When Recursive Models Finish Computing

Recursive models can continue updating their latent states beyond their nominal inference budget, so an incorrect output at that budget does not show whether computation is unfinished or has entered a persistently unsuccessful regime. We study the dynamics of completion in attention- and MLP-based Tiny Recursive Models (TRMs) on 1,000 hard Sudoku puzzles. Extending recurrence from the nominal 16 steps to 512 steps increases cumulative exact-solve accuracy from 59.2% to 87.5% for the attention model and from 74.4% to 91.9% for the MLP model, solving more than two-thirds of the puzzles unsolved in the nominal budget. Across both architectures, latent-state motion drops sharply after the first exact solution. Completed states are typically locally contractive along the trajectory direction, even though the same local Jacobian retains strongly expanding directions. We characterize this phenomenon as trajectory-conditioned anisotropic stability. Perturbation experiments confirm this directional stability across both models. The multi-step fate of the maximally expanding direction differs: it is absorbed within 16 steps in the attention model but persists longer in the MLP model. The anisotropic-stability pattern also holds for a second attention checkpoint. Together, these results distinguish nominal-budget failure from completed computation and identify a common dynamical signature of completion across two recurrent architectures.