When an auto-associative neural network is trained within any conceptual space, the many rules and schema embodied within that knowledge domain are encoded through its many connection weights and biases. For instance, if such a network's input/output exemplars consist of numerous formulas representing known chemical compounds, subsequent network training will produce connection traces that embody the many implicit rules governing the constraints between constituent elements and their allowed proportionalities. That is to say, the net has gained a statistical `insight' into the patterns of bonding, valence, and charge balance that must be observed in theorizing new chemical compounds. If that network is now made chaotic by random perturbation of its processing elements and connection weights, the resulting network activations will represent the formulas of a wide variety of plausible compounds, many of which may be considered novel from the standpoint of network training. We therefore attain an all-neural search engine for generating a stream of plausible chemical possibilities. Adding subsequent `policing' networks to associate these emerging chemical formulas with various physical and chemical properties, we are able to either filter for sought characteristics or alternatively, assemble expanding materials tabulations of potentially new compounds and their estimated properties. Here, we describe the theory, construction, function, and results of just such an autonomous materials discovery machine, tailored specifically to the search for new ultrahard binary compounds.