Semialgebraic Representation of Monotone Deep Equilibrium Models and Applications to Certification

Authors: Tong Chen, Jean B. Lasserre, Victor Magron, Edouard Pauwels

NeurIPS 2021 | Conference PDF | Archive PDF | Plain Text | LLM Run Details

Reproducibility Variable Result LLM Response
Research Type Experimental In this section, we present the experimental results of Robustness Model, Lipschitz Model and Ellipsoid Model described in Section 3 for a pretrained mon DEQ on MNIST dataset. Experimental results show that the proposed models outperform existing approaches for mon DEQ certification.
Researcher Affiliation Academia Tong Chen LAAS-CNRS Université de Toulouse 31400 Toulouse, France tchen@laas.fr Jean-Bernard Lasserre LAAS-CNRS & IMT Université de Toulouse 31400 Toulouse, France lasserre@laas.fr Victor Magron LAAS-CNRS Université de Toulouse 31400 Toulouse, France vmagron@laas.fr Edouard Pauwels IRIT & IMT Université de Toulouse 31400 Toulouse, France edouard.pauwels@irit.fr
Pseudocode No The paper describes procedures and models but does not include any explicitly labeled 'Pseudocode' or 'Algorithm' blocks or structured steps formatted as code.
Open Source Code Yes The code of all our models is available at https://github.com/Neur IPS2021Paper4075/Semi Mon DEQ.
Open Datasets Yes In this section, we present the experimental results of Robustness Model, Lipschitz Model and Ellipsoid Model described in Section 3 for a pretrained mon DEQ on MNIST dataset. Training is based on the normalized MNIST database in [45], we use the same normalization setting on each test example with mean µ = 0.1307 and standard deviation σ = 0.3081... [46] Le Cun Yann, Cortes Corinna, and Burges Christopher J. C. Mnist handwritten digit database. 2010. [ATT Labs Online].
Dataset Splits No The paper mentions using 'the first 100 test MNIST examples' and refers to 'training hyperparameters...the same as in Table D1 of [45]', but it does not explicitly detail the train/validation/test dataset splits (e.g., percentages or counts) within its own text.
Hardware Specification Yes All experiments are performed on a personal laptop with an Intel 8-Core i7-8665U CPU @ 1.90GHz Ubuntu 18.04.5 LTS, 32GB RAM.
Software Dependencies No For Certification model and Lipschitz model, we implement them in Julia [5] with Ju MP [11] package; for Ellipsoid model, we implement it in Matlab [39] with CVX [17] package. For all the three models, we use Mosek [29] as a backend to solve the targeted POPs. Only CVX [17] explicitly mentions a version number ('version 2.1'); other software components are mentioned without their specific versions.
Experiment Setup Yes The network we use consists of a fully-connected implicit layer with 87 neurons and we set its monotonicity parameter m to be 20. The training hyperparameters are set to be the same as in Table D1 of [45], where the training code (in Python) is available at https://github.com/locuslab/monotone_op_net.