Before revision:  Despite these promising theoretical results, empirical evaluation of vanilla DMF on real benchmarks exhibits poor reconstructions which we attribute to the extremely low number of samples available. We propose an explicit spectral regularization scheme that is able to make DMF models competitive on real benchmarks, while still maintaining the implicit regularization induced by gradient descent, thus enjoying the best of both worlds .
After revision:  In this work we interpret the DMF model through the lens of spectral geometry. This allows us to incorporate explicit regularization without breaking the DMF structure, thus enjoying the best of both worlds. In particular, we focus on matrix completion problems with underlying geometric or topological relations between the rows and/or columns. Such relations are prevalent in matrix completion problems that arise in many applications, such as recommender systems and drug-target interaction. Our contributions enable DMF models to exploit these relations, and make them competitive on real benchmarks, while still maintaining the implicit regularization induced by gradient descent, thus enjoying the best of both worlds .