Preserving knowledge during learning

Thesis

Humans and non-human animals live and learn in a continuous stream of information, and rarely experience catastrophic interference between currently and previously acquired knowledge. In contrast, artificial neural networks suffer from catastrophic forgetting and typically remain static once trained. In this work, we provide an analytical study of continual learning and its effects on neural representations in deep linear networks. We present a mathematical analysis of the solution manifold, illustrating how different areas result in different neural representations and computational properties; and obtain an exact expression for the continual learning dynamics under gradient descent. Based on these analyses, we derive exact continual learning rules for categorical and relational knowledge, and demonstrate how common replay- and regularisation-based algorithms either require exploding memory and computational capacity or fail to learn representations that capture the structure of experiences. Our theory predicts that any successful continual learning rule requires representational drift of previously acquired knowledge, and it makes testable predictions about the geometry and temporal evolution of drifting neural representations. Empirically, we confirm this prediction by studying relational learning in humans through functional magnetic resonance imaging, showing that a single experience can cause systematic reorganisation of representations to preserve previously acquired knowledge. Taken together, our results provide a mathematical framework for studying neural representations during continual learning in both biological and artificial neural networks.

Authors: Braun, L

• DOI: 10.5287/ora-ng2nb1nre
• Type of award: DPhil
• Level of award: Doctoral
• Awarding institution: University of Oxford
• Language: English
• Keywords: deep learning; representational drift; deep linear networks; continual learning; exact learning dynamics