9 papers
Vanilla SGD with Momentum Survives Heavy-Tailed Noise: Convergence Analysis without Gradient Clipping or Normalization
Ryusei Yamada, Naoki Sato, Hideaki Iiduka
Stochastic gradient descent (SGD) is a cornerstone of modern optimization. While its performance under heavy-tailed noise is often addressed through specialized modifications such…
Muon Converges under Heavy-Tailed Noise: Nonconvex Hölder-Smooth Empirical Risk Minimization
Hideaki Iiduka
Muon is a recently proposed optimizer that enforces orthogonality in parameter updates by projecting gradients onto the Stiefel manifold, leading to stable and efficient training i…
Lipschitz Multiscale Deep Equilibrium Models: A Theoretically Guaranteed and Accelerated Approach
Naoki Sato, Hideaki Iiduka
Deep equilibrium models (DEQs) achieve infinitely deep network representations without stacking layers by exploring fixed points of layer transformations in neural networks. Such m…
Improved Convergence Rates of Muon Optimizer for Nonconvex Optimization
Shuntaro Nagashima, Hideaki Iiduka
The Muon optimizer has recently attracted attention due to its orthogonalized first-order updates, and a deeper theoretical understanding of its convergence behavior is essential f…
Convergence Analysis of SGD under Expected Smoothness
Yuta Kawamoto, Hideaki Iiduka
Stochastic gradient descent (SGD) is the workhorse of large-scale learning, yet classical analyses rely on assumptions that can be either too strong (bounded variance) or too coars…
Convergence Bound and Critical Batch Size of Muon Optimizer
Naoki Sato, Hiroki Naganuma, Hideaki Iiduka
Muon, a recently proposed optimizer that leverages the inherent matrix structure of neural network parameters, has demonstrated strong empirical performance, indicating its potenti…
Explicit and Implicit Graduated Optimization in Deep Neural Networks
Naoki Sato, Hideaki Iiduka
Graduated optimization is a global optimization technique that is used to minimize a multimodal nonconvex function by smoothing the objective function with noise and gradually refi…
Scaled Conjugate Gradient Method for Nonconvex Optimization in Deep Neural Networks
Naoki Sato, Koshiro Izumi, Hideaki Iiduka
A scaled conjugate gradient method that accelerates existing adaptive methods utilizing stochastic gradients is proposed for solving nonconvex optimization problems with deep neura…
Momentum Does Not Reduce Stochastic Noise in Stochastic Gradient Descent
Naoki Sato, Hideaki Iiduka
For nonconvex objective functions, including those found in training deep neural networks, stochastic gradient descent (SGD) with momentum is said to converge faster and have bette…