# MoGU: Mixture-of-Gaussians with Uncertainty-based Gating for Time Series Forecasting

arXiv: https://arxiv.org/abs/2510.07459 · HTML: https://mlsanity.com/paper/2510.07459/

## 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 26 of its 32 references that are in the map.
- First posted on arXiv 8 Oct 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, 26 of 26)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [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)
- [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)
- [Reformer: The Efficient Transformer](https://mlsanity.com/paper/2001.04451/) (2020)
- [GShard: Scaling Giant Models with Conditional Computation and Automatic Sharding](https://mlsanity.com/paper/2006.16668/) (2020)
- [Are Transformers Effective for Time Series Forecasting?](https://mlsanity.com/paper/2205.13504/) (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)
- [DeepSeekMoE: Towards Ultimate Expert Specialization in Mixture-of-Experts Language Models](https://mlsanity.com/paper/2401.06066/) (2024)
- [Conformalized Quantile Regression](https://mlsanity.com/paper/1905.03222/) (2019)
- [Time Series Forecasting With Deep Learning: A Survey](https://mlsanity.com/paper/2004.13408/) (2020)
- [Accurate Uncertainties for Deep Learning Using Calibrated Regression](https://mlsanity.com/paper/1807.00263/) (2018)
- [Adaptive Conformal Inference Under Distribution Shift](https://mlsanity.com/paper/2106.00170/) (2021)
- [TimeMixer: Decomposable Multiscale Mixing for Time Series Forecasting](https://mlsanity.com/paper/2405.14616/) (2024)
- [Deep Time Series Models: A Comprehensive Survey and Benchmark](https://mlsanity.com/paper/2407.13278/) (2024)
- [Deep Learning for Multivariate Time Series Imputation: A Survey](https://mlsanity.com/paper/2402.04059/) (2024)
- [Error-quantified Conformal Inference for Time Series](https://mlsanity.com/paper/2502.00818/) (2025)
- [Relational Conformal Prediction for Correlated Time Series](https://mlsanity.com/paper/2502.09443/) (2025)
- [Extracting Uncertainty Estimates from Mixtures of Experts for Semantic Segmentation](https://mlsanity.com/paper/2509.04816/) (2025)
- [Efficient Deweather Mixture-of-Experts with Uncertainty-aware Feature-wise Linear Modulation](https://mlsanity.com/paper/2312.16610/) (2023)

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

- [Modular Foundation Models for Time-Series Perception in Digital Twins](https://mlsanity.com/paper/2607.03585/) (2026)
- [Cross-Entropy Guided Routing in Mixture-of-Experts Large Language Models](https://mlsanity.com/paper/2609.37751/) (2026)

## Abstract (arXiv)

We introduce Mixture-of-Gaussians with Uncertainty-based Gating (MoGU), a novel Mixture-of-Experts (MoE) framework designed for regression tasks. MoGU replaces standard learned gating with an intrinsic routing paradigm where expert-specific uncertainty serves as the native gating signal. By modeling each prediction as a Gaussian distribution, the system utilizes predicted variance to dynamically weight expert contributions. We validate MoGU on multivariate time-series forecasting, a domain defined by high volatility and varying noise patterns. Empirical results across multiple benchmarks, horizon lengths, and backbones demonstrate that MoGU consistently improves forecasting accuracy compared to traditional MoE. Further evaluation via conformal prediction indicates that our approach yields more efficient prediction intervals than existing baselines. These findings highlight MoGU's capacity for providing both competitive performance and reliable, high-fidelity uncertainty quantification. Our code is available at: https://github.com/yolish/moe_unc_tsf