A Mathematical Theory of Semantic Development in Deep Neural Networks
By | Andrew M. Saxe, Postdoctoral Research Associate, Department of Experimental PsychologyUniversity of Oxford
| Senior Common Room,  Level 2 (2D17), Priory Road Complex
Date | Thursday 9 May 2019
Time | 13:00

An extensive body of empirical research has revealed remarkable regularities in the acquisition, organization, deployment, and neural representation of human semantic knowledge, thereby raising a fundamental conceptual question: what are the theoretical principles governing the ability of neural networks to acquire, organize, and deploy abstract knowledge by integrating across many individual experiences? I will describe work addressing this question by mathematically analyzing the nonlinear dynamics of learning in deep linear networks. We find exact solutions to this learning dynamics that yield a conceptual explanation for the prevalence of many disparate phenomena in semantic cognition, including the hierarchical differentiation of concepts through rapid developmental transitions, the ubiquity of semantic illusions between such transitions, the emergence of item typicality and category coherence as factors controlling the speed of semantic processing, changing patterns of inductive projection over development, and the conservation of semantic similarity in neural representations across species. Furthermore, I will show that many of these phenomena only arise in deep but not shallow networks. Thus, surprisingly, this simple neural model qualitatively recapitulates many diverse regularities underlying semantic development, while providing analytic insight into how the statistical structure of an environment can interact with nonlinear deep learning dynamics to give rise to these regularities. Finally, if time permits, I will turn to a critical analysis of an intriguing recent theory of deep learning dynamics, the information bottleneck theory of deep learning.

All Welcome | Tea, coffee and cakes will be available after the seminar.