Mechanistic Foundations of Goal-Directed Control
Mechanistic interpretability has transformed the analysis of transformer circuits by decomposing model behavior into competing algorithms, identifying phase transitions during training, and deriving closed-form predictions for when and why strategies shift. However, this program has remained largely confined to sequence-prediction architectures, leaving embodied control systems without comparable mechanistic accounts. Here we extend this framework to sensorimotor-cognitive development, using infant motor learning as a model system. We show that foundational inductive biases give rise to causal control circuits, with learned gating mechanisms converging toward theoretically motivated uncertainty thresholds. The resulting dynamics reveal a clean phase transition in the arbitration gate whose commitment behavior is well described by a closed-form exponential moving-average surrogate. We identify context window k as the critical parameter governing circuit formation: below a minimum threshold (k$\leq$4) the arbitration mechanism cannot form; above it (k$\geq$8), gate confidence scales asymptotically as log k. A two-dimensional phase diagram further reveals task-demand-dependent route arbitration consistent with the prediction that prospective execution becomes advantageous only when prediction error remains within the task tolerance window. Together, these results provide a mechanistic account of how reactive and prospective control strategies emerge and compete during learning. More broadly, this work sharpens mechanistic accounts of cognitive development and provides principled guidance for the design of interpretable embodied agents.