Functional Regularisation for Continual Learning with Gaussian Processes

We introduce a framework for continual learning 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. function given by the dot product of the neural network feature vector. 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 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, so that catastrophic forgetting of earlier tasks is avoided. We demonstrate %the effectiveness of our algorithm in classification datasets, such as Split-MNIST, Permuted-MNIST and Omniglot.

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