# OLMA: One Loss for More Accurate Time Series Forecasting

arXiv: https://arxiv.org/abs/2505.11567 · HTML: https://mlsanity.com/paper/2505.11567/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 24 of its 38 references that are in the map.
- First posted on arXiv 16 May 2025.

## Builds on (most cited first, 24 of 24)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (2020)
- [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)
- [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)
- [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)
- [Time-LLM: Time Series Forecasting by Reprogramming Large Language Models](https://mlsanity.com/paper/2310.01728/) (2023)
- [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)
- [TimeXer: Empowering Transformers for Time Series Forecasting with Exogenous Variables](https://mlsanity.com/paper/2402.19072/) (2024)
- [A Dual-Stage Attention-Based Recurrent Neural Network for Time Series Prediction](https://mlsanity.com/paper/1704.02971/) (2017)
- [Diffusion-TS: Interpretable Diffusion for General Time Series Generation](https://mlsanity.com/paper/2403.01742/) (2024)
- [Towards Understanding the Spectral Bias of Deep Learning](https://mlsanity.com/paper/1912.01198/) (2019)
- [FiLM: Frequency improved Legendre Memory Model for Long-term Time Series Forecasting](https://mlsanity.com/paper/2205.08897/) (2022)
- [Is Mamba Effective for Time Series Forecasting?](https://mlsanity.com/paper/2403.11144/) (2024)
- [Generative Time Series Forecasting with Diffusion, Denoise, and Disentanglement](https://mlsanity.com/paper/2301.03028/) (2023)
- [AutoTimes: Autoregressive Time Series Forecasters via Large Language Models](https://mlsanity.com/paper/2402.02370/) (2024)
- [Fredformer: Frequency Debiased Transformer for Time Series Forecasting](https://mlsanity.com/paper/2406.09009/) (2024)
- [WPMixer: Efficient Multi-Resolution Mixing for Long-Term Time Series Forecasting](https://mlsanity.com/paper/2412.17176/) (2024)
- [Tuning Frequency Bias of State Space Models](https://mlsanity.com/paper/2410.02035/) (2024)
- [Addressing Spectral Bias of Deep Neural Networks by Multi-Grade Deep Learning](https://mlsanity.com/paper/2410.16105/) (2024)
- [Generic Variance Bounds on Estimation and Prediction Errors in Time Series Analysis: An Entropy Perspective](https://mlsanity.com/paper/1904.04765/) (2019)

## Abstract (arXiv)

Time series forecasting faces two important but often overlooked challenges. Firstly, the inherent random noise in the time series labels sets a theoretical lower bound for the forecasting error, which is positively correlated with the entropy of the labels. Secondly, neural networks exhibit a frequency bias when modeling the state-space of time series, that is, the model performs well in learning certain frequency bands but poorly in others, thus restricting the overall forecasting performance. To address the first challenge, we prove a theorem that there exists a unitary transformation that can reduce the marginal entropy of multiple correlated Gaussian processes, thereby providing guidance for reducing the lower bound of forecasting error. Furthermore, experiments confirm that Discrete Fourier Transform (DFT) can reduce the entropy in the majority of scenarios. Correspondingly, to alleviate the frequency bias, we jointly introduce supervision in the frequency domain along the temporal dimension through DFT and Discrete Wavelet Transform (DWT). This supervision-side strategy is highly general and can be seamlessly integrated into any supervised learning method. Moreover, we propose a novel loss function named OLMA, which utilizes the frequency domain transformation across both channel and temporal dimensions to enhance forecasting. Finally, the experimental results on multiple datasets demonstrate the effectiveness of OLMA in addressing the above two challenges and the resulting improvement in forecasting accuracy. The results also indicate that the perspectives of entropy and frequency bias provide a new and feasible research direction for time series forecasting. The code is available at: https://github.com/Yuyun1011/OLMA-One-Loss-for-More-Accurate-Time-Series-Forecasting.