Erase-then-Delta Attention: Decoupling Erase and Write Addresses in Delta-Rule Linear Attention

Linear attention replaces the unbounded cache of softmax attention with a fixed-size recurrent state, reducing sequence mixing to linear time and decoding to constant memory. The hard part is not just what to forget, but how to edit this compressed memory without scrambling existing associations. Delta-rule models subtract the current read before writing a new value, and Kimi Delta Attention (KDA) sharpens forgetting with channel-wise decay. But the active edit still uses a single scalar gate to control two different things: how much old content to erase on the key side and how much new content to commit on the value side. We introduce Gated DeltaNet-2, which generalizes both Gated DeltaNet and KDA by inheriting adaptive forgetting and channel-wise decay while addressing their shared limitation, the scalar tie between erasing and writing. Gated Delta Rule-2 separates these roles with a channel-wise erase gate b_t and a channel-wise write gate w_t, reducing to KDA when both gates collapse to the same scalar and to Gated DeltaNet when the decay also collapses. We derive a fast-weight update view, a chunkwise WY algorithm with channel-wise decay absorbed into asymmetric erase factors, and a gate-aware backward pass that preserves efficient parallel training. At 1.3B parameters trained on 100B FineWeb-Edu tokens, Gated DeltaNet-2 achieves the strongest overall results among Mamba-2, Gated DeltaNet, KDA, and Mamba-3 variants across language modeling, commonsense reasoning, and retrieval. Its advantage is most pronounced on long-context RULER needle-in-a-haystack benchmarks, where it improves the evaluated multi-key retrieval setting and remains strong in both recurrent and hybrid settings. Code is available at https://github.com/NVlabs/GatedDeltaNet-2.

Exact deletion from persistent language-model memory depends on whether a record's effect remains addressable after later computation. Native Kimi Delta Attention (KDA) gives a negative result for the tested receipt interface: the corpus-pooled raw recurrent contribution changes by 12-49% with the suffix and remains 8-49% after a decay-ledger correction. Native omission also changes later transition and write terms and other active caches. Frozen-input transport succeeds on its fixed-input control; the changed terms place native omission outside the tested receipt classes. Checkpoint replay supplies the evaluated recomputation path; zero residual on final logits and all 80 audited KDA arrays verifies restoration across the declared checkpoint surface. The complementary result is constructive. We retrofit support-vector memory into frozen Gemma 3 without attention transfer, low-rank recovery, distillation, adapters, or language-model parameter updates. Prefix-mass preservation and one box per prefix solve give base-matched admission at 4B with 1.85% perplexity overhead. At 1B and 4B, verified deletion agrees with its conditional retained-key refit within 1.3e-10 maximum next-token KL; behavioral attacks at 4B reach never-stored or chance baselines. Across 1B, 4B, and 12B, the 4B checkpoint uniquely combines base-matched admission with low overhead. The paper's two contributions are a negative result for native KDA's tested receipt classes and a positive training-free construction for addressable pretrained memory.

Linear attention is increasingly used in frontier language models for efficient long-context inference and constant-memory decoding. Its fixed-size recurrent memory, however, requires an online decision at each token: what to write and how strongly to overwrite existing associations before knowing which information future queries will require. Delta-rule models learn this strength from the current token embedding but do not track confidence in the memory estimate, preventing each write from adapting to accumulated evidence. To represent this uncertainty explicitly, we reformulate recurrent associative memory as a linear--Gaussian state-space model, for which the Kalman filter is the optimal recursive estimator, and introduce a new family of models, Kalman Delta Networks (KDNs). Within KDNs, the transition propagates both the memory state and its uncertainty, allowing the Kalman gain to weight each residual write by accumulated evidence and observation reliability. Under this formulation, Delta-style updates emerge as a special case that substitutes a token-wise isotropic surrogate for predictive covariance and omits covariance tracking. Exact tracking, however, entails a dense, state-dependent Riccati recursion that is poorly suited to GPU-parallel linear-attention scans. To address this issue, we introduce two scan-compatible KDN approximations. Diagonal KDN projects each one-step posterior onto the diagonal Gaussian family through online mean-field variational inference, whereas Isotropic KDN uses an isotropic approximation with a single uncertainty scalar per head. Their uncertainty recurrences are Mobius maps, enabling associative scans with logarithmic parallel depth. Across controlled pretraining at 750M and 1.3B parameters, KDN variants consistently improve perplexity and mean downstream accuracy over state-of-the-art linear-attention models.