Research map / Graph learning / GNN architectures
TopInG: Topologically Interpretable Graph Learning via Persistent Rationale Filtration
Read the paperCheck your idea against 108,967 papers
AI-extracted summary. Written by AI from the paper's full text. Numbers and claims can be wrong or missing context, so check the paper before you cite or build on it.
Proposes TopInG, an intrinsically interpretable GNN that learns a rationale filtration over edges and adds a topological discrepancy loss (bottleneck-distance-based Wasserstein between persistent homology distributions of rationale vs. complement) to identify persistent rationale subgraphs.
Problem
Intrinsically interpretable GNNs assume rationale subgraphs are nearly invariant and one-to-one with labels, which fails when rationale subgraphs are variform (vary in form, size, topology) and under spurious correlations.
Approach
Learn an edge importance filtration with a GNN that induces a graph filtration, and enforce a persistent homology gap between the topological features (H0/H1 persistence) of the rationale and complement subgraphs via a self-adjusted topological discrepancy approximated by a learnable vectorization (Kantorovich dual lower bound), plus a two-Gaussian mixture prior on edge scores.
Key results
- On Benzene interpretation AUC, TopInG (CIN++ backbone) reaches 100.00 ± 0.00 vs. 95.40 for CIN++-GSAT and 83.90 for GMT-Lin.
- On SPMotif0.5 accuracy with CIN++ backbone, TopInG achieves 79.30 ± 3.92 vs. 74.70 for GSAT (CIN++).
- On MUTAG, the GIN-based TopInG underperforms GSAT (92.92 vs. 98.28 accuracy), which the authors attribute to MUTAG's simple rationales lacking cycles; a TopInG-0 variant (0th homology only) reaches 95.18 accuracy and 99.40 AUC.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use TopInG instead of the strongest listed baseline | GIN-based interpretation models · BA-2Motifs | AUC: 98.85 $\pm$ 0.47 -> 99.57 $\pm$ 0.60 | Helped |
| Use TopInG instead of the strongest listed baseline | GIN-based interpretation models · SPMotif0.9 | AUC: 74.38 $\pm$ 0.64 -> 80.82 $\pm$ 4.22 | Helped |
| Use TopInG instead of the strongest listed baseline | GIN-based interpretation models · BA-HouseAndGrid | AUC: 99.95 $\pm$ 0.06 -> 95.35 $\pm$ 0.95 | Hurt |
| Use TopInG instead of the strongest listed baseline | GIN-based interpretation models · BA-HouseOrGrid | AUC: 99.93 $\pm$ 0.07 -> 88.56 $\pm$ 2.04 | Hurt |
| Use TopInG instead of the strongest listed baseline | GIN-based prediction models · SpuriousMotif b=0.9 | accuracy: 47.60 $\pm$ 2.06 -> 50.21 $\pm$ 3.22 | Helped |
| Use TopInG instead of the strongest listed baseline | CINpp prediction models · SpuriousMotif b=0.9 | accuracy: 65.90 $\pm$ 4.18 -> 77.68 $\pm$ 4.64 | Helped |
| Remove topological discrepancy (ablation) | TopInG · BA-2Motifs | AUC: 100.00 $\pm$ 0.00 -> 97.90 $\pm$ 1.24 | Hurt |
| Remove topological discrepancy (ablation) | TopInG · BA-HouseGrid | ACC: 100.00 $\pm$ 0.00 -> 89.24 $\pm$ 5.40 | Hurt |
| Remove prior regularization (ablation) | TopInG · BA-2Motifs | ACC: 100.00 $\pm$ 0.00 -> 53.49 $\pm$ 4.03 | Hurt |
| Remove prior regularization (ablation) | TopInG · BA-HouseGrid | AUC: 99.87 $\pm$ 0.13 -> 98.76 $\pm$ 1.53 | Hurt |
| Use TopInG-0, omitting 1-dimensional persistent homology features (ablation) | TopInG · Mutag | AUC: 96.38 $\pm$ 2.56 -> 99.40 $\pm$ 0.07 | Helped |
| Use TopInG-0, omitting 1-dimensional persistent homology features (ablation) | TopInG · Mutag | ACC: 92.92 $\pm$ 7.02 -> 95.18 $\pm$ 2.24 | Helped |
Surprising findings
- On MUTAG, adding 1st-dimensional (cycle) persistent homology hurt performance because rationales there are simple two-edge substructures without cycles.
- Using only the Gaussian prior without the topological term gave competitive results on SPMotif and BA-HouseOrGrid-nRnd interpretation.
Limitations
- Persistent homology computation is a computational bottleneck and poorly suited to GPU, with CPU-GPU transfer overhead.
- Topological discrepancy with both 0- and 1-dimensional features underperforms on molecular datasets with simple, acyclic rationales such as MUTAG.
- Relies on approximations (lower bound via Kantorovich duality and learnable vectorization) so the theoretical uniqueness guarantee is for the exact objective under stated assumptions.
Experimental setup
Datasets: BA-2Motifs BA-HouseGrid SPMotif BA-HouseAndGrid BA-HouseOrGrid Mutag Benzene BA-HouseOrGrid-nRnd
Benchmarks: BA-2Motifs BA-HouseGrid SPMotif0.5 SPMotif0.9 BA-HouseAndGrid BA-HouseOrGrid Mutag Benzene BA-HouseOrGrid-nRnd
Metrics: explanation ROC AUC classification accuracy
Baselines: GNNExplainer PGExplainer MatchExplainer MAGE DIR GSAT GMT-Lin CIN++ with GSAT CIN++ with GMT-Lin
Builds on: GSAT DIR GMT CIN++ learnable vectorization of persistence diagrams
Closest papers by meaning
- TopoGCL: Topological Graph Contrastive Learning (AAAI 2024 · similarity 0.90)
- TopER: Topological Embeddings in Graph Representation Learning (NeurIPS 2025 · similarity 0.90)
- Boosting Graph Pooling with Persistent Homology (NeurIPS 2024 · similarity 0.89)
- Topological Neural Networks go Persistent, Equivariant, and Continuous (ICML 2024 · similarity 0.88)
- Topological Blindspots: Understanding and Extending Topological Deep Learning Through the Lens of Expressivity (ICLR 2025 · similarity 0.88)
- Graph Persistence goes Spectral (NeurIPS 2025 · similarity 0.87)
Writing a paper in this area? scime draft is a free LaTeX editor with AI included, real-time co-authors and a check of your references and venue rules before you submit. It also imports OpenAI Prism projects.