Fast and Effective Robustness Certification for Recurrent Neural Networks.

We present a scalable and precise verifier for recurrent neural networks, called Prover based on two novel ideas: (i) a method to compute a set of polyhedral abstractions for the non-convex and nonlinear ... recurrent update functions by combining sampling, optimization, and Fermat's theorem, and (ii) a gradient descent based algorithm for abstraction refinement guided by the certification problem that combines ... Fig. 1 shows how our proposed R2: Robustness certifier for Recurrent neural networks proves the robustness of the model. ...

<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2005.13300v3">arXiv:2005.13300v3</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/wzopdvt3jnch5lvqsiy2psiuve">fatcat:wzopdvt3jnch5lvqsiy2psiuve</a> </span>

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This work proposes an incremental dissipativity-based robustness certificate for neural networks in the form of a linear matrix inequality for each layer. ... We also propose an equivalent spectral norm bound for this certificate which is scalable to neural networks with multiple layers. ... ACKNOWLEDGMENT The authors acknowledge comments from Julien Béguinot (Télécom Paris -Institut Polytechnique de Paris) and Léo Monbroussou ( École Normale Supérieure Paris-Saclay -Institut Polytechnique ...

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This tutorial will particularly highlight state-of-the-art techniques in adversarial attacks and robustness verification of deep neural networks (DNNs). ... We will also introduce some effective countermeasures to improve robustness of deep learning models, with a particular focus on adversarial training. ... their extension to recurrent neural networks [10] . ...

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We then propose an optimization-based approach FROWN (Fastened CROWN): a general algorithm to tighten robustness certificates for neural networks. ... Extensive experiments on various networks trained individually verify the effectiveness of FROWN in safeguarding larger robust regions. ... Acknowledgement This work is partially supported by the General Research Fund (Project 14236516) of the Hong Kong Research Grants Council, and MIT-Quest program. ...

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Specifically, we aim to train deep neural networks that not only are robust to adversarial perturbations but also whose robustness can be verified more easily. ... We explore the concept of co-design in the context of neural network verification. ... In general, the process of training a robust neural network and then formally verifying its robustness happens in two steps. • Step 1: Training 2018) , propose a method for step 2 (the certification ...

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The large majority of them verify trained neural networks and employ either SMT, optimization, or abstract interpretation techniques. ... Thanks to the availability of mature tools, their use is well established in the industry, and in particular to check safety-critical applications as they undergo a stringent certification process. ... Acknowledgements This work is partially supported by Airbus and the European Research Council under Consolidator Grant Agreement 681393 -MOPSA. ...

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It remains an open problem to quantify robustness for recurrent networks, especially LSTM and GRU. ... We demonstrate its effectiveness on different network architectures and show that the robustness quantification on individual steps can lead to new insights. ... Acknowledgment The authors would like to thank Zhuolun Leon He for useful discussion. ...

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AbstractWe present a scalable and precise verifier for recurrent neural networks, called Prover based on two novel ideas: (i) a method to compute a set of polyhedral abstractions for the non-convex and ... non-linear recurrent update functions by combining sampling, optimization, and Fermat's theorem, and (ii) a gradient descent based algorithm for abstraction refinement guided by the certification problem ... Introduction Recurrent neural networks (RNNs) are widely used to model long-term dependencies in lengthy sequential signals [11, 27, 43] . ...

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Deep neural networks (DNNs) are widely developed and applied in many areas, and the quality assurance of DNNs is critical. ... Specifically, we (1) propose a line of mutation rules, including model level mutation and specification level mutation, to effectively explore the two-dimensional input space of neural network verifiers ... and verify regular properties for recurrent neural networks. ...

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Through experiments on MNIST and CIFAR-10, we demonstrate the effectiveness of our spectral bound in improving generalization and provable robustness of deep networks. ... We show that our spectral bound is an effective regularizer and can be used to bound either the lipschitz constant or curvature values (eigenvalues of the Hessian) of neural networks. ... Dhillon, and Luca Daniel. Towards fast computation of certified robustness for relu networks. In International Conference on Machine Learning (ICML), July 2018. ...

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Training certifiable neural networks enables one to obtain models with robustness guarantees against adversarial attacks. ... We demonstrate the flexibility and effectiveness of our framework on standard benchmarks; it applies to networks of different architectures and general activation functions. ... Therefore, our method is also applicable to other network architectures, such as convolutional neural networks (CNN), residual networks (ResNet) and recurrent neural networks (RNN). III. ...

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In recent years, it has been seen that deep neural networks are lacking robustness and are likely to break in case of adversarial perturbations in input data. ... This survey also highlights the fragility of the advanced deep neural networks in NLP and the challenges in defending them. ... A new set of methods to achieve robustness were proposed in the direction of providing a certificate of robustness for a neural network, attempting to put an end to this race. ...

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This paper provides a comprehensive overview of research topics and foundational principles of research methods for adversarial robustness of deep learning models, including attacks, defenses, verification ... Adversarial robustness studies the worst-case performance of a machine learning model to ensure safety and reliability. ... Throughout this paper, we focus on adversarial robustness of neural networks for classification tasks. ...

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Deep neural networks can be fragile and sensitive to small input perturbations that might cause a significant change in the output. ... In this paper, we employ contraction theory to improve the robustness of neural ODEs (NODEs). ... Contractivity has been used to improve the well-posedness of implicit neural networks [16] and the trainability of recurrent neural networks [17] . ...

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We then propose an optimization-based approach FROWN (Fastened CROWN): a general algorithm to tighten robustness certificates for neural networks. ... Extensive experiments on various networks trained individually verify the effectiveness of FROWN in safeguarding larger robust regions. ... Acknowledgement This work is partially supported by the General Research Fund (Project 14236516) of the Hong Kong Research Grants Council, and MIT-Quest program. ...

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