A Control Theoretic Approach to Transfer Learning

Abstract: A neural network has memorized a training set if, when fed on any sample from that set, it yields the desired output. Adopting a control theoretic language, we say that the system steers each point of a learning set to its corresponding target with a common control. Transfer learning and fine tuning deal with the issue of adapting a control to memorize additional data points. We introduce here the concept of tuning without forgetting. We develop an iterative algorithm to tune the control or system parameters when the training set expands, whereby points already memorized remain so, and new training samples are additional memorized. We discuss the geometric structure underlying our approach and provide simulation results.