Abstract
The lack of interpretability is a much-criticised feature of deep
neural networks. Often, a neural network is effectively a black box.
We have recently found a group-theoretical procedure that brings
inner layer signalling into a human-readable form. We applied it to a
signal processing network used in magnetic resonance
spectroscopy, and found that the network spontaneously invents a
significant chunk of undergraduate calculus: a bandpass filter, a
notch filter, a frequency axis rescaling transformation, frequency
division multiplexing, group embedding, spectral filtering
regularisation, and a map from harmonic functions into Chebyshev
polynomials – all in ten minutes of unattended training from a
random initial guess.