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.

翻译：利用特定数据领域固有的对称性构建等变神经网络，已在数据效率和泛化能力方面取得了显著提升。然而，现有研究主要关注平面和体数据中的对称性，而时间序列这一关键数据源在很大程度上尚未被充分探索。在本工作中，我们通过利用时间序列固有的对称性来构建等变神经网络，填补了这一空白。我们识别出两个核心对称性：**尺度和平移**，并构建了用于时间序列学习的尺度-平移等变神经网络。有趣的是，我们发现尺度-平移等变映射与小波变换具有高度相似性。受此启发，我们将所提出的网络命名为小波网络，并证明它们能够执行嵌套式非线性小波类时频变换。实验结果表明，小波网络在原始波形数据上优于传统卷积神经网络，并在多个任务和时间序列类型（包括音频、环境声音和电信号）中与高度工程化的谱图技术性能相当。我们的代码已开源，见 https://github.com/dwromero/wavelet_networks。