Measuring Affordance Emergence: Design Constraints for Self-Supervised Embodied World Models

Gibson defined an affordance as a relation between agent and environment, where the same gap affords crossing for a long-legged body but not a short one. Whether such structure emerges in a world model trained only to predict its own future latent states, without reward or affordance labels, remains untested, since existing work either supervises affordance directly or probes models pretrained on demonstrations. We argue the question is not yet well-posed and report three measured obstacles. First, affordance probes are often solvable from the raw observation. Probing whether the cell ahead is blocked in MiniGrid, a randomly initialized encoder reaches ROC-AUC $1.000\pm0.000$ across 20 seeds, and the relational version fails identically since the carried object is rendered into the agent's view. Second, preventing representational collapse does not by itself produce structure. Across four self-supervised objectives at 20 seeds each, none exceeded an untrained encoder on spatial probes ($0.572\pm0.019$), including an inverse-dynamics objective that demonstrably learns yet reduces accuracy to $0.517\pm0.029$. Scale-based collapse diagnostics also mislead, since mean pairwise latent distance ranks these objectives almost opposite to effective dimensionality, which does predict probe performance (Spearman $0.64$, $p<10^{-10}$, 85 runs). Third, random exploration rarely reaches affordance-relevant states, encountering the key-and-door conjunction in 84 of 50,000 MiniGrid steps and reaching terrain obstacles in 5 of 200 BipedalWalker episodes, so competence is a precondition for generating affordance data rather than a consequence of it. We therefore propose a 2D physics benchmark satisfying all three constraints, in which a non-tipping body crosses gaps whose crossability depends on body parameters absent from the observation. Affordance is then a genuine agent–environment relation with analytic ground truth that an untrained control cannot recover, giving emergence claims a test they can actually fail.