# Why Does the Future Branch? Identifiable Closure Tests for Stochastic Physical World Models

arXiv: https://arxiv.org/abs/2608.00591 · HTML: https://mlsanity.com/paper/2608.00591/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Latent predictive world models, one of 11 directions in World models.
- Builds on 11 of its 28 references that are in the map.
- First posted on arXiv 1 Aug 2026.

## Placed in

- World models / [Latent predictive world models](https://mlsanity.com/wm/latent-predictive-world-models/)

## Builds on (most cited first, 11 of 11)

- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision?](https://mlsanity.com/paper/1703.04977/) (2017)
- [World Models](https://mlsanity.com/paper/1803.10122/) (2018)
- [Physion++: Evaluating Physical Scene Understanding that Requires Online Inference of Different Physical Properties](https://mlsanity.com/paper/2306.15668/) (2023)
- [Rethinking Aleatoric and Epistemic Uncertainty](https://mlsanity.com/paper/2412.20892/) (2024)
- [On the Benefits of Memory for Modeling Time-Dependent PDEs](https://mlsanity.com/paper/2409.02313/) (2024)
- [On Rollouts in Model-Based Reinforcement Learning](https://mlsanity.com/paper/2501.16918/) (2025)
- [What-If World: A Causal Benchmark for General World Models in Embodied Scenarios](https://mlsanity.com/paper/2605.27589/) (2026)
- [Learning Stochastic Multiscale Models](https://mlsanity.com/paper/2506.22655/) (2025)
- [STORI: A Benchmark and Taxonomy for Stochastic Environments](https://mlsanity.com/paper/2509.01793/) (2025)

## Abstract (arXiv)

A calibrated stochastic world model can reveal how uncertain a future is without revealing why it branches. The same conditional future law can arise because an observation aliases physical states or because dynamics remain random after the declared full state is fixed. We prove that ordinary transitions cannot identify these two sources, even for a perfect probabilistic predictor. ClosurePairs makes them identifiable by crossing compatible microstates with repeated exogenous disturbances and estimating state, noise, and state-noise interaction variance. The central consequence is operational: under finite hierarchical sampling, forecast difficulty governs the useful compute scale, while the alias/process composition provides complementary information about its direction-resolving the current state or sampling future randomness. ClosurePairs recovers source attribution at unchanged likelihood, reduces equal-budget decomposition error in a nonlinear interaction benchmark, and supports observation-only routing. On exact-marginal MetaWorld twins, an output-only allocator is at chance while a Closure-supervised probe on frozen JEPA-WM features routes 89.8-100%. In an independent ManiSkill PushCube confirmation, a stochastic RSSM's outputs and latents remain at chance, whereas an RGB-only Closure probe routes 100% under both ID and geometry/camera OOD over five seeds, matching direct allocation rather than exceeding it. Across five unseen allocation menus, the same Closure probe routes 92.5%/90.4% ID/OOD with no new oracle labels, versus 37.9%/32.9% for a frozen direct allocator. ClosurePairs is therefore an identifiable, reusable mechanism target that cannot be recovered from forecast quality alone.