Minming Chen

Zhouchen Lin, Minming Chen, Yi Ma

This paper proposes scalable and fast algorithms for solving the Robust PCA problem, namely recovering a low-rank matrix with an unknown fraction of its entries being arbitrarily corrupted. This problem arises in many applications, such as image processing, web data ranking, and bioinformatic data analysis. It was recently shown that under surprisingly broad conditions, the Robust PCA problem can be exactly solved via convex optimization that minimizes a combination of the nuclear norm and the $\ell^1$-norm . In this paper, we apply the method of augmented Lagrange multipliers (ALM) to solve this convex program. As the objective function is non-smooth, we show how to extend the classical analysis of ALM to such new objective functions and prove the optimality of the proposed algorithms and characterize their convergence rate. Empirically, the proposed new algorithms can be more than five times faster than the previous state-of-the-art algorithms for Robust PCA, such as the accelerated proximal gradient (APG) algorithm. Moreover, the new algorithms achieve higher precision, yet being less storage/memory demanding. We also show that the ALM technique can be used to solve the (related but somewhat simpler) matrix completion problem and obtain rather promising results too. We further prove the necessary and sufficient condition for the inexact ALM to converge globally. Matlab code of all algorithms discussed are available at http://perception.csl.illinois.edu/matrix-rank/home.html

Yuning Gong, Yifei Liu, Yifan Zhan et al.

Neural rendering, particularly 3D Gaussian Splatting (3DGS), has evolved rapidly and become a key component for building world models. However, existing viewer solutions remain fragmented, heavy, or constrained by legacy pipelines, resulting in high deployment friction and limited support for dynamic content and generative models. In this work, we present Visionary, an open, web-native platform for real-time various Gaussian Splatting and meshes rendering. Built on an efficient WebGPU renderer with per-frame ONNX inference, Visionary enables dynamic neural processing while maintaining a lightweight, "click-to-run" browser experience. It introduces a standardized Gaussian Generator contract, which not only supports standard 3DGS rendering but also allows plug-and-play algorithms to generate or update Gaussians each frame. Such inference also enables us to apply feedforward generative post-processing. The platform further offers a plug in three.js library with a concise TypeScript API for seamless integration into existing web applications. Experiments show that, under identical 3DGS assets, Visionary achieves superior rendering efficiency compared to current Web viewers due to GPU-based primitive sorting. It already supports multiple variants, including MLP-based 3DGS, 4DGS, neural avatars, and style transformation or enhancement networks. By unifying inference and rendering directly in the browser, Visionary significantly lowers the barrier to reproduction, comparison, and deployment of 3DGS-family methods, serving as a unified World Model Carrier for both reconstructive and generative paradigms.