# Addressing Spatial Indistinguishability in Spatiotemporal Prediction via Optimal Transport-Guided Masking

arXiv: https://arxiv.org/abs/2609.35021 · HTML: https://mlsanity.com/paper/2609.35021/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 22 of its 44 references that are in the map.
- First posted on arXiv 28 Sep 2026.

## Builds on (most cited first, 22 of 22)

- [BEiT: BERT Pre-Training of Image Transformers](https://mlsanity.com/paper/2106.08254/) (2021)
- [A Time Series is Worth 64 Words: Long-term Forecasting with Transformers](https://mlsanity.com/paper/2211.14730/) (2022)
- [Spatio-Temporal Graph Convolutional Networks: A Deep Learning Framework for Traffic Forecasting](https://mlsanity.com/paper/1709.04875/) (2017)
- [Graph WaveNet for Deep Spatial-Temporal Graph Modeling](https://mlsanity.com/paper/1906.00121/) (2019)
- [Adaptive Graph Convolutional Recurrent Network for Traffic Forecasting](https://mlsanity.com/paper/2007.02842/) (2020)
- [Learning Generative Models with Sinkhorn Divergences](https://mlsanity.com/paper/1706.00292/) (2017)
- [Spatial-Temporal Graph ODE Networks for Traffic Flow Forecasting](https://mlsanity.com/paper/2106.12931/) (2021)
- [Discrete Graph Structure Learning for Forecasting Multiple Time Series](https://mlsanity.com/paper/2101.06861/) (2021)
- [Spatial-Temporal Identity: A Simple yet Effective Baseline for Multivariate Time Series Forecasting](https://mlsanity.com/paper/2208.05233/) (2022)
- [PDFormer: Propagation Delay-Aware Dynamic Long-Range Transformer for Traffic Flow Prediction](https://mlsanity.com/paper/2301.07945/) (2023)
- [Graph Neural Controlled Differential Equations for Traffic Forecasting](https://mlsanity.com/paper/2112.03558/) (2021)
- [Pre-training Enhanced Spatial-temporal Graph Neural Network for Multivariate Time Series Forecasting](https://mlsanity.com/paper/2206.09113/) (2022)
- [Exploring Progress in Multivariate Time Series Forecasting: Comprehensive Benchmarking and Heterogeneity Analysis](https://mlsanity.com/paper/2310.06119/) (2023)
- [SimMTM: A Simple Pre-Training Framework for Masked Time-Series Modeling](https://mlsanity.com/paper/2302.00861/) (2023)
- [Ti-MAE: Self-Supervised Masked Time Series Autoencoders](https://mlsanity.com/paper/2301.08871/) (2023)
- [Towards Spatio-Temporal Aware Traffic Time Series Forecasting--Full Version](https://mlsanity.com/paper/2203.15737/) (2022)
- [Learning to Embed Time Series Patches Independently](https://mlsanity.com/paper/2312.16427/) (2023)
- [Spatiotemporal-aware Trend-Seasonality Decomposition Network for Traffic Flow Forecasting](https://mlsanity.com/paper/2502.12213/) (2025)
- [Heterogeneity-Informed Meta-Parameter Learning for Spatiotemporal Time Series Forecasting](https://mlsanity.com/paper/2405.10800/) (2024)
- [RNN with Particle Flow for Probabilistic Spatio-temporal Forecasting](https://mlsanity.com/paper/2106.06064/) (2021)
- [Energy Prediction using Spatiotemporal Pattern Networks](https://mlsanity.com/paper/1702.01125/) (2017)
- [Net-Ev2: A Generative Simulator for Network Event Evolution](https://mlsanity.com/paper/2606.12494/) (2026)

## Abstract (arXiv)

Spatiotemporal prediction aims to learn discriminative representations from correlated temporal signals over spatial structures for accurate future inference. A central challenge is spatial indistinguishability: different nodes may share similar historical patterns yet evolve toward divergent futures, severely degrading forecasting performance in real-world sensor networks. Existing embedding-based and graph neural network (GNN)-based approaches can partially detect such ambiguous nodes but rely on historical similarity, struggling to capture future behavioral divergence. We propose STOT (SpatioTemporal Optimal Transport), a self-supervised framework that resolves spatiotemporal ambiguity via structured masking guided by optimal transport. Our key idea treats indistinguishability as a disambiguation problem: future states are inferred by exploiting concurrent spatial correlations and their time-varying similarity. We design a similarity-aware metric for dynamic inter-node relationships and an optimal transport-based masking strategy to emphasize ambiguous positions during pre-training. A batch consistency constraint preserves semantic coherence, while a random-walk masking mechanism promotes structured context exploration. Experiments on six real-world datasets show that STOT performs competitively with state-of-the-art baselines on the evaluated benchmarks and improved interpretability through transport-plan visualizations.