# BEAT: Balanced Frequency Adaptive Tuning for Long-Term Time-Series Forecasting

arXiv: https://arxiv.org/abs/2501.19065 · HTML: https://mlsanity.com/paper/2501.19065/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 35 of its 53 references that are in the map.
- First posted on arXiv 31 Jan 2025.

## Builds on (most cited first, 30 of 35)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [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)
- [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)
- [TimesNet: Temporal 2D-Variation Modeling for General Time Series Analysis](https://mlsanity.com/paper/2210.02186/) (2022)
- [Modeling Long- and Short-Term Temporal Patterns with Deep Neural Networks](https://mlsanity.com/paper/1703.07015/) (2017)
- [N-BEATS: Neural basis expansion analysis for interpretable time series forecasting](https://mlsanity.com/paper/1905.10437/) (2019)
- [Time-LLM: Time Series Forecasting by Reprogramming Large Language Models](https://mlsanity.com/paper/2310.01728/) (2023)
- [Enhancing the Locality and Breaking the Memory Bottleneck of Transformer on Time Series Forecasting](https://mlsanity.com/paper/1907.00235/) (2019)
- [Recent Advances in Convolutional Neural Networks](https://mlsanity.com/paper/1512.07108/) (2015)
- [TimeMixer: Decomposable Multiscale Mixing for Time Series Forecasting](https://mlsanity.com/paper/2405.14616/) (2024)
- [SCINet: Time Series Modeling and Forecasting with Sample Convolution and Interaction](https://mlsanity.com/paper/2106.09305/) (2021)
- [Long-term Forecasting with TiDE: Time-series Dense Encoder](https://mlsanity.com/paper/2304.08424/) (2023)
- [Balanced Multimodal Learning via On-the-fly Gradient Modulation](https://mlsanity.com/paper/2203.15332/) (2022)
- [TSMixer: An All-MLP Architecture for Time Series Forecasting](https://mlsanity.com/paper/2303.06053/) (2023)
- [Deep Time Series Models: A Comprehensive Survey and Benchmark](https://mlsanity.com/paper/2407.13278/) (2024)
- [FITS: Modeling Time Series with 10k Parameters](https://mlsanity.com/paper/2307.03756/) (2023)
- [Frequency-domain MLPs are More Effective Learners in Time Series Forecasting](https://mlsanity.com/paper/2311.06184/) (2023)
- [FiLM: Frequency improved Legendre Memory Model for Long-term Time Series Forecasting](https://mlsanity.com/paper/2205.08897/) (2022)
- [FreDF: Learning to Forecast in the Frequency Domain](https://mlsanity.com/paper/2402.02399/) (2024)
- [TSLANet: Rethinking Transformers for Time Series Representation Learning](https://mlsanity.com/paper/2404.08472/) (2024)
- [Multilevel Wavelet Decomposition Network for Interpretable Time Series Analysis](https://mlsanity.com/paper/1806.08946/) (2018)
- [Fredformer: Frequency Debiased Transformer for Time Series Forecasting](https://mlsanity.com/paper/2406.09009/) (2024)
- [Deep Learning for Time Series Forecasting: The Electric Load Case](https://mlsanity.com/paper/1907.09207/) (2019)
- [Enhancing Foundation Models for Time Series Forecasting via Wavelet-based Tokenization](https://mlsanity.com/paper/2412.05244/) (2024)

## Abstract (arXiv)

Long-term time-series forecasting supports a wide range of applications, including weather prediction and electricity demand planning. Frequency-domain methods address this task by decomposing observations into components that describe temporal variations at different scales. However, separate representations do not by themselves provide an explicit mechanism for adjusting the training emphasis across components. Under a shared forecasting objective, the frequency-specific networks can retain different levels of coefficient prediction error, motivating an error-dependent adjustment to their gradients. To this end, we propose BEAT (Balanced frEquency Adaptive Tuning), a framework that combines frequency-specific error monitoring with adaptive gradient modulation. We design a Frequency-Specific Monitor that compares predicted and target wavelet coefficients in a common normalized space and expresses each discrepancy relative to a reference error computed from the detail components. We further introduce a Dynamical Gradient Balancer that converts these ratios into positive, bounded coefficients. Components with higher relative errors receive larger gradient weights, whereas those with lower relative errors receive smaller weights. A shared modulation-strength parameter controls the departure from unmodulated training, and the monitoring and balancing operations are used only during training. Experiments on seven real-world datasets show that BEAT achieves competitive performance against state-of-the-art forecasting methods.