Spiking and saturating dendrites differentially expand single neuron computation capacity

Part of Advances in Neural Information Processing Systems 25 (NIPS 2012)

Bibtex Metadata Paper


Romain Cazé, Mark Humphries, Boris Gutkin


The integration of excitatory inputs in dendrites is non-linear: multiple excitatory inputs can produce a local depolarization departing from the arithmetic sum of each input's response taken separately. If this depolarization is bigger than the arithmetic sum, the dendrite is spiking; if the depolarization is smaller, the dendrite is saturating. Decomposing a dendritic tree into independent dendritic spiking units greatly extends its computational capacity, as the neuron then maps onto a two layer neural network, enabling it to compute linearly non-separable Boolean functions (lnBFs). How can these lnBFs be implemented by dendritic architectures in practise? And can saturating dendrites equally expand computational capacity? To adress these questions we use a binary neuron model and Boolean algebra. First, we confirm that spiking dendrites enable a neuron to compute lnBFs using an architecture based on the disjunctive normal form (DNF). Second, we prove that saturating dendrites as well as spiking dendrites also enable a neuron to compute lnBFs using an architecture based on the conjunctive normal form (CNF). Contrary to the DNF-based architecture, a CNF-based architecture leads to a dendritic unit tuning that does not imply the neuron tuning, as has been observed experimentally. Third, we show that one cannot use a DNF-based architecture with saturating dendrites. Consequently, we show that an important family of lnBFs implemented with a CNF-architecture can require an exponential number of saturating dendritic units, whereas the same family implemented with either a DNF-architecture or a CNF-architecture always require a linear number of spiking dendritic unit. This minimization could explain why a neuron spends energetic resources to make its dendrites spike.