New algorithm reduces clustering cost in bandit feedback.
problem Discovering hidden groupings in stochastic bandit feedback.
method ACB algorithm for active clustering with non-asymptotic lower bound.
result ACB algorithm's budget matches lower bound in most regimes.
Proposes a method to compute information theory measures via Gaussianization.
problem Challenges of computing information from multidimensional data.
method Indirect computation using a multivariate Gaussianization transform.
result Proposed methods outperform existing estimators, especially in high dimensions.
We simplify information measure computation using learned features.
problem Computing information measures from raw data is computationally expensive.
method Developed a separable design for computing information measures from learned feature representations.
result A variety of information measures can be computed efficiently through learned feature representations.
We examine a class of deep learning models with a tractable method to compute information-theoretic quantities. Our contributions are three-fold: (i) We show how entropies and mutual informations can be derived from heuristic statistical physics methods, under the assumption that weight matrices are independent and ort…
Cost-effective feature selection improves network model choice.
problem Selecting informative features from noisy candidates in network models.
method Adapted feature selection methods to account for feature costs and used pilot simulations.
result Reduced computational cost by two orders of magnitude without sacrificing model accuracy.
In this paper, we propose a novel Reinforcement Learning approach for solving the Active Information Acquisition problem, which requires an agent to choose a sequence of actions in order to acquire information about a process of interest using on-board sensors. The classic challenges in the information acquisition prob…
RL policy tracks dynamic targets in partially known environments robustly.
problem Active target tracking in partially known environments.
method Deep reinforcement learning (RL) approach for in-sight tracking, navigation, and exploration.
result Unified RL policy shows robust behavior for agile and anomalous targets.
New bounds for heavy-tailed SDEs without info-theory terms.
problem Understanding generalization of heavy-tailed stochastic optimization.
method Fractional Fokker-Planck equation to estimate entropy flows.
result High-probability bounds with better dimension dependence.
This paper investigates methods for quantifying similarity between audio signals, specifically for the task of of cover song detection. We consider an information-theoretic approach, where we compute pairwise measures of predictability between time series. We compare discrete-valued approaches operating on quantised au…
The paper explores gaps in curvature-related metrics and rigidity.
problem Understanding gaps in curvature-related metrics and rigidity.
method Analyzes three types of gaps: spectral, metric-rigidity, and topological-rigidity.
result Proposes open problems in the field.
Study gap-dependent regret bounds for risk-sensitive RL.
problem Risk-sensitive reinforcement learning with entropic risk measure.
method Propose cascaded gaps to adapt to problem structures, derive regret bounds.
result Exponential improvement over existing bounds in appropriate settings.
We show how the discovery of robust scalable numerical solvers for arbitrary bounded linear operators can be automated as a Game Theory problem by reformulating the process of computing with partial information and limited resources as that of playing underlying hierarchies of adversarial information games. When the so…
Paper analyzes origami slope gaps and their distribution, finding a unique pattern.
problem Analyzing slope gaps in origami surfaces.
method Derived slope gap distribution of a specific origami by considering return times under the horocycle flow.
result Found a unique distribution of origami slope gaps, not a sum of scaled Hall distributions.
Random hyperbolic surfaces have nearly optimal spectral gaps.
problem Proving the nearly optimal spectral gap conjecture for random Belyi surfaces.
method Using the Brooks-Makover model, the authors show a spectral gap greater than 1/4 - c/log(n).
result A random hyperbolic surface in the Brooks-Makover model has a spectral gap greater than 1/4 - c/log(n).
Paper improves volume gap between minimal submanifolds and unit spheres.
problem Volume gap between minimal submanifolds and unit spheres.
method Modified Cheng-Li-Yau coefficients and applied Cheng-Yang eigenvalue estimate for Laplacian.
result Enhanced volume gap between minimal submanifolds and unit spheres.
The article proves a conjecture about the fundamental gap for horoconvex domains in hyperbolic space.
problem Proving a conjecture about the fundamental gap for horoconvex domains in hyperbolic space.
method Establishing conformal log-concavity estimates for the first eigenfunction.
result Proves a conjecture about the fundamental gap for horoconvex domains in hyperbolic space.
Kahler-Einstein metrics linked to eigenvalue gaps on Fano manifolds.
problem Existence of Kahler-Einstein metrics on Fano manifolds.
method Characterization via eigenvalue gaps of Cauchy-Riemann and Hamiltonian vector fields.
result Existence of Kahler-Einstein metrics linked to eigenvalue gaps.
