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].
Deep Neural Network Approximation of Invariant Functions through Dynamical Systems
Authors: Qianxiao Li, Ting Lin, Zuowei Shen
JMLR 2024 | Venue PDF | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Theoretical | We prove sufficient conditions for universal approximation of these functions by a controlled dynamical system, which can be viewed as a general abstraction of deep residual networks with symmetry constraints. These results not only imply the universal approximation for a variety of commonly employed neural network architectures for symmetric function approximation, but also guide the design of architectures with approximation guarantees for applications involving new symmetry requirements. |
| Researcher Affiliation | Academia | Qianxiao Li EMAIL Department of Mathematics Institute for Functional Intelligent Materials National University of Singapore 10 Lower Kent Ridge Road, Singapore, 119076 Ting Lin EMAIL School of Mathematical Sciences Peking University 5 Yiheyuan Road, Beijing, China, 100871 Zuowei Shen EMAIL Department of Mathematics National University of Singapore 10 Lower Kent Ridge Road, Singapore, 119076 |
| Pseudocode | No | The paper primarily presents mathematical theorems, proofs, definitions, and discussions of theoretical concepts. It does not include any explicitly labeled pseudocode blocks or algorithms in a structured format. |
| Open Source Code | No | The paper does not provide any statements about releasing source code, nor does it include links to code repositories. |
| Open Datasets | No | The paper is theoretical and does not conduct experiments that would involve the use of specific datasets. While it mentions applications in science and engineering using data (e.g., 'modelling structure-property relationships involving atomic systems', 'CIF form'), these are illustrative contexts for the theoretical framework rather than actual datasets used for empirical evaluation within the paper. |
| Dataset Splits | No | The paper is theoretical and does not conduct experiments, therefore, there is no mention of dataset splits for training, validation, or testing. |
| Hardware Specification | No | The paper is purely theoretical and does not describe any experimental setup or the hardware used to run experiments. |
| Software Dependencies | No | The paper is theoretical and does not describe any experimental implementation or specific software dependencies with version numbers. |
| Experiment Setup | No | The paper is theoretical, focusing on mathematical proofs and conditions for universal approximation. It does not describe any experimental setup, hyperparameters, or training configurations. |