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

arXiv: https://arxiv.org/abs/2006.05259 · HTML: https://mlsanity.com/paper/2006.05259/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Jun 2020.

## Built on by (most cited first, 6 of 6)

- [Clifford-Steerable Convolutional Neural Networks](https://mlsanity.com/paper/2402.14730/) (2024)
- [Shifting the Paradigm: A Diffeomorphism Between Time Series Data Manifolds for Achieving Shift-Invariancy in Deep Learning](https://mlsanity.com/paper/2502.19921/) (2025)
- [MS-SSM: A Multi-Scale State Space Model for Efficient Sequence Modeling](https://mlsanity.com/paper/2512.23824/) (2025)
- [Capturing Cardiac Cyclicity through Phase-Equivariant Self-Supervised Learning](https://mlsanity.com/paper/2608.21147/) (2026)
- [Transversal Pooling Neural Networks](https://mlsanity.com/paper/2609.36237/) (2026)
- [LexiCan: Lexicographic Canonicalization of Point Clouds for Machine Learning Applications](https://mlsanity.com/paper/2610.15171/) (2026)

## Abstract (arXiv)

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.