# Super-Linear: A Lightweight Pretrained Mixture of Linear Experts for Time Series Forecasting

arXiv: https://arxiv.org/abs/2509.15105 · HTML: https://mlsanity.com/paper/2509.15105/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Placed in MoE for time series and graphs, one of 12 directions in Mixture-of-experts.
- Builds on 52 of its 64 references that are in the map.
- First posted on arXiv 18 Sep 2025.

## Placed in

- Mixture-of-experts / [MoE for time series and graphs](https://mlsanity.com/moe/moe-for-time-series-and-graphs/)

## Builds on (most cited first, 30 of 52)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer](https://mlsanity.com/paper/1910.10683/) (2019)
- [Outrageously Large Neural Networks: The Sparsely-Gated Mixture-of-Experts Layer](https://mlsanity.com/paper/1701.06538/) (2017)
- [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)
- [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)
- [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)
- [Chronos: Learning the Language of Time Series](https://mlsanity.com/paper/2403.07815/) (2024)
- [Time-LLM: Time Series Forecasting by Reprogramming Large Language Models](https://mlsanity.com/paper/2310.01728/) (2023)
- [A decoder-only foundation model for time-series forecasting](https://mlsanity.com/paper/2310.10688/) (2023)
- [One Fits All:Power General Time Series Analysis by Pretrained LM](https://mlsanity.com/paper/2302.11939/) (2023)
- [Unified Training of Universal Time Series Forecasting Transformers](https://mlsanity.com/paper/2402.02592/) (2024)
- [MOMENT: A Family of Open Time-series Foundation Models](https://mlsanity.com/paper/2402.03885/) (2024)
- [A Comprehensive Survey on Pretrained Foundation Models: A History from BERT to ChatGPT](https://mlsanity.com/paper/2302.09419/) (2023)
- [SCINet: Time Series Modeling and Forecasting with Sample Convolution and Interaction](https://mlsanity.com/paper/2106.09305/) (2021)
- [Time-MoE: Billion-Scale Time Series Foundation Models with Mixture of Experts](https://mlsanity.com/paper/2409.16040/) (2024)
- [Monash Time Series Forecasting Archive](https://mlsanity.com/paper/2105.06643/) (2021)
- [Foundation Models for Time Series Analysis: A Tutorial and Survey](https://mlsanity.com/paper/2403.14735/) (2024)
- [GIFT-Eval: A Benchmark For General Time Series Forecasting Model Evaluation](https://mlsanity.com/paper/2410.10393/) (2024)
- [Timer: Generative Pre-trained Transformers Are Large Time Series Models](https://mlsanity.com/paper/2402.02368/) (2024)
- [FITS: Modeling Time Series with 10k Parameters](https://mlsanity.com/paper/2307.03756/) (2023)
- [Sundial: A Family of Highly Capable Time Series Foundation Models](https://mlsanity.com/paper/2502.00816/) (2025)
- [TEMPO: Prompt-based Generative Pre-trained Transformer for Time Series Forecasting](https://mlsanity.com/paper/2310.04948/) (2023)

## Built on by (most cited first, 2 of 2)

- [Reverso: Efficient Time Series Foundation Models for Zero-shot Forecasting](https://mlsanity.com/paper/2602.17634/) (2026)
- [XCTFormer: Leveraging Cross-Channel and Cross-Time Dependencies for Enhanced Time-Series Analysis](https://mlsanity.com/paper/2605.18534/) (2026)

## Abstract (arXiv)

Time series forecasting (TSF) is critical in domains like energy, finance, healthcare, and logistics, requiring models that generalize across diverse datasets. Large pre-trained models such as Chronos and Time-MoE show strong zero-shot (ZS) performance but suffer from high computational costs. In this work, we introduce Super-Linear, a lightweight and scalable mixture-of-experts (MoE) model for general forecasting. It replaces deep architectures with simple frequency-specialized linear experts, trained on resampled data across multiple frequency regimes. A lightweight spectral gating mechanism dynamically selects relevant experts, enabling efficient, accurate forecasting. Despite its simplicity, Super-Linear demonstrates strong performance across benchmarks, while substantially improving efficiency, robustness to sampling rates, and interpretability. The implementation of Super-Linear is available at: hrefhttps://github.com/azencot-group/SuperLinearhttps://github.com/azencot-group/SuperLinear.