Studied SGD convergence under weak conditions.
problem Convergence of SGD in nonconvex optimization.
method Analyzed biased nonconvex SGD under mild conditions.
result Provided convergence rates and complexities.
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48 results for “convergence conditions”
Study on slow convergence in geometric variational problems.
problem Slow convergence of solutions in geometric variational problems.
method Identifying necessary conditions for slowly converging solutions and characterizing their convergence rate and direction.
result Characterization of the rate and direction of convergence for slowly converging solutions.
Paper proposes a pre-conditioning technique to speed up gradient-descent convergence in distributed linear least-squares problems.
problem Expediting convergence of gradient-descent method for ill-conditioned distributed linear least-squares problems.
method Iterative pre-conditioning technique to improve convergence rate of gradient-descent method.
result Pre-conditioned gradient-descent achieves superlinear convergence for unique solutions and improved linear convergence otherwise.
Convergence of the Stochastic Heavy Ball Method With Approximate Gradients and/or Block Updatingmath.OC
Paper proves SHB convergence with biased gradients and approximate step sizes.
problem Establishing convergence of SHB with biased gradients and approximate step sizes.
method Generalizes SHB convergence conditions for biased gradients, approximate step sizes, and block updating.
result Proves convergence of SHB with new conditions for biased gradients and approximate step sizes.
COS method convergence conditions expanded for heavy-tailed distributions.
problem Ensuring convergence of the COS method for various densities.
method Analyzing truncation error and providing conditions for convergence.
result Conditions for COS method convergence extended to include heavy-tailed distributions.
SGD converges with positive probability for non-convex deep neural networks under specific conditions.
problem Convergence of SGD for non-convex deep neural networks.
method Established local convergence with positive probability under local Łojasiewicz condition and additional structural assumption.
result SGD converges with positive probability for non-convex deep neural networks under specific conditions.
Hamiltonian Monte Carlo converges to target distributions under mild conditions.
problem Establishing convergence of Hamiltonian Monte Carlo algorithms.
method Analyzing convergence for Hamiltonian Monte Carlo under mild conditions.
result Outputs converge to target distributions under specified conditions.
Uniform convergence of isotopies implies ambient isotopy, aiding knot equivalence.
problem Determining when uniform convergence of isotopies leads to ambient isotopies.
method Using a diagrammatic condition to offload uniform convergence, constructing examples of tame knots.
result Constructing tame knots with countably-many crossings, distinguishing them from wild curves.
Improved subgradient method tackles ill-conditioned composite optimization problems.
problem Slow convergence of subgradient method for composite optimization problems.
method Preconditioned subgradient method with Levenberg-Marquardt approach.
result Linear convergence rate for composite optimization problems under mild conditions.
This paper considers inference over distributed linear Gaussian models using factor graphs and Gaussian belief propagation (BP). The distributed inference algorithm involves only local computation of the information matrix and of the mean vector, and message passing between neighbors. Under broad conditions, it is show…
Paper analyzes convergence of two time-scale stochastic approximation using martingale approach.
problem Analyzing convergence of two time-scale stochastic approximation algorithms.
method Uses martingale approach to establish convergence conditions and rates.
result Establishes different rates of convergence for fast and slow subsystems.
Smooth Nested Simulation: Bridging Cubic and Square Root Convergence Rates in High Dimensionsstat.ME
New method improves simulation efficiency in high dimensions.
problem Efficiency in estimating functionals of conditional expectations in high dimensions.
method Kernel ridge regression exploiting smoothness of conditional expectation.
result Effective reduction of the curse of dimensionality, bridging convergence rates.
New analysis shows GMD can converge linearly under PL-like conditions.
problem Establishing linear convergence for generalized mirror descent.
method PL-based analysis for time-dependent mirrors, Taylor-series approach for stochastic GMD.
result Linear convergence of stochastic GMD under PL-like conditions.
Study on surfaces pinched by curvature in space forms converging under specific conditions.
problem Investigating convergence of surfaces pinched by curvature in space forms.
method Proving convergence theorems for surfaces pinched by normal curvature in 4-dimensional space forms.
result Generalizes Baker-Nguyen's convergence theorem for surfaces pinched by curvature.
New conditions ensure MMDs separate and converge to target distributions.
problem Ensuring MMDs separate and converge to target distributions.
method Deriving new sufficient and necessary conditions for MMDs on separable metric spaces.
result First KSDs that exactly metrize weak convergence to P.
Paper develops a new local convexity condition for non-isolated minima in non-convex optimization.
problem Lack of theory for non-isolated minima in non-convex optimization.
method Formulates a new local convexity condition and studies SGD convergence under this condition.
result Shows SGD can converge locally under the new condition.
