Generalization Bounds for Heavy-Tailed SDEs through the Fractional Fokker-Planck Equation
Authors: Benjamin Dupuis, Umut Simsekli
ICML 2024 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | We support our theory with experiments conducted in a variety of settings. [...] All the proofs are presented in the Appendix. The code for our numerical experiments is available at https://github.com/benji Dupuis/ heavy_tails_generalization. |
| Researcher Affiliation | Academia | 1Inria 2Ecole Normale Sup erieure, Paris, France 3PSL Research University, Paris, France 4CNRS. |
| Pseudocode | No | The paper describes the Euler Maruyama discretization formula (17) but does not present it in a formal pseudocode or algorithm block. |
| Open Source Code | Yes | The code for our numerical experiments is available at https://github.com/benji Dupuis/ heavy_tails_generalization. |
| Open Datasets | Yes | Our main experiments were conducted with 2 layers fully-connected networks (FCN2) trained on the MNIST dataset (Lecun et al., 1998). Additional experiments, using MNIST, Fasion MNIST (Xiao et al., 2017) and CIFAR10 datasets (Krizhevsky et al., 2014), as well as linear models and deeper networks, are presented in Appendix F.4. |
| Dataset Splits | No | The paper mentions training on datasets and evaluating accuracy, but does not explicitly describe train/validation/test dataset splits for reproduction. It mentions |
| Hardware Specification | No | The paper does not provide specific hardware details (e.g., CPU/GPU models, memory) used for running the experiments. It only mentions general computing environments like 'workstation' in discussion. |
| Software Dependencies | No | The paper mentions numerical approximation using 'Euler Maruyama discretization' and implicitly uses Python libraries given the GitHub link, but it does not specify versions of any software dependencies like programming languages or libraries. |
| Experiment Setup | Yes | All hyperparameters details can be found in Appendix F.1. [...] We simulate Eq. (17) with T = 5.103, γ = 10 2, η = 10 3. The last 2000 iterations were used to estimate the accuracy error, as described in Appendix F.2. |