[2604.04050] TORA: Topological Representation Alignment for 3D Shape Assembly

Computer Science > Computer Vision and Pattern Recognition arXiv:2604.04050 (cs) [Submitted on 5 Apr 2026] Title:TORA: Topological Representation Alignment for 3D Shape Assembly Authors:Nahyuk Lee, Zhiang Chen, Marc Pollefeys, Sunghwan Hong View a PDF of the paper titled TORA: Topological Representation Alignment for 3D Shape Assembly, by Nahyuk Lee and 3 other authors View PDF HTML (experimental) Abstract:Flow-matching methods for 3D shape assembly learn point-wise velocity fields that transport parts toward assembled configurations, yet they receive no explicit guidance about which cross-part interactions should drive the motion. We introduce TORA, a topology-first representation alignment framework that distills relational structure from a frozen pretrained 3D encoder into the flow-matching backbone during training. We first realize this via simple instantiation, token-wise cosine matching, which injects the learned geometric descriptors from the teacher representation. We then extend to employ a Centered Kernel Alignment (CKA) loss to match the similarity structure between student and teacher representations for enhanced topological alignment. Through systematic probing of diverse 3D encoders, we show that geometry- and contact-centric teacher properties, not semantic classification ability, govern alignment effectiveness, and that alignment is most beneficial at later transformer layers where spatial structure naturally emerges. TORA introduces zero inference overhead...