Theoretical Insights into Overparameterized Models in Multi-Task and Replay-Based Continual Learning

Multi-task learning (MTL) is a machine learning paradigm that aims to improve the generalization performance of a model on multiple related tasks by training it simultaneously on those tasks. Unlike MTL, where the model has instant access to the training data of all tasks, continual learning (CL) involves adapting to new sequentially arriving tasks over time without forgetting the previously acquired knowledge. Despite the wide practical adoption of CL and MTL and extensive literature on both areas, there remains a gap in the theoretical understanding of these methods when used with overparameterized models such as deep neural networks. This paper studies the overparameterized linear models as a proxy for more complex models. We develop theoretical results describing the effect of various system parameters on the model's performance in an MTL setup. Specifically, we study the impact of model size, dataset size, and task similarity on the generalization error and knowledge transfer. Additionally, we present theoretical results to characterize the performance of replay-based CL models. Our results reveal the impact of buffer size and model capacity on the forgetting rate in a CL setup and help shed light on some of the state-of-the-art CL methods. Finally, through extensive empirical evaluations, we demonstrate that our theoretical findings are also applicable to deep neural networks, offering valuable guidance for designing MTL and CL models in practice.

A Distinct Unsupervised Reference Model From The Environment Helps Continual Learning

The existing continual learning methods are mainly focused on fully-supervised scenarios and are still not able to take advantage of unlabeled data available in the environment. Some recent works tried to investigate semi-supervised continual learning (SSCL) settings in which the unlabeled data are available, but it is only from the same distribution as the labeled data. This assumption is still not general enough for real-world applications and restricts the utilization of unsupervised data. In this work, we introduce Open-Set Semi-Supervised Continual Learning (OSSCL), a more realistic semi-supervised continual learning setting in which out-of-distribution (OoD) unlabeled samples in the environment are assumed to coexist with the in-distribution ones. Under this configuration, we present a model with two distinct parts: (i) the reference network captures general-purpose and task-agnostic knowledge in the environment by using a broad spectrum of unlabeled samples, (ii) the learner network is designed to learn task-specific representations by exploiting supervised samples. The reference model both provides a pivotal representation space and also segregates unlabeled data to exploit them more efficiently. By performing a diverse range of experiments, we show the superior performance of our model compared with other competitors and prove the effectiveness of each component of the proposed model.