A Unified View of Piecewise Linear Neural Network Verification

By Rudy Bunel, Ilker Turkaslan, Philip H. S. Torr, Pushmeet Kohli, Pawan Kumar Mudigonda. 2017

369 citations recorded by the source corpus.

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1. Huan Zhang
2. Sergey Levine
3. Shiqi Wang
4. Hadi Salman
5. Sven Gowal
6. J. Kolter
7. Eric Wong
8. Yoshua Bengio

Citations in the corpus

• Certified Adversarial Robustness via Randomized Smoothing (2019, background): “…is a sum of mbad independent random variables each bounded between zero and one, with E[Ybad] ≤ αmbad and Var(Ybad) ≤ mbadα(1− α), Bernstein’s inequality (Blanchard, 2007) guarantees that with probability at least 1− ρ over the randomness in CERTIFY, Ybad ≤ αmbad + √ 2mbadα(1− α) log(1/ρ) +…”
• A Dual Approach to Scalable Verification of Deep Networks (2018, background): “More recently, researchers have proposed a set of approaches that make use of branch and bound algorithms either directly or via mixed-integer programming solvers [Bunel et al., 2017, Cheng et al., 2017, Tjeng and Tedrake, 2017].”
• Optimization Models for Machine Learning: A Survey (2019, background): “In [47], a branch-and-bound framework for verifying piecewiselinear neural networks is introduced.”
• Beta-CROWN: Efficient Bound Propagation with Per-neuron Split Constraints for Neural Network Robustness Verification (2021, methodology): “Many BaB based complete verifiers (Bunel et al., 2018; Lu & Kumar, 2020) use an LP solver for Eq.”
• A Convex Relaxation Barrier to Tight Robustness Verification of Neural Networks (2019, methodology): “Combining exact and relaxed verifiers, hybrid methods have shown some effectiveness (Bunel et al., 2018; Singh et al., 2019a).”
• CAQL: Continuous Action Q-Learning (2019, methodology): “Versions of this MIP model have been used in neural network verification (Cheng et al., 2017; Lomuscio & Maganti, 2017; Bunel et al., 2018; Dutta et al., 2018; Fischetti & Jo, 2018; Anderson et al., 2019; Tjeng et al., 2019) and analysis (Serra et al.”
• Provable repair of deep neural networks (2021, unknown): “Prior work on DNN verification focused on safety and robustness [4, 6, 11, 15, 18, 30, 33, 34, 49].”
• Fast and Stable Interval Bounds Propagation for Training Verifiably Robust Models (2019, methodology): “[2017], Carlini et al. [2017], Ehlers [2017]. A downside of these methods is their high computational complexity due to the NP-completeness of the problem. In consequence, vast majority of these methods do not scale well to large or even medium size networks. To speed up the training of verifiably r”
• Algorithms for Verifying Deep Neural Networks (2019, methodology): “Representative methods for search and optimization include Reluplex [30], Marabou [31], Planet [32], Sherlock [33], Venus [34], PeregriNN [35], and BaB [36] and its extensions [20], [37], [38].”
• A Statistical Approach to Assessing Neural Network Robustness (2018, background): “, 2017), and even then these solutions do not scale to, for example, common image classification architectures with input dimensions in the hundreds, or apply to networks with nonlinear activation functions (Bunel et al., 2018).”
• Strong mixed-integer programming formulations for trained neural networks (2018, unknown): “In recent years a number of authors have used MIP formulations to model trained neural networks [19,22,24,29,40,47,54,64,66,67,70,80,81], mostly applying big-M formulation techniques to ReLU-based networks.”
• Evaluating Robustness of Neural Networks with Mixed Integer Programming (2017, background): “, 2014) are linear transformations at evaluation time (Bunel et al., 2018).”