TORA: Topological Representation Alignment for 3D Shape Assembly

TL;DR

TORA is a topological representation alignment framework that improves 3D shape assembly by guiding flow-matching methods with relational structure, leading to faster convergence and better accuracy, especially in zero-shot scenarios.

Contribution

Introducing TORA, a novel topology-first representation alignment method that enhances flow-matching for 3D shape assembly without additional inference overhead.

Findings

TORA achieves up to 6.9× faster convergence.

It improves accuracy in-distribution and under domain shift.

State-of-the-art results on five diverse benchmarks.

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 while yielding two consistent benefits: faster convergence (up to 6.9$\times$) and improved accuracy in-distribution, along with greater robustness under domain shift. Experiments on five benchmarks spanning geometric, semantic, and inter-object assembly demonstrate state-of-the-art performance, with particularly pronounced gains in zero-shot transfer to unseen real-world and synthetic datasets. Project page: https://nahyuklee.github.io/tora.