Wavelet Networks: Scale-Translation Equivariant Learning From Raw Time-Series
This addresses a gap in equivariant neural networks for time-series data, offering improved data efficiency and generalization for domains such as audio processing and signal analysis.
The authors tackled the problem of learning from raw time-series data by constructing scale-translation equivariant neural networks, termed Wavelet Networks, which outperform conventional CNNs on raw waveforms and match engineered spectrogram techniques across tasks like audio and electrical signals.
Leveraging the symmetries inherent to specific data domains for the construction of equivariant neural networks has lead to remarkable improvements in terms of data efficiency and generalization. However, most existing research focuses on symmetries arising from planar and volumetric data, leaving a crucial data source largely underexplored: time-series. In this work, we fill this gap by leveraging the symmetries inherent to time-series for the construction of equivariant neural network. We identify two core symmetries: *scale and translation*, and construct scale-translation equivariant neural networks for time-series learning. Intriguingly, we find that scale-translation equivariant mappings share strong resemblance with the wavelet transform. Inspired by this resemblance, we term our networks Wavelet Networks, and show that they perform nested non-linear wavelet-like time-frequency transforms. Empirical results show that Wavelet Networks outperform conventional CNNs on raw waveforms, and match strongly engineered spectrogram techniques across several tasks and time-series types, including audio, environmental sounds, and electrical signals. Our code is publicly available at https://github.com/dwromero/wavelet_networks.