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Causality-Inspired Safe Residual Correction for Multivariate Time Series

Jianxiang Xie, Yuncheng Hua, Mingyue Cheng, Flora Salim, Hao Xue

TL;DR

The paper addresses the reliability gap in multivariate time-series forecasting by introducing CRC, a causality-inspired safe residual correction framework. It combines a direction-aware encoder that disentangles self- and cross-node dynamics with a hybrid linear–nonlinear corrector, guarded by a four-fold safety firewall to guarantee non-degradation in deployment. Empirical results across seven datasets and multiple backbones show CRC consistently improves accuracy while achieving high non-degradation rates (NDR), indicating strong deployment reliability and interpretability through directional priors. Limitations include dependence on a pre-defined adjacency prior and conservative safety mechanisms, with future work aimed at online causal discovery and adaptive safety bounds to balance safety and performance.

Abstract

While modern multivariate forecasters such as Transformers and GNNs achieve strong benchmark performance, they often suffer from systematic errors at specific variables or horizons and, critically, lack guarantees against performance degradation in deployment. Existing post-hoc residual correction methods attempt to fix these errors, but are inherently greedy: although they may improve average accuracy, they can also "help in the wrong way" by overcorrecting reliable predictions and causing local failures in unseen scenarios. To address this critical "safety gap," we propose CRC (Causality-inspired Safe Residual Correction), a plug-and-play framework explicitly designed to ensure non-degradation. CRC follows a divide-and-conquer philosophy: it employs a causality-inspired encoder to expose direction-aware structure by decoupling self- and cross-variable dynamics, and a hybrid corrector to model residual errors. Crucially, the correction process is governed by a strict four-fold safety mechanism that prevents harmful updates. Experiments across multiple datasets and forecasting backbones show that CRC consistently improves accuracy, while an in-depth ablation study confirms that its core safety mechanisms ensure exceptionally high non-degradation rates (NDR), making CRC a correction framework suited for safe and reliable deployment.

Causality-Inspired Safe Residual Correction for Multivariate Time Series

TL;DR

The paper addresses the reliability gap in multivariate time-series forecasting by introducing CRC, a causality-inspired safe residual correction framework. It combines a direction-aware encoder that disentangles self- and cross-node dynamics with a hybrid linear–nonlinear corrector, guarded by a four-fold safety firewall to guarantee non-degradation in deployment. Empirical results across seven datasets and multiple backbones show CRC consistently improves accuracy while achieving high non-degradation rates (NDR), indicating strong deployment reliability and interpretability through directional priors. Limitations include dependence on a pre-defined adjacency prior and conservative safety mechanisms, with future work aimed at online causal discovery and adaptive safety bounds to balance safety and performance.

Abstract

While modern multivariate forecasters such as Transformers and GNNs achieve strong benchmark performance, they often suffer from systematic errors at specific variables or horizons and, critically, lack guarantees against performance degradation in deployment. Existing post-hoc residual correction methods attempt to fix these errors, but are inherently greedy: although they may improve average accuracy, they can also "help in the wrong way" by overcorrecting reliable predictions and causing local failures in unseen scenarios. To address this critical "safety gap," we propose CRC (Causality-inspired Safe Residual Correction), a plug-and-play framework explicitly designed to ensure non-degradation. CRC follows a divide-and-conquer philosophy: it employs a causality-inspired encoder to expose direction-aware structure by decoupling self- and cross-variable dynamics, and a hybrid corrector to model residual errors. Crucially, the correction process is governed by a strict four-fold safety mechanism that prevents harmful updates. Experiments across multiple datasets and forecasting backbones show that CRC consistently improves accuracy, while an in-depth ablation study confirms that its core safety mechanisms ensure exceptionally high non-degradation rates (NDR), making CRC a correction framework suited for safe and reliable deployment.
Paper Structure (48 sections, 5 theorems, 14 equations, 2 figures, 3 tables)

This paper contains 48 sections, 5 theorems, 14 equations, 2 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Contributions.
  3. Related Work
  4. Forecasting and Residual Correction Models
  5. Safe and Causal Learning
  6. Our Contribution
  7. Method
  8. Overview.
  9. Structured Residual Representation via a Causality-Inspired Encoder
  10. Directional Encoding with Pairwise Interaction.
  11. Causal State Encoding
  12. Self-Dynamics.
  13. Cross-Node Dynamics.
  14. Gated Aggregation.
  15. Multi-Scale Feature Priors and Augmentation
  16. ...and 33 more sections

Key Result

Proposition 1.2

Under Assumption ass:gate-clip, if $0\le |\delta'|\le \min\{|e|,\tau\}$, then An analogous inequality holds for MSE when $\mathrm{sign}(\delta')=\mathrm{sign}(e)$ and $|\delta'|\le |e|$.

Figures (2)

  • Figure 1: Overview of the Causality-aware Residual Correction (CRC) framework. CRC exposes structured residual representations via a causality-inspired encoder, applies hybrid linear--nonlinear correction, and enforces four explicit safety mechanisms to guarantee non-degradation.
  • Figure 2: Dynamic Spatial Causality Snapshots ($N=4$). Time-evolution of learned directional influence strengths $S_t[i,j]$ ($j \!\to\! i$) by CRC (TimesNet backbone) on the Weather dataset. The encoder captures strongly non-stationary and context-dependent dependencies across four representative windows ($\Delta t = 200$).

Theorems & Definitions (9)

  • Proposition 1.2: Pointwise non-degradation under MAE
  • proof
  • Proposition 1.3: Validation-level non-degradation
  • Theorem 1.4: Probably approximately non-degrading (PAND)
  • proof : Sketch
  • Proposition 1.5: Risk upper bound with blending threshold
  • Proposition 1.6: Linear recoverability via ridge projection
  • proof : Intuition
  • Remark 1.7: Practical implications