Local gaps in Ricci shrinkers depend only on dimension.
problem Understanding local properties of Ricci shrinkers.
method Proved local versions of Ricci curvature and entropy gap theorems.
result Local gaps depend only on dimension, not global entropy.
Study shows gaps in Bitcoin order book are linked to returns but only in the short term.
problem Understanding the relationship between gaps and returns in Bitcoin order books.
method Examined the dynamics of gaps and returns in a Bitcoin order book without considering long-term causation.
result The causal relationship between gaps and returns is limited to instantaneous causation.
Researchers compute gap distributions for saddle connection directions on specific translation surfaces.
problem Computing gap distributions for saddle connection directions on translation surfaces.
method Translation to dynamical question of return times to a transversal under the horocycle flow.
result Gap distributions have support at 0 and quadratic tail decay.
Proves gap rigidity theorem for Hermitian symmetric spaces.
problem Gap rigidity problems in compact Hermitian symmetric spaces.
method Dual analogy to Mok's noncompact case theorem, theorem on higher dimensional submanifolds.
result Proves gap rigidity theorem for diagonal curves in tube type spaces.
The paper introduces gapped scale-sensitive dimensions to improve learning rate bounds.
problem Improving lower bounds on rates of convergence in statistical and online learning.
method Introducing and analyzing gapped scale-sensitive dimensions for function classes.
result Gapped dimensions lead to stronger lower bounds on offset Rademacher averages.
The article explores the fundamental gap in Bakry-Emery geometry.
problem The fundamental gap in Bakry-Emery geometry.
method Recalled Bakry-Emery geometry and connected eigenvalues with boundary conditions. Showed a connection between fundamental gap and Bakry-Emery geometry.
result Presented key ideas in Andrews's and Clutterbuck's proof of the fundamental gap conjecture.
The paper calculates gap distributions for translation surfaces, focusing on the double heptagon.
problem Calculating gap distributions for translation surfaces.
method Describes a procedure to find winning holonomy vectors and applies it to the double heptagon.
result Explicitly computed gap distribution for the regular double heptagon translation surface.
Improved gap-dependent bounds for reinforcement learning with linear approximations.
problem Achieving nearly minimax-optimal performance with linear function approximation.
method Developed and analyzed the LSVI-UCB++ algorithm and its concurrent variant.
result First gap-dependent regret bound for nearly minimax-optimal algorithm LSVI-UCB++.
We present a data-driven framework called generative adversarial privacy (GAP). Inspired by recent advancements in generative adversarial networks (GANs), GAP allows the data holder to learn the privatization mechanism directly from the data. Under GAP, finding the optimal privacy mechanism is formulated as a constrain…
Computing unlinking number is usually very difficult and complex problem, therefore we define BJ-unlinking number and recall Bernhard-Jablan conjecture stating that the classical unknotting/unlinking number is equal to the BJ-unlinking number. We compute BJ-unlinking number for various families of knots and links for w…
New methods reduce bias in estimating optimality gaps for risk-averse stochastic programs.
problem Optimality gap estimation bias in risk-averse stochastic programs.
method Two independent samples, each estimating a different component of the optimality gap.
result Our method reduces bias in estimating optimality gaps for risk-averse problems.
New conditions prevent gaps in optimal control problems.
problem Preventing gaps in optimal control problems with state constraints.
method Developed new sufficient conditions not relying on convexity.
result Derived bounds for the size of the relaxation gap.
Federated learning studies separate client data and distribution gaps.
problem Understanding performance differences in federated learning across different datasets.
method Proposed a framework to disentangle out-of-sample and participation gaps.
result Dataset synthesis strategy is crucial for realistic simulations of federated learning generalization.
The paper proves gap theorems for Yang-Mills on manifolds with positive Yamabe.
problem Yang-Mills theory on manifolds with positive Yamabe constant.
method Extending Gursky-Kelleher-Streets results to complete manifolds.
result Equality in gap theorem described in terms of basic instanton.
Study simplicial volume for fixed fundamental groups, finding gaps.
problem Understanding simplicial volume for manifolds with fixed fundamental group.
method Relate gap problem to rationality questions in bounded (co)homology.
result Show existence of gaps in simplicial volume spectrum at zero.
Study shows fundamental gap of horoconvex domains in hyperbolic space has no positive lower bound.
problem Understanding the fundamental gap of horoconvex domains in hyperbolic space.
method Analysis of fundamental gap of geodesic balls as radius goes to infinity.
result Product of fundamental gap and square of diameter has no positive lower bound for horoconvex domains.
