Improving Spatio-Temporal Residual Error Propagation by Mitigating Over-Squashing

• URL: http://arxiv.org/abs/2605.18068v1
• Date: Mon, 18 May 2026 08:51:33 GMT
• Title: Improving Spatio-Temporal Residual Error Propagation by Mitigating Over-Squashing
• Abstract summary: We introduce Teger, a structured uncertainty module that overcomes the spa- tial and temporal limitations of error-related autoregressive forecasting.<n>Teger is backbone-agnostic, requiring only the latent state produced by any autoregressive encoder.
• Score: 4.62541204592513
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Residual error propagation remains a fundamental problem in recurrent models, where small prediction inaccuracies compound over time and degrade long-horizon performance. Accurately modeling the correlation structure of such residuals is critical for reliable uncertainty quantification in probabilistic multivariate timeseries forecasting. While recent time-series deep models efficiently parametrize time-varying contemporaneous correlations, they often assume temporal independence of errors and neglect spatial correlation across the observed network. In this paper, we introduce Teger, a structured uncertainty module that overcomes the spa- tial and temporal limitations of error-correlated autoregressive forecasting. Teger proposes a spatial curvature-aware graph rewiring mechanism explicitly strengthening information-bottleneck edges identified by discrete Forman curvature. The component is integrated into a low-rank-plus-diagonal covariance head, preserving tractable inference via the Woodbury identity. Teger is backbone-agnostic, requiring only the latent state produced by any autoregressive encoder. We provide theoretical evidence of Teger, and experimentally evaluate it on LSTM, Transformer, and xLSTM backbones across four real-world spatio-temporal datasets, showing consistent improvement in Continuous Ranked Probability Score (CRPS). We further provide a formal theoretical analysis connecting curvature-aware rewiring to (i) oversquashing alleviation, (ii) improved spectral connectivity, (iii) reduced effective resistance, and (iv) improved covariance calibration bounds

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