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..
Learning Polynomials with Neural Networks
Authors: Alexandr Andoni, Rina Panigrahy, Gregory Valiant, Li Zhang
ICML 2014 | Venue PDF | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | We provide strong empirical evidence (see Fig. 1) suggesting that, for the case of n-sparse polynomials over n variables, a neural network with O(n) hidden units can learn the function. We train the net using 5n hidden units while varying n through the values 10, 20, 40, and 80. The polynomial is constructed using randomly chosen n monomials. The plots show that the training error drops significantly after a reasonable number of iterations that depends on n. |
| Researcher Affiliation | Collaboration | Alexandr Andoni EMAIL Microsoft Research Rina Panigrahy EMAIL Microsoft Research Gregory Valiant EMAIL Stanford University Li Zhang EMAIL Microsoft Research |
| Pseudocode | No | The paper is theoretical and does not include any pseudocode or algorithm blocks. |
| Open Source Code | No | The paper does not provide any concrete access information (e.g., links or explicit statements) to source code for the methodology described. |
| Open Datasets | No | The paper mentions mathematical distributions (e.g., 'C(1)n', 'Gaussian distribution N(1)', 'uniform distribution U(1)') and constructed polynomials, but does not refer to or provide access information for a publicly available or open dataset. |
| Dataset Splits | No | The paper does not specify any training, validation, or test dataset splits. It only mentions 'training error' in the empirical section without detailing how data was partitioned. |
| Hardware Specification | No | The paper does not provide specific details about the hardware used to run the experiments. |
| Software Dependencies | No | The paper does not provide specific details about software dependencies, such as library names with version numbers, used for the experiments. |
| Experiment Setup | Yes | We train the net using 5n hidden units while varying n through the values 10, 20, 40, and 80. The polynomial is constructed using randomly chosen n monomials. |