In this work, we present a local intrinsic rule that we developed, dubbed IP, inspired by the Infomax rule. Like Infomax, this rule works by controlling the gain and bias of a neuron to regulate its rate of fire. We discuss the biological plausibility of the IP rule and compare it to batch normalisation. We demonstrate that the IP rule improves learning in deep networks, and provides networks with considerable robustness to increases in synaptic learning rates. We also sample the error gradients during learning and show that the IP rule substantially increases the size of the gradients over the course of learning. This suggests that the IP rule solves the vanishing gradient problem. Supplementary analysis is provided to derive the equilibrium solutions that the neuronal gain and bias converge to using our IP rule. An analysis demonstrates that the IP rule results in neuronal information potential similar to that of Infomax, when tested on a fixed input distribution. We also show that batch normalisation also improves information potential, suggesting that this may be a cause for the efficacy of batch normalisation—an open problem at the time of this writing.