# FreIE: Low-Frequency Spectral Bias in Neural Networks for Time-Series Tasks

arXiv: https://arxiv.org/abs/2510.25800 · HTML: https://mlsanity.com/paper/2510.25800/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 29 of its 37 references that are in the map.
- First posted on arXiv 29 Oct 2025.

## Builds on (most cited first, 29 of 29)

- [Neural Tangent Kernel: Convergence and Generalization in Neural Networks](https://mlsanity.com/paper/1806.07572/) (2018)
- [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)
- [Are Transformers Effective for Time Series Forecasting?](https://mlsanity.com/paper/2205.13504/) (2022)
- [On the Spectral Bias of Neural Networks](https://mlsanity.com/paper/1806.08734/) (2018)
- [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)
- [iTransformer: Inverted Transformers Are Effective for Time Series Forecasting](https://mlsanity.com/paper/2310.06625/) (2023)
- [Temporal Fusion Transformers for Interpretable Multi-horizon Time Series Forecasting](https://mlsanity.com/paper/1912.09363/) (2019)
- [Deep Neural Networks as Gaussian Processes](https://mlsanity.com/paper/1711.00165/) (2017)
- [Fantastic Generalization Measures and Where to Find Them](https://mlsanity.com/paper/1912.02178/) (2019)
- [Non-stationary Transformers: Exploring the Stationarity in Time Series Forecasting](https://mlsanity.com/paper/2205.14415/) (2022)
- [Long-term Forecasting with TiDE: Time-series Dense Encoder](https://mlsanity.com/paper/2304.08424/) (2023)
- [TimeXer: Empowering Transformers for Time Series Forecasting with Exogenous Variables](https://mlsanity.com/paper/2402.19072/) (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)
- [Finite Depth and Width Corrections to the Neural Tangent Kernel](https://mlsanity.com/paper/1909.05989/) (2019)
- [Understanding the unstable convergence of gradient descent](https://mlsanity.com/paper/2204.01050/) (2022)
- [Multi-scale Deep Neural Network (MscaleDNN) for Solving Poisson-Boltzmann Equation in Complex Domains](https://mlsanity.com/paper/2007.11207/) (2020)
- [Phase diagram for two-layer ReLU neural networks at infinite-width limit](https://mlsanity.com/paper/2007.07497/) (2020)
- [Stochastic Training is Not Necessary for Generalization](https://mlsanity.com/paper/2109.14119/) (2021)
- [From Fourier to Koopman: Spectral Methods for Long-term Time Series Prediction](https://mlsanity.com/paper/2004.00574/) (2020)
- [Frequency Adaptive Normalization For Non-stationary Time Series Forecasting](https://mlsanity.com/paper/2409.20371/) (2024)
- [Theory of the Frequency Principle for General Deep Neural Networks](https://mlsanity.com/paper/1906.09235/) (2019)
- [Fredformer: Frequency Debiased Transformer for Time Series Forecasting](https://mlsanity.com/paper/2406.09009/) (2024)
- [The Implicit Regularization of Dynamical Stability in Stochastic Gradient Descent](https://mlsanity.com/paper/2305.17490/) (2023)
- [On the infinite width limit of neural networks with a standard parameterization](https://mlsanity.com/paper/2001.07301/) (2020)
- [Explicitizing an Implicit Bias of the Frequency Principle in Two-layer Neural Networks](https://mlsanity.com/paper/1905.10264/) (2019)
- [TSINR: Capturing Temporal Continuity via Implicit Neural Representations for Time Series Anomaly Detection](https://mlsanity.com/paper/2411.11641/) (2024)

## Built on by (most cited first, 1 of 1)

- [Autocorrelation Reintroduces Spectral Bias in KANs for Time Series Forecasting](https://mlsanity.com/paper/2604.23518/) (2026)

## Abstract (arXiv)

The inherent autocorrelation of time series data presents an ongoing challenge to multivariate time series prediction. Recently, a widely adopted approach has been the incorporation of frequency domain information to assist in long-term prediction tasks. Many researchers have independently observed the spectral bias phenomenon in neural networks, where models tend to fit low-frequency signals before high-frequency ones. However, these observations have often been attributed to the specific architectures designed by the researchers, rather than recognizing the phenomenon as a universal characteristic across models. To unify the understanding of the spectral bias phenomenon in long-term time series prediction, we conducted extensive empirical experiments to measure spectral bias in existing mainstream models. Our findings reveal that virtually all models exhibit this phenomenon. To mitigate the impact of spectral bias, we propose the FreLE (Frequency Loss Enhancement) algorithm, which enhances model generalization through both explicit and implicit frequency regularization. This is a plug-and-play model loss function unit. A large number of experiments have proven the superior performance of FreLE. Code is available at https://github.com/Chenxing-Xuan/FreLE.