Optimizing Mode Connectivity for Class Incremental Learning

Class incremental learning (CIL) is one of the most challenging scenarios in continual learning. Existing work mainly focuses on strategies like memory replay, regularization, or dynamic architecture but ignores a crucial aspect: mode connectivity. Recent studies have shown that different minima can be connected by a low-loss valley, and ensembling over the valley shows improved performance and robustness. Motivated by this, we try to investigate the connectivity in CIL and find that the high-loss ridge exists along the linear connection between two adjacent continual minima. To dodge the ridge, we propose parameter-saving OPtimizing Connectivity (OPC) based on Fourier series and gradient projection for finding the low-loss path between minima. The optimized path provides infinite low-loss solutions. We further propose EOPC to ensemble points within a local bent cylinder to improve performance on learned tasks. Our scheme can serve as a plug-in unit, extensive experiments on CIFAR-100, ImageNet-100, and ImageNet-1K show consistent improvements when adapting EOPC to existing representative CIL methods. Our code is available at https://github.com/HaitaoWen/EOPC.