Publisher Correction: A neural machine code and programming framework for the reservoir computer

From logical reasoning to mental simulation, biological and artificial neural systems possess an incredible capacity for computation. Such neural computers offer a fundamentally novel computing paradigm by representing data continuously and processing information in a natively parallel and distributed manner. To harness this computation, prior work has developed extensive training techniques to understand existing neural networks. However, the lack of a concrete and low-level machine code for neural networks precludes us from taking full advantage of a neural computing framework. Here we provide such a machine code along with a programming framework by using a recurrent neural network—a reservoir computer—to decompile, code and compile analogue computations. By decompiling the reservoir’s internal representation and dynamics into an analytic basis of its inputs, we define a low-level neural machine code that we use to program the reservoir to solve complex equations and store chaotic dynamical systems as random-access memory. We further provide a fully distributed neural implementation of software virtualization and logical circuits, and even program a playable game of pong inside of a reservoir computer. Importantly, all of these functions are programmed without requiring any example data or sampling of state space. Finally, we demonstrate that we can accurately decompile the analytic, internal representations of a full-rank reservoir computer that has been conventionally trained using data. Taken together, we define an implementation of neural computation that can both decompile computations from existing neural connectivity and compile distributed programs as new connections.