# SWORD: Scene-Grounded Wasserstein Object-Relation Distance for 3D Scene Graph Prediction

arXiv: https://arxiv.org/abs/2610.17692 · HTML: https://mlsanity.com/paper/2610.17692/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 36 references that are in the map.
- First posted on arXiv 13 Oct 2026.

## Builds on (most cited first, 10 of 10)

- [SGDR: Stochastic Gradient Descent with Warm Restarts](https://mlsanity.com/paper/1608.03983/) (2016)
- [Visual Relationship Detection with Language Priors](https://mlsanity.com/paper/1608.00187/) (2016)
- [Learning 3D Semantic Scene Graphs from 3D Indoor Reconstructions](https://mlsanity.com/paper/2004.03967/) (2020)
- [RIO: 3D Object Instance Re-Localization in Changing Indoor Environments](https://mlsanity.com/paper/1908.06109/) (2019)
- [Knowledge-Embedded Routing Network for Scene Graph Generation](https://mlsanity.com/paper/1903.03326/) (2019)
- [SceneGraphFusion: Incremental 3D Scene Graph Prediction from RGB-D Sequences](https://mlsanity.com/paper/2103.14898/) (2021)
- [Open3DSG: Open-Vocabulary 3D Scene Graphs from Point Clouds with Queryable Objects and Open-Set Relationships](https://mlsanity.com/paper/2402.12259/) (2024)
- [Exploiting Edge-Oriented Reasoning for 3D Point-based Scene Graph Analysis](https://mlsanity.com/paper/2103.05558/) (2021)
- [Object-Centric Representation Learning for Enhanced 3D Semantic Scene Graph Prediction](https://mlsanity.com/paper/2510.04714/) (2025)
- [Edge-Centric Relational Reasoning for 3D Scene Graph Prediction](https://mlsanity.com/paper/2511.15288/) (2025)

## Abstract (arXiv)

3D scene graph prediction is commonly optimized with object-node and relation-edge classification losses. These objectives encourage exact object and relation label recovery, but they do not directly optimize semantic proximity to the ground-truth scene graph: two wrong graphs can receive comparable penalties even when one is much closer in object roles and relation contexts. A direct graph-distance loss is difficult in general, since graph matching and graph edit distance require correspondence search and edit-cost design. Our key observation is that prior supervised 3D scene graph prediction protocols are conducted on fixed object-node indices and supervised edge slots. This can turn a scene graph comparison into a well-defined aligned graph-distance problem. To this end, we propose SWORD, a Scene-Grounded Wasserstein Object-Relation Distance that builds block-normalized object and relation ground distance metrics from training scene graph annotations through a deterministic base-to-context order, without external semantic priors. SWORD lifts these metrics to Wasserstein distances over aligned node and null-augmented edge marginals, providing semantic graph-distance supervision beyond exact-label penalties while preserving the ground-truth graph as the unique zero-distance solution in aligned marginal probability space. We prove that SWORD is a strict metric on aligned marginal probabilistic scene graphs, preserves scene-graph-grounded substitution ordering, controls additive graph-grounded semantic observables, and yields a surrogate upper-bounding decoded semantic error.