# Conformal Orbit-Valid Trust Horizons for Equivariant World Models

arXiv: https://arxiv.org/abs/2606.24946 · HTML: https://mlsanity.com/paper/2606.24946/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Latent predictive world models, one of 11 directions in World models.
- Builds on 18 of its 24 references that are in the map.
- First posted on arXiv 23 Jun 2026.

## Placed in

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

## Builds on (most cited first, 18 of 18)

- [Mastering Diverse Domains through World Models](https://mlsanity.com/paper/2301.04104/) (2023)
- [Group Equivariant Convolutional Networks](https://mlsanity.com/paper/1602.07576/) (2016)
- [E(n) Equivariant Graph Neural Networks](https://mlsanity.com/paper/2102.09844/) (2021)
- [A Gentle Introduction to Conformal Prediction and Distribution-Free Uncertainty Quantification](https://mlsanity.com/paper/2107.07511/) (2021)
- [Conformalized Quantile Regression](https://mlsanity.com/paper/1905.03222/) (2019)
- [Adaptive Conformal Inference Under Distribution Shift](https://mlsanity.com/paper/2106.00170/) (2021)
- [Control Barrier Functions: Theory and Applications](https://mlsanity.com/paper/1903.11199/) (2019)
- [Vector Neurons: A General Framework for SO(3)-Equivariant Networks](https://mlsanity.com/paper/2104.12229/) (2021)
- [Hamilton-Jacobi Reachability: A Brief Overview and Recent Advances](https://mlsanity.com/paper/1709.07523/) (2017)
- [e3nn: Euclidean Neural Networks](https://mlsanity.com/paper/2207.09453/) (2022)
- [Provably Strict Generalisation Benefit for Equivariant Models](https://mlsanity.com/paper/2102.10333/) (2021)
- [SO(2)-Equivariant Reinforcement Learning](https://mlsanity.com/paper/2203.04439/) (2022)
- [EquiBot: SIM(3)-Equivariant Diffusion Policy for Generalizable and Data Efficient Learning](https://mlsanity.com/paper/2407.01479/) (2024)
- [Does equivariance matter at scale?](https://mlsanity.com/paper/2410.23179/) (2024)
- [Hierarchical Planning with Latent World Models](https://mlsanity.com/paper/2604.03208/) (2026)
- [Equivariant Reinforcement Learning under Partial Observability](https://mlsanity.com/paper/2408.14336/) (2024)
- [FF-JEPA: Long-Horizon Planning in World Models with Latent Planners](https://mlsanity.com/paper/2606.09311/) (2026)
- [Symmetry, Defects, and Diffusion in Continuous-memory Recurrent Networks](https://mlsanity.com/paper/2605.03338/) (2026)

## Built on by (most cited first, 1 of 1)

- [DreamLedger: Where to Refuse World-Model Imagination Using Execution-Settled Credit](https://mlsanity.com/paper/2608.23863/) (2026)

## Abstract (arXiv)

Learned world models are useful only over horizons on which their rollout error remains controlled. We study trust-horizon certification for latent world models with known group symmetries. Given a one-step latent residual and a finite-time expansion estimate, we form a raw horizon curve and calibrate it with a split-conformal multiplicative factor. On the reproducible audit set, the conformal factor is γα=1.0: the raw certificate is already conservative under the audit protocol. Across 50 stable audits, we observe zero anti-conservative violations, corresponding to an exact-binomial 95% upper bound of 5.8% on the violation rate. Our main structural result is that exact equivariance transports a calibrated trust-horizon curve over the group orbit: when the environment dynamics, encoder, predictor, action transform, and latent metric satisfy the stated equivariance/invariance conditions, rollout errors and trust horizons are orbit-constant. Empirically, the implemented models exhibit small orbit-transport residuals, with median 1.1% and maximum 4.1% over 14 orbit audits. The certificate is also non-vacuous (median certified-to-measured horizon ratio 0.67). A certificate-level calibration-cost study shows two complementary regimes. On a symmetric 2D substrate, equivariant, plain, and augmented models are all orbit-valid from a single calibration sector -- no separation, because the substrate already makes non-equivariant baselines approximately orbit-robust. A 3D yaw audit shows the other regime: the equivariant model obtains a one-sector safe and non-vacuous orbit-valid certificate, while healthy non-equivariant baselines pay violation, slack, sharpness, or additional-sector cost. The certificate is a conservative, distributional audit rather than a global reachability guarantee, and certificate-guided subgoal spacing is not confirmed in the current 3D CEM-MPC behavior layer.