On Random Kernels of Residual Architectures

Etai Littwin, Tomer Galanti, Lior Wolf

פרסום מחקרי: פרסום בכתב עתמאמר מכנסביקורת עמיתים

תקציר

We analyze the finite corrections to the neural tangent kernel (NTK) of residual and densely connected networks, as a function of both depth and width. Surprisingly, our analysis reveals that given a fixed depth, residual networks provide the best tradeoff between the parameter complexity and the coefficient of variation (normalized variance), followed by densely connected networks and vanilla MLPs. While in networks that do not use skip connections, convergence to the NTK requires one to fix the depth, while increasing the layers’ width. Our findings show that in ResNets, convergence to the NTK may occur when depth and width simultaneously tend to infinity, provided with a proper initialization. In DenseNets, however, the convergence of the NTK to its limit as the width tends to infinity is guaranteed, at a rate that is independent of both the depth and scale of the weights. Our experiments validate the theoretical results and demonstrate the advantage of deep ResNets and DenseNets for kernel regression with random gradient features.

שפה מקוריתאנגלית
עמודים (מ-עד)897-907
מספר עמודים11
כתב עתProceedings of Machine Learning Research
כרך161
סטטוס פרסוםפורסם - 2021
אירוע37th Conference on Uncertainty in Artificial Intelligence, UAI 2021 - Virtual, Online
משך הזמן: 27 יולי 202130 יולי 2021

ASJC Scopus subject areas

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