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..
Why Deep Neural Networks for Function Approximation?
Authors: Shiyu Liang, R. Srikant
ICLR 2017 | Venue PDF | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Theoretical | We show that, for a large class of piecewise smooth functions, the number of neurons needed by a shallow network to approximate a function is exponentially larger than the corresponding number of neurons needed by a deep network for a given degree of function approximation. First, we consider univariate functions on a bounded interval and require a neural network to achieve an approximation error of ε uniformly over the interval. We show that shallow networks (i.e., networks whose depth does not depend on ε) require Ω(poly(1/ε)) neurons while deep networks (i.e., networks whose depth grows with 1/ε) require O(polylog(1/ε)) neurons. We then extend these results to certain classes of important multivariate functions. Our results are derived for neural networks which use a combination of rectifier linear units (Re LUs) and binary step units, two of the most popular type of activation functions. Our analysis builds on a simple observation: the multiplication of two bits can be represented by a Re LU. |
| Researcher Affiliation | Academia | Shiyu Liang & R. Srikant Coordinated Science Laboratory and Department of Electrical and Computer Engineering University of Illinois at Urbana-Champaign Urbana, IL 61801, USA |
| Pseudocode | No | The paper does not contain any structured pseudocode or algorithm blocks. |
| Open Source Code | No | The paper does not provide any statement or link regarding the availability of open-source code for the described methodology. |
| Open Datasets | No | The paper is theoretical and does not conduct empirical studies using datasets, therefore, no training datasets are mentioned. |
| Dataset Splits | No | The paper is theoretical and does not involve empirical validation on datasets, thus no dataset split information is provided. |
| Hardware Specification | No | The paper is theoretical and does not involve empirical experiments, therefore no hardware specifications are mentioned. |
| Software Dependencies | No | The paper is theoretical and does not involve empirical experiments, therefore no software dependencies with version numbers are mentioned. |
| Experiment Setup | No | The paper is theoretical and does not describe any experimental setup or training configurations. |