  In this short note, we reify the connection between work on the storage
capacity problem in wide two-layer treelike neural networks and the
rapidly-growing body of literature on kernel limits of wide neural networks.
Concretely, we observe that the "effective order parameter" studied in the
statistical mechanics literature is exactly equivalent to the infinite-width
Neural Network Gaussian Process Kernel. This correspondence connects the
expressivity and trainability of wide two-layer neural networks.