The aim of this paper is to present a further contribution to the analysis of absolute convergence (and), associated with the neoclassical theory, and conditional, associated with endogenous growth theory, of the sectoral productivity at regional level. Presenting some empirical evidence of absolute convergence of prod…
We prove that if the initial hypersurface of the mean curvature flow in spheres satisfies a sharp pinching condition, then the solution of the flow converges to a round point or a totally geodesic sphere. Our result improves the famous convergence theorem due to Huisken [9]. Moreover, we prove a convergence theorem und…
We study convergence rates of variational posterior distributions for nonparametric and high-dimensional inference. We formulate general conditions on prior, likelihood, and variational class that characterize the convergence rates. Under similar "prior mass and testing" conditions considered in the literature, the rat…
Study stability of curvature-dimension condition for negative dimensions.
problem Stability of curvature-dimension condition with negative dimension parameters.
method Introduced CD(K, N)-condition for N < 0, defined distance d_{\mathsf{iKRW}}, proved convergence stability.
result Limit structure of converging metric measure spaces remains CD(K, N) for N < 0.
Improved KL bounds and Wasserstein guarantees for diffusion flow matching under minimal conditions.
problem Theoretical convergence properties of Brownian motion based diffusion flow matching.
method Refined analysis under Kullback-Leibler and 2-Wasserstein distances.
result State-of-the-art scaling in KL convergence bounds under minimal conditions.
The paper examines the neural tangent kernel for PINNs solving general PDEs and finds convergence conditions.
problem Analyzing the convergence of neural tangent kernel for PINNs solving general PDEs.
method Analysis of NTK initialization and convergence during training for general PDEs using PINNs.
result Homogeneity of differential operators is crucial for NTK convergence.
Scalable method completes ill-conditioned matrices from few samples.
problem Matrix completion from few samples for ill-conditioned matrices.
method Iterative algorithm combining IRLS, smoothing Newton, and proximal gradient methods.
result Local quadratic convergence rate and well-conditioned linear systems.
Willmore flow converges globally for surfaces with rotational symmetry below a specific energy threshold.
problem Global existence and convergence of Willmore flow with Dirichlet boundary conditions.
method Considered surfaces with rotational symmetry, proved global existence and convergence for initial data below a sharp energy threshold.
result Sharp threshold for global existence and convergence of Willmore flow depends on boundary conditions.
New approach proves convergence of SA and SGD with weaker conditions.
problem Proving convergence of SA and SGD with relaxed noise conditions.
method Introduces GSLLN to decouple function and noise properties.
result Derives sufficient conditions for convergence of SA and SGD.
Recent studies have shown that proximal gradient (PG) method and accelerated gradient method (APG) with restarting can enjoy a linear convergence under a weaker condition than strong convexity, namely a quadratic growth condition (QGC). However, the faster convergence of restarting APG method relies on the potentially …
Improved convergence for overparameterized low-rank matrix sensing.
problem Overparameterized low-rank matrix sensing with unknown rank and ill-conditioning.
method ScaledGD() - preconditioned gradient descent method.
result ScaledGD() converges at a constant linear rate after a logarithmic number of iterations.
Near-Exponential Convergence Rates for kNN Classification
problem Convergence rates for kNN classification
method Introducing Boltzmann margin
result First near-exponential convergence rates for kNN classification
Paper proposes a pre-conditioning method to speed up gradient descent in multi-agent optimization.
problem Speed up convergence of gradient descent in multi-agent optimization problems.
method Iterative pre-conditioning approach to mitigate the effect of problem conditioning.
result Significant improvement in convergence speed of gradient descent method.
Study uses SGD to learn operators in Hilbert spaces with convergence analysis.
problem Learning operators in general Hilbert spaces with SGD.
method Proposes weak and strong regularity conditions for convergence analysis.
result SGD converges to best linear approximation of nonlinear operators.
Aim of this paper is to discuss convergence of pointed metric measure spaces in absence of any compactness condition. We propose various definitions, show that all of them are equivalent and that for doubling spaces these are also equivalent to the well known measured-Gromov-Hausdorff convergence. Then we show that the…
We analyze the local convergence of proximal splitting algorithms to solve optimization problems that are convex besides a rank constraint. For this, we show conditions under which the proximal operator of a function involving the rank constraint is locally identical to the proximal operator of its convex envelope, hen…
The paper proves conditions for smooth convergence of hyperkaehler 4-manifolds with boundary.
problem Compactness of hyperkaehler 4-manifolds with boundary.
method Analyzes sequences of hyperkaehler triples under topological and curvature conditions.
result Smooth convergence of hyperkaehler triples up to diffeomorphisms if boundary restrictions converge.
