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We study the implicit regularization effects of deep learning in tensorfactorization. While implicit regularization in deep matrix and 'shallow'tensor factorization via linear and certain type of non-linear neural networkspromotes low-rank solutions with at most quadratic growth, we show that itseffect in deep tensor factorization grows polynomially with the depth of thenetwork. This provides a remarkably faithful description of the observedexperimental behaviour. Using numerical experiments, we demonstrate thebenefits of this implicit regularization in yielding a more accurate estimationand better convergence properties.

Implicit Regularization with Polynomial Growth in Deep Tensor Factorization