A Persistent-State Dataflow Accelerator for Memory-Bound Linear Attention Decode on FPGA

Linear attention models eliminate the quadratic prefix computation and context-growing KV cache of softmax attention by replacing pairwise token interactions with recurrent state updates. However, existing decoding implementations often materialize and write back the full recurrent state after every generated token, making state maintenance a major source of memory traffic, especially for models with large states and many heads. This paper presents DeltaLog, a recurrent-state decoding scheme that reduces this overhead without changing the model semantics. Specifically, DeltaLog represents the recurrent state as a dense base state together with a bounded log of recent compact updates. Most decode steps append only compact update factors to this log, while periodic merge steps fold the accumulated updates back into the dense base state. Thus, the model observes the same dense state as in eager decoding, but most full-state write-backs are replaced by lightweight append operations. We implement DeltaLog for GDN, KDA, and RWKV6 and integrate it into a prototype serving stack. Across these models, DeltaLog accelerates the recurrent-state update kernel by up to $1.86\times$, reduces profiled recurrent-state write traffic by up to $7.83\times$, and achieves $1.05$--$1.20\times$ end-to-end serving speedups over dense recurrent baselines.

Recent LLMs increasingly adopt hybrid designs that replace standard attention with linear attention, such as Gated DeltaNet (GDN) and Kimi Delta Attention (KDA). Although they compress the context into a fixed-size recurrent state and substantially reduce the cost of long-context processing, repeatedly reading and updating that state remains a major inference bottleneck. Quantization offers a natural way to reduce this cost, but can significantly degrade model quality, due to the accumulation of rounding errors and the presence of outlier rows and columns in the state. To address these challenges, we propose LeapQuant, a training-free method that achieves near-lossless performance under 8-bit recurrent-state quantization. First, to mitigate error accumulation, we propose per-window quantization, which leaps over a window of tokens and quantizes the state only once at its end. Within a window, outputs are computed from the fixed low-bit state together with high-precision buffered updates. Second, to reduce the error introduced by each quantization, LeapQuant retains the state's largest outliers as a few high-precision Compensator Tokens, which share the update path of real tokens. We then smooth the remaining residual before quantization to further reduce the error. Comprehensive experiments across the Qwen, Kimi, and GLM model families show that LeapQuant substantially reduces memory and compute costs during inference. With accuracy comparable to the FP32 baseline, it achieves average speedups of 2.05--3.70$\times$ at the kernel level and 1.47$\times$ for end-to-end inference on NVIDIA B200, RTX PRO 6000, and RTX 5090 GPUs.

Long-context language modeling remains central to modern sequence modeling, but the quadratic cost of Transformer attention makes scaling computationally prohibitive. Linear recurrent models address this bottleneck by compressing the context into a fixed-size state, making the rule that forgets, writes, and edits information a central design problem. To address state maintenance, Gated DeltaNet (GDN) combines gated state decay with delta-rule residual writes, using a learnable coefficient to balance forgetting and update magnitude. However, this coefficient is learned empirically rather than derived from the underlying objective, which can lead to suboptimal update magnitudes. We revisit the online-regression objective underlying GDN and, inspired by the Kaczmarz projection method, derive the key-norm-normalized dynamic step size $β_t = η_t / (\|k_t\|_2^2 + ε)$ for residual updates. We propose Kaczmarz Linear Attention (KLA), a one-scalar modification of GDN that preserves the state shape, gates, linear recurrence, and chunkwise parallel algorithm. At the 0.4B scale with a 1B-token budget, KLA achieves the lowest validation perplexity among evaluated linear-time baselines, 8.09 versus 8.50 for GDN, and remains stable up to 65K tokens. On controlled tasks, KLA reaches 100% on single-needle-in-a-haystack retrieval, improves 8x multi-query associative recall by 7.03 points over GDN, and delivers 2.1x higher decode throughput at 32K context. These results suggest that the key-norm-normalized Kaczmarz coefficient is a first-order design axis for delta-rule sequence models: it improves accuracy, extrapolation, and decoding efficiency without changing the recurrent state or hardware kernel.