7 papers
Acceleration and its Limits in Gaussian Variational Inference
Jaesung R. Park, Uijeong Jang, Yifan Chen
We study whether the classical momentum-based acceleration that improves the condition-number dependence of gradient descent from to for strongly convex, smooth object…
Higher-Order Derivatives Do Not Accelerate the Computation of Fixed Points
Uijeong Jang, Ernest K. Ryu
The Picard iteration converges to the unique fixed point of a -contractive operator at a linear rate , and a lower bound with an affine construction shows that no determini…
Optimal Acceleration for Proximal Minimization of the Sum of Convex and Strongly Convex Functions
Govind M. Chari, Uijeong Jang, Ernest K. Ryu +1
When minimizing the sum of a convex and a strongly convex function, or when finding the zero of the sum of a monotone operator and a strongly monotone operator, Chambolle and Pock…
ALiA: Adaptive Linearized ADMM
Uijeong Jang, Kaizhao Sun, Wotao Yin +1
We propose ALiA, a novel adaptive variant of the alternating direction method of multipliers (ADMM). Specifically, ALiA is a variant of function-linearized proximal ADMM (FLiP ADMM…
Point Convergence of Nesterov's Accelerated Gradient Method: An AI-Assisted Proof
Uijeong Jang, Ernest K. Ryu
The Nesterov accelerated gradient method, introduced in 1983, has been a cornerstone of optimization theory and practice. Yet the question of its point convergence had remained ope…
Sharpness-Aware Minimization Can Hallucinate Minimizers
Chanwoong Park, Uijeong Jang, Ernest K. Ryu +1
Sharpness-Aware Minimization (SAM) is widely used to seek flatter minima -- often linked to better generalization. In its standard implementation, SAM updates the current iterate u…
LoRA Training in the NTK Regime has No Spurious Local Minima
Uijeong Jang, Jason D. Lee, Ernest K. Ryu
Low-rank adaptation (LoRA) has become the standard approach for parameter-efficient fine-tuning of large language models (LLM), but our theoretical understanding of LoRA has been l…