Adaptive Uncertainty Quantification on Simplicial Complexes with Conformalized Simplicial Neural Networks

Abstract

Simplicial neural networks (SNNs) are powerful tools for prediction tasks on higher-order relational datasets stored on simplicial complexes (SCs), a higher-order generalization of graphs. However, SNNs usually lack rigorous uncertainty quantification (UQ), limiting their usefulness in high-stakes scenarios. We propose conformalized SNN (CF-SNN), a framework that, given a simplicial-complex entity with m prediction targets, generates prediction sets for all m targets simultaneously. Under mild assumptions, CF-SNN guarantees that, for each target, the prediction set contains the true label with a user-specified nominal coverage probability, and the realized miscoverage proportion across all m targets is guaranteed to remain close to the nominal level with high probability. Extensive experiments across a wide range of SC prediction tasks demonstrate that CF-SNN is a flexible UQ framework that achieves user-specified coverage while producing informative prediction sets of small size.

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BibTeX RIS

BibTeX

@misc{wang2026adaptive,
  title = {{Adaptive Uncertainty Quantification on Simplicial Complexes with Conformalized Simplicial Neural Networks}},
  author = {Lekun Wang and Jaidev Goel and Yulia R. Gel and Yao Xie},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.41166},
  eprint = {2610.41166},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.41166},
}

RIS

TY  - UNPB
TI  - Adaptive Uncertainty Quantification on Simplicial Complexes with Conformalized Simplicial Neural Networks
AU  - Lekun Wang
AU  - Jaidev Goel
AU  - Yulia R. Gel
AU  - Yao Xie
PY  - 2026
DA  - 2026/10/30
PB  - arXiv
DO  - 10.48550/arxiv.2610.41166
UR  - https://arxiv.org/abs/2610.41166
AB  - Simplicial neural networks (SNNs) are powerful tools for prediction tasks on higher-order relational datasets stored on simplicial complexes (SCs), a higher-order generalization of graphs. However, SNNs usually lack rigorous uncertainty quantification (UQ), limiting their usefulness in high-stakes scenarios. We propose conformalized SNN (CF-SNN), a framework that, given a simplicial-complex entity with m prediction targets, generates prediction sets for all m targets simultaneously. Under mild assumptions, CF-SNN guarantees that, for each target, the prediction set contains the true label with a user-specified nominal coverage probability, and the realized miscoverage proportion across all m targets is guaranteed to remain close to the nominal level with high probability. Extensive experiments across a wide range of SC prediction tasks demonstrate that CF-SNN is a flexible UQ framework that achieves user-specified coverage while producing informative prediction sets of small size.
ER  -

Abstract

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