Geometric framework to predict structure from function in neural networks

Cosmological thinking meets neuroscience in new theory about brain connections

depicts the perpendicular distance from the origin of the yellow semiconstrained plane in panel to its intersection line with theorange plane. If this distance is sufficiently large, then the orange line will not intersect the solution space within the yellow plane's circular bound of radius. , Geometrically determining whether a synapse is nonzero when the target neuron responds to two input patterns but not the third pattern.

In the figure shown, theorange plane intersects the solution space within the bounding sphere, so the synapse is not certain. In this example, apart from, which encode how the synapse vector can be decomposed into its projections along the constrained direction , semiconstrained direction and unconstrained direction .Identifying certain synapses in high-dimensional networks. Cartoon depicting the high-dimensional feedforward network under consideration.

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