Probabilistic Graph Cuts

2025-11-04

AI Summary

Existing probabilistic graph-cut methods are largely restricted to RatioCut and lack theoretical foundations, differentiability guarantees, and numerical stability for general graph-cut objectives such as Normalized Cut (NCut). Method: We propose the first unified probabilistic graph-cut framework, achieved via probabilistic relaxation, integral representation, and modeling with the Gaussian hypergeometric function—enabling end-to-end differentiable optimization without spectral decomposition. Contribution/Results: Our framework provides rigorous analytical upper bounds and closed-form gradients for a broad class of graph-cut objectives—including NCut—ensuring both theoretical soundness and computational efficiency. Experiments demonstrate significant improvements in convergence stability and generalization across clustering and contrastive learning tasks. Moreover, the method supports large-scale online learning, establishing a principled foundation for differentiable graph learning.

Technology Category

• Machine Learning: Probabilistic Circuits and Graphical Models
• Reasoning under Uncertainty: Graphical Models
• Computer Vision: Learning & Optimization for CV

Application Category

• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Semantics and Knowledge: Scalable techniques for the creation, curation, publication, maintenance, and consumption of large, Web-based, structured, reusable, knowledge graphs and ontologies

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.

Problem

• Develops probabilistic graph cuts for differentiable clustering without eigendecompositions
• Provides unified framework with tight bounds for multiple cut types
• Enables scalable differentiable graph partitioning for clustering objectives

Innovation

• Probabilistic framework for various graph cuts
• Analytic bounds using integral and hypergeometric functions
• Differentiable graph partitioning with stable gradients