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..
Heavy-Ball Momentum Method in Continuous Time and Discretization Error Analysis
Authors: Bochen Lyu, Xiaojing Zhang, Fangyi Zheng, He Wang, Zheng Wang, Zhanxing Zhu
NeurIPS 2025 | Venue PDF | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | This paper establishes a continuous time approximation, a piece-wise continuous differential equation, for the discrete Heavy-Ball (HB) momentum method with explicit discretization error. ... Our theoretical findings are further supported by numerical experiments. |
| Researcher Affiliation | Collaboration | a University of Southampton b Data Canvas c Pony.ai d University College London e University of Leeds |
| Pseudocode | No | The paper describes mathematical equations and methodology in text but does not include any clearly labeled 'Pseudocode' or 'Algorithm' blocks, nor does it present structured steps formatted like code. |
| Open Source Code | No | The paper does not provide an unambiguous statement of releasing its own source code or a direct link to a code repository. While it mentions using 'open-source data' in the NeurIPS checklist, this refers to external datasets, not the authors' implementation code for the methodology. |
| Open Datasets | Yes | For the experiment of Figure 1, we conduct observation on the comparison of directional smoothness for HB and GD on the CIFAR-10 dataset Krizhevsky et al. (2009). ... We conduct experiments of Fig. 2(b) in the MNIST dataset... |
| Dataset Splits | No | For the experiment of Figure 1, ... MLP on CIFAR10 5k Subset (full-batch)... For the discrete learning dynamics of HB and GD, we set the step size as η and the momentum factor is µ. For the continuous approximations, we use ηEuler = η/10 as the Euler step sizes to approximate the dynamics. These hyper-parameters are listed in Table 2. ... The batch size is 60,000 and the momentum factor µ (0.7, 0.8). |
| Hardware Specification | Yes | The experiments are conducted on a Cent OS Linux 7.9.2 platform equipped with an Intel(R) Xeon CPU E5-2683 at 3.00 GHz, 256GB of RAM, and an NVIDIA Tesla A100 graphics card. |
| Software Dependencies | No | The paper mentions 'PyTorch' in the introduction but does not specify its version or any other software libraries with their version numbers used in the experiments. |
| Experiment Setup | Yes | A multilayer perceptron with two hidden layers (each of width 200) is trained for 2000 epochs using full-batch GD and HB (µ = 0.9), and the step size is set to 0.1. ... Hyper-parameters for 2-d model: η 5e-3, µ 0.7, ηEuler 5e-4. ... For the MNIST dataset, The batch size is 60,000 and the momentum factor µ (0.7, 0.8). The learning rate is η = 0.01. |