Analytical Bounds on the Local Lipschitz Constants of ReLU Networks

Avant, Trevor; Morgansen, Kristi A.

doi:10.1109/tnnls.2023.3273228

Cited by 3 publications

(1 citation statement)

References 13 publications

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“…isSaf e ← F alse; Szegedy et al 2014). Here we extend the result in (Avant and Morgansen 2021) to Lipschitz constant estimation for BNNs. The n x in Line 10 denotes the system dimension.…”

Section: Safe Weight Set Construction For Bnnmentioning

confidence: 57%

Safety Verification of Nonlinear Systems with Bayesian Neural Network Controllers

Zeng

Yang

Zhang

et al. 2023

AAAI

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Bayesian neural networks (BNNs) retain NN structures with a probability distribution placed over their weights. With the introduced uncertainties and redundancies, BNNs are proper choices of robust controllers for safety-critical control systems. This paper considers the problem of verifying the safety of nonlinear closed-loop systems with BNN controllers over unbounded-time horizon. In essence, we compute a safe weight set such that as long as the BNN controller is always applied with weights sampled from the safe weight set, the controlled system is guaranteed to be safe. We propose a novel two-phase method for the safe weight set computation. First, we construct a reference safe control set that constraints the control inputs, through polynomial approximation to the BNN controller followed by polynomial-optimization-based barrier certificate generation. Then, the computation of safe weight set is reduced to a range inclusion problem of the BNN on the system domain w.r.t. the safe control set, which can be solved incrementally and the set of safe weights can be extracted. Compared with the existing method based on invariant learning and mixed-integer linear programming, we could compute safe weight sets with larger radii on a series of linear benchmarks. Moreover, experiments on a series of widely used nonlinear control tasks show that our method can synthesize large safe weight sets with probability measure as high as 95% even for a large-scale system of dimension 7.

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Section: Safe Weight Set Construction For Bnnmentioning

confidence: 57%

Safety Verification of Nonlinear Systems with Bayesian Neural Network Controllers

Zeng

Yang

Zhang

et al. 2023

AAAI

View full text Add to dashboard Cite

show abstract

Chordal Sparsity for Lipschitz Constant Estimation of Deep Neural Networks

Xue

Lindemann

Robey

et al. 2022

2022 IEEE 61st Conference on Decision and Control (CDC)

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Multivalued Classification of Computer Attacks Using Artificial Neural Networks with Multiple Outputs

Shelukhin,

Rakovsky

2023

jour

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Modern computer networks (CN), having a complex and often heterogeneous structure, generate large volumes of multi-dimensional multi-label data. Accounting for information about multi-label experimental data (ED) can improve the efficiency of solving a number of information security problems: from CN profiling to detecting and preventing computer attacks on CN. The aim of the work is to develop a multi-label artificial neural network (ANN) architecture for detecting and classifying computer attacks in multi-label ED, and its comparative analysis with known analogues in terms of binary metrics for assessing the quality of classification. A formalization of ANN in terms of matrix algebra is proposed, which allows taking into account the case of multi-label classification and the new architecture of ANN with multiple output using the proposed formalization. The advantage of the proposed formalization is the conciseness of a number of entries associated with the ANN operating mode and learning mode. Proposed architecture allows solving the problems of detecting and classifying multi-label computer attacks, on average, 5% more efficiently than known analogues. The observed gain is due to taking into account multi-label patterns between class labels at the training stage through the use of a common first layer. The advantages of the proposed ANN architecture are scalability to any number of class labels and fast convergence.

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Analytical Bounds on the Local Lipschitz Constants of ReLU Networks

Cited by 3 publications

References 13 publications

Safety Verification of Nonlinear Systems with Bayesian Neural Network Controllers

Safety Verification of Nonlinear Systems with Bayesian Neural Network Controllers

Chordal Sparsity for Lipschitz Constant Estimation of Deep Neural Networks

Multivalued Classification of Computer Attacks Using Artificial Neural Networks with Multiple Outputs

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