DAMP: Decay-Aware Mixed-Precision Recurrent-State Quantization

Linear attention replaces growing KV caches with fixed-size recurrent states, yet these persistent states can become a substantial memory bottleneck under concurrent serving. Directly quantizing recurrent states to low precision often leads to severe accuracy degradation, as quantization errors propagate through successive state updates. We discover that the impact of these errors depends on two complementary dimensions: temporally, errors in long-lived memory can persist across many decoding steps; spatially, errors in different key rows affect model outputs differently, while state magnitudes vary substantially along both rows and columns. Motivated by these observations, we propose STEPQuant, a spatial-temporal post-training quantization framework for Delta-rule recurrent states. STEPQuant allocates precision according to error magnitude and memory lifetime, and jointly fits key-row and value-column scales based on state distributions and key-row impact on output error. Experiments on Qwen3.8-27B and Kimi-Linear-48B-A3B-Instruct across both long- and short-generation benchmarks show that STEPQuant closely matches FP32-state accuracy under a nominal 6-bit budget and outperforms uniform INT8 in its 4-bit configuration. Integrated into SGLang with optimized GPU kernels, 6-bit STEPQuant achieves over 5x recurrent-state compression and reduces total serving memory by up to 68.7%. Our code is available at https://github.com/Dreamer-Toby/STEPQuant.

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.

Hybrid linear-attention architectures have recently scaled to large open-weight models, offering quality competitive with full attention while substantially reducing key/value (KV) cache growth. However, their in-place recurrent-state updates complicate cache management: prefix reuse requires state checkpoints alongside full-attention KV, while storing state checkpoints in full increases memory pressure, leading to more evictions and repeated prefill. By analyzing the decay structure of Gated DeltaNet (GDN) and Kimi Delta Attention (KDA), we find that different heads and channels retain prefix information over markedly different timescales, which we term \emph{retention horizons}. This variation suggests substantial compression potential in persistent state checkpoints. Building on this observation, we introduce \emph{Decay-Aware State Compression} (DASC), which derives retention horizons from model weights, selects long-horizon state units, and packs them into a ragged state checkpoint layout. To integrate efficiently with tensor-parallel inference engines, DASC furtherly balances compressed state checkpoints across TP ranks. On reuse, DASC either zero-fills omitted units or refreshes them from a bounded suffix with additional compute cost. Across retrieval and end-to-end reasoning benchmarks on Kimi-Linear, conservative DASC configurations remain close to full caching while compressing KDA recurrent state checkpoints by $2.63\times$. Under fixed state checkpoint memory budgets, the resulting capacity gains reduce mean Time to First Token (TTFT) by 42.6% and improve input throughput by 68.4%. At larger compression ratio, suffix refresh recovers much of the accuracy lost to more aggressive omission, at the cost of additional replay computation. Qwen with GDN exhibits a similar quality--efficiency trend, showing that DASC extends from channel-wise KDA to head-wise GDN.