  In singular models, the optimal set of parameters forms an analytic set with
singularities and classical statistical inference cannot be applied to such
models. This is significant for deep learning as neural networks are singular
and thus "dividing" by the determinant of the Hessian or employing the Laplace
approximation are not appropriate. Despite its potential for addressing
fundamental issues in deep learning, singular learning theory appears to have
made little inroads into the developing canon of deep learning theory. Via a
mix of theory and experiment, we present an invitation to singular learning
theory as a vehicle for understanding deep learning and suggest important
future work to make singular learning theory directly applicable to how deep
learning is performed in practice.
