Forcing-Consistency Training Constraint

1. Exact integration point: add this objective to supervised or actor-critic training for a recurrent policy, world-model controller, or event-based transformer. Construct minibatch groups $\mathcal{H}_o$ containing different hidden-state histories that share the same observable event sequence. 2. Pseudocode: sample histories; group them by $P(h)$; compute policy distributions $q_\theta$; compute the group-average distribution $\bar q$; add Jensen-Shannon disagreement to the task loss; use the world model to enumerate or sample latent states in each belief group; calculate the minimum safety margin for each candidate forcing mask; add the hinge penalty when no candidate has margin $m$; optimize policy and model parameters, optionally stopping gradients through the safety model initially. Do not union independently safe masks across groups, because forcing consistency need not be closed under union. 3. Computed versus estimated: observational equivalence and the consistency loss are exact for logged histories; belief sets, safety margins, and latent transitions are estimated from the world model or simulator. Maintain an explicit empty-intersection label whenever every candidate mask fails at least one latent state. 4. First cheap experiment: train GRU policies on a partially observed safety gridworld with aliased rooms and hidden obstacle states, comparing task loss alone, latent-state contrastive regularization, and the proposed loss. Sweep $\lambda$ and observation aliasing. The predicted signature is monotone reduction of $\widehat{\kappa}(o)$, with a transition when the safety term becomes large enough to collapse contradictory action distributions. Empirically, violation probability should correlate with the measured empty-intersection rate, and policies trained with the constraint should preserve safety under held-out hidden-state permutations even if nominal reward is matched.