ICLR 2025 Papers

Continual learning (CL) has garnered significant attention because of its ability to adapt to new tasks that arrive over time. Catastrophic forgetting (of old tasks) has been identified as a major issue in CL, as the model adapts to new tasks. The Mixture-of-Experts (MoE) model has recently been shown to effectively mitigate catastrophic forgetting in CL, by employing a gating network to sparsify and distribute diverse tasks among multiple experts. However, there is a lack of theoretical analysis of MoE and its impact on the learning performance in CL. This paper provides the first theoretical results to characterize the impact of MoE in CL via the lens of overparameterized linear regression tasks. We establish the benefit of MoE over a single expert by proving that the MoE model can diversify its experts to specialize in different tasks, while its router learns to select the right expert for each task and balance the loads across all experts. Our study further suggests an intriguing fact that the MoE in CL needs to terminate the update of the gating network after sufficient training rounds to attain system convergence, which is not needed in the existing MoE studies that do not consider the continual task arrival. Furthermore, we provide explicit expressions for the expected forgetting and overall generalization error to characterize the benefit of MoE in the learning performance in CL. Interestingly, adding more experts requires additional rounds before convergence, which may not enhance the learning performance. Finally, we conduct experiments on both synthetic and real datasets to extend these insights from linear models to deep neural networks (DNNs), which also shed light on the practical algorithm design for MoE in CL.

Humans can naturally learn new and varying tasks in a sequential manner. Continual learning is a class of learning algorithms that updates its learned model as it sees new data (on potentially new tasks) in a sequence. A key challenge in continual learning is that as the model is updated to learn new tasks, it becomes susceptible to \textit{catastrophic forgetting}, where knowledge of previously learned tasks is lost. A popular approach to mitigate forgetting during continual learning is to maintain a small buffer of previously-seen samples, and to replay them during training. However, this approach is limited by the small buffer size and, while forgetting is reduced, it is still present. In this paper, we propose a novel loss function STAR that exploits the worst-case parameter perturbation that reduces the KL-divergence of model predictions with that of its local parameter neighborhood to promote stability and alleviate forgetting. STAR can be combined with almost any existing rehearsal-based methods as a plug-and-play component. We empirically show that STAR consistently improves performance of existing methods by up to $\sim15\\%$ across varying baselines, and achieves superior or competitive accuracy to that of state-of-the-art methods aimed at improving rehearsal-based continual learning. Our implementation is available at https://github.com/Gnomy17/STAR_CL.