  The human ability to track musical downbeats is robust to changes in tempo,
and it extends to tempi never previously encountered. We propose a
deterministic time-warping operation that enables this skill in a convolutional
neural network (CNN) by allowing the network to learn rhythmic patterns
independently of tempo. Unlike conventional deep learning approaches, which
learn rhythmic patterns at the tempi present in the training dataset, the
patterns learned in our model are tempo-invariant, leading to better tempo
generalisation and more efficient usage of the network capacity. We test the
generalisation property on a synthetic dataset created by rendering the Groove
MIDI Dataset using FluidSynth, split into a training set containing the
original performances and a test set containing tempo-scaled versions rendered
with different SoundFonts (test-time augmentation). The proposed model
generalises nearly perfectly to unseen tempi (F-measure of 0.89 on both
training and test sets), whereas a comparable conventional CNN achieves similar
accuracy only for the training set (0.89) and drops to 0.54 on the test set.
The generalisation advantage of the proposed model extends to real music, as
shown by results on the GTZAN and Ballroom datasets.
