# Moirai-MoE: Empowering Time Series Foundation Models with Sparse Mixture of Experts

arXiv: https://arxiv.org/abs/2410.10469 · HTML: https://mlsanity.com/paper/2410.10469/

## Key facts

- Cited by 95 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 30 of its 35 references that are in the map.
- First posted on arXiv 14 Oct 2024.

## 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 30)

- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Segment Anything](https://mlsanity.com/paper/2304.02643/) (2023)
- [Outrageously Large Neural Networks: The Sparsely-Gated Mixture-of-Experts Layer](https://mlsanity.com/paper/1701.06538/) (2017)
- [Switch Transformers: Scaling to Trillion Parameter Models with Simple and Efficient Sparsity](https://mlsanity.com/paper/2101.03961/) (2021)
- [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)
- [Mixtral of Experts](https://mlsanity.com/paper/2401.04088/) (2024)
- [Autoformer: Decomposition Transformers with Auto-Correlation for Long-Term Series Forecasting](https://mlsanity.com/paper/2106.13008/) (2021)
- [GShard: Scaling Giant Models with Conditional Computation and Automatic Sharding](https://mlsanity.com/paper/2006.16668/) (2020)
- [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)
- [DeepSeekMoE: Towards Ultimate Expert Specialization in Mixture-of-Experts Language Models](https://mlsanity.com/paper/2401.06066/) (2024)
- [Chronos: Learning the Language of Time Series](https://mlsanity.com/paper/2403.07815/) (2024)
- [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)
- [Large Language Models Are Zero-Shot Time Series Forecasters](https://mlsanity.com/paper/2310.07820/) (2023)
- [MOMENT: A Family of Open Time-series Foundation Models](https://mlsanity.com/paper/2402.03885/) (2024)
- [DeepSpeed-MoE: Advancing Mixture-of-Experts Inference and Training to Power Next-Generation AI Scale](https://mlsanity.com/paper/2201.05596/) (2022)
- [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)
- [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)
- [Timer: Generative Pre-trained Transformers Are Large Time Series Models](https://mlsanity.com/paper/2402.02368/) (2024)
- [TEMPO: Prompt-based Generative Pre-trained Transformer for Time Series Forecasting](https://mlsanity.com/paper/2310.04948/) (2023)
- [UniTime: A Language-Empowered Unified Model for Cross-Domain Time Series Forecasting](https://mlsanity.com/paper/2310.09751/) (2023)
- [LLaMA-MoE: Building Mixture-of-Experts from LLaMA with Continual Pre-training](https://mlsanity.com/paper/2406.16554/) (2024)
- [AutoMixer for Improved Multivariate Time-Series Forecasting on Business and IT Observability Data](https://mlsanity.com/paper/2310.20280/) (2023)
- [Cross-Frequency Time Series Meta-Forecasting](https://mlsanity.com/paper/2302.02077/) (2023)

