From their inception in the 1950s, artificial neural networks (ANNs) started using the so-called point neuron model then prevalent in neuroscience, hoping that this analogy would allow for a better emulation of brain function. Over the years the neuroscience literature has shown that the point neuron model is too simplistic to properly represent many fundamental neural processes; however, the standard neuron model in ANNs still remains the same. Here we substitute it by a very recent model of cortical cells and demonstrate through theoretical analyses and experimental results how, simply by using a more realistic neural unit element without augmenting the number of parameters, the resulting ANNs offer a number of important advantages that include increases in expressivity, robustness and learning speed, and a reduction in memorization and the amount of training data needed.