FG2-GDN: Enhancing Long-Context Gated Delta Networks with Doubly Fine-Grained Control

Linear attention mechanisms have emerged as promising alternatives to softmax attention, offering linear-time complexity during inference. Recent advances such as Gated DeltaNet (GDN) and Kimi Delta Attention (KDA) have demonstrated that the delta rule, an online gradient descent update, enables superior associative recall compared to simple additive updates. While KDA refined the coarse head-wise decay gate into channel-wise decay, the learning rate βt in the delta update remains a scalar, limiting the model's capacity for dimension-specific adaptation. We introduce FG2-GDN, which replaces the scalar βt with a channel-wise vector analogous to the transition from SGD to per-coordinate adaptive optimizers such as AdaGrad and Adam. We further propose FG2-GDN+, which decouples the scaling for keys and values, enabling independent control of erasure strength and write strength. Experiments on synthetic and real-world benchmarks show that FG2-GDN and its variant improve associative recall and long-context understanding over GDN and KDA, with comparable computational efficiency.