Guess-Verify-Refine: Data-Aware Top-K for Sparse-Attention Decoding on Blackwell via Temporal Correlation

Sparse-attention decoders rely on exact Top-K selection to choose the most important key-value entries for each query token. In long-context LLM serving, this Top-K stage runs once per decode query and becomes a meaningful latency bottleneck even when the indexer and attention kernels are already highly optimized. We present Guess-Verify-Refine (GVR), a data-aware exact Top-K algorithm for sparse-attention decoding on NVIDIA Blackwell. GVR exploits temporal correlation across consecutive decode steps: it uses the previous step's Top-K as a prediction signal, computes pre-indexed statistics, narrows to a valid threshold by secant-style counting in 1-2 global passes, verifies candidates with a ballot-free collector, and finishes exact selection in shared memory. We connect this behavior to the Toeplitz / RoPE structure of DeepSeek Sparse Attention (DSA) indexer scores and validate the design on real DeepSeek-V3.2 workloads integrated into TensorRT-LLM. GVR achieves an average 1.88x single-operator speedup over the production radix-select kernel, with up to 2.42x per layer per step, while preserving bit-exact Top-K outputs. In controlled TEP8 min-latency deployment, it improves end-to-end TPOT by up to 7.52% at 100K context, with larger gains at longer contexts and smaller but still positive gains under speculative decoding. While implemented and validated in the current TensorRT-LLM DSA stack on Blackwell, the same principle may extend to sparse-attention decoders whose decode-phase Top-K exhibits temporal stability.