Error Correction in Trained TTT Layers

Abstract

Test-time-training (TTT) layers update fast-weight memory while processing an input sequence. A gradient-based update, however, does not by itself establish how the memory revises an existing association. We study the structure and empirical role of prediction-derived updates in released TTT implementations. For dot-product objectives, we characterize the absence of a prediction-error residual and establish conditions under which inner-loop ascent and descent are equivalent after reparameterization. For the LayerNorm-based squared-error objective used by TTT-Linear and TTT-MLP, we derive the inner gradient and identify a prediction-derived component that cancels at the released initialization in the zero-epsilon limit. We then measure the full normalized prediction's contribution on three trained checkpoints. Removing this contribution while retaining the LayerNorm Jacobian gives a mean gradient norm ratio of 0.25 to 0.32 across the models. On 100,303 tokens from War and Peace, the same intervention with local per-token norm matching raises perplexity by 2.8-2.9% on TTT-Linear-760M and 1.3B, whereas freezing all fast-weight updates raises it by factors of 4.2-4.5. Separate synthetic tests illustrate the dependence of plain delta-rule overwriting on step size. The results distinguish a prediction-derived update from its behavioral value and show why implementation analysis and live interventions are both needed to assess test-time memory.