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Register a new userDeepSplit: Scalable Verification of Deep Neural Networks via Operator Splitting
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Added by
Shaoru Chen
Publication date
2021
fields
Informatics Engineering
and research's language is
English
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Analyzing the worst-case performance of deep neural networks against input perturbations amounts to solving a large-scale non-convex optimization problem, for which several past works have proposed convex relaxations as a promising alternative. However, even for reasonably-sized neural networks, these relaxations are not tractable, and so must be replaced by even weaker relaxations in practice. In this work, we propose a novel operator splitting method that can directly solve a convex relaxation of the problem to high accuracy, by splitting it into smaller sub-problems that often have analytical solutions. The method is modular and scales to problem instances that were previously impossible to solve exactly due to their size. Furthermore, the solver operations are amenable to fast parallelization with GPU acceleration. We demonstrate our method in obtaining tighter bounds on the worst-case performance of large convolutional networks in image classification and reinforcement learning settings.
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Despite the functional success of deep neural networks (DNNs), their trustworthiness remains a crucial open challenge. To address this challenge, both testing and verification techniques have been proposed. But these existing techniques provide either scalability to large networks or formal guarantees, not both. In this paper, we propose a scalable quantitative verification framework for deep neural networks, i.e., a test-driven approach that comes with formal guarantees that a desired probabilistic property is satisfied. Our technique performs enough tests until soundness of a formal probabilistic property can be proven. It can be used to certify properties of both deterministic and randomized DNNs. We implement our approach in a tool called PROVERO and apply it in the context of certifying adversarial robustness of DNNs. In this context, we first show a new attack-agnostic measure of robustness which offers an alternative to purely attack-based methodology of evaluating robustness being reported today. Second, PROVERO provides certificates of robustness for large DNNs, where existing state-of-the-art verification tools fail to produce conclusive results. Our work paves the way forward for verifying properties of distributions captured by real-world deep neural networks, with provable guarantees, even where testers only have black-box access to the neural network.
This paper addresses the problem of formally verifying desirable properties of neural networks, i.e., obtaining provable guarantees that neural networks satisfy specifications relating their inputs and outputs (robustness to bounded norm adversarial perturbations, for example). Most previous work on this topic was limited in its applicability by the size of the network, network architecture and the complexity of properties to be verified. In contrast, our framework applies to a general class of activation functions and specifications on neural network inputs and outputs. We formulate verification as an optimization problem (seeking to find the largest violation of the specification) and solve a Lagrangian relaxation of the optimization problem to obtain an upper bound on the worst case violation of the specification being verified. Our approach is anytime i.e. it can be stopped at any time and a valid bound on the maximum violation can be obtained. We develop specialized verification algorithms with provable tightness guarantees under special assumptions and demonstrate the practical significance of our general verification approach on a variety of verification tasks.
Convolutional Neural Networks (CNN) have redefined the state-of-the-art in many real-world applications, such as facial recognition, image classification, human pose estimation, and semantic segmentation. Despite their success, CNNs are vulnerable to adversarial attacks, where slight changes to their inputs may lead to sharp changes in their output in even well-trained networks. Set-based analysis methods can detect or prove the absence of bounded adversarial attacks, which can then be used to evaluate the effectiveness of neural network training methodology. Unfortunately, existing verification approaches have limited scalability in terms of the size of networks that can be analyzed. In this paper, we describe a set-based framework that successfully deals with real-world CNNs, such as VGG16 and VGG19, that have high accuracy on ImageNet. Our approach is based on a new set representation called the ImageStar, which enables efficient exact and over-approximative analysis of CNNs. ImageStars perform efficient set-based analysis by combining operations on concrete images with linear programming (LP). Our approach is implemented in a tool called NNV, and can verify the robustness of VGG networks with respect to a small set of input states, derived from adversarial attacks, such as the DeepFool attack. The experimental results show that our approach is less conservative and faster than existing zonotope methods, such as those used in DeepZ, and the polytope method used in DeepPoly.
Graph Neural Networks (GNN) is an emerging field for learning on non-Euclidean data. Recently, there has been increased interest in designing GNN that scales to large graphs. Most existing methods use graph sampling or layer-wise sampling techniques to reduce training time. However, these methods still suffer from degrading performance and scalability problems when applying to graphs with billions of edges. This paper presents GBP, a scalable GNN that utilizes a localized bidirectional propagation process from both the feature vectors and the training/testing nodes. Theoretical analysis shows that GBP is the first method that achieves sub-linear time complexity for both the precomputation and the training phases. An extensive empirical study demonstrates that GBP achieves state-of-the-art performance with significantly less training/testing time. Most notably, GBP can deliver superior performance on a graph with over 60 million nodes and 1.8 billion edges in less than half an hour on a single machine. The codes of GBP can be found at https://github.com/chennnM/GBP .
Formal verification of neural networks is an active topic of research, and recent advances have significantly increased the size of the networks that verification tools can handle. However, most methods are designed for verification of an idealized model of the actual network which works over real arithmetic and ignores rounding imprecisions. This idealization is in stark contrast to network quantization, which is a technique that trades numerical precision for computational efficiency and is, therefore, often applied in practice. Neglecting rounding errors of such low-bit quantized neural networks has been shown to lead to wrong conclusions about the networks correctness. Thus, the desired approach for verifying quantized neural networks would be one that takes these rounding errors into account. In this paper, we show that verifying the bit-exact implementation of quantized neural networks with bit-vector specifications is PSPACE-hard, even though verifying idealized real-valued networks and satisfiability of bit-vector specifications alone are each in NP. Furthermore, we explore several practical heuristics toward closing the complexity gap between idealized and bit-exact verification. In particular, we propose three techniques for making SMT-based verification of quantized neural networks more scalable. Our experiments demonstrate that our proposed methods allow a speedup of up to three orders of magnitude over existing approaches.
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