Control Theoretic Approach to Fine-Tuning and Transfer Learning

Abstract

Given a training set in the form of a paired (X,Y), we say that the control system x = f(x,u) has learned the paired set via the control u^* if the system steers each point of X to its corresponding target in Y. If the training set is expanded, most existing methods for finding a new control u^* require starting from scratch, resulting in a quadratic increase in complexity with the number of points. To overcome this limitation, we introduce the concept of tuning without forgetting. We develop an iterative algorithm to tune the control u^* when the training set expands, whereby points already in the paired set are still matched, and new training samples are learned. At each update of our method, the control u^* is projected onto the kernel of the end-point mapping generated by the controlled dynamics at the learned samples. It ensures keeping the end-points for the previously learned samples constant while iteratively learning additional samples.

Tasks

Reproductions