Impact of dendritic non-linearities on the computational capabilities of neurons

These nonlinearities have motivated mathematical descriptions of single neurons as a two-layer computational units, which have been shown to increase substantially the computational abilities of neurons, compared to linear dendritic integration. However, current analytical studies are restricted to neurons with unconstrained synaptic weights and unplausible dendritic nonlinearities. Here we introduce a two-layer model with sign-constrained synaptic weights and a biologically plausible form of dendritic nonlinearity and investigate its properties using both statistical physics methods and numerical simulations. We find that the dendritic nonlinearity enhances both the number of possible learned input-output associations and the learning velocity. We characterize how capacity and learning speed depend on the implemented nonlinearity and the levels of dendritic and somatic inhibition. We calculate analytically the distribution of synaptic weights in networks close to maximal capacity and find that the dendritic nonlinearity increases the fraction of zero-weight (“silent” or “potential”) synapses, compared with the standard perceptron model, when no or weak robustness constraints are present, while the opposite occurs with strong robustness constraints. We test our model on standard real-world benchmark datasets and observe empirically that the nonlinearity provides an enhancement in generalization performance and that it enables to capture more complex input-output relations, compared to the perceptron model.