Probabilistic Graph Cuts
This work addresses the need for scalable and differentiable graph partitioning in clustering and contrastive learning, offering a rigorous foundation but is incremental as it builds on prior probabilistic relaxations.
The paper tackles the problem of making graph cuts differentiable for end-to-end and online learning by introducing a unified probabilistic framework that covers a wide class of cuts, including Normalized Cut, and provides tight analytic upper bounds on expected discrete cuts with closed-form forward and backward passes.
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.