Efficient inference for adaptive data with directional stability condition.
problem Efficient inference on scalar targets after adaptive data collection.
method Introduces directional stability, a weaker condition than i.i.d. data, and shows asymptotic normality and efficiency of estimators.
result Estimators remain asymptotically normal and semiparametrically efficient under directional stability.
The study examines stability of Sobolev inequalities on manifolds with Ricci bounds.
problem Stability of Sobolev inequalities on Riemannian manifolds with Ricci curvature lower bounds.
method Combines techniques from smooth and non-smooth geometry, focusing on direct strategies.
result Effective methods revealed for stability of Sobolev inequalities on manifolds with non-negative Ricci curvature and Euclidean volume growth.
Unified framework for stability and generalization of Push-Sum in decentralized learning over directed graphs.
problem Understanding stability and generalization of Push-Sum in decentralized learning over directed networks.
method Developed a unified uniform-stability framework for SGP algorithm, incorporating imbalance-aware consistency bounds.
result Established finite-iteration stability and optimization guarantees for convex and non-convex objectives.
In this paper, the concepts and the direct theorems of stability in the sense of Liapunov, within the framework of Birkhoffian dynamical systems on manifolds, are considered. The Liapunov-type functions are constructed for linear and nonlinear LC and RLC electrical networks, to prove stability under certain conditions.
This paper analyzes quantiles of heavy-tailed distributions, separating projection direction and quantile threshold effects.
problem Analyzing quantiles of heavy-tailed distributions with estimated parameters.
method Introduces a Q-Q orthogonality formulation to separate projection-direction and quantile-threshold effects.
result Decomposes the difference between empirical and population quantiles into three terms.
Mirror descent linked to information ratio via Bayesian regret bounds.
problem Understanding stability in mirror descent and its relation to information ratio.
method Developed a connection between mirror descent and information ratio using Bayesian regret bounds.
result Mirror descent with suitable estimators and distributions achieves bounds similar to information-directed sampling.
New method accelerates neural network training by focusing on flat directions.
problem Improving neural network training speed and stability.
method Bulk-SGD, interpolated gradient methods.
result Updates along the Dominant subspace can accelerate convergence but compromise stability.
Graph braid groups' complexity stabilizes for most graphs.
problem Stabilization of topological complexity in graph braid groups.
method Geometric lower bounds on configuration spaces.
result Topological complexity stabilizes for most graphs.
Study fixed angle inverse scattering with Riemannian metrics, proving uniqueness and stability.
problem Inverse scattering problem with Riemannian metrics.
method Direct problem via progressing wave expansion; inverse problem using symmetry assumptions.
result Uniqueness and stability results for inverse scattering with Riemannian metrics.
Market activity scales near a constant of 0.632 in intrinsic time.
problem Understanding the stability of market scaling laws.
method Modeling market directional changes as a memoryless exponential hazard process and identifying the intrinsic time scaling constant.
result The intrinsic time scaling constant is 1−1/e=0.632. Gradient descent near stability threshold exhibits sharpness oscillations.
problem Understanding sharpness behavior near stability threshold in non-Euclidean norms.
method Interpreted EoS through Directional Smoothness and generalized sharpness under arbitrary norms.
result Non-Euclidean GD with generalized sharpness shows sharpness oscillations near 2/η. We formulate a notion of K-stability for Kähler manifolds, and prove one direction of the Yau-Tian-Donaldson conjecture in this setting. More precisely, we prove that the Mabuchi functional being bounded below (resp. coercive) implies K-semistability (resp. uniformly K-stable). In particular this shows that the existen…
Inspired by work of Colding-Minicozzi on mean curvature flow, Zhang introduced a notion of entropy stability for harmonic map flow. We build further upon this work in several directions. First we prove the equivalence of entropy stability with a more computationally tractable F-stability. Then, focusing on t…
Gradient descent near stability threshold shows sharpness oscillations.
problem Understanding sharpness and stability in non-Euclidean norms during gradient descent.
method Interpreted EoS through Directional Smoothness, defined generalized sharpness for arbitrary norms.
result Non-Euclidean GD exhibits sharpness oscillations around the stability threshold.
