Efficiency of local learning rules in threshold-linear associative networks

We derive the Gardner storage capacity for associative networks of threshold linear units, and show that with Hebbian learning they can operate closer to such Gardner bound than binary networks, and even surpass it. This is largely achieved through a sparsification of the retrieved patterns, which we analyze for theoretical and empirical distributions of activity. As reaching the optimal capacity via non-local learning rules like backpropagation requires slow and neurally implausible training procedures, our results indicate that one-shot self-organized Hebbian learning can be just as efficient.