7 papers · 1 filter
Spectral Deflation for Factorization-Free Matrix Filtering in Muon and Semidefinite Programming
Haoran Sun, Shucheng Kang, Heng Yang
GPU implementations of the Muon optimizer and of first-order semidefinite programming (SDP) solvers share one computational pattern: a matrix factorization is replaced by a fixed-d…
Afterimage Slow Regions in First-Order Methods for Linear Conic Programming
Shucheng Kang, Heng Yang
First-order methods for linear conic programming often stall on long plateaus. Existing analyses characterize when during a run or on which problem instances slow convergence occur…
Trajectory Optimization via Schrödinger Bridge Sampling
Mattia Mosso, Yang Liu, Heng Yang
We take a new look at the relation between finite-horizon trajectory optimization and Schrödinger bridge sampling. Viewed as inference, KL-regularized trajectory optimization is so…
Hard-Constrained Sampling on Embedded Riemannian Manifolds via Adjoint Schrödinger Bridges
Mattia Mosso, Jaemoo Choi, Heng Yang
A variety of tasks require sampling from unnormalized Boltzmann distributions supported on manifolds. Building upon the foundations of adjoint matching and adjoint Schrödinger brid…
Adam at the Edge of Stability: Adaptive Feedback, Provable Oscillation, and Gradient Reversal
Yiman Fong, Heng Yang
The edge-of-stability (EoS) phenomenon of full-batch Adam has been widely observed, yet its underlying dynamical mechanism remains poorly understood. In this paper, we identify Ada…
Simplicial Regularizability of the Pseudo-Moment Cone and Carathéodory-Type Atomic Decomposition of Moment Matrices
Shucheng Kang, Heng Yang
We study the facial geometry of the homogeneous pseudo-moment cone \(Σ_{n,2d}^*\) and its implications for atomic decomposition of moment matrices. For fixed \(d \ge 2\), we show t…
Local Second-Order Limit Dynamics of the Alternating Direction Method of Multipliers for Semidefinite Programming
Shucheng Kang, Heng Yang
The alternating direction method of multipliers (ADMM) is widely used for solving large-scale semidefinite programs (SDPs), yet on instances with multiple primal-dual optimal solut…