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Deep rectified neural networks are over-parameterized in the sense that scaling of the weights in one layer, can be compensated for exactly in the subsequent layer. This paper introduces Path-SGD, a simple modification to the SGD update rule, whose update is invariant to such rescaling. The method is derived from the proximal form of gradient descent, whereby a constraint term is added which preserves the norm of the "product weight" formed along each path in the network (from input to output node). Path-SGD is thus principled and shown to yield faster convergence for a standard 2 layer rectifier network, across a variety of dataset (MNIST, CIFAR-10, CIFAR-100, SVHN). As an algorithm, Path-SGD appears effective, simple to implement and addresses an obvious flaw in first-order updates to ReLU networks.