A Second-Order Perspective on Model Compositionality and Incremental Learning#

We examine how fine-tuning deep pre-trained models yields compositional modules in non-linear networks, using a second-order Taylor approximation of the loss. Our findings show that staying within the pre-training basin is key for preserving composability. Building on this, we propose two incremental training strategies: ITA, where each task is handled by an individually trained module; and IEL, a complementary approach that jointly optimizes the composed model. Both methods foster an accurate multi-task model with flexible editing capabilities, enabling specialization or unlearning for specific tasks.