Notice: The reproducibility variables underlying each score are classified using an automated LLM-based pipeline, validated against a manually labeled dataset. LLM-based classification introduces uncertainty and potential bias; scores should be interpreted as estimates. Full accuracy metrics and methodology are described in Coakley et alK. L. Coakley, T. Snelleman, H. Hoos, and O. E. Gundersen, "The embrace of open science: An analysis of a decade of AI research and 56 800 conference papers," Under Review, 2026..
Keep the Momentum: Conservation Laws beyond Euclidean Gradient Flows
Authors: Sibylle Marcotte, Rémi Gribonval, Gabriel Peyré
ICML 2024 | Venue PDF | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | We consider here a 3-layer MLP trained for classification on the MNIST dataset (Le Cun et al., 2010) with the cross entropy loss function and a ReLU non-linearity... Figure 1, left, shows the evolution of the loss for a range of step size δ up to almost no convergence... Figure 2 shows how the evolution of the loss and the preserved quantities for GF is impacted by the momentum parameter µ = 1/τ. |
| Researcher Affiliation | Academia | Sibylle Marcotte 1 Rémi Gribonval 2 Gabriel Peyré 1 3 1ENS PSL Univ. 2Univ Lyon, Ens L, UCBL, CNRS, Inria, LIP. 3CNRS. Correspondence to: Sibylle Marcotte <EMAIL>. |
| Pseudocode | No | The paper does not contain any pseudocode or clearly labeled algorithm blocks. |
| Open Source Code | Yes | Our code to compute them is available at https://github.com/sibyllema/Conservation_laws_ICML. |
| Open Datasets | Yes | We consider here a 3-layer MLP trained for classification on the MNIST dataset (Le Cun et al., 2010). |
| Dataset Splits | No | The paper mentions using training and test sets from MNIST but does not specify a validation set or explicit split percentages for training, validation, and testing. |
| Hardware Specification | No | The paper does not specify the hardware used for running the experiments, such as specific GPU or CPU models. |
| Software Dependencies | No | We used the software Sage Math (The Sage Developers, 2022), which relies on a Python interface. |
| Experiment Setup | Yes | We consider the following time discretization of the flows, where time at step k is t = kδ and δ > 0 is the time step... This can be re-written in the usual form of a gradient descent with momentum θk+1 = θk αMk EZ(θk) + β(θk θk 1) where α := δ ν + µ/δ and β := µ δν + µ < 1. Here β [0, 1) is the momentum (extrapolation) parameter, so that β = 0 corresponds to usual gradient descent, and setting β = 1 is maximum momentum (which is not in general ensured to converge). Figure 1, left, shows the evolution of the loss for a range of step size δ... Figure 2 shows how the evolution of the loss and the preserved quantities for GF is impacted by the momentum parameter µ = 1/τ. |