Topological Continual Learning with Wasserstein Distance and Barycenter

TL;DR

This paper introduces a topological regularization method based on Wasserstein distance and barycenter to promote modularity in neural networks, thereby reducing catastrophic forgetting in continual learning.

Contribution

It proposes a novel topological regularization using persistent homology and optimal transport, combined with episodic memory, to improve continual learning performance.

Findings

Effective in shallow and deep networks

Reduces catastrophic forgetting

Improves performance on image classification datasets

Abstract

Continual learning in neural networks suffers from a phenomenon called catastrophic forgetting, in which a network quickly forgets what was learned in a previous task. The human brain, however, is able to continually learn new tasks and accumulate knowledge throughout life. Neuroscience findings suggest that continual learning success in the human brain is potentially associated with its modular structure and memory consolidation mechanisms. In this paper we propose a novel topological regularization that penalizes cycle structure in a neural network during training using principled theory from persistent homology and optimal transport. The penalty encourages the network to learn modular structure during training. The penalization is based on the closed-form expressions of the Wasserstein distance and barycenter for the topological features of a 1-skeleton representation for the network. Our topological continual learning method combines the proposed regularization with a tiny episodic memory to mitigate forgetting. We demonstrate that our method is effective in both shallow and deep network architectures for multiple image classification datasets.