Plenary II: The Local Geometry of Deep Learning

We study the geometry of deep learning through the lens of approximation theory via splines. The enabling insight is that a large class of deep networks can be written as a composition of continuous piecewise affine (CPA) spline operators, which provides a powerful portal through which to interpret and analyze their inner workings. Our particular focus is the local geometry of the spline partition of the network’s input space, which opens up new avenues to study how deep networks organize signals in a hierarchical, multiscale fashion. Applications include the analysis of the deep network optimization landscape, explaining batch normalization, and debiasing pre-trained generative networks.