LIGHT CONES FOR VISION: SIMPLE CAUSAL PRIORS FOR VISUAL HIERARCHY

Manglam Kartik, Neel Tushar Shah

Track: tiny paper (up to 4 pages)

Keywords: Object-Centric Learning, Lorentzian Spacetime, Visual Hierarchy, Geometric Deep Learning, Inductive Biases, Causal Structure, Minkowski Metric

TL;DR: We demonstrate that hierarchical object discovery requires Lorentzian causal structure, showing that a minimalist 11K-parameter model succeeds where identical Euclidean architectures consistently fail.

Abstract: Standard vision models treat objects as independent points in Euclidean space, unable to capture hierarchical structure like parts within wholes. We introduce Worldline Slot Attention, which models objects as persistent trajectories through spacetime worldlines, where each object has multiple slots at different hierarchy levels sharing the same spatial position but differing in temporal coordinates. This architecture consistently fails without geometric structure: Euclidean worldlines achieve 0.078 level accuracy, below random chance (0.33), while Lorentzian worldlines achieve 0.479-0.661 across three datasets: a 6x improvement replicated over 20+ independent runs. Lorentzian geometry also outperforms hyperbolic embeddings showing visual hierarchies require causal structure (temporal dependency) rather than tree structure (radial branching). Our results demonstrate that hierarchical object discovery requires geometric structure encoding asymmetric causality, an inductive bias absent from Euclidean space but natural to Lorentzian light cones, achieved with only 11K parameters. The code is available at: https://github.com/iclrsubmissiongram/loco.

Anonymization: This submission has been anonymized for double-blind review via the removal of identifying information such as names, affiliations, and identifying URLs.

Submission Number: 95