Learning Polynomials with Neural Networks
Authors: Alexandr Andoni, Rina Panigrahy, Gregory Valiant, Li Zhang
ICML 2014 | Conference PDF | Archive PDF | Plain Text | 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 ANDONI@MICROSOFT.COM Microsoft Research Rina Panigrahy RINA@MICROSOFT.COM Microsoft Research Gregory Valiant GREGORY.VALIANT@GMAIL.COM Stanford University Li Zhang LZHA@MICROSOFT.COM 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. |