Optimizers Select Algorithms: Update Geometry Controls Memory Strategy in Associative Recall

Optimizers do not merely dictate convergence speed; they actively select the computational algorithm a network uses. We introduce RP-MQAR, placing memorization and in-context retrieval in direct competition, and study algorithm selection across seven sequence architectures and a broad spectrum of optimizers—ranging from coordinate-adaptive Adam to spectrally orthogonal Muon, and the continuous geometric family in between. Architecture strongly constrains which strategies are available; where both are learned, optimizer choice can switch the model between parametric and contextual recall. Orthogonalizing Adam-like updates strongly favors contextual retrieval. Parametric memory consistently forms first, and the final strategy tracks whether contextual retrieval later displaces it. Update geometry therefore selects the learned algorithm, not merely its convergence speed.