The Orthogonalized Read Is a Removable Training Scaffold for Recurrent Memory

Abstract

Orthogonalizing the mLSTM memory matrix at read time with five differentiable Newton-Schulz iterations improves noisy associative recall. We replicate this effect and investigate its mechanism. Training on MAD noisy recall exhibits a long chance-level plateau followed by a sharp increase in accuracy. The orthogonalized read improves conditioning during this plateau and can be removed after escape. Ablations support three findings. First, the benefit requires a self-consistent read and gradient: an exact recursive least-squares read (the Mesa layer) yields a similar benefit, while straight-through variants, delta-rule writes, frozen random keys, and Frobenius normalization show no improvement over baseline. Second, across a learning-rate x task-difficulty grid, orthogonalization multiplies escape hazard roughly six-fold, with no detectable dependence on difficulty, and widens the range of learning rates that produce successful runs. Third, adding orthogonalization at inference leaves chance-level failures unresolved, while removing it gradually after escape yields standard mLSTMs at near-perfect accuracy. Schedule changes alone recover much of the reported gain. A batch-size x learning-rate analysis separates the effects of per-step learning rate and gradient noise on escape hazard (elasticities +3.0 and -1.65, respectively), linking the original vocab-96 result to its large-batch training regime. Direct decoding of the memory state recovers roughly half of the associations in behaviorally failed models, indicating a readout-learning limitation despite substantial stored information. These results show that fixed-budget recall benchmarks are sensitive to trainability and provide a tractable setting for investigating abrupt behavioral transitions through measurements of internal representations.