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 Coakley et alK. L. Coakley, T. Snelleman, H. Hoos, and O. E. Gundersen, "The embrace of open science: An analysis of a decade of AI research and 56 800 conference papers," Under Review, 2026..
On topological descriptors for graph products
Authors: Mattie Ji, Amauri H. Souza, Vikas Garg
NeurIPS 2025 | Venue PDF | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | To evaluate the empirical power of topological descriptors for graph products, we run three sets of experiments. The first investigates their effectiveness on BREC datasets [49] and minimal Cayley graphs [11] with varying number of nodes, which are popular benchmarks for assessing the expressive power of graph models. The second examines the runtime performance of the algorithms described in Theorems 4 and 5, using the BREC datasets. Finally, the third demonstrates how these descriptors can be integrated with GNNs for graph classification tasks. |
| Researcher Affiliation | Collaboration | Mattie Ji University of Pennsylvania EMAIL Amauri H. Souza Federal Institute of Ceará EMAIL Vikas Garg Aalto University Yai Yai Ltd EMAIL |
| Pseudocode | Yes | Algorithm 1 Computing the 0-dim PH Diagrams in Product of Vertex-Level Filtrations Algorithm 2 Computing the 0-dim PH Diagrams in Product of Edge-Level Filtrations Algorithm 3 Computing the 0-dim PH Diagrams in Product of Vertex-Level Filtrations (Symmetric) |
| Open Source Code | Yes | Code is available at https://github.com/Aalto-Qu ML/tda_graph_product. |
| Open Datasets | Yes | BREC is a benchmark designed to evaluate the expressiveness of graph neural networks (GNNs). It comprises 800 non-isomorphic graphs organized into 400 pairs, grouped into four categories: Basic, Regular, Extension, and CFI. For completeness, we also considered minimal Cayley graphs. These datasets have been used to assess the expressivity of graph models [2] and can be found at https://houseofgraphs.org/ meta-directory/minimal-cayley . With the exception of ZINC, all datasets originate from the TUDataset repository a comprehensive benchmark suite commonly employed for assessing graph kernel methods and GNNs. The datasets can be accessed at https://chrsmrrs.github.io/datasets/docs/datasets/. |
| Dataset Splits | Yes | For the TU datasets, we use a random 80/10/10% (train/validation/test) split, which varies with the random seed (i.e., a different split is used for each of the five runs). All models are trained with an initial learning rate of 10 3, which is halved if the validation accuracy does not improve for 10 consecutive epochs. For ZINC, we use the publicly available train/validation/test splits; for the remaining datasets, we adopt a random 80/10/10% split. |
| Hardware Specification | Yes | The runtime experiments were conducted on Google Colab and written in Python. For all experiments, we use Tesla V100 GPU cards and consider a memory budget of 64GB of RAM. |
| Software Dependencies | Yes | We implement all models using the Py Torch Geometric Library [17]. Similarly, for the edge-level product filtration, we compare three counterparts: our method (Theorem 5), a union-find PH implementation on the graph product, and the gudhi-based approach. The GUDHI Project. GUDHI User and Reference Manual. GUDHI Editorial Board, 3.11.0 edition, 2025. URL https://gudhi.inria.fr/doc/3.11.0/. |
| Experiment Setup | Yes | All models are trained with an initial learning rate of 10 3, which is halved if the validation accuracy does not improve for 10 consecutive epochs. We employ early stopping with a patience of 40 epochs and train for up to 500 epochs using the Adam optimizer [31]. A batch size of 64 and batch normalization are used in all experiments. |