New method recovers curvature from heat diffusion data.
problem Recovering Riemannian curvature from heat diffusion.
method Information-theoretic approach using relative entropy.
result Local curvature determined by heat diffusion.
On-device research index
arXiv research
A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
168,742 papers · 148 categories
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48 results for “curvature information”
CuBAS selects informative data points based on curvature for better classification.
problem Lack of efficient sampling strategies for maximizing dataset informativeness.
method Information-geometric framework using curvature scores to select labeled data.
result Consistent and statistically significant improvements over random and uncertainty-based sampling.
The article examines entropy-information inequalities for continuous-time Markov chains under curvature-dimension conditions.
problem Proving Li-Yau inequalities and modified logarithmic Sobolev inequalities for reversible Markov chains.
method Introducing the condition and deriving entropy-information inequalities.
result Derives functional inequalities relating entropy to Fisher information.
Paper proposes a new method to efficiently incorporate curvature information in stochastic optimization.
problem Minimizing nonconvex functions with limited curvature information.
method Structured stochastic quasi-Newton method using partial Hessian information.
result Global convergence to stationary point and local superlinear convergence rate established.
Defines curvature for metric triples in metric spaces.
problem No standard curvature for metric triples in general metric spaces.
method Defines curvature using side lengths and distances to points in .
result Curvature enables isometric embedding into model spaces.
Deep Curvature Suitestat.ML
Deep Curvature Suite offers a PyTorch package for neural network curvature analysis.
problem Insufficient use of curvature information in neural networks.
method Implementation of Lanczos algorithm for neural network curvature analysis.
result Our package outperforms existing methods for similar purposes.
We review basic notions in the field of information geometry such as Fisher metric on statistical manifold, -connection and corresponding curvature following Amari's work . We show application of information geometry to asymptotic statistical inference.
Study submanifolds in spheres with Ricci curvature bounds.
problem Topology of submanifolds in spheres with Ricci curvature constraints.
method Investigates submanifolds in spheres with Ricci curvature lower bounds.
result Strong additional information on submanifold geometry.
The paper refines classical covariance asymptotics using geometric information geometry.
problem Deviation of finite-sample behavior from classical predictions in curved models.
method Develops a curvature-aware refinement by viewing parametric families as Riemannian manifolds with Fisher-Rao metric.
result Derives an \(n^{-2}\) correction to the leading \(n^{-1}I(θ)^{-1}\) covariance term for score-root estimators.
New neural network solves Nirenberg problem for curvature on sphere.
problem Prescribing Gaussian curvature on for metrics conformal to the round metric.
method Mesh-free physics-informed neural network (PINN) that directly parametrises the conformal factor.
result Neural network achieves very low losses for realisable curvatures, distinguishing them from non-realisable ones.
Research characterizes critical points of scalar curvature functionals.
problem Characterizing critical points of scalar curvature functionals.
method Translation and analysis of a previous Russian paper.
result Provides insights into critical points of scalar curvature functionals.
Partial Counterfactual Identification of Continuous Outcomes with a Curvature Sensitivity Modelstat.ML
Proposes a new model to identify unknown counterfactual outcomes for continuous variables.
problem Counterfactual inference for continuous outcomes with strong assumptions.
method Curvature Sensitivity Model to relax assumptions and provide informative bounds.
result Demonstrates effectiveness of the Curvature Sensitivity Model in identifying counterfactual outcomes.
Negative step sizes improve second-order methods for neural networks.
problem Second-order methods discard negative curvature, limiting their effectiveness.
method Introduce negative step sizes in second-order methods combined with Wolfe line search.
result Negative step sizes lead to global convergence and improved performance.
The question of how to incorporate curvature information in stochastic approximation methods is challenging. The direct application of classical quasi- Newton updating techniques for deterministic optimization leads to noisy curvature estimates that have harmful effects on the robustness of the iteration. In this paper…
We obtain new topological information about the local structure of collapsing under a lower sectional curvature bound. As an application we prove a new sphere theorem and obtain a partial result towards the conjecture that not every Alexandrov space can be obtained as a limit of a sequence of Riemannian manifolds with …
ITF improves DSR but inflates curvature, while marginal likelihood reduces it, affecting QoIs.
problem Curvature mismatch between teacher forcing and marginal likelihood in chaotic dynamical systems.
method Comparing objective-induced curvatures of ITF and marginal likelihood in a probabilistic switching augmentation of AL-RNNs.
result Curvature inflation by ITF and reduction by marginal likelihood affect dynamical quantities of interest.
