ST-GFM: Spectral-Temporal Graph Forecasting with Measured Perturbation Bounds and Masked Spectral Reconstruction
Abstract
Graph forecasters for sensor networks are trained in one regime and deployed in others, where sensor coupling and signal frequency content both change. We split this spectral shift into an operator channel and a frequency channel, each with a dimensionless measure. ST-GFM (Spectral-Temporal Graph Forecasting Model) filters every input step with Chebyshev and bidirectional diffusion filters on one learned, non-symmetric operator and alternates them with per-node temporal attention. For the operator channel we prove Frobenius-norm perturbation bounds for both graph branches, show that the Chebyshev bound is attained to first order, and compute its constant from the trained weights and the measured operator norm: 17.9 on METR-LA and 21.5 on PEMS-BAY. Under random edge dropout the trained layer moves by 2.0% to 3.1% of this bound. Masked Spectral Reconstruction (MSR), a self-supervised loss active in the first 40 epochs, matches the log power spectrum of the encoder output to that of the input. For small log-spectral residuals on unclamped bins it is proportional to an Itakura-Saito divergence to leading order. Removing it raises the 60-minute MAE by 0.30 on METR-LA, close to the 0.33 lost when all three self-supervised losses go. Under one shared evaluation pipeline, the 60-minute MAE of ST-GFM is 3.5% below a retrained STAEformer on METR-LA and 13.0% below it on PEMS-BAY. Its 60-minute MAE is 3.0980.017 on METR-LA (five seeds) and 1.5760.006 on PEMS-BAY (three seeds), the lowest PEMS-BAY MAE among twelve published baselines.
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BibTeX
@misc{bohra2026stgfm,
title = {{ST-GFM: Spectral-Temporal Graph Forecasting with Measured Perturbation Bounds and Masked Spectral Reconstruction}},
author = {Aashish Bohra and Vivek Vijay},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.03512},
eprint = {2611.03512},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.03512},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - ST-GFM: Spectral-Temporal Graph Forecasting with Measured Perturbation Bounds and Masked Spectral Reconstruction
AU - Aashish Bohra
AU - Vivek Vijay
PY - 2026
DA - 2026/11/02
PB - arXiv
DO - 10.48550/arxiv.2611.03512
UR - https://arxiv.org/abs/2611.03512
AB - Graph forecasters for sensor networks are trained in one regime and deployed in others, where sensor coupling and signal frequency content both change. We split this spectral shift into an operator channel and a frequency channel, each with a dimensionless measure. ST-GFM (Spectral-Temporal Graph Forecasting Model) filters every input step with Chebyshev and bidirectional diffusion filters on one learned, non-symmetric operator and alternates them with per-node temporal attention. For the operator channel we prove Frobenius-norm perturbation bounds for both graph branches, show that the Chebyshev bound is attained to first order, and compute its constant from the trained weights and the measured operator norm: 17.9 on METR-LA and 21.5 on PEMS-BAY. Under random edge dropout the trained layer moves by 2.0% to 3.1% of this bound. Masked Spectral Reconstruction (MSR), a self-supervised loss active in the first 40 epochs, matches the log power spectrum of the encoder output to that of the input. For small log-spectral residuals on unclamped bins it is proportional to an Itakura-Saito divergence to leading order. Removing it raises the 60-minute MAE by 0.30 on METR-LA, close to the 0.33 lost when all three self-supervised losses go. Under one shared evaluation pipeline, the 60-minute MAE of ST-GFM is 3.5% below a retrained STAEformer on METR-LA and 13.0% below it on PEMS-BAY. Its 60-minute MAE is 3.0980.017 on METR-LA (five seeds) and 1.5760.006 on PEMS-BAY (three seeds), the lowest PEMS-BAY MAE among twelve published baselines.
ER -