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..
Minimum Width for Deep, Narrow MLP: A Diffeomorphism Approach
Authors: Geonho Hwang
NeurIPS 2025 | Venue PDF | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Theoretical | We prove that deep, narrow MLPs with a width of d, employing the Leaky-Re LU activation function, can approximate any C2-diffeomorphisms on Rd. Furthermore, for more general activation functions, we demonstrate that deep, narrow MLPs with width d + 1 using Re LU and d + 2 employing a general activation function, respectively, can approximate any C2-diffeomorphisms uniformly on Rd. We propose the purely topological quantity w(dx, dy), representing the optimal minimum width for achieving the UAP of deep, narrow MLPs employing the Leaky-Re LU activation function. Building upon the aforementioned results, we prove that deep, narrow MLPs with a width of max(2dx + 1, dy) + α(σ) can approximate any continuous function in C(Rdx, Rdy) uniformly on a compact domain, where 0 α(σ) 2 is a constant depending on the activation function. We prove that when the input dimension is 2k and the output dimension is 4k 1, the optimal minimum width is 4k. We demonstrate that a width of 4 is the optimal minimum width for deep, narrow MLPs to approximate arbitrary continuous function mapping [0, 1]2 to R2. |
| Researcher Affiliation | Academia | Geonho Hwang Department of Mathematical Sciences Gwangju Institute for Science and Technology Gwangju, Buk-gu 61005 EMAIL |
| Pseudocode | No | The paper only contains mathematical definitions, theorems, lemmas, and proofs. There are no structured pseudocode or algorithm blocks. |
| Open Source Code | No | The paper does not contain any statements about open-source code availability, nor does it provide links to any code repositories. |
| Open Datasets | No | The paper is a theoretical work and does not describe any experiments that would use datasets, therefore no dataset information is provided. |
| Dataset Splits | No | The paper is a theoretical work and does not involve empirical experiments or datasets, thus there is no mention of dataset splits. |
| Hardware Specification | No | The paper is theoretical and does not describe any computational experiments that would require specific hardware. Therefore, no hardware specifications are mentioned. |
| Software Dependencies | No | The paper is theoretical and does not describe any computational experiments that would require specific software dependencies. Therefore, no software dependencies are mentioned. |
| Experiment Setup | No | The paper is a theoretical work and does not detail any experimental setups, hyperparameters, or system-level training settings. |