6 papers
Mixing times of Langevin dynamics for spiked matrix models
Reza Gheissari, Curtis Grant, Tianmin Yu
We investigate the Langevin dynamics for Wigner matrices with a spherical spike, in the regime where the signal-to-noise ratio is large, but order one. For large, order-, si…
DiffATS: Diffusion in Aligned Tensor Space
Jinhua Lyu, Tianmin Yu, Brian Kim +3
Direct diffusion modeling of high-resolution spatiotemporal fields is computationally challenging. Parameter-efficient primitives address this by representing high-dimensional data…
Scalable Mean-Field Variational Inference via Preconditioned Primal-Dual Optimization
Jinhua Lyu, Tianmin Yu, Ying Ma +1
In this work, we investigate the large-scale mean-field variational inference (MFVI) problem from a mini-batch primal-dual perspective. By reformulating MFVI as a constrained finit…
An entropy formula for the Deep Linear Network
Govind Menon, Tianmin Yu
We study the Riemannian geometry of the Deep Linear Network (DLN) as a foundation for a thermodynamic description of the learning process. The main tools are the use of group actio…
Siegel Brownian motion
Govind Menon, Tianmin Yu
We construct an analogue of Dyson Brownian motion in the Siegel half-space H that we term Siegel Brownian motion. Given βin (0,\infty], a stochastic flow for Z_t in H is introduced…
Riemannian Langevin Monte Carlo schemes for sampling PSD matrices with fixed rank
Tianmin Yu, Shixin Zheng, Jianfeng Lu +2
This paper introduces two explicit schemes to sample matrices from Gibbs distributions on , the manifold of real positive semi-definite (PSD) matrices of size $…