Sparse attention limits the keys used by each query, but finding those keys can still require a full-prefix scan at every layer. We introduce , a training-free method that shares candidate search while retaining each consumer’s own scoring and selection. A producer publishes a top- pool larger than the attention budget ; subsequent layers select their own top- from that pool. Measurements across three sparse-attention model families show substantially higher coverage from broad pools than overlap between final selections. We implement layerwise sharing, persistent decode reuse, and a coarse producer in vLLM for DeepSeek-V4-Flash. Across four long-context suites, three consumer layers per producer give – speedups and – lower GPU energy, with observed accuracy changes of to percentage points in single runs. More extensive sharing exposes task-dependent quality losses. Sampled prefill traces also reveal recurring selected KV positions across query groups and layers. We characterize this shared working-set structure and use it to motivate Top-, an exploratory bounded pool construction for prefill. Its deployment, task accuracy, and serving benefits remain open.

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