## Built on by (most cited first, 30 of 95)

- [Moirai 2.0: When Less Is More for Time Series Forecasting](https://mlsanity.com/paper/2511.11698/) (2025)
- [This Time is Different: An Observability Perspective on Time Series Foundation Models](https://mlsanity.com/paper/2505.14766/) (2025)
- [Timer-S1: A Billion-Scale Time Series Foundation Model with Serial Scaling](https://mlsanity.com/paper/2603.04791/) (2026)
- [Foundation Models for Spatio-Temporal Data Science: A Tutorial and Survey](https://mlsanity.com/paper/2503.13502/) (2025)
- [MIRA: Medical Time Series Foundation Model for Real-World Health Data](https://mlsanity.com/paper/2506.07584/) (2025)
- [True Zero-Shot Inference of Dynamical Systems Preserving Long-Term Statistics](https://mlsanity.com/paper/2505.13192/) (2025)
- [TempoPFN: Synthetic Pre-training of Linear RNNs for Zero-shot Time Series Forecasting](https://mlsanity.com/paper/2510.25502/) (2025)
- [BLAST: Balanced Sampling Time Series Corpus for Universal Forecasting Models](https://mlsanity.com/paper/2505.17871/) (2025)
- [Empowering Time Series Analysis with Synthetic Data: A Survey and Outlook in the Era of Foundation Models](https://mlsanity.com/paper/2503.11411/) (2025)
- [SciTS: Scientific Time Series Understanding and Generation with LLMs](https://mlsanity.com/paper/2510.03255/) (2025)
- [CauKer: Classification Time Series Foundation Models Can Be Pretrained on Synthetic Data](https://mlsanity.com/paper/2508.02879/) (2025)
- [TiRex-2: Generalizing TiRex to Multivariate Data and Streaming](https://mlsanity.com/paper/2607.01204/) (2026)
- [VisionTS++: Cross-Modal Time Series Foundation Model with Continual Pre-trained Vision Backbones](https://mlsanity.com/paper/2508.04379/) (2025)
- [TS-Reasoner: Aligning Time Series Foundation Models with LLM Reasoning](https://mlsanity.com/paper/2510.03519/) (2025)
- [Learning Soft Sparse Shapes for Efficient Time-Series Classification](https://mlsanity.com/paper/2505.06892/) (2025)
- [Can TabPFN Compete with GNNs for Node Classification via Graph Tabularization?](https://mlsanity.com/paper/2512.08798/) (2025)
- [Kairos: Toward Adaptive and Parameter-Efficient Time Series Foundation Models](https://mlsanity.com/paper/2509.25826/) (2025)
- [Learning the Context of Errors: Black-Box Online Adaptation of Time Series Foundation Models](https://mlsanity.com/paper/2606.14222/) (2026)
- [Xihe: Scalable Zero-Shot Time Series Learner Via Hierarchical Interleaved Block Attention](https://mlsanity.com/paper/2510.21795/) (2025)
- [MoTime: A Dataset Suite for Multimodal Time Series Forecasting](https://mlsanity.com/paper/2505.15072/) (2025)
- [TimeRecipe: A Time-Series Forecasting Recipe via Benchmarking Module Level Effectiveness](https://mlsanity.com/paper/2506.06482/) (2025)
- [TRACE: Grounding Time Series in Context for Multimodal Embedding and Retrieval](https://mlsanity.com/paper/2506.09114/) (2025)
- [SEMPO: Lightweight Foundation Models for Time Series Forecasting](https://mlsanity.com/paper/2510.19710/) (2025)
- [Synapse: Adaptive Arbitration of Complementary Expertise in Time Series Foundational Models](https://mlsanity.com/paper/2511.05460/) (2025)
- [Unlocking Pretrained Vision Transformers for Time Series Classification](https://mlsanity.com/paper/2506.08641/) (2025)
- [CoRA: Covariate-Aware Adaptation of Time Series Foundation Models](https://mlsanity.com/paper/2510.12681/) (2025)
- [The Seismic Wavefield Common Task Framework](https://mlsanity.com/paper/2512.19927/) (2025)
- [CITRAS: Covariate-Informed Transformer for Time Series Forecasting](https://mlsanity.com/paper/2503.24007/) (2025)
- [Byte Pair Encoding for Efficient Time Series Forecasting](https://mlsanity.com/paper/2505.14411/) (2025)
- [CTF4Nuclear: Common Task Framework for Nuclear Fission and Fusion Models](https://mlsanity.com/paper/2605.15549/) (2026)

## Abstract (arXiv)

Time series foundation models have demonstrated impressive performance as zero-shot forecasters. However, achieving effectively unified training on time series remains an open challenge. Existing approaches introduce some level of model specialization to account for the highly heterogeneous nature of time series data. For instance, Moirai pursues unified training by employing multiple input/output projection layers, each tailored to handle time series at a specific frequency. Similarly, TimesFM maintains a frequency embedding dictionary for this purpose. We identify two major drawbacks to this human-imposed frequency-level model specialization: (1) Frequency is not a reliable indicator of the underlying patterns in time series. For example, time series with different frequencies can display similar patterns, while those with the same frequency may exhibit varied patterns. (2) Non-stationarity is an inherent property of real-world time series, leading to varied distributions even within a short context window of a single time series. Frequency-level specialization is too coarse-grained to capture this level of diversity. To address these limitations, this paper introduces Moirai-MoE, using a single input/output projection layer while delegating the modeling of diverse time series patterns to the sparse mixture of experts (MoE) within Transformers. With these designs, Moirai-MoE reduces reliance on human-defined heuristics and enables automatic token-level specialization. Extensive experiments on 39 datasets demonstrate the superiority of Moirai-MoE over existing foundation models in both in-distribution and zero-shot scenarios. Furthermore, this study conducts comprehensive model analyses to explore the inner workings of time series MoE foundation models and provides valuable insights for future research.