Deep Learning is Singular, and That's Good
This addresses fundamental theoretical issues in deep learning for researchers, but it is incremental as it builds on existing singular learning theory.
The paper tackles the problem that neural networks are singular models, making classical statistical inference methods inappropriate, and presents singular learning theory as a framework for understanding deep learning, suggesting future work for practical application.
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.