Leveraging the two-timescale regime to demonstrate convergence of neural networks
Authors: Pierre Marion, Raphaël Berthier
NeurIPS 2023 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Experimental illustration is provided, showing that the stochastic gradient descent behaves according to our description of the gradient flow and thus converges to a global optimum in the two-timescale regime, but can fail outside of this regime. Section 6 presents numerical experiments showing that the SGD dynamics follow closely those of the gradient flow in the two-timescale regime, and therefore exhibit convergence to a global optimum. |
| Researcher Affiliation | Academia | Pierre Marion Sorbonne Université, CNRS, Laboratoire de Probabilités, Statistique et Modélisation, LPSM, F-75005 Paris, France pierre.marion@sorbonne-universite.fr Raphaël Berthier EPFL, Switzerland raphael.berthier@epfl.ch |
| Pseudocode | No | The paper provides mathematical equations for gradient flow and SGD updates but no structured pseudocode or algorithm block. |
| Open Source Code | Yes | Our code is available at https://github.com/Pierre Marion23/two-timescale-nn. |
| Open Datasets | No | The paper uses a synthetic target function defined as 'f = 1 on [0., 0.2], [0.35, 0.5], [0.65, 0.8], f = 2 on [0.5, 0.65] and f = 4 elsewhere.' This is a custom-generated function, not a publicly available dataset with a direct link or citation for access. |
| Dataset Splits | No | The paper describes the generation of noisy observations for SGD, but does not specify any explicit training, validation, or test dataset splits (percentages or sample counts) for a fixed dataset. |
| Hardware Specification | No | No specific hardware details such as GPU models (e.g., NVIDIA A100), CPU models (e.g., Intel Xeon), or cloud instance types were mentioned in the paper. |
| Software Dependencies | No | The paper mentions that 'Our code is available at https://github.com/Pierre Marion23/two-timescale-nn.', but it does not list any specific software dependencies or their version numbers (e.g., Python 3.x, PyTorch 1.x). |
| Experiment Setup | Yes | In Section C, 'Experimental details and additional experiments', the paper provides tables (Table 1, Table 2, Table 3, Table 4) that list specific parameters used in the experiments, such as 'm 20', 'ε 2 10 5', 'h 10 5', 'Additive noise Uniform on [ 1, 1]', 'P 300', 'η 10 2'. |