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

How neurons integrate the myriad synaptic inputs scattered across their dendrites is a fundamental question in neuroscience. Multiple neurophysiological experiments have shown that dendritic non-linearities can have a strong influence on synaptic input integration. These non-linearities have motivated mathematical descriptions of single neuron 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 non-linearities. Here, we introduce a two-layer model with sign-constrained synaptic weights and a biologically plausible form of dendritic non-linearity, and investigate its properties using both statistical physics methods and numerical simulations. We find that the dendritic non-linearity 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 non-linearity 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 a large fraction of zero-weight ('silent' or 'potential') synapses naturally emerge in neurons with sign-constrained synapses, as a consequence of non-linear dendritic integration. Non-linearly induced sparsity comes with a second central advantage for neuronal information processing, i.e. input and synaptic noise robustness. We test our model on standard real-world benchmark datasets and observe empirically that the non-linearity provides an enhancement in generalization performance, showing that it enables to capture more complex input/output relations.

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