Proves uniqueness of measure of maximal entropy for geodesic flows on surfaces.
problem Proving uniqueness of measure of maximal entropy for geodesic flows on surfaces.
method Analyzes geodesic flows on closed orientable C^∞ surfaces, proving uniqueness of measure of maximal entropy and at most one SRB measure.
result Proves uniqueness of measure of maximal entropy for geodesic flows on surfaces, covering previous results and new examples.
We prove the existence of manifolds with almost maximal volume entropy which are not hyperbolic.
Maximal representations show strong entropy rigidity.
problem Entropy rigidity for maximal representations.
method Measurable hypertransversality, Gromov product, Bowen-Margulis-Sullivan measure.
result Strong entropy rigidity proved for maximal representations.
New algorithm estimates semi-continuous data density using entropy maximization.
problem Estimating density functions for semi-continuous data.
method Maximum entropy principle, requiring only constraint function samples.
result Estimate has significantly less bias compared to existing methods.
Entropy minimization has been widely used in unsupervised domain adaptation (UDA). However, existing works reveal that entropy minimization only may result into collapsed trivial solutions. In this paper, we propose to avoid trivial solutions by further introducing diversity maximization. In order to achieve the possib…
The paper proves a quantitative rigidity result for spaces with specific curvature bounds.
problem Understanding the rigidity of spaces with almost maximal volume entropy.
method Analyzing Riemannian manifolds and RCD-spaces with specific curvature conditions. result Spaces with almost maximal volume entropy are closely related to hyperbolic space forms.
Improved pre-trained embeddings through effective entropy maximization.
problem Developing high-quality pre-trained embeddings for future tasks.
method E2MC criterion defined in terms of low-dimensional constraints.
result Significant improvement in downstream performance.
Estimate relaxation times in nonextensive systems using gradient flow for Tsallis entropy maximization.
problem Estimating relaxation times in financial market dynamics.
method Developing a method using EGF for maximizing Tsallis entropy.
result Longer relaxation times for nonextensive systems compared to Shannon entropy.
Study geodesic flows on hyperbolic manifolds without conjugate points, proving unique measure of maximal entropy.
problem Proving uniqueness of measure of maximal entropy for geodesic flows on specific manifolds.
method Analyzing geodesic flows on closed Riemannian manifolds without conjugate points, using properties of Gromov hyperbolic and residually finite groups.
result Proves geodesic flow has a unique measure of maximal entropy under appropriate assumptions.
Quantitative rigidity theorem for Alexandrov spaces with curvature bounds.
problem Quantifying rigidity in Alexandrov spaces with curvature constraints.
method Using Gromov-Hausdorff distance and properties of Alexandrov spaces.
result Alexandrov spaces with curvature bounds are close to hyperbolic manifolds.
New measure of maximal entropy found for a class of geometrically finite groups.
problem Finding a measure of maximal entropy for relatively Anosov groups.
method Constructing reparameterizations and using exponential expansion along unstable foliations.
result The Bowen-Margulis-Sullivan measure is finite and unique for relatively Anosov groups.
Paper proposes a policy-search algorithm to learn entropy-maximizing exploration policies in reward-free environments.
problem Reward-free learning in high-dimensional, continuous-control domains.
method Maximum Entropy POLicy optimization (MEPOL) algorithm that maximizes a non-parametric state entropy estimate.
result MEPOL learns a maximum-entropy exploration policy that facilitates learning various reward-based tasks.
Stokes' theorem's boundary maximizes entropy.
problem Characterizing the boundary of a manifold using entropy.
method Maximizing entropy for codimension-1 submanifolds satisfying Stokes' theorem.
result The boundary of a manifold maximizes the entropy functional.
New method detects changes by maximizing cross-entropy, outperforming existing techniques.
problem Detecting abrupt changes in data streams without labeled examples.
method Maximizes cross-entropy between segments to find change points, using dynamic programming.
result Outperforms three state-of-the-art approaches on challenging datasets.
The study proves the uniqueness of entropy-maximizing measures for geodesic flows on specific manifolds.
problem Uniqueness of entropy-maximizing measures for geodesic flows on rank 1 manifolds.
method Symbolic dynamics applied to countable topological Markov flows.
result Proof of the uniqueness of the measure of maximal entropy.
Geodesic flows on compact manifolds without conjugate points are shown to have a unique measure of maximal entropy.
problem Analyzing geodesic flows on compact manifolds without conjugate points and with visibility universal covering.
method Using topological mixing, local product structure, and properties of geodesic flows, the authors prove the existence of an expansive factor and uniqueness of measure of maximal entropy.
result The geodesic flow on compact manifolds without conjugate points has a unique measure of maximal entropy.
