Abstract
The interactions of large groups of spiking neurons have been difficult to understand or visualise. Using simple geometric pictures, we here illustrate the spike-by-spike dynamics of networks based on efficient spike coding, and we highlight the conditions under which they can preserve their function against various perturbations. We show that their dynamics are confined to a small geometric object, a ‘convex polytope’, in an abstract error space. Changes in network parameters (such as number of neurons, dimensionality of the inputs, firing thresholds, synaptic weights, or transmission delays) can all be understood as deformations of this polytope. Using these insights, we show that the core functionality of these network models, just like their biological counterparts, is preserved as long as perturbations do not destroy the shape of the geometric object. We suggest that this single principle—efficient spike coding—may be key to understanding the robustness of neural systems at the circuit level.
Competing Interest Statement
The authors have declared no competing interest.