  We introduce a framework for Continual Learning (CL) based on Bayesian
inference over the function space rather than the parameters of a deep neural
network. This method, referred to as functional regularisation for Continual
Learning, avoids forgetting a previous task by constructing and memorising an
approximate posterior belief over the underlying task-specific function. To
achieve this we rely on a Gaussian process obtained by treating the weights of
the last layer of a neural network as random and Gaussian distributed. Then,
the training algorithm sequentially encounters tasks and constructs posterior
beliefs over the task-specific functions by using inducing point sparse
Gaussian process methods. At each step a new task is first learnt and then a
summary is constructed consisting of (i) inducing inputs -- a fixed-size subset
of the task inputs selected such that it optimally represents the task -- and
(ii) a posterior distribution over the function values at these inputs. This
summary then regularises learning of future tasks, through Kullback-Leibler
regularisation terms. Our method thus unites approaches focused on
(pseudo-)rehearsal with those derived from a sequential Bayesian inference
perspective in a principled way, leading to strong results on accepted
benchmarks.
