We introduce a new type of neural network activation function based on recent physiological rate models for complex cells in visual area V1. A single-hidden-layer neural network of this kind of model achieves 1.5% error on MNIST. We also introduce an existing criterion for learning slow, decorrelated features as a pretraining strategy for image models. This pretraining strategy results in orientation-selective features, similar to the receptive fields of complex cells. With this pretraining, the same single-hidden-layer model achieves better generalization error, even though the pretraining sample distribution is very different from the fine-tuning distribution. To implement this pretraining strategy, we derive a fast algorithm for online learning of decorrelated features such that each iteration of the algorithm runs in linear time with respect to the number of features.