相关论文: Accelerated Schr\"odinger-F\"ollmer samplers

Score-based generative modeling with probability flow ordinary differential equations (ODEs) has achieved remarkable success in a variety of applications. While various fast ODE-based samplers have been proposed in the literature and…

In this work, we propose a method for speeding up linear regression distributively, while ensuring security. We leverage randomized sketching techniques, and improve straggler resilience in asynchronous systems. Specifically, we apply a…

We propose a simple and efficient clustering method for high-dimensional data with a large number of clusters. Our algorithm achieves high-performance by evaluating distances of datapoints with a subset of the cluster centres. Our…

In this paper a new Runge-Kutta type scheme is introduced for nonlinear stochastic partial differential equations (SPDEs) with multiplicative trace class noise. The proposed scheme converges with respect to the computational effort with a…

The $O(N)$ stochastic propagation method, which relies on the numerical solution of the time-dependent Schr\"odinger equation using random initial states, is widely used in large-scale first-principles calculations. In this work, we…

We study the approximation of a square-integrable function from a finite number of evaluations on a random set of nodes according to a well-chosen distribution. This is particularly relevant when the function is assumed to belong to a…

We establish an averaging principle for a structural multiscale stochastic nonlinear fractional Schr\"odinger system on the one-dimensional torus driven by a multiplicative Wiener noise. The slow component is governed by a fractional…

We propose an enhanced zeroth-order stochastic Frank-Wolfe framework to address constrained finite-sum optimization problems, a structure prevalent in large-scale machine-learning applications. Our method introduces a novel double variance…

We consider the problem of minimizing the sum of two convex functions. One of those functions has Lipschitz-continuous gradients, and can be accessed via stochastic oracles, whereas the other is "simple". We provide a Bregman-type algorithm…

The sampling of probability distributions specified up to a normalization constant is an important problem in both machine learning and statistical mechanics. While classical stochastic sampling methods such as Markov Chain Monte Carlo…

Score-based diffusion models have emerged as powerful tools in generative modeling, yet their theoretical foundations remain underexplored. In this work, we focus on the Wasserstein convergence analysis of score-based diffusion models.…

Deep generative models based on neural differential equations have quickly become the state-of-the-art for numerous generation tasks across many different applications. These models rely on ODE/SDE solvers which integrate from a prior…

Stochastic Gradient Descent (SGD) is an important algorithm in machine learning. With constant learning rates, it is a stochastic process that, after an initial phase of convergence, generates samples from a stationary distribution. We show…

We theoretically analyzed the convergence behavior of Riemannian stochastic gradient descent (RSGD) and found that using an increasing batch size leads to faster convergence than using a constant batch size, not only with a constant…

Diffusion models suffer from slow sample generation at inference time. Despite recent efforts, improving the sampling efficiency of stochastic samplers for diffusion models remains a promising direction. We propose Splitting Integrators for…

Time-of-flight (ToF) devices have greatly propelled the advancement of various multi-modal perception applications. However, achieving accurate rendering of time-resolved information remains a challenge, particularly in scenes involving…

We give algorithms for sampling several structured logconcave families to high accuracy. We further develop a reduction framework, inspired by proximal point methods in convex optimization, which bootstraps samplers for regularized…

In this paper, we derive a strong convergence rate of spatial finite difference approximations for both focusing and defocusing stochastic cubic Schr\"odinger equations driven by a multiplicative $Q$-Wiener process. Beyond the uniform…

We consider the Sherrington-Kirkpatrick model of spin glasses at high-temperature and no external field, and study the problem of sampling from the Gibbs distribution $\mu$ in polynomial time. We prove that, for any inverse temperature…

Random Feature Models (RFMs) have become a powerful tool for approximating multivariate functions and solving partial differential equations efficiently. Sparse Random Feature Expansions (SRFE) improve traditional RFMs by incorporating…