Title: FOLIAGE: a Latent World Model for Accretive Surface Growth
Primary area: applications to computer vision, audio, language, and other modalities
Keywords: Surface Growth, World Model, Multimodal

Abstract: Accretive surfaces grow by adding material and changing rest metrics, producing emergent, complex, and changing morphologies. We introduce FOLIAGE, a geometry-centric latent world model that infers a deployable state from heterogeneous, partial sensors and predicts its action-conditioned evolution. The perception stack aligns images, point clouds, and meshes through correspondence-constrained fusion and age features, then pools into global and young-region summaries that emphasize where change will occur next. Dynamics input act only on the latent, taking material coefficients and a horizon code to produce counterfactual roll-outs without entangling perception with control. Training-time physics guides representation via a target encoder that receives per-vertex energies and energy-gated message passing, while the deployable path relies solely on observable inputs. On the SURF-GARDEN data platform and the SURF-BENCH suite, FOLIAGE improves mesh topology classification by ~3 pp, reduces dense-correspondence geodesic error by ~10\%, lifts cross-modal retrieval by ~25\% mAP@100, increases growth-stage recognition by ~8 pp, lowers 5-step Chamfer by ~20\%, and cuts inverse-material error by ~40\% relative to strong baselines. Stress tests show graceful degradation under sensor loss, stable long-horizon roll-outs, and gains from train-only physics without test-time privileges. Code and datasets used in this study will be made publicly available upon publication to facilitate reproducibility and further research.

TL;DR: We present FOLIAGE, a latent world model for unbounded accretive surface evolution