# Conformal Graph Prediction with Z-Gromov-Wasserstein Distances

arXiv: https://arxiv.org/abs/2603.02460 · HTML: https://mlsanity.com/paper/2603.02460/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 41 references that are in the map.
- First posted on arXiv 2 Mar 2026.

## Builds on (most cited first, 24 of 24)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Conformalized Quantile Regression](https://mlsanity.com/paper/1905.03222/) (2019)
- [ChemBERTa: Large-Scale Self-Supervised Pretraining for Molecular Property Prediction](https://mlsanity.com/paper/2010.09885/) (2020)
- [Optimal Transport for structured data with application on graphs](https://mlsanity.com/paper/1805.09114/) (2018)
- [ChemBERTa-2: Towards Chemical Foundation Models](https://mlsanity.com/paper/2209.01712/) (2022)
- [Fused Gromov-Wasserstein distance for structured objects: theoretical foundations and mathematical properties](https://mlsanity.com/paper/1811.02834/) (2018)
- [Uncertainty Quantification over Graph with Conformalized Graph Neural Networks](https://mlsanity.com/paper/2305.14535/) (2023)
- [Relationformer: A Unified Framework for Image-to-Graph Generation](https://mlsanity.com/paper/2203.10202/) (2022)
- [MassSpecGym: A benchmark for the discovery and identification of molecules](https://mlsanity.com/paper/2410.23326/) (2024)
- [A Unified Comparative Study with Generalized Conformity Scores for Multi-Output Conformal Regression](https://mlsanity.com/paper/2501.10533/) (2025)
- [Learning to Predict Graphs with Fused Gromov-Wasserstein Barycenters](https://mlsanity.com/paper/2202.03813/) (2022)
- [Optimal Transport-based Conformal Prediction](https://mlsanity.com/paper/2501.18991/) (2025)
- [Conformal Prediction for Network-Assisted Regression](https://mlsanity.com/paper/2302.10095/) (2023)
- [The Z-Gromov-Wasserstein Distance](https://mlsanity.com/paper/2408.08233/) (2024)
- [Conformal Structured Prediction](https://mlsanity.com/paper/2410.06296/) (2024)
- [Certainty in Uncertainty: Reasoning over Uncertain Knowledge Graphs with Statistical Guarantees](https://mlsanity.com/paper/2510.24754/) (2025)
- [The quest for the GRAph Level autoEncoder (GRALE)](https://mlsanity.com/paper/2505.22109/) (2025)
- [Any2Graph: Deep End-To-End Supervised Graph Prediction With An Optimal Transport Loss](https://mlsanity.com/paper/2402.12269/) (2024)
- [Predicate-Conditional Conformalized Answer Sets for Knowledge Graph Embeddings](https://mlsanity.com/paper/2505.16877/) (2025)
- [Breaking the Modality Barrier: Generative Modeling for Accurate Molecule Retrieval from Mass Spectra](https://mlsanity.com/paper/2511.06259/) (2025)
- [Small molecule retrieval from tandem mass spectrometry: what are we optimizing for?](https://mlsanity.com/paper/2602.16507/) (2026)
- [Conformal Prediction Sets for Populations of Graphs](https://mlsanity.com/paper/2404.18862/) (2024)
- [Neural Optimal Transport Meets Multivariate Conformal Prediction](https://mlsanity.com/paper/2509.25444/) (2025)
- [SpecBridge: Bridging Mass Spectrometry and Molecular Representations via Cross-Modal Alignment](https://mlsanity.com/paper/2601.17204/) (2026)

## Built on by (most cited first, 2 of 2)

- [Manifold Constrained Conformal Prediction for Spatial Events](https://mlsanity.com/paper/2607.10008/) (2026)
- [Graph Matching Relaxations and Amortization for Supervised Graph Prediction](https://mlsanity.com/paper/2609.15437/) (2026)

## Abstract (arXiv)

Supervised graph prediction addresses regression problems where the outputs are structured graphs. Although several approaches exist for graph-valued prediction, principled uncertainty quantification remains limited. We propose a conformal prediction framework for graph-valued outputs, providing distribution-free coverage guarantees in structured output spaces. Our method defines nonconformity via the Z-Gromov-Wasserstein distance, instantiated in practice through Fused Gromov-Wasserstein (FGW), enabling permutation invariant comparison between predicted and candidate graphs. To obtain adaptive prediction sets, we introduce Score Conformalized Quantile Regression (SCQR), an extension of Conformalized Quantile Regression (CQR) to handle complex output spaces such as graph-valued outputs. We evaluate the proposed approach on a synthetic task and a real problem of molecule identification.