The paper studies geometric structures of curvature radii on Riemannian manifolds.
problem Exploring geometric structures of curvature radii on Riemannian manifolds.
method The main method involves constructing a pair of global vector fields that encode intrinsic geometry.
result Existence of sub-Riemannian manifolds associated with curvature radii and investigation of their properties.
We show that gamma distributions provide models for departures from randomness since every neighbourhood of an exponential distribution contains a neighbourhood of gamma distributions, using an information theoretic metric topology. We derive also the information geometry of the 3-manifold of McKay bivariate gamma dist…
Novel coarse extrinsic curvature for Riemannian submanifolds.
problem Understanding extrinsic curvature of submanifolds.
method Derived from Wasserstein 1-distance between probability measures.
result New insights and approximation of mean curvature from data.
We classify the algebraic curvature tensors which are both Osserman and complex Osserman in all but a finite number of exceptional dimensions.Information concerning the possible eigenvalue structures, which is provided by methods of algebraic topology, plays a central role in the analysis.
Estimates for VPMCF show ancient MCF solutions and finite-time behavior.
problem Volume Preserving Mean Curvature Flow (VPMCF) behavior and singularities.
method Nonlocal estimates and blowup analysis.
result Ancient solutions to MCF and finite-time behavior of VPMCF.
Characterizes metrics with finite total Q-curvature and introduces new volume entropy.
problem Understanding metrics with finite total Q-curvature and their geometric properties.
method Characterization of metrics through total Q-curvature and introduction of new volume entropy.
result Controlled volume growth for complete metrics with finite total Q-curvature and bounded scalar curvature.
Statistical Bergman geometrymath.CV
The paper connects Bergman geometry with information geometry.
problem Exploring the Bergman geometry of complex domains.
method Introducing a mapping Φ and using Fisher information metrics.
result Established a new statistical curvature formula for the Bergman metric.
Paper proposes LCP for structural encodings, outperforming existing methods.
problem Improving Graph Neural Networks performance through effective structural encodings.
method Geometric perspective, Local Curvature Profiles (LCP) for structural encodings, combining with global positional encodings, comparing with rewiring techniques.
result LCP significantly outperforms existing structural encodings and combining LCP with global positional encodings improves performance.
Positive curvature forces foliation leaf spaces to have boundaries.
problem Understanding boundaries in foliated leaf spaces with positive curvature.
method Analyzing singular Riemannian foliations with positive sectional curvature.
result Polar foliations of positively curved manifolds have leaf spaces with nonempty boundaries.
The paper studies 3D manifolds with positive scalar curvature and volume growth.
problem Understanding the geometry of 3D manifolds with positive scalar curvature.
method Analyzes volume and geometric properties of 3D complete manifolds with positive scalar curvature, considering different curvature conditions.
result Volume growth estimates for 3D manifolds with positive scalar curvature, answering Gromov's question affirmatively.
The abstract aims to generalize classical curve concepts to uniquely define complex curves.
problem Lack of sufficient information to distinguish between different curves.
method Generalizing classical concepts of curvature and torsion to higher algebraic curvatures.
result Each analytic branch of a complex curve is uniquely defined by higher algebraic curvatures.
Graph networks struggle with multi-task learning due to varying property loss surface curvatures.
problem Graph networks underperform in multi-task learning for crystal and molecule properties.
method Assessed curvature of property loss surfaces via spectral properties of Hessians, matrix-free using randomized numerical linear algebra.
result Varying curvature of property loss surfaces explains graph networks' multi-task learning inefficiency.
Study reveals how to determine area and curvature from fluid flow resonances.
problem Determining geometric properties from fluid flow data.
method Asymptotic expansion of heat kernel and Steklov spectral invariants.
result Area and total mean curvature can be inferred from Steklov eigenvalues.
In this note we discuss the fundamental groups and diameters of positively Ricci curved -manifolds. We use a method combining the results about equivarient Hausdorff convergence developed by Fukaya and Yamaguchi with the Ricci version of splitting theorem by Cheeger and Colding to give new information on the topolog…
Paper explores duality in DPPs using embedding structure analysis.
problem Understanding the geometric structure of determinantal point processes.
method Analyzes the exponential family embedding of DPPs and uses the e-embedding curvature tensor.
result Discovers the duality between marginal and L-ensemble kernels.
DEO uses gradient information to escape saddle points in neural networks.
problem Training deep neural networks struggles with flat regions and saddle points.
method Dimer-Enhanced Optimization (DEO) uses gradient information to estimate curvature and escape saddle points.
result DEO improves training efficiency and performance compared to standard first-order methods.
