Feedback connections play a prominent role in the human brain but have not received much attention in artificial neural network research. Here, a biologically inspired feedback mechanism which gates rectified linear units is proposed. On the MNIST dataset, autoencoders with feedback show faster convergence, better performance, and more robustness to noise compared to their counterparts without feedback. Some benefits, although less pronounced and less consistent, can be observed when networks with feedback are applied on the CIFAR-10 dataset.