Notice: This website is continuously updated as new conference proceedings and journal volumes are published. Consequently, the figures presented here may differ from those reported in our publications.
A brief overview of our methodology is provided on the Methods page, along with references to publications documenting our approach and links to the code and data used in each study.
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.
Vocabulary for Universal Approximation: A Linguistic Perspective of Mapping Compositions
Authors: Yongqiang Cai
ICML 2024 | Venue PDF | LLM Run Details | Input Tokens: 27,157 Total number of tokens sent to the LLM as input for this paper's analysis. | Output Tokens: 3,662 Total number of tokens produced by the LLM (including reasoning/thinking tokens) for this paper's analysis.
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Theoretical | In this article, we investigate the finite case and constructively prove the existence of a finite vocabulary V = {ϕi : Rd Rd | i = 1, ..., n} with n = O(d2) for the universal approximation. Our proof for Theorem 2.2 is constructive, by considering the flow maps of ODEs. |
| Researcher Affiliation | Academia | School of Mathematical Sciences, Laboratory of Mathematics and Complex Systems, MOE, Beijing Normal University, Beijing, 100875, China. Correspondence to: Yongqiang Cai <EMAIL>. |
| Pseudocode | No | No pseudocode or algorithm blocks are present. The paper describes mathematical constructions and proofs. |
| Open Source Code | No | The paper does not mention providing open-source code for the described methodology. |
| Open Datasets | No | The paper is theoretical and does not use or reference any datasets for training or evaluation. |
| Dataset Splits | No | The paper is theoretical and does not describe training, validation, or test dataset splits. |
| Hardware Specification | No | The paper is theoretical and does not describe any hardware specifications used for experiments. |
| Software Dependencies | No | The paper is theoretical and does not list any specific software dependencies with version numbers. |
| Experiment Setup | No | The paper is theoretical and does not describe any experimental setup details, hyperparameters, or training settings. |