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Beyond Immediate Activation: Temporally Decoupled Backdoor Attacks on Time Series Forecasting

Zhixin Liu, Xuanlin Liu, Sihan Xu, Yaqiong Qiao, Ying Zhang, Xiangrui Cai

TL;DR

This work addresses the limitation of existing backdoor attacks on multivariate time series forecasting, which require rigid, synchronous activation of trigger and target patterns. It introduces Temporally Decoupled Backdoor Attack (TDBA), a framework with a position-guided trigger generation module and a position-aware optimization module that enable delayed and dimension-specific activation of target patterns within forecast windows. TDBA employs a Position Guidance Matrix and two trigger-generation variants (GCN-based and Inverse Forecasting) to align triggering with desired activation positions, while a soft-identification-based loss emphasizes attack effectiveness on targeted regions and stealth in non-target regions. Extensive experiments on five real-world datasets demonstrate superior attack effectiveness and stealthiness compared to baselines, with ablations confirming the necessity of both positional guidance and pose-aware optimization. The results underscore security risks in MTS forecasting systems and motivate future work on multi-target learning and cross-domain transferability of backdoor triggers.

Abstract

Existing backdoor attacks on multivariate time series (MTS) forecasting enforce strict temporal and dimensional coupling between triggers and target patterns, requiring synchronous activation at fixed positions across variables. However, realistic scenarios often demand delayed and variable-specific activation. We identify this critical unmet need and propose TDBA, a temporally decoupled backdoor attack framework for MTS forecasting. By injecting triggers that encode the expected location of the target pattern, TDBA enables the activation of the target pattern at any positions within the forecasted data, with the activation position flexibly varying across different variable dimensions. TDBA introduces two core modules: (1) a position-guided trigger generation mechanism that leverages smoothed Gaussian priors to generate triggers that are position-related to the predefined target pattern; and (2) a position-aware optimization module that assigns soft weights based on trigger completeness, pattern coverage, and temporal offset, facilitating targeted and stealthy attack optimization. Extensive experiments on real-world datasets show that TDBA consistently outperforms existing baselines in effectiveness while maintaining good stealthiness. Ablation studies confirm the controllability and robustness of its design.

Beyond Immediate Activation: Temporally Decoupled Backdoor Attacks on Time Series Forecasting

TL;DR

This work addresses the limitation of existing backdoor attacks on multivariate time series forecasting, which require rigid, synchronous activation of trigger and target patterns. It introduces Temporally Decoupled Backdoor Attack (TDBA), a framework with a position-guided trigger generation module and a position-aware optimization module that enable delayed and dimension-specific activation of target patterns within forecast windows. TDBA employs a Position Guidance Matrix and two trigger-generation variants (GCN-based and Inverse Forecasting) to align triggering with desired activation positions, while a soft-identification-based loss emphasizes attack effectiveness on targeted regions and stealth in non-target regions. Extensive experiments on five real-world datasets demonstrate superior attack effectiveness and stealthiness compared to baselines, with ablations confirming the necessity of both positional guidance and pose-aware optimization. The results underscore security risks in MTS forecasting systems and motivate future work on multi-target learning and cross-domain transferability of backdoor triggers.

Abstract

Existing backdoor attacks on multivariate time series (MTS) forecasting enforce strict temporal and dimensional coupling between triggers and target patterns, requiring synchronous activation at fixed positions across variables. However, realistic scenarios often demand delayed and variable-specific activation. We identify this critical unmet need and propose TDBA, a temporally decoupled backdoor attack framework for MTS forecasting. By injecting triggers that encode the expected location of the target pattern, TDBA enables the activation of the target pattern at any positions within the forecasted data, with the activation position flexibly varying across different variable dimensions. TDBA introduces two core modules: (1) a position-guided trigger generation mechanism that leverages smoothed Gaussian priors to generate triggers that are position-related to the predefined target pattern; and (2) a position-aware optimization module that assigns soft weights based on trigger completeness, pattern coverage, and temporal offset, facilitating targeted and stealthy attack optimization. Extensive experiments on real-world datasets show that TDBA consistently outperforms existing baselines in effectiveness while maintaining good stealthiness. Ablation studies confirm the controllability and robustness of its design.
Paper Structure (30 sections, 14 equations, 2 figures, 4 tables)

This paper contains 30 sections, 14 equations, 2 figures, 4 tables.

Table of Contents

  1. Introduction
  2. Related Work
  3. Multivariate Time Series Forecasting.
  4. Backdoor Attacks in Deep Learning.
  5. Notations and Preliminaries
  6. Multivariate Time Series Forecasting
  7. Threat Model and Attack Scenario
  8. Temporally Decoupled Backdoor Attack
  9. Temporally Decoupled Injection Strategy
  10. Position-guided Trigger Injection
  11. Position Guidance Matrix.
  12. GCN-based Trigger Generator with Position Guidance.
  13. Inverse Forecasting Trigger Generator with Position Guidance.
  14. Position-aware Backdoor Optimization
  15. Position-aware Soft Identification.
  16. ...and 15 more sections

Figures (2)

  • Figure 1: (a) Theoretical trigger injections at $t_0$ activating cone-shaped target patterns at $t_1$, $t_2$, and $t_3$ across $F_1$, $F_2$, and $F_3$. (b) Corresponding real-world traffic scenario where control at $t_0$ induces congestion on three roads. $F_1$–$F_3$ in (a) correspond to flow sensors on roads 1–3 in (b).
  • Figure 2: Visualization of the TDBA on the PEMS04 dataset using Autoformer. Four dimensions (163, 164, 166, 168) are attacked, each with its own assigned positional offset. The auxiliary lines in the figure captions are used to connect the trigger or target pattern to the clean data at both ends, maintaining visual uniformity.