Conformal Orbit-Valid Trust Horizons for Equivariant World Models
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 $γ_α=1.0$: 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.
Code (0)
등록된 구현이 없습니다.
Similar Papers 제목 키워드 기반
eCP: Equivariant Conformal Prediction with pre-trained models
Conformal prediction, a post-hoc, distribution-free, finite-sample method of uncertainty quantification that offers formal coverage guarantees under the assumption of data exchangeability. Unfortunately, the resulting un…
Trajectory PredictionCertified World Models: Predictability Across Configuration, Horizon, and Resolution
Scale buys interpolation; structure buys certifiable transfer. A world model's average error does not say whether a particular rollout can be trusted, or for how long. For equivariant latent world models we give a predic…
Symmetry-Protected Lyapunov Neutral Modes in Equivariant Recurrent Networks
Recurrent networks that store position, phase, or other continuous variables need state-space directions that remain neutral over long horizons. We give a symmetry-based account of when such neutral directions are guaran…
AdS-GNN -- a Conformally Equivariant Graph Neural Network
Conformal symmetries, i.e.\ coordinate transformations that preserve angles, play a key role in many fields, including physics, mathematics, computer vision and (geometric) machine learning. Here we build a neural networ…
Graph Neural NetworkOrbit-Equivariant Graph Neural Networks
Equivariance is an important structural property that is captured by architectures such as graph neural networks (GNNs). However, equivariant graph functions cannot produce different outputs for similar nodes, which may …