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1. The Case for Scalable Quantitative Neural Network Analysis

   https://doi.org/10.1145/3617574.3617862  

   Downing, Mara; Bultan, Tevfik (December 2023, ACM)

   Neural networks are an increasingly common tool for solving problems that require complex analysis and pattern matching, such as identifying stop signs in a self driving car or processing medical imagery during diagnosis. Accordingly, verification of neural networks for safety and correctness is of great importance, as mispredictions can have catastrophic results in safety critical domains. As neural networks are known to be sensitive to small changes in input, leading to vulnerabilities and adversarial attacks, analyzing the robustness of networks to small changes in input is a key piece of evaluating their safety and correctness. However, there are many real-world scenarios where the requirements of robustness are not clear cut, and it is crucial to develop measures that assess the level of robustness of a given neural network model and compare levels of robustness across different models, rather than using a binary characterization such as robust vs. not robust. We believe there is great need for developing scalable quantitative robustness verification techniques for neural networks. Formal verification techniques can provide guarantees of correctness, but most existing approaches do not provide quantitative robustness measures and are not effective in analyzing real-world network sizes. On the other hand, sampling-based quantitative robustness is not hindered much by the size of networks but cannot provide sound guarantees of quantitative results. We believe more research is needed to address the limitations of both symbolic and sampling-based verification approaches and create sound, scalable techniques for quantitative robustness verification of neural networks. 

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2. NNV2.0: The neural network verification tool

   Diego Manzanas Lopez; Sung Woo Choi; Hoang-Dung Tran; Taylor T. Johnson (July 2023, The 35th International Conference on Computer-Aided Verification)

   This manuscript presents the updated version of the Neural Network Verification (NNV) tool. NNV is a formal verification software tool for deep learning models and cyber-physical systems with neural network components. NNV was first introduced as a verification framework for feedforward and convolutional neural networks, as well as for neural network control systems. Since then, numerous works have made significant improvements in the verification of new deep learning models, as well as tackling some of the scalability issues that may arise when verifying complex models. In this new version of NNV, we introduce verification support for multiple deep learning models, including neural ordinary differential equations, semantic segmentation networks and recurrent neural networks, as well as a collection of reachability methods that aim to reduce the computation cost of reachability analysis of complex neural networks. We have also added direct support for standard input verification formats in the community such as VNNLIB (verification properties), and ONNX (neural networks) formats. We present a collection of experiments in which NNV verifies safety and robustness properties of feedforward, convolutional, semantic segmentation and recurrent neural networks, as well as neural ordinary differential equations and neural network control systems. Furthermore, we demonstrate the capabilities of NNV against a commercially available product in a collection of benchmarks from control systems, semantic segmentation, image classification, and time-series data. 

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3. Global optimization of objective functions represented by ReLU networks

   https://doi.org/10.1007/s10994-021-06050-2  

   Strong, Christopher A.; Wu, Haoze; Zeljić, Aleksandar; Julian, Kyle D.; Katz, Guy; Barrett, Clark; Kochenderfer, Mykel J. (October 2021, Machine Learning)

   Neural networks can learn complex, non-convex functions, and it is challenging to guarantee their correct behavior in safety-critical contexts. Many approaches exist to find failures in networks (e.g., adversarial examples), but these cannot guarantee the absence of failures. Verification algorithms address this need and provide formal guarantees about a neural network by answering "yes or no" questions. For example, they can answer whether a violation exists within certain bounds. However, individual "yes or no" questions cannot answer qualitative questions such as “what is the largest error within these bounds”; the answers to these lie in the domain of optimization. Therefore, we propose strategies to extend existing verifiers to perform optimization and find: (i) the most extreme failure in a given input region and (ii) the minimum input perturbation required to cause a failure. A naive approach using a bisection search with an off-the-shelf verifier results in many expensive and overlapping calls to the verifier. Instead, we propose an approach that tightly integrates the optimization process into the verification procedure, achieving better runtime performance than the naive approach. We evaluate our approach implemented as an extension of Marabou, a state-of-the-art neural network verifier, and compare its performance with the bisection approach and MIPVerify, an optimization-based verifier. We observe complementary performance between our extension of Marabou and MIPVerify 

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4. Robustness Certificates for Implicit Neural Networks: A Mixed Monotone Contractive Approach

   Jafarpour, S; Abate, M.; Davydov A.; Bullo, F.; Coogan S. (May 2022, Proceedings of The 4th Annual Learning for Dynamics and Control Conference, PMLR)

   Implicit neural networks are a general class of learning models that replace the layers in traditional feedforward models with implicit algebraic equations. Compared to traditional learning models, implicit networks offer competitive performance and reduced memory consumption. However, they can remain brittle with respect to input adversarial perturbations. This paper proposes a theoretical and computational framework for robustness verification of implicit neural networks; our framework blends together mixed monotone systems theory and contraction theory. First, given an implicit neural network, we introduce a related embedded network and show that, given an infinity-norm box constraint on the input, the embedded network provides an infinity-norm box overapproximation for the output of the original network. Second, using infinity-matrix measures, we propose sufficient conditions for well-posedness of both the original and embedded system and design an iterative algorithm to compute the infinity-norm box robustness margins for reachability and classification problems. Third, of independent value, we show that employing a suitable relative classifier variable in our analysis will lead to tighter bounds on the certified adversarial robustness in classification problems. Finally, we perform numerical simulations on a Non-Euclidean Monotone Operator Network (NEMON) trained on the MNIST dataset. In these simulations, we compare the accuracy and run time of our mixed monotone contractive approach with the existing robustness verification approaches in the literature for estimating the certified adversarial robustness. 

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5. First three years of the international verification of neural networks competition (VNN-COMP)

   https://doi.org/10.1007/s10009-023-00703-4  

   Brix, Christopher; Müller, Mark Niklas; Bak, Stanley; Johnson, Taylor T.; Liu, Changliu (May 2023, International Journal on Software Tools for Technology Transfer)

   This paper presents a summary and meta-analysis of the first three iterations of the annual International Verification of Neural Networks Competition (VNN-COMP), held in 2020, 2021, and 2022. In the VNN-COMP, participants submit software tools that analyze whether given neural networks satisfy specifications describing their input-output behavior. These neural networks and specifications cover a variety of problem classes and tasks, corresponding to safety and robustness properties in image classification, neural control, reinforcement learning, and autonomous systems. We summarize the key processes, rules, and results, present trends observed over the last three years, and provide an outlook into possible future developments. 

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