13 papers
Understanding Parallel Samplers in Masked Diffusion via Random Walks on Graphs
Vansh Bansal, Cho Cholyeon, Syamantak Kumar +2
In this paper, we propose using random walks on graphs as a verifiable sandbox to study different parallel sampling strategies in masked diffusion models (MDMs). We train an MDM on…
On the Curse of Dimensionality in Private Sparse Covariance Estimation and PCA
Syamantak Kumar, Shourya Pandey, Purnamrita Sarkar +1
We study high-dimensional differentially private (DP) covariance estimation in the operator norm, and principal component analysis (PCA), under -row-column sparsity (-RCS) of…
Combinatorial Sparse PCA Beyond the Spiked Identity Model
Syamantak Kumar, Purnamrita Sarkar, Kevin Tian +1
Sparse PCA is one of the most well-studied problems in high-dimensional statistics. In this problem, we are given samples from a distribution with covariance , whose top eigenv…
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…
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…
Nonparametric Evaluation of Noisy ICA Solutions
Syamantak Kumar, Purnamrita Sarkar, Peter Bickel +1
Independent Component Analysis (ICA) was introduced in the 1980's as a model for Blind Source Separation (BSS), which refers to the process of recovering the sources underlying a m…