Study on utility maximization with Tsallis entropy in reinforcement learning.
problem Exploring utility maximization with Tsallis entropy in reinforcement learning.
method Introducing Tsallis entropy regularizer to induce exploration, investigating specific examples, characterizing well-posedness, designing reinforcement learning algorithm.
result Characterized well-posedness and provided semi-closed-form solutions for specific examples, found distinct optimal strategies.
A new algorithm learns MAGs from data more efficiently using entropy.
problem Learning MAGs from data is unstable and computationally expensive.
method Uses entropy estimation and refined Markov property to score MAGs.
result Algorithm is polynomial in number of nodes and outperforms existing methods.
Entropy regularization is used to get improved optimization performance in reinforcement learning tasks. A common form of regularization is to maximize policy entropy to avoid premature convergence and lead to more stochastic policies for exploration through action space. However, this does not ensure exploration in th…
Neural network MCMC sampler maximizes proposal entropy for efficient sampling.
problem Inefficient sampling from complex probability distributions.
method Proposes a neural network MCMC sampler that maximizes proposal entropy.
result Significantly higher efficiency in various sampling tasks.
The study shows almost maximal volume entropy rigidity for certain manifolds with integral Ricci curvature.
problem Volume entropy rigidity for manifolds with lower integral Ricci curvature bound.
method Analyzing manifolds with specific integral Ricci curvature bounds, diameter, and volume entropy.
result The universal cover of the manifold is close to a hyperbolic space form under certain conditions.
New RL approach uses future state and action visitation measures for better exploration.
problem Improving exploration in reinforcement learning.
method Intrinsic reward based on future state and action visitation measures, using contraction operators.
result Policies achieve good state-action space coverage and high performance.
New bandit algorithm maximizes information gain.
problem Optimizing decision-making in uncertain environments.
method Approximates information maximization using entropy and free energy principles.
result Asymptotic optimality proven for two-armed bandit problem.
Paper proposes a new method to learn distribution kernels via entropy maximization.
problem Challenges in applying kernel methods to distribution regression tasks.
method Proposes a novel objective for unsupervised learning of data-dependent distribution kernels based on entropy maximization.
result Demonstrates the effectiveness of the learned kernel across different modalities.
This paper improves test-time adaptation for distribution shifts using confidence maximization and input transformation.
problem Improving deep networks' performance on data shifted from the training distribution.
method Proposes a novel loss function combining confidence maximization and batch-wise entropy maximization with an input transformation module.
result Significantly improves robustness of pretrained networks to corruptions on benchmarks like ImageNet-C.
Maximizes Rényi entropy for efficient exploration in reward-free RL.
problem Challenges of exploration in reward-free reinforcement learning.
method Maximizes Rényi entropy over state-action space in exploration phase; uses batch RL for planning phase.
result Effective and sample-efficient exploration leading to superior policies.
In this paper, we present a new class of Markov decision processes (MDPs), called Tsallis MDPs, with Tsallis entropy maximization, which generalizes existing maximum entropy reinforcement learning (RL). A Tsallis MDP provides a unified framework for the original RL problem and RL with various types of entropy, includin…
The paper extends entropy maximization to multiscale settings and applies it to neural networks.
problem Achieving optimal risk bounds in neural networks using multiscale entropy.
method Generalizing maximum entropy to multiscale settings and applying it to neural networks.
result The multiscale Gibbs posterior can achieve a smaller excess risk than the single-scale Gibbs posterior in a teacher-student scenario.
This paper controls a boundary term in Huisken's formula for entropy.
problem Entropy of translators and its behavior under mean curvature flow.
method Geometrically natural control of the boundary term in Huisken's monotonicity formula.
result Entropy of compact translators is bounded by boundary entropy and maximal cone density.
We prove that for closed surfaces M with Riemannian metrics without conjugate points and genus ≥2 the geodesic flow on the unit tangent bundle T1M has a unique measure of maximal entropy. Furthermore, this measure is fully supported on T1M and the flow is mixing with respect to this measure. We formulate …
Cross-entropy loss linked to metric learning, outperforming complex pairwise losses.
problem Improving metric learning performance without complex optimization schemes.
method Theoretical analysis linking cross-entropy to pairwise losses, showing cross-entropy as an upper bound and equivalent to mutual information maximization.
result Minimizing cross-entropy is equivalent to maximizing mutual information, leading to state-of-the-art performance.
In this note we give a short proof to the rigidity of volume entropy. The result says that for a closed manifold with Ricci curvature bounded from below, if the universal cover has maximal volume entropy, then it is the space form. This theorem was first proved by F. Ledrappier and X. Wang in [1].
