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. |