Transformer residual streams evolve through additive updates. Although a sufficiently expressive residual block can represent content replacement, standard architectures do not parameterize reading, comparison, and replacement as an explicit residual operation. We introduce Deep Delta Learning (DDL), a structured residual update that preserves the identity path while enabling target-seeking edits to the residual state. Each layer reads the current state along a learned direction, compares the resulting readout with a learned target, and writes back a gated rank-1 correction along the same direction. Closing the gate recovers the identity map, while fully opening it exactly overwrites the selected residual readout. We instantiate DDL with both scalar and expanded residual states. The expanded formulation provides multiple persistent value channels while keeping attention and MLP computation at the original model width, thereby separating residual-state capacity from backbone compute width. Controlled LLM pretraining experiments show that DDL improves language-modeling quality and average one-shot downstream performance over additive residual baselines in the reported runs, while introducing explicit memory and throughput tradeoffs. These results suggest that depth-wise delta-rule updates provide a useful inductive bias for managing Transformer residual streams.

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