Low-Rank Filtering and Smoothing for Sequential Deep Learning

Learning multiple tasks sequentially requires neural networks to balance retaining knowledge, yet being flexible enough to adapt to new tasks. Regularizing network parameters is a common approach, but it rarely incorporates prior knowledge about task relationships, and limits information flow to future tasks only. We propose a Bayesian framework that treats the network's parameters as the state space of a nonlinear Gaussian model, unlocking two key capabilities: (1) A principled way to encode domain knowledge about task relationships, allowing, e.g., control over which layers should adapt between tasks. (2) A novel application of Bayesian smoothing, allowing task-specific models to also incorporate knowledge from models learned later. This does not require direct access to their data, which is crucial, e.g., for privacy-critical applications. These capabilities rely on efficient filtering and smoothing operations, for which we propose diagonal plus low-rank approximations of the precision matrix in the Laplace approximation (LR-LGF). Empirical results demonstrate the efficiency of LR-LGF and the benefits of the unlocked capabilities.