Computer Sciences Commons^™

Improved Generalisation Bounds For Deep Learning Through L∞ Covering Numbers, Antoine Ledent, Yunwen Lei, Marius Kloft

Research Collection School Of Computing and Information Systems

Using proof techniques involving L∞ covering numbers, we show generalisation error bounds for deep learning with two main improvements over the state of the art. First, our bounds have no explicit dependence on the number of classes except for logarithmic factors. This holds even when formulating the bounds in terms of the L 2 norm of the weight matrices, while previous bounds exhibit at least a square-root dependence on the number of classes in this case. Second, we adapt the Rademacher analysis of DNNs to incorporate weight sharing—a task of fundamental theoretical importance which was previously attempted only under very …