Gradient descent with logistic loss can interpolate deep networks with smoothed ReLU activations under certain conditions.
problem Conditions for gradient descent to drive logistic loss to zero in deep networks with smoothed ReLU activations.
method Gradient descent applied to fixed-width deep networks with smoothed ReLU approximations (e.g., Swish, Huberized ReLU).
result Gradient descent can drive logistic loss to zero under specific conditions, providing bounds on convergence rate.
Paper constructs flows converging to cones and foliations.
problem Understanding mean curvature flow convergence to cones and foliations.
method Constructs a family of mean curvature flows converging to cones and foliations under specific conditions.
result Flow converges to area minimizing, strictly stable hypercone and Hardt-Simon foliation of the cone.
Paper shows how solutions to Allen-Cahn converge to multiphase mean curvature flow.
problem Convergence of Allen-Cahn solutions to multiphase mean curvature flow.
method Conditional convergence result of Allen-Cahn solutions to De Giorgi type BV-solutions of multiphase mean curvature flow.
result De Giorgi type BV-solutions are unique in a weak-strong sense.
Consider the problem of learning, from non-experimental data, the causal (Markov equivalence) structure of the true, unknown causal Bayesian network (CBN) on a given, fixed set of (categorical) variables. This learning problem is known to be so hard that there is no learning algorithm that converges to the truth for al…
Convergence of continuous-time stochastic gradient descent with applications to deep neural networkscs.LG
Continuous-time SGD converges under certain conditions, useful for deep learning.
problem Minimizing population expected loss in learning problems.
method Continuous-time approximation of stochastic gradient descent.
result Establishes sufficient conditions for convergence, applicable to overparametrized neural networks.
New algorithm ensures global convergence in deep neural networks beyond NTK regime.
problem Existing global convergence guarantees do not apply to practical deep networks.
method Proposes an algorithm with global convergence guarantees under the expressivity condition.
result Algorithm ensures global convergence in practical settings beyond NTK regime.
Paper shows SVM can achieve super fast convergence rates.
problem Understanding fast convergence rates for SVM.
method Presented a simple mechanism to obtain fast convergence rates for SVM.
result SVM can exhibit exponential convergence rates without hard Tsybakov margin condition.
The paper analyzes the convergence of CART under a SID condition, improving previous results.
problem Investigating the convergence rate of CART under a sufficient impurity decrease condition.
method Established an upper bound on prediction error under SID condition, introduced easily verifiable conditions.
result Improved convergence rate of CART under SID condition, demonstrated examples of error bound limitations.
New insights into convergence of optimization methods for DAG structure learning.
problem Unclear convergence properties of optimization methods for structure learning.
method Examined the convergence of augmented Lagrangian method (ALM) and quadratic penalty method (QPM) for structure learning.
result Standard convergence result of ALM does not hold in various cases, and QPM is prone to ill-conditioning.
In this paper, we consider the convergence of an abstract inexact nonconvex and nonsmooth algorithm. We promise a pseudo sufficient descent condition and a pseudo relative error condition, which are both related to an auxiliary sequence, for the algorithm; and a continuity condition is assumed to hold. In fact, a lot o…
Delay stochastic interest rate model with jump and strong convergence in Monte Carlo simulationsq-fin.RM
Study on interest rate model with jumps, proving strong convergence in simulations.
problem Analytical solutions for complex interest rate models with jumps are difficult.
method Employed truncated Euler-Maruyama techniques to prove strong convergence.
result Justified strong convergence for Monte Carlo calibration and valuation.
The paper examines conditions for Gromov-Hausdorff convergence of metric quotients and provides examples of conic-flat surfaces.
problem Conditions for Gromov-Hausdorff convergence of metric quotients.
method Analyzes sufficient conditions for Gromov-Hausdorff convergence of metric quotients of a metric space.
result Concrete examples of sequences of two-dimensional conic-flat spheres converging to spheres with singularities.
Nonexistence of spacelike foliations and the dominant energy condition in Lorentzian geometrymath.DG
We show that many Lorentzian manifolds of dimension >2 do not admit a spacelike codimension-one foliation, and that almost every manifold of dimension >2 which admits a Lorentzian metric at all admits one which satisfies the dominant energy condition and the timelike convergence condition. These two seemingly unrelated…
FlexCodeTS is a flexible time series density estimator.
problem Estimating conditional densities for time series data.
method Nonparametric conditional density estimator based on arbitrary regression methods.
result FlexCodeTS adapts its convergence rate based on the chosen regression method.
SGD converges to global minimum for structured non-convex functions.
problem Optimizing non-convex functions using SGD with slow convergence rates.
method Convergence theorems for SGD on structured non-convex functions, including Quasar and PL conditions.
result SGD converges to global minimum for specific non-convex functions under certain conditions.