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arXiv 2604.03427cs.LGcs.SYeess.SY
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深度状态空间模型在预测中的对抗鲁棒性

Adversarial Robustness of Deep State Space Models for Forecasting

University of Pennsylvania(宾夕法尼亚大学);KTH Royal Institute of Technology(瑞典皇家理工学院)

Sribalaji C. Anand, George J. Pappas

AI总结:

本文研究深度状态空间模型在预测中的对抗鲁棒性,通过控制理论视角,提出基于Spacetime SSM的鲁棒预测器设计方法,并推导出对抗预测误差的闭式界。

摘要:

状态空间模型(SSM)在时间序列预测中表现出色,但其对抗扰动下的鲁棒性尚不明确。本文通过控制理论视角,聚焦最近提出的Spacetime SSM预测器,证明解码器-only Spacetime架构在自回归数据生成过程中可表示最优卡尔曼预测器。基于此,将鲁棒预测器设计建模为Stackelberg博弈,针对最坏情况的隐形对手,受限于检测预算,通过对抗训练解决。推导出对抗预测误差的闭式界,揭示开环不稳定、闭环不稳定和解码器状态维度如何放大脆弱性,提供鲁棒预测器设计的可行原则。最后证明即使对手无法访问预测器,也可通过利用模型的局部线性输入输出行为构造有效攻击,无需梯度计算。实验表明,无模型攻击在无梯度计算时可导致至少33%的误差增加。

英文摘要:

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.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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