SYNTOLOGY HomeExplorerAtlasCodeMethodologyAboutDevelopersFeedPricing
Paper · 2205.10287 · 2022

On the SDEs and Scaling Rules for Adaptive Gradient Algorithms

arXiv · PDF · Open in the Atlas

Code that ran

We have not lifted any functions out of this paper's repositories yet, so there is nothing we have run. If it links a repository, it is listed below.

Repositories linked to this paper

Some links come from the archived Papers with Code dataset (CC BY-SA 4.0): attribution and licence.

Abstract

Approximating Stochastic Gradient Descent (SGD) as a Stochastic Differential Equation (SDE) has allowed researchers to enjoy the benefits of studying a continuous optimization trajectory while carefully preserving the stochasticity of SGD. Analogous study of adaptive gradient methods, such as RMSprop and Adam, has been challenging because there were no rigorously proven SDE approximations for these methods. This paper derives the SDE approximations for RMSprop and Adam, giving theoretical guarantees of their correctness as well as experimental validation of their applicability to common large-scaling vision and language settings. A key practical result is the derivation of a $\textit{square root scaling rule}$ to adjust the optimization hyperparameters of RMSprop and Adam when changing batch size, and its empirical validation in deep learning settings.

For agents

The same record, over MCP at https://syntology.ai/mcp:

get_harvested_code_for_paper("2205.10287")
get_code_for_paper("2205.10287")
have("2205.10287")

Connect an agent — have() is free.