# Neuralized Multi-Wavelet Decomposition for Time Series Classification and Forecasting

arXiv: https://arxiv.org/abs/2609.29317 · HTML: https://mlsanity.com/paper/2609.29317/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 28 of its 60 references that are in the map.
- First posted on arXiv 24 Sep 2026.

## Builds on (most cited first, 28 of 28)

- [Informer: Beyond Efficient Transformer for Long Sequence Time-Series Forecasting](https://mlsanity.com/paper/2012.07436/) (2020)
- [A Time Series is Worth 64 Words: Long-term Forecasting with Transformers](https://mlsanity.com/paper/2211.14730/) (2022)
- [Autoformer: Decomposition Transformers with Auto-Correlation for Long-Term Series Forecasting](https://mlsanity.com/paper/2106.13008/) (2021)
- [Are Transformers Effective for Time Series Forecasting?](https://mlsanity.com/paper/2205.13504/) (2022)
- [FEDformer: Frequency Enhanced Decomposed Transformer for Long-term Series Forecasting](https://mlsanity.com/paper/2201.12740/) (2022)
- [TimesNet: Temporal 2D-Variation Modeling for General Time Series Analysis](https://mlsanity.com/paper/2210.02186/) (2022)
- [DeepAR: Probabilistic Forecasting with Autoregressive Recurrent Networks](https://mlsanity.com/paper/1704.04110/) (2017)
- [End-to-End Multi-Task Learning with Attention](https://mlsanity.com/paper/1803.10704/) (2018)
- [A Transformer-based Framework for Multivariate Time Series Representation Learning](https://mlsanity.com/paper/2010.02803/) (2020)
- [The UCR Time Series Archive](https://mlsanity.com/paper/1810.07758/) (2018)
- [Unsupervised Scalable Representation Learning for Multivariate Time Series](https://mlsanity.com/paper/1901.10738/) (2019)
- [TSMixer: An All-MLP Architecture for Time Series Forecasting](https://mlsanity.com/paper/2303.06053/) (2023)
- [Multiwavelet-based Operator Learning for Differential Equations](https://mlsanity.com/paper/2109.13459/) (2021)
- [MINIROCKET: A Very Fast (Almost) Deterministic Transform for Time Series Classification](https://mlsanity.com/paper/2012.08791/) (2020)
- [Neural Rough Differential Equations for Long Time Series](https://mlsanity.com/paper/2009.08295/) (2020)
- [HIVE-COTE 2.0: a new meta ensemble for time series classification](https://mlsanity.com/paper/2104.07551/) (2021)
- [Pathformer: Multi-scale Transformers with Adaptive Pathways for Time Series Forecasting](https://mlsanity.com/paper/2402.05956/) (2024)
- [TS-CHIEF: A Scalable and Accurate Forest Algorithm for Time Series Classification](https://mlsanity.com/paper/1906.10329/) (2019)
- [Multilevel Wavelet Decomposition Network for Interpretable Time Series Analysis](https://mlsanity.com/paper/1806.08946/) (2018)
- [TimesURL: Self-supervised Contrastive Learning for Universal Time Series Representation Learning](https://mlsanity.com/paper/2312.15709/) (2023)
- [Omni-Scale CNNs: a simple and effective kernel size configuration for time series classification](https://mlsanity.com/paper/2002.10061/) (2020)
- [STDEN: Towards Physics-Guided Neural Networks for Traffic Flow Prediction](https://mlsanity.com/paper/2209.00225/) (2022)
- [BasisFormer: Attention-based Time Series Forecasting with Learnable and Interpretable Basis](https://mlsanity.com/paper/2310.20496/) (2023)
- [AlphaStock: A Buying-Winners-and-Selling-Losers Investment Strategy using Interpretable Deep Reinforcement Attention Networks](https://mlsanity.com/paper/1908.02646/) (2019)
- [Inherently Interpretable Time Series Classification via Multiple Instance Learning](https://mlsanity.com/paper/2311.10049/) (2023)
- [Bridging Traffic State and Trajectory for Dynamic Road Network and Trajectory Representation Learning](https://mlsanity.com/paper/2502.06870/) (2025)
- [Neural Decomposition of Time-Series Data for Effective Generalization](https://mlsanity.com/paper/1705.09137/) (2017)
- [Understanding Urban Dynamics via Context-aware Tensor Factorization with Neighboring Regularization](https://mlsanity.com/paper/1905.00702/) (2019)

## Abstract (arXiv)

Time series analysis is fundamental in domains such as finance, healthcare, and meteorology. Real-world time series often exhibit multiscale characteristics shaped by diverse latent factors, resulting in intricate temporal patterns and rich frequency structures. However, existing approaches typically focus on either frequency-domain decomposition or time-domain pattern extraction in isolation, neglecting their joint structure. This decoupled modeling limits representation expressiveness and undermines performance in tasks requiring simultaneous temporal and spectral reasoning. To address this gap, we propose m-WCN, a novel end-to-end deep learning framework that neuralizes multi-wavelet decomposition for joint extraction of temporal patterns and frequency components. By approximating the classical GHM multi-wavelet transform with trainable convolutional operators and enforcing orthogonality constraints, m-WCN produces interpretable multi-resolution representations. Built on this foundation, we introduce two task-specific architectures: TFBC for time series classification, which boosts discriminative features across frequency scales, and FTB for forecasting, which ensembles frequency-aware predictors. Extensive experiments on 64 UCR datasets and seven public forecasting benchmarks demonstrate the effectiveness of our approach. Built on the neuralized m-WCN, our TFBC and FTB outperform various baseline models across diverse datasets, achieving average improvements of 19.97% in classification and 19.92% in forecasting tasks.