SketchSSM: Write to the Full State, Read from a Compact Sketch

Hybrid-attention models replace most softmax attention layers with linear attention, reducing KV-cache growth and enabling larger decode batches where recurrent-state access becomes a major bottleneck. ReplaySSM amortizes state updates by buffering keys and values, but each new query still requires a full-state read even though the state remains unchanged between state updates. We observe that low-rank state-weighted query approximation accurately preserves state-read outputs. Although future queries are unknown, the basis vectors used to approximate them can be fixed offline. Based on this observation, we introduce SketchSSM, which preserves full-state updates while approximating reads. At each state update, SketchSSM reads the full state once to precompute outputs for these basis vectors, storing them in a compact sketch. Each subsequent decode step combines the sketch vectors with query-dependent coefficients to reconstruct the output without a full-state read. Across four Mamba-2-, GDN-, and KDA-based models, SketchSSM reduces state-access traffic by approximately 10$\times$ while largely preserving average accuracy across four decode benchmarks and recall on four RULER retrieval tasks. On one NVIDIA B300, linear-attention kernel speedups over the standard vLLM baseline reach 7.78$\times$, 5.22$\times$, and 5.20$\times$ for Mamba-2, GDN, and KDA, respectively, with up to 2.64$\times$ higher decode throughput on Nemotron 3 Super.