  Deep neural networks suffer from the catastrophic forgetting problem in the
field of continual learning (CL). To address this challenge, we propose
MGSER-SAM, a novel memory replay-based algorithm specifically engineered to
enhance the generalization capabilities of CL models. We first intergrate the
SAM optimizer, a component designed for optimizing flatness, which seamlessly
fits into well-known Experience Replay frameworks such as ER and DER++. Then,
MGSER-SAM distinctively addresses the complex challenge of reconciling
conflicts in weight perturbation directions between ongoing tasks and
previously stored memories, which is underexplored in the SAM optimizer. This
is effectively accomplished by the strategic integration of soft logits and the
alignment of memory gradient directions, where the regularization terms
facilitate the concurrent minimization of various training loss terms integral
to the CL process. Through rigorous experimental analysis conducted across
multiple benchmarks, MGSER-SAM has demonstrated a consistent ability to
outperform existing baselines in all three CL scenarios. Comparing to the
representative memory replay-based baselines ER and DER++, MGSER-SAM not only
improves the testing accuracy by $24.4\%$ and $17.6\%$ respectively, but also
achieves the lowest forgetting on each benchmark.
