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..
Convergence Analysis of Fractional Gradient Descent
Authors: Ashwani Aggarwal
TMLR 2024 | Venue PDF | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Finally, empirical results will be presented on the potential speed up of fractional gradient descent over standard gradient descent as well as some preliminary theoretical results explaining this speed up. Figure 1 depicts convergence on a quadratic function for standard gradient descent as well as AT-CFGD and the method in Corollary 15 labeled Fractional Descent guided by Gradient. For specifically picked hyperparameters, both of these fractional methods can significantly outperform standard gradient descent. |
| Researcher Affiliation | Academia | Ashwani Aggarwal Department of Computer Science University of California, Los Angeles EMAIL |
| Pseudocode | No | The paper describes the fractional gradient descent method mathematically (e.g., "xt+1 = xt ηt Cδα,β ct f(xt)"), but it does not contain explicit pseudocode or algorithm blocks with structured formatting or labels. |
| Open Source Code | No | No explicit statement or link for open-source code release for the methodology described in this paper was found. |
| Open Datasets | No | The paper conducts experiments on synthetic quadratic functions such as "f(x, y) = 10x2 + y2" and "f(x) = x T diag([10, 1, 1, 1, 1])x". These are synthetic functions, not publicly available datasets, and no specific access information is provided for them. |
| Dataset Splits | No | The experiments in this paper are conducted on synthetic quadratic functions like f(x, y) = 10x2 + y2, which do not involve standard dataset splits for training, validation, or testing. |
| Hardware Specification | No | No specific hardware details (such as CPU/GPU models, processor types, or memory amounts) used for running the experiments were mentioned in the paper. |
| Software Dependencies | No | No specific software dependencies or version numbers (e.g., library names with versions like Python 3.8, PyTorch 1.9) were mentioned for replicating the experiments. |
| Experiment Setup | Yes | Figure 1: Convergence of descent methods on function f(x, y) = 10x2 + y2 beginning at x = 1, y = 10. In all cases, the optimal (not theoretical) step size is used. AT-CFGD is as described in Shin et al. (2021) with x( 1) = 1.5, y( 1) = 10.5, α = 1/2, β = 4/10. Fractional Descent guided by Gradient is the method discussed in Corollary 15 with α = 1/2, β = 4/10, λt = 0.0675(t+1)0.2 in xt ct = λt f(xt). Also, Figure 3 and 4 specify "Hyper-parameters as in Corollary 15 are α = 1/2, β = 4/10, λt = 0.0675". |