Metric Space Magnitude and Generalisation in Neural Networks

Understand

Deep learning models have seen significant successes in numerous applications, but their inner workings remain elusive.

• The purpose of this work is to quantify the learning process of deep neural networks through the lens of a novel topological invariant called magnitude.
• Magnitude is an isometry invariant; its properties are an active area of research as it encodes many known invariants of a metric space.
• We use magnitude to study the internal representations of neural networks and propose a new method for determining their generalisation capabilities.