Grounding Spatial Relations in a Compact World Model: Instruction Leakage and a Goal-Free Dynamics Fix

Compact world models that condition on a language goal promise to ground relations such as ``put the red block left of the blue block'' using a sparse set of explicit \emph{reference anchors}.

We ask when such references actually ground a relation, and identify a trap: a goal-conditioned predictor reaches a striking $0.90$ relation-readout accuracy, yet this is \emph{instruction transcription}, not perception.

Withholding the goal collapses it to chance ($0.90\!\to\!0.27$, three seeds) and a counterfactual instruction makes the predicted anchors follow the \emph{false} instruction $94.5\%$ of the time (true scene $2.3\%$; $N{=}256$).

Tested across three settings and a within-task ablation, our central claim characterizes the confound: \textbf{instruction leakage occurs when the scored quantity is transcribable from the instruction (when the instruction names the answer) and is essentially independent of how predictive the non-instruction inputs are.} Our tabletop and the external BabyAI benchmark leak, whereas a Language-Table forward-dynamics world model whose instruction names \emph{referents} does not, until the instruction is augmented to name the direction; and degrading the action never increases leakage, the opposite of what predictor-competition predicts.

The diagnosis prescribes the fix: keep the goal out of the dynamics (it belongs to the planner's cost) and supervise the \emph{read} path, recovering genuine, instruction-independent grounding ($0.88$, identical with and without the goal).

The detection protocol and remedy apply to any goal-conditioned world model whose instruction names the scored quantity.