# Learning the Dynamic Correlations and Mitigating Noise by Hierarchical Convolution for Long-term Sequence Forecasting

arXiv: https://arxiv.org/abs/2312.16790 · HTML: https://mlsanity.com/paper/2312.16790/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 27 references that are in the map.
- First posted on arXiv 28 Dec 2023.

## Builds on (most cited first, 14 of 14)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Billion-scale similarity search with GPUs](https://mlsanity.com/paper/1702.08734/) (2017)
- [Informer: Beyond Efficient Transformer for Long Sequence Time-Series Forecasting](https://mlsanity.com/paper/2012.07436/) (2020)
- [Autoformer: Decomposition Transformers with Auto-Correlation for Long-Term Series Forecasting](https://mlsanity.com/paper/2106.13008/) (2021)
- [An Empirical Evaluation of Generic Convolutional and Recurrent Networks for Sequence Modeling](https://mlsanity.com/paper/1803.01271/) (2018)
- [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)
- [DeepAR: Probabilistic Forecasting with Autoregressive Recurrent Networks](https://mlsanity.com/paper/1704.04110/) (2017)
- [Enhancing the Locality and Breaking the Memory Bottleneck of Transformer on Time Series Forecasting](https://mlsanity.com/paper/1907.00235/) (2019)
- [Think Globally, Act Locally: A Deep Neural Network Approach to High-Dimensional Time Series Forecasting](https://mlsanity.com/paper/1905.03806/) (2019)
- [FiLM: Frequency improved Legendre Memory Model for Long-term Time Series Forecasting](https://mlsanity.com/paper/2205.08897/) (2022)
- [Triformer: Triangular, Variable-Specific Attentions for Long Sequence Multivariate Time Series Forecasting--Full Version](https://mlsanity.com/paper/2204.13767/) (2022)
- [Bayesian Inference and Learning in Gaussian Process State-Space Models with Particle MCMC](https://mlsanity.com/paper/1306.2861/) (2013)
- [Deep Portfolio Optimization via Distributional Prediction of Residual Factors](https://mlsanity.com/paper/2012.07245/) (2020)

## Abstract (arXiv)

Deep learning algorithms, especially Transformer-based models, have achieved significant performance by capturing long-range dependencies and historical information. However, the power of convolution has not been fully investigated. Moreover, most existing works ignore the dynamic interaction among variables and evolutionary noise in series. Addressing these issues, we propose a Hierarchical Memorizing Network (HMNet). In particular, a hierarchical convolution structure is introduced to extract the information from the series at various scales. Besides, we propose a dynamic variable interaction module to learn the varying correlation and an adaptive denoising module to search and exploit similar patterns to alleviate noises. These modules can cooperate with the hierarchical structure from the perspective of fine to coarse grain. Experiments on five benchmarks demonstrate that HMNet significantly outperforms the state-of-the-art models by 10.6% on MSE and 5.7% on MAE. Our code is released at https://github.com/yzhHoward/HMNet.