A Characterization Theorem for Equivariant Networks with Point-wise Activations
Authors: Marco Pacini, Xiaowen Dong, Bruno Lepri, Gabriele Santin
ICLR 2024 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Theoretical | Equivariant neural networks have shown improved performance, expressiveness and sample complexity on symmetrical domains. But for some specific symmetries, representations, and choice of coordinates, the most common point-wise activations, such as Re LU, are not equivariant, hence they cannot be employed in the design of equivariant neural networks. The theorem we present in this paper describes all possible combinations of finite-dimensional representations, choice of coordinates and point-wise activations to obtain an exactly equivariant layer, generalizing and strengthening existing characterizations. |
| Researcher Affiliation | Academia | Marco Pacini Fondazione Bruno Kessler, Italy mpacini@fbk.eu; Xiaowen Dong University of Oxford, United Kingdom xdong@robots.ox.ac.uk; Bruno Lepri Fondazione Bruno Kessler, Italy lepri@fbk.eu; Gabriele Santin University of Venice, Italy gabriele.santin@unive.it |
| Pseudocode | No | The paper is theoretical and focuses on characterization theorems; it does not include any pseudocode or algorithm blocks. |
| Open Source Code | No | The paper does not contain any statement about releasing source code for the methodology, nor does it provide a link to a code repository. |
| Open Datasets | No | The paper is theoretical and does not describe empirical experiments using datasets for training. It mentions 'training data' in a general context but does not refer to a specific dataset used in this work. |
| Dataset Splits | No | The paper is theoretical and does not involve empirical experiments with datasets, thus no training, validation, or test splits are described. |
| Hardware Specification | No | The paper is theoretical and does not describe any experiments that would require specific hardware. Therefore, no hardware specifications are mentioned. |
| Software Dependencies | No | The paper is theoretical and does not describe any experiments or implementations that would necessitate detailing specific software dependencies or their versions. |
| Experiment Setup | No | The paper is theoretical and presents a characterization theorem; it does not describe an experimental setup, hyperparameters, or training configurations. |