5 papers
Streaming PCA: averaging from a geometric perspective
Tuan Pham, Alessandro Rinaldo, Purnamrita Sarkar
We study principal component analysis (PCA) under memory constraints, a setting that is increasingly important in large-scale data analysis. Our focus is on Oja's algorithm, which…
Low-Dimensional Adaptation of Rectified Flow: A Diffusion and Stochastic Localization Perspective
Saptarshi Roy, Alessandro Rinaldo, Purnamrita Sarkar
In recent years, Rectified flow (RF) has gained considerable popularity largely due to its generation efficiency and state-of-the-art performance. In this paper, we investigate the…
A note on time-uniform concentration inequality for matrix products
Tuan Pham, Alessandro Rinaldo
This short note contains a simple argument that allows us to go from fixed-time to any-time bounds for the concentration of matrix products. The result presented here is motivated…
Time-uniform concentration bounds for iterative algorithms
Tuan Pham, Alessandro Rinaldo, Purnamrita Sarkar
We develop a new framework for deriving time-uniform concentration bounds for the output of stochastic sequential algorithms satisfying certain recursive inequalities akin to those…
On the Convergence and Straightness of Rectified Flow
Vansh Bansal, Saptarshi Roy, Alessandro Rinaldo +1
Flow Matching has become a cornerstone of modern generative models like Stable Diffusion 3, largely due to the efficiency of its Rectified Flow (RF) variant. The success of RF hing…