TY - JOUR

T1 - Double Double Descent

T2 - On Generalization Errors in Transfer Learning between Linear Regression Tasks

AU - Dar, Y

AU - Baraniuk, RG

PY - 2022/12/31

Y1 - 2022/12/31

N2 - We study the transfer learning process between two linear regression problems. An important and timely special case is when the regressors are overparameterized and perfectly interpolate their training data. We examine a parameter transfer mechanism whereby a subset of the parameters of the target task solution are constrained to the values learned for a related source task. We analytically characterize the generalization error of the target task in terms of the salient factors in the transfer learning architecture, i.e., the number of examples available, the number of (free) parameters in each of the tasks, the number of parameters transferred from the source to target task, and the relation between the two tasks. Our nonasymptotic analysis shows that the generalization error of the target task follows a two-dimensional double descent trend (with respect to the number of free parameters in each of the tasks) that is controlled by the transfer learning factors. Our analysis points to specific cases where the transfer of parameters is beneficial as a substitute for extra overparameterization (i.e., additional free parameters in the target task). Specifically, we show that the usefulness of a transfer learning setting is fragile and depends on a delicate interplay among the set of transferred parameters, the relation between the tasks, and the true solution. We also demonstrate that overparameterized transfer learning is not necessarily more beneficial when the source task is closer or identical to the target task.

AB - We study the transfer learning process between two linear regression problems. An important and timely special case is when the regressors are overparameterized and perfectly interpolate their training data. We examine a parameter transfer mechanism whereby a subset of the parameters of the target task solution are constrained to the values learned for a related source task. We analytically characterize the generalization error of the target task in terms of the salient factors in the transfer learning architecture, i.e., the number of examples available, the number of (free) parameters in each of the tasks, the number of parameters transferred from the source to target task, and the relation between the two tasks. Our nonasymptotic analysis shows that the generalization error of the target task follows a two-dimensional double descent trend (with respect to the number of free parameters in each of the tasks) that is controlled by the transfer learning factors. Our analysis points to specific cases where the transfer of parameters is beneficial as a substitute for extra overparameterization (i.e., additional free parameters in the target task). Specifically, we show that the usefulness of a transfer learning setting is fragile and depends on a delicate interplay among the set of transferred parameters, the relation between the tasks, and the true solution. We also demonstrate that overparameterized transfer learning is not necessarily more beneficial when the source task is closer or identical to the target task.

KW - Double descent

KW - Linear regression

KW - Overparameterized learning

KW - Transfer learning

UR - https://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=bgu-pure&SrcAuth=WosAPI&KeyUT=WOS:000978251900010&DestLinkType=FullRecord&DestApp=WOS

U2 - 10.1137/22M1469559

DO - 10.1137/22M1469559

M3 - Article

SN - 2577-0187

SP - 1447

EP - 1472

JO - SIAM Journal on Mathematics of Data Science

JF - SIAM Journal on Mathematics of Data Science

ER -