Beyond Spectral Clustering: Probabilistic Cuts for Differentiable Graph Partitioning

Ayoub Ghriss
Proceedings of The 29th International Conference on Artificial Intelligence and Statistics, PMLR 300:3997-4005, 2026.

Abstract

Probabilistic relaxations of graph cuts offer a differentiable alternative to spectral clustering, enabling end-to-end and online learning without eigendecompositions, yet prior work centered on RatioCut and lacked general guarantees and principled gradients. We present a unified probabilistic framework that covers a wide class of cuts, including Normalized Cut. Our framework provides tight analytic upper bounds on expected discrete cuts via integral representations and Gauss hypergeometric functions with closed-form forward and backward. Together, these results deliver a rigorous, numerically stable foundation for scalable, differentiable graph partitioning covering a wide range of clustering and contrastive learning objectives.

Cite this Paper

BibTeX
@InProceedings{pmlr-v300-ghriss26a, title = { Beyond Spectral Clustering: Probabilistic Cuts for Differentiable Graph Partitioning }, author = {Ghriss, Ayoub}, booktitle = {Proceedings of The 29th International Conference on Artificial Intelligence and Statistics}, pages = {3997--4005}, year = {2026}, editor = {Khan, Emtiyaz and Li, Yingzhen and Solin, Arno and Ramdas, Aaditya}, volume = {300}, series = {Proceedings of Machine Learning Research}, month = {02--05 May}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v300/main/assets/ghriss26a/ghriss26a.pdf}, url = {https://proceedings.mlr.press/v300/ghriss26a.html}, abstract = { Probabilistic relaxations of graph cuts offer a differentiable alternative to spectral clustering, enabling end-to-end and online learning without eigendecompositions, yet prior work centered on RatioCut and lacked general guarantees and principled gradients. We present a unified probabilistic framework that covers a wide class of cuts, including Normalized Cut. Our framework provides tight analytic upper bounds on expected discrete cuts via integral representations and Gauss hypergeometric functions with closed-form forward and backward. Together, these results deliver a rigorous, numerically stable foundation for scalable, differentiable graph partitioning covering a wide range of clustering and contrastive learning objectives. } }
Endnote
%0 Conference Paper %T Beyond Spectral Clustering: Probabilistic Cuts for Differentiable Graph Partitioning %A Ayoub Ghriss %B Proceedings of The 29th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2026 %E Emtiyaz Khan %E Yingzhen Li %E Arno Solin %E Aaditya Ramdas %F pmlr-v300-ghriss26a %I PMLR %P 3997--4005 %U https://proceedings.mlr.press/v300/ghriss26a.html %V 300 %X Probabilistic relaxations of graph cuts offer a differentiable alternative to spectral clustering, enabling end-to-end and online learning without eigendecompositions, yet prior work centered on RatioCut and lacked general guarantees and principled gradients. We present a unified probabilistic framework that covers a wide class of cuts, including Normalized Cut. Our framework provides tight analytic upper bounds on expected discrete cuts via integral representations and Gauss hypergeometric functions with closed-form forward and backward. Together, these results deliver a rigorous, numerically stable foundation for scalable, differentiable graph partitioning covering a wide range of clustering and contrastive learning objectives.
APA
Ghriss, A.. (2026). Beyond Spectral Clustering: Probabilistic Cuts for Differentiable Graph Partitioning . Proceedings of The 29th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 300:3997-4005 Available from https://proceedings.mlr.press/v300/ghriss26a.html.

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