Paper analyzes SGD dynamics in high-dimensional linear networks

By PulseAugur Editorial · [2 sources] · 2026-05-16 22:26

A new paper details the high-dimensional behavior of stochastic gradient descent (SGD) on diagonal linear networks. The research shows that in high dimensions, SGD dynamics can be accurately modeled by a stochastic differential equation. This allows for the derivation of a deterministic partial differential equation that tracks key statistics like risk and curvature, ultimately demonstrating exponential convergence to zero risk. AI

IMPACT Provides theoretical insights into the optimization of neural network components, potentially informing future model training strategies.

RANK_REASON Academic paper published on arXiv detailing theoretical analysis of optimization methods in machine learning.

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Newsworthiness bucket: Research; Academic paper published on arXiv detailing theoretical analysis of optimization methods in machine learning.
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arXiv stat.ML TIER_1 English(EN) · Bego\~na Garc\'ia Malaxechebarr\'ia, Courtney Paquette, Maryam Fazel, Dmitriy Drusvyatskiy · 2026-05-19 04:00

High-dimensional Limit of SGD for Diagonal Linear Networks

arXiv:2605.17177v1 Announce Type: cross Abstract: Understanding the behavior of stochastic gradient methods is a central problem in modern machine learning. Recent work has highlighted diagonal linear networks as a simplified yet expressive setting for analyzing the optimization …
arXiv stat.ML TIER_1 English(EN) · Dmitriy Drusvyatskiy · 2026-05-16 22:26

High-dimensional Limit of SGD for Diagonal Linear Networks

Understanding the behavior of stochastic gradient methods is a central problem in modern machine learning. Recent work has highlighted diagonal linear networks as a simplified yet expressive setting for analyzing the optimization and generalization properties of neural models. In…