# FTMixer: Frequency and Time Domain Representations Fusion for Time Series Modeling

arXiv: https://arxiv.org/abs/2405.15256 · HTML: https://mlsanity.com/paper/2405.15256/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 35 of its 53 references that are in the map.
- First posted on arXiv 24 May 2024.

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

- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Xception: Deep Learning with Depthwise Separable Convolutions](https://mlsanity.com/paper/1610.02357/) (2016)
- [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)
- [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)
- [Modeling Long- and Short-Term Temporal Patterns with Deep Neural Networks](https://mlsanity.com/paper/1703.07015/) (2017)
- [Temporal Fusion Transformers for Interpretable Multi-horizon Time Series Forecasting](https://mlsanity.com/paper/1912.09363/) (2019)
- [N-BEATS: Neural basis expansion analysis for interpretable time series forecasting](https://mlsanity.com/paper/1905.10437/) (2019)
- [One Fits All:Power General Time Series Analysis by Pretrained LM](https://mlsanity.com/paper/2302.11939/) (2023)
- [Non-stationary Transformers: Exploring the Stationarity in Time Series Forecasting](https://mlsanity.com/paper/2205.14415/) (2022)
- [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)
- [Kernel and Rich Regimes in Overparametrized Models](https://mlsanity.com/paper/2002.09277/) (2020)
- [Learning in the Frequency Domain](https://mlsanity.com/paper/2002.12416/) (2020)
- [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)
- [Koopa: Learning Non-stationary Time Series Dynamics with Koopman Predictors](https://mlsanity.com/paper/2305.18803/) (2023)
- [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)
- [The Implicit Bias of Depth: How Incremental Learning Drives Generalization](https://mlsanity.com/paper/1909.12051/) (2019)
- [An Analysis of Linear Time Series Forecasting Models](https://mlsanity.com/paper/2403.14587/) (2024)
- [Implicit Sparse Regularization: The Impact of Depth and Early Stopping](https://mlsanity.com/paper/2108.05574/) (2021)
- [Fully Learnable Deep Wavelet Transform for Unsupervised Monitoring of High-Frequency Time Series](https://mlsanity.com/paper/2105.00899/) (2021)
- [ConvTimeNet: A Deep Hierarchical Fully Convolutional Model for Multivariate Time Series Analysis](https://mlsanity.com/paper/2403.01493/) (2024)
- [Mamba4Rec: Towards Efficient Sequential Recommendation with Selective State Space Models](https://mlsanity.com/paper/2403.03900/) (2024)
- [High-Dimensional Linear Regression via Implicit Regularization](https://mlsanity.com/paper/1903.09367/) (2019)

## Built on by (most cited first, 4 of 4)

- [Patch-wise Structural Loss for Time Series Forecasting](https://mlsanity.com/paper/2503.00877/) (2025)
- [Disentangled Parameter-Efficient Linear Model for Long-Term Time Series Forecasting](https://mlsanity.com/paper/2411.17257/) (2024)
- [FSMLP: Modelling Channel Dependencies With Simplex Theory Based Multi-Layer Perceptions In Frequency Domain](https://mlsanity.com/paper/2412.01654/) (2024)
- [Multi-Term Fourier Graph Neural Network with Sample Relationship Learning for Enhanced Remaining Useful Life Prediction](https://mlsanity.com/paper/2609.25179/) (2026)

## Abstract (arXiv)

Time series data can be represented in both the time and frequency domains, with the time domain emphasizing local dependencies and the frequency domain highlighting global dependencies. To harness the strengths of both domains in capturing local and global dependencies, we propose the Frequency and Time Domain Mixer (FTMixer). To exploit the global characteristics of the frequency domain, we introduce the Frequency Channel Convolution (FCC) module, designed to capture global inter-series dependencies. Inspired by the windowing concept in frequency domain transformations, we present the Windowing Frequency Convolution (WFC) module to capture local dependencies. The WFC module first applies frequency transformation within each window, followed by convolution across windows. Furthermore, to better capture these local dependencies, we employ channel-independent scheme to mix the time domain and frequency domain patches. Notably, FTMixer employs the Discrete Cosine Transformation (DCT) with real numbers instead of the complex-number-based Discrete Fourier Transformation (DFT), enabling direct utilization of modern deep learning operators in the frequency domain. Extensive experimental results across seven real-world long-term time series datasets demonstrate the superiority of FTMixer, in terms of both forecasting performance and computational efficiency.