A new framework selects information sources to test hypotheses robustly, even with misclassifications.
problem Robust hypothesis testing with misclassification penalties.
method Introduces a misclassification penalty framework and an efficient greedy algorithm.
result Proposes a submodular surrogate metric for better selection.
The paper calculates Betti numbers for special geometric manifolds with curvature constraints.
problem Estimating Betti numbers for nearly and nearly Kähler manifolds with curvature bounds.
method Using Weitzenböck formulas and bounds on sectional curvature to estimate Betti numbers.
result Sufficient conditions for vanishing certain Betti numbers based on sectional curvature bounds.
Study on curvature functions for compact manifolds with boundary.
problem Understanding curvature functions on compact manifolds with boundary.
method Proves necessary and sufficient conditions for geodesic and Gaussian curvature, solves problems in the pointwise conformal case.
result New existence and nonexistence results for metrics with prescribed curvature, depending on Euler characteristic.
Study angle structures on pseudo 3-manifolds, proving existence for some cases.
problem Determining if hyperbolic 3-manifolds can have angle structures.
method Examined triangulated pseudo 3-manifolds with area-curvature angle structures, establishing sufficient and necessary conditions.
result Compact hyperbolic 3-manifolds with totally geodesic boundary can have angle structures.
This paper studies an acceleration technique for incremental aggregated gradient ({\sf IAG}) method through the use of \emph{curvature} information for solving strongly convex finite sum optimization problems. These optimization problems of interest arise in large-scale learning applications. Our technique utilizes a c…
We introduce a notion of measuring scales for quantum abelian gauge systems. At each measuring scale a finite dimensional affine space stores information about the evaluation of the curvature on a discrete family of surfaces. Affine maps from the spaces assigned to finer scales to those assigned to coarser scales play …
Singular 3-manifolds in math.DG
Study 3D shapes in 5D space with sharp points.
problem Understanding shapes with sharp points in higher dimensions.
method Define curvature locus using fundamental forms at sharp points.
result Local second order geometrical information captured.
The Riemannian Bures metric on the space of (normalized) complex positive matrices is used for parameter estimation of mixed quantum states based on repeated measurements just as the Fisher information in classical statistics. It appears also in the concept of purifications of mixed states in quantum physics. Here we d…
A lightweight framework improves convergence and stability of PINNs for complex PDEs.
problem Training instability and reduced accuracy in PINNs for complex PDEs.
method Adaptive curvature correction using secant information to optimize first-order optimizers.
result Consistent improvements in convergence speed, stability, and accuracy over standard optimizers.
New method efficiently learns positive-definite curvature for neural nets.
problem Efficiently learn positive-definite curvature for neural net training.
method Spectral-factorized positive-definite curvature learning approach.
result Efficiently applies arbitrary matrix roots and generic curvature learning.
In this paper, we study some classes of submanifolds of codimension one and two in the Page space. These submanifolds are totally geodesic. We also compute their curvature and show that some of them are constant curvature spaces. Finally we give information on how the Page space is related to some other metrics on the …
Optimal transport and information geometry both study geometric structures on spaces of probability distributions. Optimal transport characterizes the cost-minimizing movement from one distribution to another, while information geometry originates from coordinate-invariant properties of statistical inference. Their con…
Fractal Lipschitz-Killing curvature measures C^f_k(F,.), k = 0, ..., d, are determined for a large class of self-similar sets F in R^d. They arise as weak limits of the appropriately rescaled classical Lipschitz-Killing curvature measures C_k(F_r,.) from geometric measure theory of parallel sets F_r for small distances…
AngularGrad: A New Optimization Technique for Angular Convergence of Convolutional Neural Networkscs.LG
AngularGrad optimizes CNNs by considering gradient direction, improving convergence.
problem Dying gradient problem and inefficiency in exploiting gradient curvature.
method AngularGrad considers gradient direction/angle, generating a score for step size control.
result AngularGrad outperforms state-of-the-art optimizers in benchmark tests.
Gradient-based optimization methods are the most popular choice for finding local optima for classical minimization and saddle point problems. Here, we highlight a systemic issue of gradient dynamics that arise for saddle point problems, namely the presence of undesired stable stationary points that are no local optima…
The Freund family of distributions becomes a Riemannian 4-manifold with Fisher information as metric; we derive the induced -geometry, i.e., the -curvature, -Ricci curvature with its eigenvales and eigenvectors, the -scalar curvature etc. We show that the Freund manifold has a positive constant 0-scalar cur…