Biological neural networks face homeostatic and resource constraints that restrict the allowed configurations of connection weights. If a constraint is tight it defines a very small solution space, and the size of these constraint spaces determines their potential overlap with the solutions for computational tasks. We study the geometry of the solution spaces for constraints on neurons' total synaptic weight and on individual synaptic weights, characterizing the connection degrees (numbers of partners) that maximize the size of these solution spaces. We then hypothesize that the size of constraints' solution spaces could serve as a cost function governing neural circuit development. We develop analytical approximations and bounds for the model evidence of the maximum entropy degree distributions under these cost functions. We test these on a published electron microscopic connectome of an associative learning center in the fly brain, finding evidence for a developmental progression in circuit structure.
We examine the hypothesis that the entropy of solution spaces for constraints on synaptic weights (the "flexibility" of the constraint) could serve as a cost function for neural circuit development.