相关论文: Global Convergence of ESPRIT with Preconditioned F…

Randomly initialized first-order optimization algorithms are the method of choice for solving many high-dimensional nonconvex problems in machine learning, yet general theoretical guarantees cannot rule out convergence to critical points of…

The stable principal component pursuit (SPCP) problem is a non-smooth convex optimization problem, the solution of which has been shown both in theory and in practice to enable one to recover the low rank and sparse components of a matrix…

Sign-based algorithms (e.g. signSGD) have been proposed as a biased gradient compression technique to alleviate the communication bottleneck in training large neural networks across multiple workers. We show simple convex counter-examples…

We present a novel, practical, and provable approach for solving diagonally constrained semi-definite programming (SDP) problems at scale using accelerated non-convex programming. Our algorithm non-trivially combines acceleration motions…

Reconstructing a sequence of sharp images from the blurry input is crucial for enhancing our insights into the captured scene and poses a significant challenge due to the limited temporal features embedded in the image. Spike cameras,…

We consider a wide range of regularized stochastic minimization problems with two regularization terms, one of which is composed with a linear function. This optimization model abstracts a number of important applications in artificial…

Adaptive Gradient Descent with Energy (AEGD) is a variant of gradient descent (GD) designed to mitigate step-size sensitivity through an energy-based formulation. AEGD is notable for its unconditional energy stability, which guarantees…

Discrete diffusion models excel at visual synthesis but rely on slow, iterative decoding. Existing single-step distillation methods attempt to bypass this bottleneck, either by training auxiliary score networks that effectively double…

Detecting the source model of AI-generated images is a growing accountability problem. AI fingerprinting techniques address this by detecting imperceptible patterns in the images that are unique to each model, achieving high detection…

Deep learning models are dominating almost all artificial intelligence tasks such as vision, text, and speech processing. Stochastic Gradient Descent (SGD) is the main tool for training such models, where the computations are usually…

The quality of microscopy images often suffers from optical aberrations. These aberrations and their associated point spread functions have to be quantitatively estimated to restore aberrated images. The recent state-of-the-art method…

Recovering high-dimensional statistical structure from limited measurements is a fundamental challenge in hyperspectral imaging, where capturing full-resolution data is often infeasible due to sensor, bandwidth, or acquisition constraints.…

This paper proposes {\sf AEPG-SPIDER}, an Adaptive Extrapolated Proximal Gradient (AEPG) method with variance reduction for minimizing composite nonconvex finite-sum functions. It integrates three acceleration techniques: adaptive…

3D Gaussian Splatting (3DGS) demonstrates unparalleled superior performance in 3D scene reconstruction. However, 3DGS heavily relies on the sharp images. Fulfilling this requirement can be challenging in real-world scenarios especially when…

We consider the problem of principal component analysis (PCA) in a streaming stochastic setting, where our goal is to find a direction of approximate maximal variance, based on a stream of i.i.d. data points in $\reals^d$. A simple and…

Decoding extracellular recordings is a crucial task in electrophysiology and brain-computer interfaces. Spike sorting, which distinguishes spikes and their putative neurons from extracellular recordings, becomes computationally demanding…

We present a unified convergence theory for gradient-based training of neural network methods for partial differential equations (PDEs), covering both physics-informed neural networks (PINNs) and the Deep Ritz method. For linear PDEs, we…

Blind super-resolution can be cast as a low rank matrix recovery problem by exploiting the inherent simplicity of the signal and the low dimensional structure of point spread functions. In this paper, we develop a simple yet efficient…

Stochastic Gradient Descent (SGD) is a known stochastic iterative method popular for large-scale convex optimization problems due to its simple implementation and scalability. Some objectives, such as those found in complex-valued neural…

Fine-grained object retrieval aims to learn discriminative representation to retrieve visually similar objects. However, existing top-performing works usually impose pairwise similarities on the semantic embedding spaces or design a…