# HiMoE: Heterogeneity-Informed Mixture-of-Experts for Fair Spatial-Temporal Forecasting

arXiv: https://arxiv.org/abs/2412.00316 · HTML: https://mlsanity.com/paper/2412.00316/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in MoE for time series and graphs, one of 12 directions in Mixture-of-experts.
- Builds on 41 of its 58 references that are in the map.
- First posted on arXiv 30 Nov 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 41)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [Outrageously Large Neural Networks: The Sparsely-Gated Mixture-of-Experts Layer](https://mlsanity.com/paper/1701.06538/) (2017)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [Spatio-Temporal Graph Convolutional Networks: A Deep Learning Framework for Traffic Forecasting](https://mlsanity.com/paper/1709.04875/) (2017)
- [GLaM: Efficient Scaling of Language Models with Mixture-of-Experts](https://mlsanity.com/paper/2112.06905/) (2021)
- [Graph WaveNet for Deep Spatial-Temporal Graph Modeling](https://mlsanity.com/paper/1906.00121/) (2019)
- [Scaling Vision with Sparse Mixture of Experts](https://mlsanity.com/paper/2106.05974/) (2021)
- [Connecting the Dots: Multivariate Time Series Forecasting with Graph Neural Networks](https://mlsanity.com/paper/2005.11650/) (2020)
- [Adaptive Graph Convolutional Recurrent Network for Traffic Forecasting](https://mlsanity.com/paper/2007.02842/) (2020)
- [GMAN: A Graph Multi-Attention Network for Traffic Prediction](https://mlsanity.com/paper/1911.08415/) (2019)
- [Deep Spatio-Temporal Residual Networks for Citywide Crowd Flows Prediction](https://mlsanity.com/paper/1610.00081/) (2016)
- [A Survey on Mixture of Experts in Large Language Models](https://mlsanity.com/paper/2407.06204/) (2024)
- [Spatial-Temporal Graph ODE Networks for Traffic Flow Forecasting](https://mlsanity.com/paper/2106.12931/) (2021)
- [OpenMoE: An Early Effort on Open Mixture-of-Experts Language Models](https://mlsanity.com/paper/2402.01739/) (2024)
- [Spatial-Temporal Transformer Networks for Traffic Flow Forecasting](https://mlsanity.com/paper/2001.02908/) (2020)
- [Efficient Large Scale Language Modeling with Mixtures of Experts](https://mlsanity.com/paper/2112.10684/) (2021)
- [Graph Neural Networks for Graphs with Heterophily: A Survey](https://mlsanity.com/paper/2202.07082/) (2022)
- [Spatio-Temporal Graph Neural Networks for Predictive Learning in Urban Computing: A Survey](https://mlsanity.com/paper/2303.14483/) (2023)
- [Graph Neural Controlled Differential Equations for Traffic Forecasting](https://mlsanity.com/paper/2112.03558/) (2021)
- [Decoupled Dynamic Spatial-Temporal Graph Neural Network for Traffic Forecasting](https://mlsanity.com/paper/2206.09112/) (2022)
- [M3ViT: Mixture-of-Experts Vision Transformer for Efficient Multi-task Learning with Model-Accelerator Co-design](https://mlsanity.com/paper/2210.14793/) (2022)
- [Spatio-Temporal Meta-Graph Learning for Traffic Forecasting](https://mlsanity.com/paper/2211.14701/) (2022)
- [Spatio-Temporal Self-Supervised Learning for Traffic Flow Prediction](https://mlsanity.com/paper/2212.04475/) (2022)
- [Multi-Range Attentive Bicomponent Graph Convolutional Network for Traffic Forecasting](https://mlsanity.com/paper/1911.12093/) (2019)
- [PM2.5-GNN: A Domain Knowledge Enhanced Graph Neural Network For PM2.5 Forecasting](https://mlsanity.com/paper/2002.12898/) (2020)
- [TrafficStream: A Streaming Traffic Flow Forecasting Framework Based on Graph Neural Networks and Continual Learning](https://mlsanity.com/paper/2106.06273/) (2021)
- [Joint Air Quality and Weather Prediction Based on Multi-Adversarial Spatiotemporal Networks](https://mlsanity.com/paper/2012.15037/) (2020)
- [Generative Image Modeling Using Spatial LSTMs](https://mlsanity.com/paper/1506.03478/) (2015)

## Abstract (arXiv)

Achieving both accurate and consistent predictive performance across spatial nodes is crucial for ensuring the validity and reliability of outcomes in fair spatial-temporal forecasting tasks. However, existing training methods treat heterogeneous nodes with a fully averaged perspective, resulting in inherently biased prediction targets. Balancing accuracy and consistency is particularly challenging due to the multi-objective nature of spatial-temporal forecasting. To address this issue, we propose a novel Heterogeneity-Informed Mixture-of-Experts (HiMoE) framework that delivers both uniform and precise spatial-temporal predictions. From a model architecture perspective, we design the Heterogeneity-Informed Graph Convolutional Network (HiGCN) to address trend heterogeneity, and we introduce the Node-wise Mixture-of-Experts (NMoE) module to handle cardinality heterogeneity across nodes. From an evaluation perspective, we propose STFairBench, a benchmark that handles fairness in spatial-temporal prediction from both training and evaluation stages. Extensive experiments on four real-world datasets demonstrate that HiMoE achieves state-of-the-art performance, outperforming the best baseline by at least 9.22% across all evaluation metrics.