相关论文: Weak Convergence Of Tamed Exponential Integrators …

Recent work across many machine learning disciplines has highlighted that standard descent methods, even without explicit regularization, do not merely minimize the training error, but also exhibit an implicit bias. This bias is typically…

We propose and analyse a boundary-preserving numerical scheme for the weak approximation for some stochastic partial differential equations (SPDEs) with bounded state-space. We impose regularity assumptions on the drift and diffusion…

This paper presents a comprehensive analysis of a broad range of variations of the stochastic proximal point method (SPPM). Proximal point methods have attracted considerable interest owing to their numerical stability and robustness…

Stochastic gradient-based descent (SGD), have long been central to training large language models (LLMs). However, their effectiveness is increasingly being questioned, particularly in large-scale applications where empirical evidence…

We study multiplicative SDEs perturbed by an additive fractional Brownian motion on another probability space. Provided the Hurst parameter is chosen in a specified regime, we establish existence of probabilistically weak solutions to the…

In this paper, we apply the tamed technique to the Milstein numerical scheme to investigate Neutral Stochastic Delay Differential Equations(NSDDEs) with highly nonlinear coefficients. Under the local Lipschitz condition and Khasminskii…

The gradient discretisation method (GDM) -- a generic framework encompassing many numerical methods -- is studied for a general stochastic Stefan problem with multiplicative noise. The convergence of the numerical solutions is proved by…

PGD adversarial training, the standard robustness method, can reduce Jacobian Frobenius norm yet worsen clean-input geometry (e.g., TDI 1.336 vs. ERM 1.093). We show this is not an implementation artifact but a theorem-level consequence of…

Although generative diffusion models (GDMs) are widely used in practice, their theoretical foundations remain limited, especially concerning the impact of different discretization schemes applied to the underlying stochastic differential…

In this paper, we design and analyze a new family of adaptive subgradient methods for solving an important class of weakly convex (possibly nonsmooth) stochastic optimization problems. Adaptive methods that use exponential moving averages…

An estimation problem of fundamental interest is that of phase synchronization, in which the goal is to recover a collection of phases using noisy measurements of relative phases. It is known that in the Gaussian noise setting, the maximum…

In recent years, an intensive study of strong approximation of stochastic differential equations (SDEs) with a drift coefficient that may have discontinuities in space has begun. In many of these results it is assumed that the drift…

Black-box variational inference (BBVI) with Gaussian mixture families offers a flexible approach for approximating complex posterior distributions without requiring gradients of the target density. However, standard numerical optimization…

We study the convergence of accelerated stochastic gradient descent for strongly convex objectives under the growth condition, which states that the variance of stochastic gradient is bounded by a multiplicative part that grows with the…

Probabilistic ordinary differential equation (ODE) solvers have been introduced over the past decade as uncertainty-aware numerical integrators. They typically proceed by assuming a functional prior to the ODE solution, which is then…

Gradient normalization and soft clipping are two popular techniques for tackling instability issues and improving convergence of stochastic gradient descent (SGD) with momentum. In this article, we study these types of methods through the…

Regression with a spherical response is challenging due to the absence of linear structure, making standard regression models inadequate. Existing methods, mainly parametric, lack the flexibility to capture the complex relationship induced…

Prior work on computable defect-based local error estimators for (linear) time-reversible integrators is extended to nonlinear and nonautonomous evolution equations. We prove that the asymptotic results from the linear case [W. Auzinger and…

In the present work, strong approximation errors are analyzed for both the spatial semi-discretization and the spatio-temporal fully discretization of stochastic wave equations (SWEs) with cubic polynomial nonlinearities and additive…

In the last few years, various communication compression techniques have emerged as an indispensable tool helping to alleviate the communication bottleneck in distributed learning. However, despite the fact biased compressors often show…