# Attractor Memory for Long-Term Time Series Forecasting: A Chaos Perspective

arXiv: https://arxiv.org/abs/2402.11463 · HTML: https://mlsanity.com/paper/2402.11463/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- Builds on 27 of its 68 references that are in the map.
- First posted on arXiv 18 Feb 2024.

## Builds on (most cited first, 27 of 27)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Mamba: Linear-Time Sequence Modeling with Selective State Spaces](https://mlsanity.com/paper/2312.00752/) (2023)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [Efficiently Modeling Long Sequences with Structured State Spaces](https://mlsanity.com/paper/2111.00396/) (2021)
- [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)
- [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)
- [DeepAR: Probabilistic Forecasting with Autoregressive Recurrent Networks](https://mlsanity.com/paper/1704.04110/) (2017)
- [iTransformer: Inverted Transformers Are Effective for Time Series Forecasting](https://mlsanity.com/paper/2310.06625/) (2023)
- [Simplified State Space Layers for Sequence Modeling](https://mlsanity.com/paper/2208.04933/) (2022)
- [One Fits All:Power General Time Series Analysis by Pretrained LM](https://mlsanity.com/paper/2302.11939/) (2023)
- [HiPPO: Recurrent Memory with Optimal Polynomial Projections](https://mlsanity.com/paper/2008.07669/) (2020)
- [Hopfield Networks is All You Need](https://mlsanity.com/paper/2008.02217/) (2020)
- [Time Series Forecasting With Deep Learning: A Survey](https://mlsanity.com/paper/2004.13408/) (2020)
- [Non-stationary Transformers: Exploring the Stationarity in Time Series Forecasting](https://mlsanity.com/paper/2205.14415/) (2022)
- [Multiwavelet-based Operator Learning for Differential Equations](https://mlsanity.com/paper/2109.13459/) (2021)
- [FiLM: Frequency improved Legendre Memory Model for Long-term Time Series Forecasting](https://mlsanity.com/paper/2205.08897/) (2022)
- [UniTime: A Language-Empowered Unified Model for Cross-Domain Time Series Forecasting](https://mlsanity.com/paper/2310.09751/) (2023)
- [Koopa: Learning Non-stationary Time Series Dynamics with Koopman Predictors](https://mlsanity.com/paper/2305.18803/) (2023)
- [Large Models for Time Series and Spatio-Temporal Data: A Survey and Outlook](https://mlsanity.com/paper/2310.10196/) (2023)
- [Generalized Teacher Forcing for Learning Chaotic Dynamics](https://mlsanity.com/paper/2306.04406/) (2023)
- [SegRNN: Segment Recurrent Neural Network for Long-Term Time Series Forecasting](https://mlsanity.com/paper/2308.11200/) (2023)
- [Koopman Neural Forecaster for Time Series with Temporal Distribution Shifts](https://mlsanity.com/paper/2210.03675/) (2022)
- [RWKV-TS: Beyond Traditional Recurrent Neural Network for Time Series Tasks](https://mlsanity.com/paper/2401.09093/) (2024)
- [Sequence Modeling with Multiresolution Convolutional Memory](https://mlsanity.com/paper/2305.01638/) (2023)

## Built on by (most cited first, 17 of 17)

- [Time-MoE: Billion-Scale Time Series Foundation Models with Mixture of Experts](https://mlsanity.com/paper/2409.16040/) (2024)
- [Kimi Linear: An Expressive, Efficient Attention Architecture](https://mlsanity.com/paper/2510.26692/) (2025)
- [DUET: Dual Clustering Enhanced Multivariate Time Series Forecasting](https://mlsanity.com/paper/2412.10859/) (2024)
- [Time-SSM: Simplifying and Unifying State Space Models for Time Series Forecasting](https://mlsanity.com/paper/2405.16312/) (2024)
- [Vision-Enhanced Time Series Forecasting via Latent Diffusion Models](https://mlsanity.com/paper/2502.14887/) (2025)
- [LETS Forecast: Learning Embedology for Time Series Forecasting](https://mlsanity.com/paper/2506.06454/) (2025)
- [Multi-Order Wavelet Derivative Transform for Deep Time Series Forecasting](https://mlsanity.com/paper/2505.11781/) (2025)
- [Baguan-TS: A Sequence-Native In-Context Learning Model for Time Series Forecasting with Covariates](https://mlsanity.com/paper/2603.17439/) (2026)
- [Toward Physics-guided Time Series Embedding](https://mlsanity.com/paper/2410.06651/) (2024)
- [TwinS: Revisiting Non-Stationarity in Multivariate Time Series Forecasting](https://mlsanity.com/paper/2406.03710/) (2024)
- [Time Series Forecasting Through the Lens of Dynamics](https://mlsanity.com/paper/2507.15774/) (2025)
- [A Deep Learning Framework for Heat Demand Forecasting using Time-Frequency Representations of Decomposed Features](https://mlsanity.com/paper/2603.01137/) (2026)
- [Parallel BiLSTM-Transformer networks for forecasting chaotic dynamics](https://mlsanity.com/paper/2510.23685/) (2025)
- [The Spectrum Is Not Enough: When Context Helps Time-Series Forecasting](https://mlsanity.com/paper/2607.13006/) (2026)
- [POEM: Phase-Aware SO(2) Feature Rotation for Time Series Forecasting Under Periodicity Drift](https://mlsanity.com/paper/2608.03630/) (2026)
- [Correct then Forecast: Observer State-Space Models for Time Series Forecasting](https://mlsanity.com/paper/2609.33566/) (2026)
- [XMatch: Enhancing Covariate-Aware Time Series Forecasting through Tree-Structured Exogenous Matching](https://mlsanity.com/paper/2609.34939/) (2026)

## Abstract (arXiv)

In long-term time series forecasting (LTSF) tasks, an increasing number of models have acknowledged that discrete time series originate from continuous dynamic systems and have attempted to model their dynamical structures. Recognizing the chaotic nature of real-world data, our model, textbftextitAttraos, incorporates chaos theory into LTSF, perceiving real-world time series as observations from unknown high-dimensional chaotic dynamic systems. Under the concept of attractor invariance, Attraos utilizes non-parametric Phase Space Reconstruction embedding and the proposed multi-scale dynamic memory unit to memorize historical dynamics structure and predicts by a frequency-enhanced local evolution strategy. Detailed theoretical analysis and abundant empirical evidence consistently show that Attraos outperforms various LTSF methods on mainstream LTSF datasets and chaotic datasets with only one-twelfth of the parameters compared to PatchTST.