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 [1].
Proximal Mean Field Learning in Shallow Neural Networks
Authors: Alexis Teter, Iman Nodozi, Abhishek Halder
TMLR 2024 | Venue PDF | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | We demonstrate the proposed computational framework of interacting weighted particle evolution on binary and multi-class classification. Our algorithm performs gradient descent of the free energy associated with the risk functional. We then report numerical case studies in Sec. 4 and Sec. 5 for binary and multi-class classifications, respectively. |
| Researcher Affiliation | Academia | Alexis M.H. Teter EMAIL Department of Applied Mathematics University of California, Santa Cruz Iman Nodozi EMAIL Department of Electrical and Computer Engineering University of California, Santa Cruz Abhishek Halder EMAIL Department of Aerospace Engineering Iowa State University |
| Pseudocode | Yes | Algorithm 1 Proximal Algorithm Algorithm 2 Euler-Maruyama Algorithm |
| Open Source Code | Yes | A Git Hub repository containing our code for the implementation of these applications can be found at https://github.com/zalexis12/Proximal-Mean-Field-Learning.git. |
| Open Datasets | Yes | We apply the proposed algorithm to perform a binary classification on the Wisconsin Diagnostic Breast Cancer (henceforth, WDBC) data set available at the UC Irvine machine learning repository (Dua & Graff, 2017). We next apply the proposed proximal algorithm to a ten-class classification problem using the Semeion Handwritten Digit (hereafter SHD) Data Set (Dua & Graff, 2017). |
| Dataset Splits | Yes | We use 70% of the entire data set as training data. As discussed in Sec. 3, we learn the mean field parameter distribution via weighted scattered point cloud evolution using Prox Learn. We then use the confusion matrix method (Visa et al., 2011) to evaluate the accuracy of the obtained model over the test data, which is the remaining 30% of the full data set, containing ntest points. We take the first ndata = 1000 images as training data, reserving the remaining ntest = 593 images as test data, and execute 30 independent runs of our code, each for 10^6 proximal recursions. |
| Hardware Specification | Yes | Our first implementation is on a PC with 3.4 GHz 6-Core Intel Core i5 processor, and 8 GB RAM. For runtime improvement, we then use a Jetson TX2 with a NVIDIA Pascal GPU with 256 CUDA cores, 64-bit NVIDIA Denver and ARM Cortex-A57 CPUs. |
| Software Dependencies | No | In line 6 of Algorithm 2, Euler Maruyama uses the automatic differentiation module of Py Torch Library, Backward (Paszke et al., 2017), to calculate the gradients needed to update Θk 1 to Θk k N. |
| Experiment Setup | Yes | We set the number of samples N = 1000, numerical tolerance δ = 10 3, the maximum number of iterations L = 300, and the regularizing parameter ε = 1. Additionally, we set the time step to h = 10 3. We set the inverse temperature β = 0.5, ϵ = 10, the step size h = 10 3, and N = 100. |