  Waveform-based deep learning faces a dilemma between nonparametric and
parametric approaches. On one hand, convolutional neural networks (convnets)
may approximate any linear time-invariant system; yet, in practice, their
frequency responses become more irregular as their receptive fields grow. On
the other hand, a parametric model such as LEAF is guaranteed to yield Gabor
filters, hence an optimal time-frequency localization; yet, this strong
inductive bias comes at the detriment of representational capacity. In this
paper, we aim to overcome this dilemma by introducing a neural audio model,
named multiresolution neural network (MuReNN). The key idea behind MuReNN is to
train separate convolutional operators over the octave subbands of a discrete
wavelet transform (DWT). Since the scale of DWT atoms grows exponentially
between octaves, the receptive fields of the subsequent learnable convolutions
in MuReNN are dilated accordingly. For a given real-world dataset, we fit the
magnitude response of MuReNN to that of a well-established auditory filterbank:
Gammatone for speech, CQT for music, and third-octave for urban sounds,
respectively. This is a form of knowledge distillation (KD), in which the
filterbank ''teacher'' is engineered by domain knowledge while the neural
network ''student'' is optimized from data. We compare MuReNN to the state of
the art in terms of goodness of fit after KD on a hold-out set and in terms of
Heisenberg time-frequency localization. Compared to convnets and Gabor
convolutions, we find that MuReNN reaches state-of-the-art performance on all
three optimization problems.
