Sequential Function-Space Variational Inference via Gaussian Mixture Approximation

Continual learning is learning from a sequence of tasks with the aim of learning new tasks without forgetting old tasks. Sequential function-space variational inference (SFSVI) is a continual learning method based on variational inference which uses a Gaussian variational distribution to approximate the distribution of the outputs of a finite number of selected inducing points. Since the posterior distribution of a neural network is multi-modal, a Gaussian distribution could only match one mode of the posterior distribution, and a Gaussian mixture distribution could be used to better approximate the posterior distribution. We propose an SFSVI method which uses a Gaussian mixture variational distribution. We also compare different types of variational inference methods with and without a fixed pre-trained feature extractor. We find that in terms of final average accuracy, Gaussian mixture methods perform better than Gaussian methods and likelihood-focused methods perform better than prior-focused methods.

On Sequential Loss Approximation for Continual Learning

We introduce for continual learning Autodiff Quadratic Consolidation (AQC), which approximates the previous loss function with a quadratic function, and Neural Consolidation (NC), which approximates the previous loss function with a neural network. Although they are not scalable to large neural networks, they can be used with a fixed pre-trained feature extractor. We empirically study these methods in class-incremental learning, for which regularization-based methods produce unsatisfactory results, unless combined with replay. We find that for small datasets, quadratic approximation of the previous loss function leads to poor results, even with full Hessian computation, and NC could significantly improve the predictive performance, while for large datasets, when used with a fixed pre-trained feature extractor, AQC provides superior predictive performance. We also find that using tanh-output features can improve the predictive performance of AQC. In particular, in class-incremental Split MNIST, when a Convolutional Neural Network (CNN) with tanh-output features is pre-trained on EMNIST Letters and used as a fixed pre-trained feature extractor, AQC can achieve predictive performance comparable to joint training.