problem number of topics in Topic Modeling is discussed. We proposed idea that Renyi and Tsallis entropy can be used for identification of optimal number in large textual collections. We also report results of numerical experiments of Semantic stability for 4 topic mode…

The study shows a finite number of groups acting on hyperbolic spaces with bounded entropy and compact quotient.

The paper studies the growth of closed geodesics on hyperbolic surface amalgams.

Entropy measures geodesic flow complexity.

Paper proposes a Renyi entropy-based method for tuning hierarchical topic models.

We present a new method of generating mixture models for data with categorical attributes. The keys to this approach are an entropy-based density metric in categorical space and annealing of high-entropy/low-density components from an initial state with many components. Pruning of low-density components using the entro…

Improved exploration methods for reinforcement learning with reduced sample complexity.

Modernizes Thurston's proof of entropy theorem for traintrack maps.

In this paper we study the deformation of strictly convex real projective structures on a closed surface. Specially we study the deformation in terms of the entropy on bulging deformations. As a byproduct we construct a sequence of divergent structures whose topological entropy converges to a designated number between …

The entropy of minimal surfaces is minimized in hyperbolic manifolds.

Study minimax regret in sequential probability assignment with and without side information.

The paper analyzes ESS metrics and their connections to entropy families.

We investigate entropy as a financial risk measure. Entropy explains the equity premium of securities and portfolios in a simpler way and, at the same time, with higher explanatory power than the beta parameter of the capital asset pricing model. For asset pricing we define the continuous entropy as an alternative meas…

State entropy regularization improves robustness in reinforcement learning, especially under structured perturbations.

The approximability of a convex body is a number which measures the difficulty to approximate that body by polytopes. We prove that twice the approximability is equal to the volume entropy for a Hilbert geometry in dimension two end three and that in higher dimension it is a lower bound of the entropy. As a corollary w…

We prove the compactness of self-shrinkers in $\mathbb R^3$ with bounded entropy and fixed genus. As a corollary, we show that numbers of ends of such surfaces are uniformly bounded by the entropy and genus.

Entropy Search (ES) and Predictive Entropy Search (PES) are popular and empirically successful Bayesian Optimization techniques. Both rely on a compelling information-theoretic motivation, and maximize the information gained about the $\arg\max$ of the unknown function; yet, both are plagued by the expensive computatio…

Paper proves causal direction can be inferred from data with limited randomness.

We study the sparse entropy-regularized reinforcement learning (ERL) problem in which the entropy term is a special form of the Tsallis entropy. The optimal policy of this formulation is sparse, i.e.,~at each state, it has non-zero probability for only a small number of actions. This addresses the main drawback of the …

Study positive entropy actions by higher-rank lattices, proving rigidity and conjugacy results.

Study detects anomalies in financial markets using GNN and nonextensive entropy.

Gibbs sampler contracts entropy under strong log-concavity, improving mixing time.

The study evaluates different probability models for uncertainty visualization using entropy calculations.

We introduce on any smooth oriented minimal surface in Euclidean $3$-space a meromorphic quadratic differential, $P$, which we call the entropy differential. This differential arises naturally in a number of different contexts. Of particular interest is the realization of its real part as a conservation law for a natur…

Topological entropy measures the number of distinguishable orbits in a dynamical system, thereby quantifying the complexity of chaotic dynamics. One approach to computing topological entropy in a two-dimensional space is to analyze the collective motion of an ensemble of system trajectories taking into account how traj…

A new algorithm learns MAGs from data more efficiently using entropy.

Entropy regularization improves interpretability of probabilistic clustering models.

We study the problem of existence of F-structures on compact complex surfaces, giving a complete classification modulo the gap in the classification of surfaces of class VII. We then use these results to study the minimal entropy problem for compact complex surfaces. For instance we prove that compact Kahler surfaces o…

Paper introduces ENZ to measure significant coefficients in sparse recovery, improving over classical methods.

MESSY estimation recovers symbolic density functions from samples using maximum entropy.

The paper studies minimal surface entropy on hyperbolic 3-manifolds and compares it to the hyperbolic case.

Estimates open sets for fibrations, leading to volume vanishing results.

Entropy-based decoding improves DLM sampling efficiency.

Final version. To appear in Discrete and Continuous Dynamical Systems - A.

This paper optimizes matrix-based Renyi's entropy computation for large datasets.

Maps on infinite-type surfaces linked to 3-manifold flows.

ELBO converges to a sum of entropies for many generative models.

Improved pre-trained embeddings through effective entropy maximization.

We prove that there exists a positive, explicit function $F(k, E)$ such that, for any group $G$ admitting a $k$-acylindrical splitting and any generating set $S$ of $G$ with $\mathrm{Ent}(G,S)<E$, we have $|S| \leq F(k, E)$. We deduce corresponding finiteness results for classes of groups possessing acylindrical splitt…

We study the problem of finding probability densities that match given European call option prices. To allow prior information about such a density to be taken into account, we generalise the algorithm presented in Neri and Schneider (2011) to find the maximum entropy density of an asset price to the relative entropy c…

Unique entropy measure found for convex projective manifolds.

The topological entropy of a braid is the infimum of the entropies of all homeomorphisms of the disc which have a finite invariant set represented by the braid. When the isotopy class represented by the braid is pseudo-Anosov or is reducible with a pseudo-Anosov component, this entropy is positive. Fried and Kolev prov…