Wavelet Networks: Scale-Translation Equivariant Learning From Raw Time-Series

TL;DR

This paper introduces Wavelet Networks, a novel class of scale-translation equivariant neural networks for time-series data, inspired by wavelet transforms, improving performance on various raw time-series tasks.

Contribution

The paper constructs scale-translation equivariant neural networks for time-series, inspired by wavelet transforms, filling a gap in symmetry-based neural network research.

Findings

Wavelet Networks outperform CNNs on raw waveforms.

They match spectrogram-based methods across multiple tasks.

The approach is effective for diverse time-series data.

Abstract

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.