  In this paper we explore the possibility of maximizing the information
represented in spectrograms by making the spectrogram basis functions
trainable. We experiment with two different tasks, namely keyword spotting
(KWS) and automatic speech recognition (ASR). For most neural network models,
the architecture and hyperparameters are typically fine-tuned and optimized in
experiments. Input features, however, are often treated as fixed. In the case
of audio, signals can be mainly expressed in two main ways: raw waveforms
(time-domain) or spectrograms (time-frequency-domain). In addition, different
spectrogram types are often used and tailored to fit different applications. In
our experiments, we allow for this tailoring directly as part of the network.
  Our experimental results show that using trainable basis functions can boost
the accuracy of Keyword Spotting (KWS) by 14.2 percentage points, and lower the
Phone Error Rate (PER) by 9.5 percentage points. Although models using
trainable basis functions become less effective as the model complexity
increases, the trained filter shapes could still provide us with insights on
which frequency bins are important for that specific task. From our
experiments, we can conclude that trainable basis functions are a useful tool
to boost the performance when the model complexity is limited.