We prove a theorem on structural stability of smooth attractor-repellor endomorphisms of compact manifolds, with singularities. By attractor-repellor, we mean that the non-wandering set of the dynamics f is the disjoint union of a repulsive compact subset with a hyperbolic attractor on which f acts bijectively. The…
We survey some recent developments in the direction of the Yau-Tian-Donaldson conjecture, which relates the existence of constant scalar curvature Kähler metrics to the algebro-geometric notion of K-stability. The emphasis is put on the use of pluripotential theory and the interpretation of K-stability in terms of non-…
Study on stability of quaternion-Kähler manifolds using eigenvalue estimates.
problem Stability problem for positive quaternion-Kähler manifolds.
method Description of infinitesimal Einstein deformations and destabilising directions in terms of Laplace eigenfunctions and symmetric 2-tensors. Improved eigenvalue estimates for the Hodge-Laplacian on 2-forms.
result Sharp lower bound for the first non-zero eigenvalue on the parallel subbundle Sym^2 E of the 2-form bundle.
The paper presents a model-free method for stabilizing unknown control systems.
problem Stabilizing unknown control systems in engineering.
method Solving discounted LQR problems with increasing discount factors.
result The method efficiently recovers a stabilizing controller for linear and smooth nonlinear systems.
The paper improves bounds on how many squares can fit in a rectangle and still have stable homology.
problem Homological stability in the space direction of square configurations.
method Analyzing the ordered configuration space of squares in a rectangle.
result Most rectangles can be almost entirely filled with squares and still have stable homology.
GD at EoS edge minimizes logistic loss without monotonic convergence.
problem Understanding GD's implicit bias at the edge of stability.
method Theoretical analysis of logistic regression with constant stepsize GD.
result GD with any constant stepsize minimizes logistic loss over long time scales.
Uniform Ding stability implies existence of Kähler-Einstein metric on big anticanonical manifolds.
problem Existence of Kähler-Einstein metrics on manifolds with big anticanonical class.
method Developed a theory of Deligne functionals and slope formulas for singular metrics, proving a slope formula for the Ding functional in the big setting.
result Existence of a unique Kähler-Einstein metric implies uniform Ding stability.
In these notes we give a shortened and more direct proof of Goto's generalized Kaehler stability theorem stating that if (J_1,J_2) is a generalized kaehler structure for which J_2 is determined by a nowhere vanishing closed form, then small deformations of J_1 can be coupled with small deformations of J_2 so that the p…
Sharp stability estimate for tensor tomography in non-positive curvature.
problem Stability estimate for tensor tomography on manifolds with non-positive curvature.
method Pestov identity with localized frequency boundary term.
result Stability estimate of the form L2↦HT1/2. The paper analyzes stability and convergence rates of entropic and Sinkhorn potentials.
problem Stability and convergence rates of entropic and Sinkhorn potentials.
method Semiconcavity properties of entropic potentials and Schrödinger bridges.
result Exponential convergence rates for gradient and Hessian of Sinkhorn iterates.
We develop and study stability properties of a hybrid approximation of functionals of the Bates jump model with stochastic interest rate that uses a tree method in the direction of the volatility and the interest rate and a finite-difference approach in order to handle the underlying asset price process. We also propos…
The paper explores maximal destabilizers for both K-stability and Chow-stability in unstable situations.
problem Exploring maximal destabilizers for K-stability and Chow-stability in unstable situations.
method Using non-Archimedean pluripotential theory and idealistic assumptions, the paper provides a route to show that maximal K-destabilizers are quantized by maximal Chow-destabilizers.
result Maximal K-destabilizers are quantized by maximal Chow-destabilizers.
In this article, we introduce a new method (based on Perelman's lambda-functional) to study the stability of compact Ricci-flat metrics. Under the assumption that all infinitesimal Ricci-flat deformations are integrable we prove: (A) a Ricci-flat metric is a local maximizer of lambda in a C^2,alpha-sense iff its Lichne…
Variant of Seiberg-Witten equations for multiple-spinors connects to stability of holomorphic bundles.
problem Detecting stability of holomorphic vector bundles using Seiberg-Witten equations.
method Abelian gauge-theoretic variant of Seiberg-Witten equations for multiple-spinors.
result Constructs a numerical invariant related to φ−stability of SU(n)−holomorphic vector bundles. Study on stability of α-harmonic maps and their applications.
problem Investigating the stability of α-harmonic maps and their physical applications.
method Non-existence theorem, conformal deformation, Ricci curvature analysis, α-stable manifolds.
result Investigation of the instability of non-constant α-harmonic maps and their physical applications.
We review the notion of Gieseker stability for torsion-free Higgs sheaves. This notion is a natural generalization of the classical notion of Gieseker stability for torsion-free coherent sheaves. We prove some basic properties that are similar to the classical ones for torsion-free coherent sheaves over projective alge…
Paper proves linear convergence of SCMS algorithm for directional data.
problem Identifying density ridges in directional data.
method Generalized SCMS algorithm to directional data, derived from SCGA with adaptive step size.
result Linear convergence of the proposed directional SCMS algorithm.
