Value Magnitude Does Not Survive the Recurrence: Diagnosing and Repairing a Mamba World Model for Latent Search
Abstract
A selective state-space world model that advances a chess position one ply per recurrent step under-reads the material swings that decide games. After a queen capture the frozen evaluator it was distilled from reads −0.453; the model reads −0.12. The obvious hypothesis, that the information reaches the hidden state and the value head fails to extract it, had real evidence: a cosine of +0.80 between the model's consistency projection and the evaluator's embedding. Two fine-tunes that sharpened the value target moved the reading to −0.067 and then −0.056, each further from the truth. A single probe then settled it: decoding the same hidden state through the evaluator's own value head returns −0.039, so the magnitude was never in the state. The cause is architectural: move tokens are from-square and to-square pairs, so a capture emits the same token as a quiet move, and the selective scan's decay gate, exp(ΔA) < 1, shrinks whatever magnitude the board encoding injects. The repair computes material from the real board the planner already holds and trains the head on the residual only. It adds no parameters and moves the usable un-anchored rollout horizon from three plies to eight. The repaired model is the world model inside a planner that beats a PUCT search reading the identical evaluator by +52 Elo over 1,040 games at less wall-clock; the repair itself converts to about zero Elo, because the planner's root guard already catches at play time the hangs the repair fixes. The same guard is why an on-policy correction round for what the repair leaves returned nothing: it removes the positions the round was meant to collect from the planner's own games, by a measured factor of 3.5.