We show it depends on the precise way in which the limit is taken, and in particular on how the quantityofdata,thehiddenlayerwidth,&thelearningratescalesasd .

This beseenasminimizing26], which function [17]. Figure estimated (left) free but inhigh trib perform the Model-fr bors.

We initiate the study of stochastic optimization with oblivious noise, broadly generalizing the standard heavy-tailed noise setup.

In Fig. Ateveryexistingx inside selected, wedra 5

Generative adversarial networks (GANs) typically require ample data for training in order to synthesize high-fidelity images.

A version ofthis bound becomes tight under certain assumptions.

MPNNs have been studied extensively in theory and practice [Böker et al., 2023, Gilmer et al., 2017,