Study spectral gaps in hyperbolic rational homology spheres.
problem Finding spectral gaps in hyperbolic rational homology spheres.
method Construction of families of hyperbolic rational homology spheres with coexact 1-form spectral gaps.
result Provided intervals containing limit points of spectral gaps, with the rightmost interval being [0.8196, 0.8277].
New convex domains in hyperbolic space can have lower fundamental gap than constant potentials.
problem Finding convex domains with lower fundamental gap than constant potentials.
method Constructing specific convex domains and potentials with controlled eigenfunctions.
result Fundamental gap of −Δ+V can be strictly smaller than −Δ for convex domains. The study finds larger gaps in mean curvature for biharmonic submanifolds in spheres.
problem Understanding gaps in mean curvature for biharmonic submanifolds.
method Analyzing proper biharmonic submanifolds with parallel mean curvature vector field in Euclidean spheres.
result Determining larger gaps in mean curvature for specific biharmonic submanifolds.
Solves clustering contradictions by high-dimensional embedding with wide gaps.
problem Kleinberg's clustering axioms are contradictory.
method Embedding in high-dimensional space with wide gaps between clusters.
result Handles clustering contradictions by design.
The paper establishes pressure gaps for manifolds with flat subtori singularities.
problem Understanding phase transitions in nonpositively curved manifolds with flat subtori.
method Derives a pressure gap criterion for closed rank 1 manifolds with specific singular sets and proves Hölder continuity of geometric potentials.
result Geometric potentials have pressure gaps and no phase transitions under certain curvature constraints.
In their celebrated work, B. Andrews and J. Clutterbuck proved the fundamental gap (the difference between the first two eigenvalues) conjecture for convex domains in the Euclidean space and conjectured similar results holds for spaces with constant sectional curvature. We prove the conjecture for the sphere. Namely wh…
Proves effective slope gaps for lattice surfaces.
problem Proving effective slope gaps for lattice surfaces.
method Proves effective slope gap distribution for square torus and general lattice surfaces.
result Effective slope gap distribution result for lattice surfaces.
GSP improves global average pooling for deep metric learning by learning weights and selecting semantic entities.
problem Improving global average pooling for deep metric learning.
method Generalized Sum Pooling (GSP) method that learns weights and selects semantic entities.
result GSP improves metric learning performance on 4 popular benchmarks.
This paper improves Q-learning bounds using reference-advantage decomposition.
problem Improving Q-learning bounds in MDPs with positive suboptimality gaps.
method Develops a novel error decomposition framework to prove gap-dependent regret bounds.
result Establishes logarithmic gap-dependent regret bounds for Q-learning.
Abstract: Unknown status of Jacobian Conjecture, proof has a gap.
problem Status of Jacobian Conjecture
method Analysis of proof of theorem 2.1
result Proof of theorem 2.1 contains a gap
Sharp spectral gap estimates on manifolds with integral curvature bounds.
problem Proving spectral gap estimates on manifolds with integral curvature bounds.
method Generalizing previous results to include integral curvature bounds.
result Confirms a conjecture about spectral gap estimates on manifolds with integral curvature bounds.
Fundamental gap vanishes for convex domains in hyperbolic space.
problem Behavior of fundamental gap in convex domains in hyperbolic space.
method Proof for Laplace operator with Dirichlet boundary conditions.
result Fundamental gap can be arbitrarily small for domains of any diameter.
Uniform spectral gap found for stable commutator length in hyperbolic 2-orbifolds.
problem Understanding stable commutator length in 3-manifolds.
method Explicit quasimorphisms for generic case, hyperbolic geometry for exceptional case.
result Explicit uniform gap of 1/36 for all orbifolds except a sphere with three cone points.
Study calculates eigenvalues and eigenfunctions for spherical triangles and finds fundamental gap behavior.
problem Understanding eigenvalues and gaps in spherical triangles.
method Explicit computation of Dirichlet eigenvalues and eigenfunctions for spherical lunes and triangles.
result Fundamental gap of spherical triangles increases as the angle of the lune decreases.
The paper proves lower bounds for Gaussian-weighted curvature integrals of self-shrinkers.
problem Proving lower bounds for Gaussian-weighted \(L^2\)-curvature integrals of self-shrinkers.
method Combining normal coordinate functions with weighted Poincaré inequalities and first-eigenvalue estimates.
result Explicit lower bounds in terms of entropy for closed self-shrinkers, leading to curvature gaps.