Latent Trajectory Steering Unlocks Trapped Capacity in Recursive Reasoning

Recursive reasoning models such as HRM and TRM achieve strong performance on structured reasoning tasks with far fewer parameters than LLMs, yet their inference dynamics are not well understood. We analyze their latent trajectories from a dynamical-systems perspective and find distinct stable basins for successful and failed rollouts, with high-stretching finite-time Lyapunov exponent (FTLE) ridges concentrated near transitions between them. Based on this observation, we propose a training-free inference method that identifies these ridge locations along the unperturbed trajectory, applies controlled perturbations to induce basin crossings, and aggregates the resulting trajectories through Gibbs-weighted selection. Without updating model parameters or using ground-truth labels, our method improves the accuracy of TRM in Sudoku-Extreme from 87.4% to 98.43% and in Maze from 85.3% to 91.0%, with consistent gains in HRM. These results identify dynamical trapping as a major failure mode in recursive reasoning: redirecting a failed latent trajectory across a high-FTLE boundary can recover the correct solution without retraining the model. Compared to existing alternatives, such as PTRM, our method locates a more precise point of intervention in the latent reasoning trajectory, such that much fewer rollouts and augmentation are needed.