# Beyond Spectral Clustering: Probabilistic Cuts for Differentiable Graph Partitioning

arXiv: https://arxiv.org/abs/2511.02272 · HTML: https://mlsanity.com/paper/2511.02272/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- First posted on arXiv 4 Nov 2025.

## Abstract (arXiv)

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.