Task Confusion and Catastrophic Forgetting in Class-Incremental Learning: A Mathematical Framework for Discriminative and Generative Modelings

In class-incremental learning (class-IL), models must classify all previously seen classes at test time without task-IDs, leading to task confusion. Despite being a key challenge, task confusion lacks a theoretical understanding. We present a novel mathematical framework for class-IL and prove the Infeasibility Theorem, showing optimal class-IL is impossible with discriminative modeling due to task confusion. However, we establish the Feasibility Theorem, demonstrating that generative modeling can achieve optimal class-IL by overcoming task confusion. We then assess popular class-IL strategies, including regularization, bias-correction, replay, and generative classifier, using our framework. Our analysis suggests that adopting generative modeling, either for generative replay or direct classification (generative classifier), is essential for optimal class-IL.

Fast Federated Learning by Balancing Communication Trade-Offs

Federated Learning (FL) has recently received a lot of attention for large-scale privacy-preserving machine learning. However, high communication overheads due to frequent gradient transmissions decelerate FL. To mitigate the communication overheads, two main techniques have been studied: (i) local update of weights characterizing the trade-off between communication and computation and (ii) gradient compression characterizing the trade-off between communication and precision. To the best of our knowledge, studying and balancing those two trade-offs jointly and dynamically while considering their impacts on convergence has remained unresolved even though it promises significantly faster FL. In this paper, we first formulate our problem to minimize learning error with respect to two variables: local update coefficients and sparsity budgets of gradient compression who characterize trade-offs between communication and computation/precision, respectively. We then derive an upper bound of the learning error in a given wall-clock time considering the interdependency between the two variables. Based on this theoretical analysis, we propose an enhanced FL scheme, namely Fast FL (FFL), that jointly and dynamically adjusts the two variables to minimize the learning error. We demonstrate that FFL consistently achieves higher accuracies faster than similar schemes existing in the literature.