Deep neural networks and mixed integer linear optimization

By Matteo Fischetti, Jason Jo. 2018

320 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Computer Vision and Pattern Recognition

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Citations in the corpus

Certified Adversarial Robustness via Randomized Smoothing (2019, methodology): “Exact methods are usually based on Satisfiability Modulo Theories (Katz et al., 2017; Carlini et al., 2017; Ehlers, 2017; Huang et al., 2017) or mixed integer linear programming (Cheng et al., 2017; Lomuscio & Maganti, 2017; Dutta et al., 2017; Fischetti & Jo, 2018; Bunel et al., 2018).”
Training verified learners with learned verifiers (2018, neutral): “Algorithms based on formal verification [7, 10, 14] and mixed integer programming [9, 27] have been proposed to solve this problem for networks with piecewise linear activation functions (like ReLUs and maxpooling).”
Abduction-Based Explanations for Machine Learning Models (2018, methodology): “As a result, a recently proposed encoding of NNs into Mixed Integer Linear Programming is used (Fischetti and Jo 2018).”
Lipschitz-Certifiable Training with a Tight Outer Bound (2020, methodology): “Thus, many veriﬁcation methods are proposed to guarantee stable prediction of input within a perturbation set [18, 5, 9, 16, 38, 34, 23, 11, 3, 30, 8, 43, 2].”
Provable Certificates for Adversarial Examples: Fitting a Ball in the Union of Polytopes (2019, methodology): “Binary networks were trained to distinguish a subset of 1’s and 7’s from the full MNIST dataset.”
On Relating Explanations and Adversarial Examples (2019, methodology): “Also, extracting a smallest size hitting set is NP-hard as well and can be done with the use of modern optimization procedures, e.g. mixed integer programming (MILP) [20] or maximum satisﬁability (MaxSAT) [31].”
Strong mixed-integer programming formulations for trained neural networks (2018, background): “Our contributions are depicted in Figure 1. It serves as a roadmapof the paper. 1.3 Relevant prior work 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”
CAQL: Continuous Action Q-Learning (2019, methodology): “…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., 2018; Kumar et al., 2019), but its application to RL is…”
Globally-Robust Neural Networks (2021, background): “L G ] 11 J un 2021 small models (Fischetti & Jo, 2018; Fromherz et al., 2021; Gehr et al., 2018; Jordan et al., 2019; Tjeng & Tedrake, 2017), requiring several orders of magnitude more time than a typical forward pass of a network; on moderately-large CNNs, these techniques either time out after…”
Optimization Models for Machine Learning: A Survey (2019, methodology): “ adversarial examples in BNNs by maximizing the dierence between the activation of the targeted label ˜0and the predicted label ˜of the input x0, in the nal layer (namely, maxxL ˜0 x L). Contrary to [95], the MIP of [137] does not impose limitations on the 19 search of adversarial examples, apart fr”
IPBoost - Non-Convex Boosting via Integer Programming (2020, methodology): “Moreover, neural network verification via integer programming has been treated in [34, 17].”