On Sequential Maximum a Posteriori Inference for Continual Learning

TL;DR

This paper introduces two novel methods for continual learning based on sequential MAP inference, demonstrating their effectiveness on classical and image classification tasks with fixed feature extractors.

Contribution

It formulates continual learning as recursive loss function approximation and proposes two coreset-free methods, one quadratic and one neural, for this purpose.

Findings

Neural consolidation performs well on small input dimension tasks.

Autodiff quadratic consolidation is effective on image tasks with fixed features.

Both methods achieve performance comparable to joint MAP training.

Abstract

We formulate sequential maximum a posteriori inference as a recursion of loss functions and reduce the problem of continual learning to approximating the previous loss function. We then propose two coreset-free methods: autodiff quadratic consolidation, which uses an accurate and full quadratic approximation, and neural consolidation, which uses a neural network approximation. These methods are not scalable with respect to the neural network size, and we study them for classification tasks in combination with a fixed pre-trained feature extractor. We also introduce simple but challenging classical task sequences based on Iris and Wine datasets. We find that neural consolidation performs well in the classical task sequences, where the input dimension is small, while autodiff quadratic consolidation performs consistently well in image task sequences with a fixed pre-trained feature extractor, achieving comparable performance to joint maximum a posteriori training in many cases.