Positional Encoding meets Persistent Homology on Graphs
Authors: Yogesh Verma, Amauri H Souza, Vikas K Garg
ICML 2025 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | To demonstrate the effectiveness of our proposal, we conduct rigorous empirical evaluations on various tasks, including molecule property prediction, out-of-distribution generalization, and synthetic tree tasks. In Section 5.1, we evaluate the expressivity of persistent homology and its combination with positional encoding on unattributed graphs. In Section 5.2, we assess its effectiveness in predicting properties of drug molecules and performing real-world graph classification. In Section 5.3 we evaluate Pi PE s robustness by benchmarking its ability to handle domain shifts in data, and Section 5.4 shows the performance of Pi PE on synthetic tree-structured tasks. |
| Researcher Affiliation | Collaboration | 1Department of Computer Science, Aalto University, Finland 2Federal Institute of Ceará 3Yai Yai Ltd. |
| Pseudocode | No | The paper describes the proposed method using mathematical equations and text, but it does not include a clearly labeled pseudocode or algorithm block. |
| Open Source Code | Yes | Code is available at https: //github.com/Aalto-Qu ML/PIPE. |
| Open Datasets | Yes | We used the ZINC (Dwivedi et al., 2023) and Alchemy (Chen et al., 2019) datasets, containing quantum mechanical properties of drug molecules... For graph classification, we used OGBG-MOLTOX21 (Huang et al., 2017; Wu et al., 2018)... OGBG-MOLHIV (Hu et al., 2020)... and OGBG-MOLPCBA (Wang et al., 2012; Wu et al., 2018)... To evaluate our method s ability to handle domain shifts, we used Drug OOD, an out-of-distribution (OOD) benchmark (Ji et al., 2023)... We conducted an empirical study to assess the expressivity of standard 0-dim PH and PH+LPE on the BREC dataset (Wang & Zhang, 2023). |
| Dataset Splits | Yes | We followed the data preparation strategy of Huang et al. (2024) with GIN as the base model for a fair comparison. For graph classification, we followed the experimental setup of Dwivedi et al. (2022)... The Drug OOD dataset is divided into five parts: training set, in-distribution (ID) validation/test sets, and out-of-distribution (OOD) validation/test sets. We followed the data-preparation strategy of Kogkalidis et al. (2024) and utilized same splits and hyperparameters. |
| Hardware Specification | Yes | We trained all the methods on a single NVIDIA V100 GPU. |
| Software Dependencies | No | Pi PE is implemented in Py Torch (Paszke et al., 2019)... The paper mentions PyTorch but does not specify its version or any other software dependencies with version numbers. |
| Experiment Setup | Yes | Pi PE is implemented in Py Torch (Paszke et al., 2019) with same training configuration as the competing baselines. More details in Appendix D. We adhered to the precise hyperparameters and training configuration outlined in Huang et al. (2024) for predicting drug molecule properties and in Dwivedi et al. (2022) for classifying real-world graphs in our experiments. We adhered to the precise hyperparameters and training configuration outlined in Huang et al. (2024) for Drug OOD benchmark. We adhered to the hyper-parameters and training configuration used in Kogkalidis et al. (2024) and utilized same splits and hyperparameters. Appendix D provides tables for default hyperparameters for the Re PHINE/VC method, including 'PH embed dim', 'Num Filt', and 'Hiden Filtration' with specific values. |