Linear attention and state space models (SSMs) offer efficient alternatives to softmax attention by maintaining a fixed-size recurrent state, but this design requires careful management to preserve useful historical associations and limit interference. The delta rule helps reduce interference through correction of the value associated with each key, but it does not explicitly account for how related value features are distributed across the state.
We observe that a state $\boldsymbol{S}\in\mathbb{R}^{d_k\times d_v}$ can be viewed as a bank of $d_k$ addresses storing $d_v$-dimensional values. While a key-side read $\boldsymbol{S}^\top\boldsymbol{k}$ retrieves the value associated with $\boldsymbol{k}$, a value-side read $\boldsymbol{S}\boldsymbol{e}$ aggregates addresses whose stored value features match the selector $\boldsymbol{e}$.
Based on this observation, we propose Dual DeltaNet (DDN), which extends Kimi Delta Attention (KDA) with a two-sided delta rule. The key-side delta rule reads with the current key to correct its associated value, while the complementary value-side delta rule reads with selected features of the current value to reorganize the addresses it occupies. We derive a chunkwise parallel training algorithm and a rank-2 recurrence that increases arithmetic intensity during inference.
Compared with KDA, GDN-2, and Mamba-3, DDN achieves the strongest overall performance across language modeling, zero-shot downstream tasks, and retrieval, while incurring modest training and inference overhead relative to KDA. Code: https://github.com/ReichtumQian/DualDeltaNet