Provable Lipschitz Certification for Generative Models
Authors: Matt Jordan, Alex Dimakis
ICML 2021 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | To fairly compare our work against existing Lipschitz estimation techniques, we first compare the estimated Lipschitz value and runtime of our algorithm on networks of increasing size trained on a toy dataset. We observe that our approach favorably trades-off accuracy for efficiency and yields tighter bounds compared to previous techniques. Further, it can significantly improve the runtime of exact Lipschitz computations. We scale our technique to generative models on MNIST and CIFAR-10, using well-known architectures like DCGAN and VAEs with both fully-connected and convolutional layers (Kingma & Welling, 2013; Radford et al., 2015). Our approach yields much tighter bounds compared to any other technique that can handle vector-valued networks and can scale to such architecture sizes. |
| Researcher Affiliation | Academia | Matt Jordan 1 Alexandros G. Dimakis 1 1University of Texas at Austin. Correspondence to: Matt Jordan <mjordan@cs.utexas.edu>. |
| Pseudocode | No | The paper describes algorithms in prose (e.g., in Section 6 'Vertical-Parallelogram fitting problem'), but does not include any formal pseudocode blocks or figures labeled as 'Algorithm' or 'Pseudocode'. |
| Open Source Code | No | The paper does not contain an explicit statement about releasing its source code or provide a link to a code repository for the methodology described. |
| Open Datasets | Yes | We scale our technique to generative models on MNIST and CIFAR-10, using well-known architectures like DCGAN and VAEs with both fully-connected and convolutional layers (Kingma & Welling, 2013; Radford et al., 2015). We present results on the 2-dimensional Circle dataset from (Aziznejad et al., 2020). |
| Dataset Splits | No | The paper mentions evaluating on input sets surrounding images taken from the 'test set' and 'random inputs from the training distribution' for generative models, and uses a 'test set' for toy network benchmarks. However, it does not specify explicit dataset split percentages (e.g., 80/10/10) or sample counts for training, validation, or test sets. |
| Hardware Specification | No | The acknowledgements mention 'computing resources from TACC', but no specific hardware details such as GPU/CPU models, memory, or specific cloud instances are provided in the paper. |
| Software Dependencies | No | The paper does not list any specific software dependencies with version numbers (e.g., 'Python 3.8', 'PyTorch 1.9'). |
| Experiment Setup | Yes | We consider the L( ,| |)(f, X) Lipschitz constant for fully-connected networks f with input dimension 2 and a varying amount of layers of width 100 and the Re LU nonlinearity. We train multiple VAEs and GANs using fully-connected and convolutional layers and the Re LU and tanh nonlinearities (Kingma & Welling, 2013; Radford et al., 2015). We train multiple VAEs and GANs using fully-connected and convolutional layers and the Re LU and tanh nonlinearities. For GAN evaluation, we consider ℓ balls surrounding random inputs from the training distribution and evaluate L( ,1)(f, X) of the generator. Table 1 displays results for random inputs with ℓ radius of 0.05. Full experimental details are presented in the Appendix, as well as experiments with input sets of different radii. |