Recovery Guarantees for Compressible Signals with Adversarial Noise

Authors: Jasjeet Dhaliwal, Kyle Hambrook
Published: 2019-07-15 | Updated: 2019-08-07

Source: https://arxiv.org/abs/1907.06565

PDF: https://arxiv.org/pdf/1907.06565

Labels Predicted by AI

アルゴリズム設計 深層学習手法 敵対的攻撃

Please note that these labels were automatically added by AI. Therefore, they may not be entirely accurate.
For more details, please see the About the Literature Database page.

Abstract

We provide recovery guarantees for compressible signals that have been corrupted with noise and extend the framework introduced in to defend neural networks against ℓ₀-norm, ℓ₂-norm, and ℓ_∞-norm attacks. Our results are general as they can be applied to most unitary transforms used in practice and hold for ℓ₀-norm, ℓ₂-norm, and ℓ_∞-norm bounded noise. In the case of ℓ₀-norm noise, we prove recovery guarantees for Iterative Hard Thresholding (IHT) and Basis Pursuit (BP). For ℓ₂-norm bounded noise, we provide recovery guarantees for BP and for the case of ℓ_∞-norm bounded noise, we provide recovery guarantees for Dantzig Selector (DS). These guarantees theoretically bolster the defense framework introduced in for defending neural networks against adversarial inputs. Finally, we experimentally demonstrate the effectiveness of this defense framework against an array of ℓ₀, ℓ₂ and ℓ_∞ norm attacks.