CSTs improve stability in covariance spectrum analysis without training.
problem Stability and expressiveness in covariance spectrum analysis.
method Sequential application of covariance wavelet filters to input data.
result Stable and expressive hierarchical representations in low-data settings.
Momentum affects optimization differently at small vs large batch sizes near instability.
problem Understanding how momentum impacts optimization near the edge of stability.
method Demonstrated through batch-size dependent behavior of SGD with momentum.
result Momentum operates in two distinct regimes: amplifying stochastic fluctuations at small batch sizes and stabilizing at large batch sizes.
DAGgr aggregates multiple DAGs to stabilize causal structure learning.
problem Stability in learning causal structure from data.
method Model averaging of candidate DAGs weighted by predictive likelihood, with acyclicity enforced.
result DAGgr consistently outperforms individual DAGs and bootstrap-aggregation baselines.
New findings show mini-batch SGD operates in a 'Edge of Stochastic Stability' regime.
problem Understanding the stability and convergence of mini-batch SGD.
method Analyzing the mini-batch Hessian and its directional curvature.
result Mini-batch SGD operates in a different stability regime (Edge of Stochastic Stability) compared to full-batch GD.
Improves CNN stability by translating classical signal denoising methods.
problem Stability of CNNs is poorly understood.
method Interprets classical signal denoising methods as ResNet architectures.
result Translates diffusivities, shrinkage functions, and regularizers into CNN activation functions.
For a holomorphic vector bundle E over a polarised Kähler manifold, we establish a direct link between the slope stability of E and the asymptotic behaviour of Donaldson's functional, by defining the Quot-scheme limit of Fubini-Study metrics. In particular, we provide an explicit estimate which proves that Donaldso…
Paper derives formulas for static Einstein spaces, linking Neumann data to stability.
problem Stability of conformally compact static spaces.
method First and second variation formulas for renormalized area.
result Negativity of Neumann data implies instability.
New algorithms improve causal direction inference accuracy using parallel ensemble methods.
problem Stability of causal direction inference results from observational data.
method Parallel ensemble frameworks to map and improve inference accuracy.
result Significant improvement in accuracy of causal direction inference.
New approach to Z-stability and critical metrics on Kähler manifolds.
problem Determining Z-stability and existence of Z-critical metrics on Kähler manifolds. method Equivariant localisation applied to integrals over test configurations.
result Existence of Z-critical metrics is equivalent to Z-stability. Signed Evidence Flow (SEF) combines fitted prediction with signed feature attributions to measure evidence conflict and stability.
problem Modern data analysis lacks mechanisms to show the clarity, conflict, or stability of evidence behind predictions.
method Signed Evidence Flow (SEF) combines fitted prediction with signed feature attributions.
result SEF measures conflict and stability, and shows that conflict can improve loss prediction beyond confidence.
In this paper, we address the issue of linear stability of Schwarzschild space- time subject to certain axisymmetric perturbations. In particular, we prove that associ- ated solutions to the linearized vacuum Einstein equations centered at a Schwarzschild metric, with suitably regular initial data, decay to a linearize…
Grokking occurs at numerical stability edge, requiring regularization to prevent.
problem Delayed generalization in deep learning models.
method Identified Softmax Collapse (SC) as the cause of grokking without regularization.
result Mitigating SC enables grokking without regularization.
Kuwert and Schätzle showed in 2001 that the Willmore flow converges to a standard round sphere, if the initial energy is small. In this situation, we prove stability estimates for the barycenter and the quadratic moment of the surface. Moreover, in codimension one we obtain stability bounds for the enclosed volume and …
Classifies geodesic vectors in low-dimensional Lie algebras.
problem Stability of geodesic vectors in Lie algebras.
method Complete classification of Lyapunov stable and unstable geodesic vectors.
result Classification for metric Lie algebras of dimension 3 and 4.
This work studies an explicit embedding of the set of probability measures into a Hilbert space, defined using optimal transport maps from a reference probability density. This embedding linearizes to some extent the 2-Wasserstein space, and enables the direct use of generic supervised and unsupervised learning algorit…
An important "stability" theorem in shape theory, due to D.A. Edwards and R. Geoghegan, characterizes those compacta having the same shape as a finite CW complex. In this note we present straightforward and self-contained proof of that theorem.
Generative adversarial networks are used to generate images but still their convergence properties are not well understood. There have been a few studies who intended to investigate the stability properties of GANs as a dynamical system. This short writing can be seen in that direction. Among the proposed methods for s…