Axiomatic information retrieval (IR) seeks a set of principle properties desirable in IR models. These properties when formally expressed provide guidance in the search for better relevance estimation functions. Neural ranking models typically contain a large number of parameters. The training of these models involve a search for appropriate parameter values based on large quantities of labeled examples. Intuitively, axioms that can guide the search for better traditional IR models should also help in better parameter estimation for machine learning based rankers. This work explores the use of IR axioms to augment the direct supervision from labeled data for training neural ranking models. We modify the documents in our dataset along the lines of well-known axioms during training and add a regularization loss based on the agreement between the ranking model and the axioms on which version of the document—the original or the perturbed—should be preferred. Our experiments show that the neural ranking model achieves faster convergence and better generalization with axiomatic regularization.