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 [1].
Universal Approximation of Functions on Sets
Authors: Edward Wagstaff, Fabian B. Fuchs, Martin Engelcke, Michael A. Osborne, Ingmar Posner
JMLR 2022 | Venue PDF | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Theoretical | We provide a theoretical analysis of Deep Sets which shows that this universal approximation property is only guaranteed if the model s latent space is sufficiently high-dimensional. If the latent space is even one dimension lower than necessary, there exist piecewise-affine functions for which Deep Sets performs no better than a na ıve constant baseline, as judged by worst-case error. ... In this work, we contribute to this theoretical understanding by considering how the dimension of a Deep Sets model s latent space affects its expressive capacity. ... This work provides a theoretical characterisation of the representation and approximation of permutation-invariant functions. |
| Researcher Affiliation | Academia | Edward Wagstaff EMAIL Fabian B. Fuchs EMAIL Martin Engelcke EMAIL Michael A. Osborne EMAIL Ingmar Posner EMAIL Department of Engineering Science University of Oxford Oxford, UK |
| Pseudocode | No | The paper primarily presents theoretical analysis, proofs, and mathematical discussions of function representation and approximation. It does not contain any structured pseudocode or algorithm blocks. |
| Open Source Code | No | The paper does not explicitly state that source code for the described methodology is available, nor does it provide a link to a code repository. The paper focuses on theoretical analysis rather than empirical implementation. |
| Open Datasets | No | The paper is theoretical in nature, focusing on mathematical properties of functions on sets. It does not use or make available any specific real-world or synthetic datasets for empirical evaluation. The discussions involve abstract mathematical spaces such as RM or [0, 1]M. |
| Dataset Splits | No | The paper is a theoretical work and does not perform experiments on specific datasets. Therefore, it does not provide any information regarding training, test, or validation dataset splits. |
| Hardware Specification | No | This paper presents a theoretical analysis and does not involve empirical experiments requiring computational hardware. Therefore, no hardware specifications are mentioned. |
| Software Dependencies | No | The paper is a theoretical study focused on mathematical proofs and analysis. It does not describe any implemented software or require specific software dependencies with version numbers for experimental reproduction. |
| Experiment Setup | No | The paper is purely theoretical, providing a mathematical characterization of functions on sets. It does not describe any empirical experiments, hyperparameters, training configurations, or system-level settings. |