MDND: Unsupervised Learning Guided by Non-Differentiable Refinement for Shape Correspondence

• URL: http://arxiv.org/abs/2607.15887v1
• Date: Fri, 17 Jul 2026 12:03:06 GMT
• Title: MDND: Unsupervised Learning Guided by Non-Differentiable Refinement for Shape Correspondence
• Abstract summary: We introduce MDND, a novel DFM paradigm built on the principle of merging differentiable and non-differentiable components.<n>Our framework facilitates unsupervised learning guided by an internal, non-differentiable refinement.<n> MDND sets a new state-of-the-art, demonstrating remarkable robustness on shapes with non-isometric deformations and topological noise.
• Score: 5.524462085802735
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• Abstract: Deep functional map frameworks (DFM) for shape correspondence are powerful, yet fundamentally limited by their reliance on end-to-end differentiability. This constraint prevents the integration of highly accurate, non-differentiable refinement techniques, capping their overall performance, especially on challenging non-isometric shapes. To overcome this, we introduce MDND, a novel DFM paradigm built on the principle of merging differentiable and non-differentiable components. Our framework facilitates unsupervised learning guided by an internal, non-differentiable refinement. Specifically, MDND employs a dual-branch architecture: a non-differentiable refinement branch leverages a novel, multiscale iterative solver to produce highly robust correspondences, acting as a refined target. Concurrently, a fully differentiable branch learns to predict correspondences from features. The entire system is trained end-to-end without supervision by enforcing a consistency loss that compels the differentiable branch to learn from the superior, refined results of the non-differentiable branch. Extensive experiments show that MDND sets a new state-of-the-art, demonstrating remarkable robustness on shapes with non-isometric deformations and topological noise.

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