Passive Dendrites Enable Single Neurons to Compute Linearly Non-separable Functions
Figure 3
Two strategies to implement a linearly non-separable function.
On top, the name of two possible strategies to implement the feature binding problem (FBP) based either on its DNF or CNF expression: the colored part of these expressions is the term or the clauses implemented by the dendritic sub-unit. Below, three schematics which represent parameter sets implementing FBP using either a spiking (green) or a saturating (blue) dendritic sub-unit. In circles are the value of synaptic weights (Black∶linear, green∶spiking, blue∶saturating); in colored squares (green∶spiking; blue∶saturating) are the parameters of the dendritic activation function [threshold;height], in black squares is the threshold of the somatic sub-unit. Left, the local implementation strategy; Right, the global implementation strategy; note that a neuron cannot implement the FBP using the local strategy with a saturating dendritic sub-unit. Bottom, truth tables where the
column is the input vectors,
columns describe the neuron's input-output function, here the FBP. The int. column is the result of synaptic integration of each dendritic sub-unit (black∶linear, green∶spiking, blue∶saturating). In bold and italic are the maximum possible outputs for each sub-unit, note that for the global strategy a maximal output from a dendritic sub-unit may not trigger a somatic spike.