Provably Shorter Scratchpads in Hybrid DeltaNet-Attention Decoders

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.

Hybrid large language models interleave full-attention layers with linear-attention layers to reduce the cost of long-context inference. This structure complicates prefix caching: full-attention key-value caches are token-addressable, whereas linear-attention layers maintain recurrent states that cannot be rolled back to arbitrary prefix boundaries. Existing hybrid prefix caching methods address this mismatch by storing recurrent-state checkpoints. As a result, token-level matches are directly usable only at positions aligned with stored checkpoints, constraining prefix reuse to a discrete set of boundaries. We present Tail-Replay, a prefix caching mechanism that enables unconstrained token-level prefix reuse in hybrid large language models. The key insight is that linear-attention mechanisms such as Gated DeltaNet can be viewed as a structured, lossy compression of the input prefix: gated recurrent updates progressively attenuate the contributions of earlier inputs. Consequently, the recurrent state of a matched prefix can be well approximated by replaying only a short, recent suffix of that prefix. Tail-Replay exploits this property by caching the exact full-attention key-value cache while omitting recurrent-state checkpoints. On a cache hit, it reconstructs the linear-attention states by replaying a short, recent suffix of the matched prefix. As a result, the reuse boundary is determined by the shared tokens rather than by recurrent-state checkpoints. We evaluate Tail-Replay on three Gated DeltaNet-based hybrid models using the LongBench and RULER benchmarks. With only a 5--10% replay budget, it retains 92.8--99.9% of full-prefill quality on LongBench and RULER. For serving efficiency, we evaluate time-to-first-token speedups across multiple matched-prefix lengths---8K, 16K, and 32K. The speedup grows with prefix length, reaching $9.1$--$14.3\times$ over full prefill at 32K.

Self-attention lets each token retrieve information from the full context, but its quadratic cost in sequence length limits training and inference at long context. This paper presents a comparative study of softmax attention and four recent recurrent linear-attention architectures: DeltaNet, Gated DeltaNet, Kimi Delta Attention, and Gated DeltaNet-2. We express these mechanisms in a common recurrent-memory notation, making explicit how they differ in expressivity, memory decay, erase and write control, training throughput, and implementation complexity. Our experiments center on 350M-parameter models trained for 15B tokens, and include optimizer and learning-rate comparisons, hybrid-versus-pure stack comparisons, sequence-length runtime measurements, larger DeltaNet runs at 1.3B and 3B parameters, and a small set of downstream evaluations. The reported speed results measure training throughput and iteration time; we do not provide an empirical inference-speed benchmark. Within the reported 350M-parameter, 15B-token sweep, Kimi Delta Attention with Muon reaches the lowest final validation loss, a pure Gated DeltaNet stack trained with AdamW has the highest normalized training throughput, hybrid stacks generally improve loss at a throughput cost, and Muon consistently lowers final validation loss relative to AdamW in the matched architecture settings we evaluate. We introduce and evaluate lightweight cross-layer routing mechanisms for DeltaNet-style memories. The most natural DeltaNet-inspired formulation, forwarding a lower layer's delta-rule write error into the next layer's value target, does not improve over matched baselines. Routing into the aligned hidden stream and forwarding the write value instead yields a modest improvement in the matched runs we report: Cross-Layer Value Routing (CLVR) lowers final validation loss for both DeltaNet and Gated DeltaNet.