# Learning with Calibration: Exploring Test-Time Computing of Spatio-Temporal Forecasting

arXiv: https://arxiv.org/abs/2506.00635 · HTML: https://mlsanity.com/paper/2506.00635/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 59 of its 104 references that are in the map.
- First posted on arXiv 31 May 2025.

## Builds on (most cited first, 30 of 59)

- [A Time Series is Worth 64 Words: Long-term Forecasting with Transformers](https://mlsanity.com/paper/2211.14730/) (2022)
- [Are Transformers Effective for Time Series Forecasting?](https://mlsanity.com/paper/2205.13504/) (2022)
- [Spatio-Temporal Graph Convolutional Networks: A Deep Learning Framework for Traffic Forecasting](https://mlsanity.com/paper/1709.04875/) (2017)
- [Does Reinforcement Learning Really Incentivize Reasoning Capacity in LLMs Beyond the Base Model?](https://mlsanity.com/paper/2504.13837/) (2025)
- [Do We Really Need to Access the Source Data? Source Hypothesis Transfer for Unsupervised Domain Adaptation](https://mlsanity.com/paper/2002.08546/) (2020)
- [Graph WaveNet for Deep Spatial-Temporal Graph Modeling](https://mlsanity.com/paper/1906.00121/) (2019)
- [Continual Test-Time Domain Adaptation](https://mlsanity.com/paper/2203.13591/) (2022)
- [A Comprehensive Survey on Test-Time Adaptation under Distribution Shifts](https://mlsanity.com/paper/2303.15361/) (2023)
- [ClimaX: A foundation model for weather and climate](https://mlsanity.com/paper/2301.10343/) (2023)
- [Test-Time Training with Masked Autoencoders](https://mlsanity.com/paper/2209.07522/) (2022)
- [FITS: Modeling Time Series with 10k Parameters](https://mlsanity.com/paper/2307.03756/) (2023)
- [Spatial-Temporal Transformer Networks for Traffic Flow Forecasting](https://mlsanity.com/paper/2001.02908/) (2020)
- [Spatial-Temporal Identity: A Simple yet Effective Baseline for Multivariate Time Series Forecasting](https://mlsanity.com/paper/2208.05233/) (2022)
- [A Survey on Graph Neural Networks for Time Series: Forecasting, Classification, Imputation, and Anomaly Detection](https://mlsanity.com/paper/2307.03759/) (2023)
- [Spatio-Temporal Graph Neural Networks for Predictive Learning in Urban Computing: A Survey](https://mlsanity.com/paper/2303.14483/) (2023)
- [FourierGNN: Rethinking Multivariate Time Series Forecasting from a Pure Graph Perspective](https://mlsanity.com/paper/2311.06190/) (2023)
- [Learning by Transduction](https://mlsanity.com/paper/1301.7375/) (2013)
- [LargeST: A Benchmark Dataset for Large-Scale Traffic Forecasting](https://mlsanity.com/paper/2306.08259/) (2023)
- [Exploring Progress in Multivariate Time Series Forecasting: Comprehensive Benchmarking and Heterogeneity Analysis](https://mlsanity.com/paper/2310.06119/) (2023)
- [The Surprising Effectiveness of Test-Time Training for Few-Shot Learning](https://mlsanity.com/paper/2411.07279/) (2024)
- [Test-Time Training on Nearest Neighbors for Large Language Models](https://mlsanity.com/paper/2305.18466/) (2023)
- [UniST: A Prompt-Empowered Universal Model for Urban Spatio-Temporal Prediction](https://mlsanity.com/paper/2402.11838/) (2024)
- [UrbanGPT: Spatio-Temporal Large Language Models](https://mlsanity.com/paper/2403.00813/) (2024)
- [OneNet: Enhancing Time Series Forecasting Models under Concept Drift by Online Ensembling](https://mlsanity.com/paper/2309.12659/) (2023)
- [Test-Time Adaptation via Self-Training with Nearest Neighbor Information](https://mlsanity.com/paper/2207.10792/) (2022)
- [PM2.5-GNN: A Domain Knowledge Enhanced Graph Neural Network For PM2.5 Forecasting](https://mlsanity.com/paper/2002.12898/) (2020)
- [Deciphering Spatio-Temporal Graph Forecasting: A Causal Lens and Treatment](https://mlsanity.com/paper/2309.13378/) (2023)
- [Learning Fast and Slow for Online Time Series Forecasting](https://mlsanity.com/paper/2202.11672/) (2022)
- [PastNet: Introducing Physical Inductive Biases for Spatio-temporal Video Prediction](https://mlsanity.com/paper/2305.11421/) (2023)
- [TrafficStream: A Streaming Traffic Flow Forecasting Framework Based on Graph Neural Networks and Continual Learning](https://mlsanity.com/paper/2106.06273/) (2021)

## Built on by (most cited first, 9 of 9)

- [STReasoner: Empowering LLMs for Spatio-Temporal Reasoning in Time Series via Spatial-Aware Reinforcement Learning](https://mlsanity.com/paper/2601.03248/) (2026)
- [Learning to Factorize and Adapt: A Versatile Approach Toward Universal Spatio-Temporal Foundation Models](https://mlsanity.com/paper/2601.12083/) (2026)
- [Test-Time Learning of Causal Structure from Interventional Data](https://mlsanity.com/paper/2602.19131/) (2026)
- [UrbanFM: Scaling Urban Spatio-Temporal Foundation Models](https://mlsanity.com/paper/2602.20677/) (2026)
- [From XXLTraffic to EvoXXLTraffic: Scaling Traffic Forecasting to Sensor-Evolving Networks](https://mlsanity.com/paper/2605.29768/) (2026)
- [Select, then Balance: Exploring Exogenous Variable Modeling of Spatio-Temporal Forecasting](https://mlsanity.com/paper/2509.05779/) (2025)
- [Learning from Complexity: Exploring Dynamic Sample Pruning of Spatio-Temporal Training](https://mlsanity.com/paper/2602.19113/) (2026)
- [A2TTA: Anchored-and-Agile Test-Time Adaptation for Evolving Traffic Sensor Networks](https://mlsanity.com/paper/2607.25875/) (2026)
- [More Sensors Only One Field: Rethinking Continual Spatio-Temporal Forecasting](https://mlsanity.com/paper/2609.31325/) (2026)

## Abstract (arXiv)

Spatio-temporal forecasting is crucial in many domains, such as transportation, meteorology, and energy. However, real-world scenarios frequently present challenges such as signal anomalies, noise, and distributional shifts. Existing solutions primarily enhance robustness by modifying network architectures or training procedures. Nevertheless, these approaches are computationally intensive and resource-demanding, especially for large-scale applications. In this paper, we explore a novel test-time computing paradigm, namely learning with calibration, ST-TTC, for spatio-temporal forecasting. Through learning with calibration, we aim to capture periodic structural biases arising from non-stationarity during the testing phase and perform real-time bias correction on predictions to improve accuracy. Specifically, we first introduce a spectral-domain calibrator with phase-amplitude modulation to mitigate periodic shift and then propose a flash updating mechanism with a streaming memory queue for efficient test-time computation. ST-TTC effectively bypasses complex training-stage techniques, offering an efficient and generalizable paradigm. Extensive experiments on real-world datasets demonstrate the effectiveness, universality, flexibility and efficiency of our proposed method.