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].
Separation Power of Equivariant Neural Networks
Authors: Marco Pacini, Xiaowen Dong, Bruno Lepri, Gabriele Santin
ICLR 2025 | Venue PDF | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Theoretical | In this paper, we analyze the separation power of equivariant neural networks, such as convolutional and permutation-invariant networks. We first present a complete characterization of inputs indistinguishable by models derived by a given architecture. From this results, we derive how separability is influenced by hyperparameters and architectural choices such as activation functions, depth, hidden layer width, and representation types. Notably, all non-polynomial activations, including Re LU and sigmoid, are equivalent in expressivity and reach maximum separation power. Depth improves separation power up to a threshold, after which further increases have no effect. Adding invariant features to hidden representations does not impact separation power. Finally, block decomposition of hidden representations affects separability, with minimal components forming a hierarchy in separation power that provides a straightforward method for comparing the separation power of models. All proofs are provided in the Appendix. |
| Researcher Affiliation | Academia | Marco Pacini1,2 Xiaowen Dong3 Bruno Lepri2 Gabriele Santin4 1University of Trento, 2Fondazione Bruno Kessler, 3University of Oxford, 4University of Venice |
| Pseudocode | No | The paper presents mathematical definitions, theorems, and proofs but does not include any explicitly labeled pseudocode or algorithm blocks. The methods are described mathematically rather than algorithmically in a structured code-like format. |
| Open Source Code | No | The paper does not contain any explicit statements about releasing source code, nor does it provide links to any code repositories in the main text or appendices. |
| Open Datasets | No | The paper is theoretical in nature and focuses on characterizing the separation power of neural networks. While it refers to general concepts and types of neural networks (e.g., Invariant Graph Networks, Circular CNNs), it does not describe or use specific datasets for its own empirical evaluation or provide access information for any datasets. Mentions of datasets like "Open Catalyst 2020 (OC20)" or contexts like "galaxy morphology prediction" appear in the related work section as examples of applications where equivariant models are used, not as datasets utilized in the paper's own research. |
| Dataset Splits | No | The paper focuses on theoretical analysis and does not conduct experiments involving datasets, therefore, no dataset splits are discussed or provided. |
| Hardware Specification | No | The paper does not mention any specific hardware used for experiments, such as GPU or CPU models, memory, or cloud computing resources. The research is theoretical in nature. |
| Software Dependencies | No | The paper is theoretical and does not describe any experimental setup that would require specific software dependencies with version numbers. |
| Experiment Setup | No | The paper is theoretical and focuses on mathematical characterization and proofs. It does not describe any practical experiments, hyperparameters, or training configurations. |