In this talk, I’ll present an overview of the Laplace approximation for quantifying uncertainty in Bayesian neural networks. I’ll then introduce our work, name Sparse Function-space Representation (SFR), which can be viewed as a function-space Laplace approximation for BNNs. I’ll demonstrate the proposed approach for quantifying uncertainty in supervised learning, maintaining an expressive functional representation for continual learning, and guiding exploration in model-based reinforcement learning.