# Light Cones For Vision: Simple Causal Priors For Visual Hierarchy

arXiv: https://arxiv.org/abs/2603.24753 · HTML: https://mlsanity.com/paper/2603.24753/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 14 references that are in the map.
- First posted on arXiv 25 Mar 2026.

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

- [CLEVR: A Diagnostic Dataset for Compositional Language and Elementary Visual Reasoning](https://mlsanity.com/paper/1612.06890/) (2016)
- [Object-Centric Learning with Slot Attention](https://mlsanity.com/paper/2006.15055/) (2020)
- [Dynamic Routing Between Capsules](https://mlsanity.com/paper/1710.09829/) (2017)
- [Poincar'e Embeddings for Learning Hierarchical Representations](https://mlsanity.com/paper/1705.08039/) (2017)
- [MONet: Unsupervised Scene Decomposition and Representation](https://mlsanity.com/paper/1901.11390/) (2019)
- [Multi-Object Representation Learning with Iterative Variational Inference](https://mlsanity.com/paper/1903.00450/) (2019)
- [Conditional Object-Centric Learning from Video](https://mlsanity.com/paper/2111.12594/) (2021)
- [Hyperbolic Entailment Cones for Learning Hierarchical Embeddings](https://mlsanity.com/paper/1804.01882/) (2018)
- [Illiterate DALL-E Learns to Compose](https://mlsanity.com/paper/2110.11405/) (2021)
- [Invariant Slot Attention: Object Discovery with Slot-Centric Reference Frames](https://mlsanity.com/paper/2302.04973/) (2023)

## Abstract (arXiv)

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.