提出可微图划分新框架，支持多种聚类目标且计算稳定。
Beyond Spectral Clustering: Probabilistic Cuts for Differentiable Graph Partitioning
- 基于概率松弛构建统一框架，覆盖RatioCut、Normalized Cut等
- 给出期望离散切割的紧致解析上界，支持闭式前向后向传播
- 无需特征分解，适合端到端与在线学习，适用于对比学习
概率松弛的图切割提供了谱聚类的可微替代方案，可在不进行特征分解的情况下实现端到端和在线学习。然而，以往工作主要聚焦于RatioCut，缺乏通用保证和合理的梯度设计。本文提出一个统一的概率框架，涵盖广泛的切割类型，包括Normalized Cut。该框架通过积分表示和高斯超几何函数，为期望离散切割提供紧致的解析上界，并实现闭式前向与反向传播。这些结果共同构建了一个严谨、数值稳定的可扩展可微图划分基础，适用于多种聚类与对比学习目标。
原文摘要 · Abstract (English)
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.
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