I just skimmed over the paper (don't really have time to sit and read it down right now), but it seems it's about like this: 1. They captured the ECoG of peopl

I just skimmed over the paper (don't really have time to sit and read it down right now), but it seems it's about like this: 1. They captured the ECoG of people hearing stories (for training). They also captured ECoG of people saying numbers 0 to 9. 2. They trained the vocoder with those parameters as an autoencoder that goes from 516 parameters down to 256 and back again to 516. The 516 parameters are spectral envelope, pitch, voicing and aperiodicity. 3. They trained the models to receive as input the HG and LF signals (from the ECoG I think -- don't really know wht these names mean, just what the figures on the paper show). The (expected) output for the models was either the audio spectrogram or the vocoders 256 encoding. So I'd go with "opaque ML approach" to answer your last question. As for the mathematical operations involved (in general), I dind't read the detailed explanation (if there is one) of how the networks are working, but probably ReLU activations and summation over parameters, like most DNNs.