  This paper defines geometric criteria which are then used to establish
sufficient conditions for persistency of excitation with vector functions
constructed from single hidden-layer neural networks with step or ReLU
activation functions. We show that these conditions hold when employing
reference system tracking, as is commonly done in adaptive control. We
demonstrate the results numerically on a system with linearly parameterized
activations of this type and show that the parameter estimates converge to the
true values with the sufficient conditions met.
