Evaluation of Koopman Operator Neural Decoding Scheme

Neural activity correlates with a wide variety of phenomena relating to the animal originating the activity. It is possible to exploit those correlations by measuring the activity and mathematically transforming it via a so-called decoding process to determine what, physically, the activity represented. The signals measured are typically nonlinear, and though classical statistical techniques exist for handling these signals, increasingly influential methods including neural networks and the Koopman operator formalism provide new avenues to explore for handling such nonlinear problems. We propose a method of decoding utilizing a neural network representation of the Koopman operator and test it on the task of decoding a rat’s physical position from the activity of place cells in its hippocampus. We find that although it is not yet competitive with existing methods, the technique has merit and can be improved