Safety Verification and Robustness Analysis of Neural Networks via Quadratic Constraints and Semidefinite Programming

Fazlyab, Mahyar; Morari, Manfred; Pappas, George J.

doi:10.48550/arxiv.1903.01287

Cited by 21 publications

(61 citation statements)

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“…Here we follow the general approach in [8], [9], introducing the updates needed for multiple ellipsoidally bounded inputs. Consider the following general neural network with hidden layers,…”

Section: Robustness Of Predictionmentioning

confidence: 99%

“…Our goal is to bound the resulting output π(z 0 ) of the neural network by an ellipsoid. To this end, we first abstract the neural network via Quadratic Constraints (QC) [9] and then use the S-procedure to propagate the q input ellipsoids through the network. We begin with the following definition.…”

Section: Robustness Of Predictionmentioning

confidence: 99%

“…The quadratic constraint for the activation layers, denoted by Q is presented in [9] (Lemma 4) and remains unchanged in our formulation. Now consider the implicit equation Bz = φ(Az + b) in ( 10) describing the neural network, where φ satisfies the quadratic constraint defined by Q.…”

Section: Robustness Of Predictionmentioning

confidence: 99%

“…In this context, tuning of the detector is important to balance the sensitivity of the detector with the prevalence of false alarms and while data-driven techniques are not new to fault detection, tuning to-date has been done empirically. In this paper we leverage recent results to quantify the robustness of neural networks [8], [9] to develop a novel data-driven anomaly detector with guarantees on the upper limit of the false alarm rate.…”

Section: Introductionmentioning

confidence: 99%

“…Quantifying the robustness of neural networks is originally motivated by their vulnerability to adversarial attacks, i.e., carefully chosen small input perturbations that can drastically change their output. To this end, a plethora of tools have been developed to bound the output of neural networks for a given range of inputs (e.g., the set of plausible attacks) [9]- [16]. Our particular interest in this paper is the uncertainty propagation technique put forth in [8], in which the authors develop a semi-definite program that propagates an input ellipsoid (e.g., confidence region of a density function) through the neural network to obtain guaranteed ellipsoidal over-approximation of the output set.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Performance Bounds for Neural Network Estimators: Applications in Fault Detection

Hashemi¹,

Fazlyab

Ruths³

2021

2021 American Control Conference (ACC)

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We exploit recent results in quantifying the robustness of neural networks to input variations to construct and tune a model-based anomaly detector, where the datadriven estimator model is provided by an autoregressive neural network. In tuning, we specifically provide upper bounds on the rate of false alarms expected under normal operation. To accomplish this, we provide a theory extension to allow for the propagation of multiple confidence ellipsoids through a neural network. The ellipsoid that bounds the output of the neural network under the input variation informs the sensitivity -and thus the threshold tuning -of the detector. We demonstrate this approach on a linear and nonlinear dynamical system.

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Section: Robustness Of Predictionmentioning

confidence: 99%

Section: Robustness Of Predictionmentioning

confidence: 99%

Section: Robustness Of Predictionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%