Neural Networks and Rational Functions
Authors: Matus Telgarsky
ICML 2017 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Theoretical | The main theorem here states that Re LU networks and rational functions approximate each other well in the sense... Theorem 1.1. Theorem 1.2. Lemma 1.3. Corollary 1.4. Proposition 1.5. The goal of the present work is to characterize neural networks more finely by finding a class of functions which is not only well-approximated by neural networks, but also well-approximates neural networks. In all these demonstrations, rational functions and polynomials have degree 9 unless otherwise marked. Re LU networks have two hidden layers each with 3 nodes. This is not exactly apples to apples (e.g., the rational function has twice as many parameters as the polynomial), but still reasonable as most of the approximation literature fixes polynomial and rational degrees in comparisons. Of course, this is only a qualitative demonstration, but still lends some intuition. |
| Researcher Affiliation | Academia | Matus Telgarsky 1University of Illinois, Urbana-Champaign; work completed while visiting the Simons Institute. Correspondence to: your friend <mjt@illinois.edu>. |
| Pseudocode | No | The paper contains mathematical descriptions and proofs, but no structured pseudocode or algorithm blocks. |
| Open Source Code | No | The paper does not provide any concrete access information (links, explicit statements) for the open-source code of the described methodology. |
| Open Datasets | No | The paper is theoretical and does not conduct experiments involving dataset training; therefore, no public dataset access information is provided. |
| Dataset Splits | No | The paper is theoretical and does not conduct experiments involving validation splits; therefore, no specific dataset split information for validation is provided. |
| Hardware Specification | No | The paper is theoretical and does not report on computational experiments that would require specific hardware specifications. |
| Software Dependencies | No | The paper is theoretical and does not report on computational experiments that would require specific software dependencies with version numbers. |
| Experiment Setup | No | The paper is theoretical and does not describe an experimental setup with specific hyperparameters or training configurations for models. |