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.
PAN improves graph neural networks using path integrals.
problem Efficiency and performance of graph neural networks.
method PAN uses path integrals to generalize graph Laplacian, incorporating all paths between nodes.
result PAN achieves state-of-the-art performance on benchmark tasks.
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.
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.
A streamlined DRL algorithm improves sample efficiency without entropy maximization.
problem Improving sample efficiency in off-policy DRL algorithms.
method Output normalization and non-uniform sampling.
result Proposed algorithm matches SAC's performance without entropy maximization and improves sample efficiency.
In this paper we study the ergodic theory of the geodesic flow on negatively curved geometrically finite manifolds. We prove that the measure theoretic entropy is upper semicontinuous when there is no loss of mass. In case we are losing mass, the critical exponents of parabolic subgroups of the fundamental group have a…
Persistent entropy detects phase transitions in complex systems.
problem Detecting phase transitions in complex systems.
method Established a general theorem for persistent entropy to reliably detect phase transitions, introduced operational framework for finite-time computations.
result Persistent entropy exhibits an asymptotically non-vanishing gap across phases, robust numerical signatures across experiments.
PAN uses path integrals for graph convolution and pooling, improving GNN performance.
problem Designing efficient graph convolution and pooling for graph neural networks.
method Path integral based graph convolution and pooling using learnable weights for path lengths.
result PAN achieves state-of-the-art performance on various graph classification/regression tasks.
Entropy tracking reveals class commitment transitions in diffusion models.
problem Diffusion models lack reliable methods to detect semantic structure transitions.
method Tracking class-conditional entropy of latent variables.
result Entropy isolates noise regimes critical for semantic structure formation.
Proposes MEDM to balance entropy minimization and diversity maximization for better domain adaptation.
problem Trivial solutions in entropy minimization for unsupervised domain adaptation.
method Introduces diversity maximization to balance with entropy minimization, controlled by deep embedded validation.
result MEDM outperforms state-of-the-art methods on four domain adaptation datasets.
This paper presents a Bayesian image segmentation model based on Potts prior and loopy belief propagation. The proposed Bayesian model involves several terms, including the pairwise interactions of Potts models, and the average vectors and covariant matrices of Gauss distributions in color image modeling. These terms a…
Proves constraints on groups extending Möbius transformations on spheres.
problem Constraints on groups extending Möbius transformations on spheres.
method Proved constraints through group transitivity and topological entropy analysis.
result Groups must be 4-transitive or arc 4-transitive, and contain elements of positive topological entropy.
Study shows depth improves generalization in deep learning models.
problem Understanding why and when depth improves generalization in deep learning.
method Implementation-agnostic state-transition model to analyze depth and generalization.
result Identifies geometric and semigroup mechanisms that keep entropy contribution saturated or polynomial, clarifying depth's statistical advantage.
New algorithm reduces performance loss in IRL with mismatched transition dynamics.
problem Performance degradation in inverse reinforcement learning due to mismatched transition dynamics.
method Proposed a robust Maximum Causal Entropy (MCE) IRL algorithm leveraging robust reinforcement learning insights.
result Empirically demonstrated stable performance improvement under transition dynamics mismatches.
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.
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.
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.
This work improves policy optimization by maximizing entropy of state distribution, leading to better exploration.
problem Lack of exploration in state space when maximizing policy entropy.
method Proposes maximizing the entropy of a lower bound approximation to the state weighting distribution, based on latent space representation.
result Entropy regularization based on marginal state distribution achieves superior state space coverage and better performance in various domains.
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.
Stochastic kernel based dimensionality reduction approaches have become popular in the last decade. The central component of many of these methods is a symmetric kernel that quantifies the vicinity between pairs of data points and a kernel-induced Markov chain on the data. Typically, the Markov chain is fully specified…
Method detects phase transitions in financial markets using eigenvalue decomposition.
problem Detecting tipping points and fluctuation patterns in financial markets.
method Eigenvalue decomposition and eigen-entropy from cross-correlation matrix.
result Market events undergo phase separation and order-disorder transitions.
Order-flow entropy predicts price magnitude without directionality.
problem Predicting price magnitude in financial markets.
method Real-time order-flow entropy computed from a 15-state Markov transition matrix.
result Order-flow entropy predicts the magnitude of intraday returns with high accuracy.
The main result of this article is that if a 3-manifold M supports an Anosov flow, then the number of conjugacy classes in the fundamental group of M grows exponentially fast with the length of the shortest orbit representative, hereby answering a question raised by Plante and Thurston in 1972. In fact we show 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.
State entropy regularization improves robustness in reinforcement learning, especially under structured perturbations.
problem Structured and spatially correlated perturbations in reinforcement learning.
method State entropy regularization, compared to policy entropy.
result State entropy regularization provides better robustness to structured and spatially correlated perturbations.
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.
EVODiff optimizes DM inference by reducing conditional entropy, improving image generation.
problem Slow and inaccurate inference in diffusion models.
method Entropy-aware variance optimization for efficient inference.
result Significant improvement in image generation quality and efficiency.
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.
New method identifies common cause in causal insufficiency, revealing complex phase transitions.
problem Identifying common cause in causal insufficiency with observed joint probability.
method Generalized maximum likelihood method, closely related to maximum entropy principle.
result Identifies consistent common cause that aligns with the common cause principle.
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.
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.
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 …