Transformer residual streams evolve by additive accumulation: each layer appends a feature update to a shared hidden state, but has no direct mechanism for replacing content that has become obsolete or conflicting. We introduce Deep Delta Learning (DDL), a residual update rule that preserves the identity path while giving every layer the ability to selectively rewrite residual content. DDL reads the current state along a learned direction, compares it with a learned target value, and writes back a gated correction along the same direction. When the gate is closed, the update reduces to the identity; when the gate is fully open, the selected component is overwritten, yielding a depth-wise delta-rule generalization of standard residual addition. We integrate DDL in decoder-only language models with both scalar and expanded residual states, while keeping attention and MLP sublayers at the original compute width. Controlled pretraining and downstream evaluations show that residual rewrite operations improve language modeling quality relative to pure additive accumulation introduced in ResNet, suggesting that a learned delta-rule update is an effective mechanism for managing Transformer residual streams.