We address the issue of learning multi-layered perceptrons (MLPs) in a discriminative, inductive, multiclass, parametric, and semi-supervised fashion. We introduce a novel objective function that, when optimized, simultaneously encourages 1) accuracy on the labeled points, 2) respect for an underlying graph-represented manifold on all points, 3) smoothness via an entropic regularizer of the classifier outputs, and 4) simplicity via an l2 regularizer. Our approach provides a simple, elegant, and computationally efficient way to bring the benefits of semi-supervised learning (and what is typically an enormous amount of unlabeled training data) to MLPs, which are one of the most widely used pattern classifiers in practice. Our objective has the property that efficient learning is possible using stochastic gradient descent even on large datasets. Results demonstrate significant improvements compared both to a baseline supervised MLP, and also to a previous non-parametric manifold-regularized reproducing kernel Hilbert space classifier.