Figure 1.

Computations in two dimensions with non-orthogonal features. Each dot represents a high dimensional stimulus that has been projected onto this relevant subspace with axes s₁ and s₂ recovered by STC method. The red dots are stimuli for which y = 1 and the blue circles are those for which y = 0. Both logical OR (A) and logical AND operations (B) with two non-orthogonal features v₁ and v₂ are defined by two thresholds (dashed lines) which lie perpendicular to the feature directions. In the case of logical OR, any stimulus above either threshold causes a spike (corrupted by Gaussian noise), whereas for a logical AND function stimuli must be above all thresholds to elicit spikes. In both panels the parts of the thresholds that determine spiking behavior are shown in black and the irrelevant parts in gray. Note that logical OR nonlinearity leads to the “crescent-shape” distribution of spike-eliciting inputs that are common in sensory systems (Fairhall et al., 2006).