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Adversarial Robustness of Deep State Space Models for Forecasting

arXiv:2604.03427v1 Announce Type: new Abstract: State-space model (SSM) for time-series forecasting have demonstrated strong empirical performance on benchmark datasets, yet their robustness under adversarial perturbations is poorly understood. We address this gap through a control-theoretic lens, focusing on the recently proposed Spacetime SSM forecaster. We first establish that the decoder-only Spacetime architecture can represent the optimal Kalman predictor when the underlying data-generating process is autoregressive - a property no other SSM possesses. Building on this, we formulate robust forecaster design as a Stackelberg game against worst-case stealthy adversaries constrained by a detection budget, and solve it via adversarial training. We derive closed-form bounds on adversarial forecasting error that expose how open-loop instability, closed-loop instability, and decoder state dimension each amplify vulnerability - offering actionable principles towards robust forecaster de

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Sribalaji C. Anand, George J. Pappas · · 1 min read · 13 views
#cs.LG #cs.SY #eess.SY

arXiv:2604.03427v1 Announce Type: new Abstract: State-space model (SSM) for time-series forecasting have demonstrated strong empirical performance on benchmark datasets, yet their robustness under adversarial perturbations is poorly understood. We address this gap through a control-theoretic lens, focusing on the recently proposed Spacetime SSM forecaster. We first establish that the decoder-only Spacetime architecture can represent the optimal Kalman predictor when the underlying data-generating process is autoregressive - a property no other SSM possesses. Building on this, we formulate robust forecaster design as a Stackelberg game against worst-case stealthy adversaries constrained by a detection budget, and solve it via adversarial training. We derive closed-form bounds on adversarial forecasting error that expose how open-loop instability, closed-loop instability, and decoder state dimension each amplify vulnerability - offering actionable principles towards robust forecaster design. Finally, we show that even adversaries with no access to the forecaster can nonetheless construct effective attacks by exploiting the model's locally linear input-output behavior, bypassing gradient computations entirely. Experiments on the Monash benchmark datasets highlight that model-free attacks, without any gradient computation, can cause at least 33% more error than projected gradient descent with a small step size.

Executive Summary

This article explores the adversarial robustness of deep state space models for time-series forecasting, filling a significant gap in understanding their vulnerabilities under adversarial perturbations. The authors employ a control-theoretic lens to analyze the recently proposed Spacetime SSM forecaster, demonstrating its unique ability to represent the optimal Kalman predictor. By formulating robust forecaster design as a Stackelberg game and solving it via adversarial training, they derive closed-form bounds on adversarial forecasting error and propose actionable principles for robust forecaster design. The article also highlights the effectiveness of model-free attacks in causing significant errors, underscoring the need for robustness in time-series forecasting models.

Key Points

  • ▸ The Spacetime SSM forecaster can represent the optimal Kalman predictor when the underlying data-generating process is autoregressive.
  • ▸ Robust forecaster design is formulated as a Stackelberg game against worst-case stealthy adversaries constrained by a detection budget.
  • ▸ Closed-form bounds on adversarial forecasting error are derived, exposing the amplifying effects of open-loop instability, closed-loop instability, and decoder state dimension.

Merits

Strength in Formulation

The article's formulation of robust forecaster design as a Stackelberg game provides a clear and actionable framework for robustness analysis.

Insight into Model Vulnerabilities

The authors' identification of the unique vulnerabilities of the Spacetime SSM forecaster sheds light on the need for robustness in time-series forecasting models.

Demerits

Limited Experimental Scope

The article's experimental evaluation is limited to the Monash benchmark datasets, which may not be representative of the broader range of time-series forecasting applications.

Model-Free Attack Implications

The article's findings on the effectiveness of model-free attacks may have significant implications for the development of robust time-series forecasting models, but these implications are not fully explored.

Expert Commentary

This article makes a significant contribution to the field of adversarial robustness in deep learning, shedding light on the unique vulnerabilities of the Spacetime SSM forecaster. The authors' formulation of robust forecaster design as a Stackelberg game provides a clear and actionable framework for robustness analysis, and their findings on the effectiveness of model-free attacks have significant implications for the development of robust time-series forecasting models. However, the article's experimental evaluation is limited to the Monash benchmark datasets, and the implications of the findings on model-free attacks are not fully explored. Nonetheless, this article is a valuable addition to the literature on adversarial robustness in deep learning, and its findings have significant implications for both practical applications and policy-making.

Recommendations

  • ✓ Future research should focus on expanding the experimental scope of the article to include a broader range of time-series forecasting applications.
  • ✓ The development of robust time-series forecasting models should be prioritized in areas such as finance, healthcare, and energy management, where forecasting reliability is critical.

Sources

Original: arXiv - cs.LG

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