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From Geometry to Generalization: Why Row Normalization Can Beat Adam and Muon
Jihwan Kim, Dogyoon Song, Chulhee Yun
Different optimizers can fit the same training data while selecting classifiers with substantially different geometries, but whether this difference provably affects population per…
Implicit Bias and Loss of Plasticity in Matrix Completion: Depth Promotes Low-Rankness
Baekrok Shin, Chulhee Yun
We study matrix completion via deep matrix factorization (a.k.a. deep linear neural networks) as a simplified testbed to examine how network depth influences training dynamics. Des…
Scaling Laws of SignSGD in Linear Regression: When Does It Outperform SGD?
Jihwan Kim, Dogyoon Song, Chulhee Yun
We study scaling laws of signSGD under a power-law random features (PLRF) model that accounts for both feature and target decay. We analyze the population risk of a linear model tr…
Minor First, Major Last: A Depth-Induced Implicit Bias of Sharpness-Aware Minimization
Chaewon Moon, Dongkuk Si, Chulhee Yun
We study the implicit bias of Sharpness-Aware Minimization (SAM) when training -layer linear diagonal networks on linearly separable binary classification. For linear models ($L…
Uniform Spectral Growth and Convergence of Muon in LoRA-Style Matrix Factorization
Changmin Kang, Jihun Yun, Baekrok Shin +2
Spectral gradient descent (SpecGD) orthogonalizes the matrix parameter updates and has inspired practical optimizers such as Muon. They often perform well in large language model (…