Improved exploration methods for reinforcement learning with reduced sample complexity.
problem Challenges in reinforcement learning exploration in unknown environments.
method Proposed game-theoretic and trajectory entropy algorithms with improved sample complexity.
result Established statistical advantage of entropy-regularized MDPs for exploration and reduced sample complexity.
Minimal surfaces and average area ratio found to be maximized by hyperbolic metrics.
problem Finding sharp relations between minimal surface entropy and average area ratio.
method Ricci flow with surgery and invariant measures.
result Minimal surface entropy maximized by hyperbolic metrics among metrics with scalar curvature ≥ -6.
Unique entropy measure found for convex projective manifolds.
problem Entropy measure for convex projective manifolds.
method Developed Patterson--Sullivan densities and mixing theory.
result Unique mixing measure of maximal entropy exists.
The paper studies minimal surface entropy on hyperbolic 3-manifolds and compares it to the hyperbolic case.
problem Minimal surface entropy on hyperbolic 3-manifolds and its comparison to the hyperbolic case.
method Analysis of Ricci flow convergence and comparison of metrics with sectional and scalar curvature constraints.
result The entropy is maximized at the hyperbolic metric under certain curvature conditions.
Empirical evidence suggests that even the most competitive markets are not strictly efficient. Price histories can be used to predict near future returns with a probability better than random chance. Many markets can be considered as {\it favorable games}, in the sense that there is a small probabilistic edge that smar…
DAC enhances exploration in reinforcement learning with entropy regularization.
problem Improving exploration efficiency in reinforcement learning.
method Sample-aware entropy regularization using replay buffer action distributions.
result DAC significantly outperforms existing algorithms in reinforcement learning tasks.
LITE efficiently estimates Gaussian PoM with linear time and memory complexity.
problem Estimating the probability of maximality (PoM) of Gaussian vectors efficiently.
method LITE: entropy-regularized UCB approach for almost-linear time and memory complexity.
result Achieves state-of-the-art accuracy with significantly faster performance than existing methods.
Paper develops MRCs for supervised classification using generalized maximum entropy.
problem Developing robust classifiers for decision problems.
method Generalized maximum entropy principle applied to minimax risk classifiers.
result Learning techniques for determining MRCs with performance guarantees.
Max entropy exploration guides reinforcement learning agents to pursue achievable goals.
problem Achieving distant test-time goals in long-horizon tasks.
method Optimize entropy of historical achieved goals by focusing on sparsely explored areas.
result Order of magnitude better sample efficiency on long-horizon multi-goal tasks.
Geodesics in curved spaces spread evenly over time.
problem Equidistribution of geodesics in negatively curved spaces.
method Proving equidistribution of geodesic flow orbits towards measures of maximal entropy and Bowen-Margulis measure.
result Equidistribution of divergent geodesics in negative curvature as their complexity increases.
The study calculates Weyl entropy in spacetime regions and shows its monotonic behavior.
problem Calculating and understanding Weyl entropy in spacetime regions.
method Introducing a candidate density for Weyl entropy in perfect fluid regions and analyzing its behavior in compact spacetime regions.
result Weyl entropy is shown to be monotonic in time and maximal in vacuum static metrics.
For a given quantum field theory, provided the area of the entangling surface is fixed, what surface maximizes entanglement entropy? We analyze the answer to this question in four and higher dimensions. Surprisingly, in four dimensions the answer is related to a mathematical problem of finding surfaces which minimize t…
Maximum entropy modeling is a flexible and popular framework for formulating statistical models given partial knowledge. In this paper, rather than the traditional method of optimizing over the continuous density directly, we learn a smooth and invertible transformation that maps a simple distribution to the desired ma…
Maximizes mixing efficiency in surface braids.
problem Finding the maximum mixing efficiency in surface braids.
method Introduced an efficient algorithm to compute topological entropy and TEPO for surface braids.
result Conjectured a novel candidate braid to have maximal mixing efficiency.
The paper proves rigidity results for Einstein manifolds with specific geometric constraints.
problem Understanding the rigidity of Einstein manifolds under bounded covering geometry.
method Analyzing Einstein manifolds with bounded covering geometry to prove rigidity results.
result Compact Einstein manifolds with specific geometric properties are isometric to space forms.
This paper optimizes trading strategies to minimize risk and maximize profit while accounting for market uncertainty.
problem Optimizing trading strategies to minimize risk and maximize profit while accounting for market uncertainty.
method Relative entropy-regularized robust optimal control problem, modeled as a stochastic differential game.
result Analytical expressions for optimal strategy and trajectory are derived under specific assumptions.