Late-interaction visual document retrievers preserve fine-grained page evidence by storing many token embeddings per page, but the resulting storage and query-time interaction costs make large-scale deployment expensive. Pooling document tokens before indexing offers a natural remedy, yet static pooling must decide which visual evidence to preserve before the query is known. We study an alternative: a heavily compressed hot-path index generates candidates, after which query-aware token budgeting operates on the original token sets of the shortlisted pages. We formulate this stage-two selection as a budgeted MaxSim coverage problem, show that a clipped version is monotone submodular, and compare coverage-only, cluster-guided, token-wise, and marginal-gain policies. On ten ViDoRe tasks with ColModernVBERT, direct static pooling reduces macro normalized discounted cumulative gain at rank five from 0.6309 without compression to 0.4738 at a thirty-two-fold pool factor. Under the same candidate-generation regime and a pool-factor-eight-equivalent reranking budget, token top-k recovers 93.93 percent of the full-token score, while greedy marginal-gain selection recovers 98.39 percent. Held-out and leave-one-dataset-out evaluations yield positive greedy improvements over token top-k on every dataset. The latency analysis reveals two useful operating points: token top-k for interactive retrieval and the naive greedy implementation as a quality upper envelope. Together, these results show that late-interaction visual retrieval benefits from query-aware allocation rather than query-agnostic pooling alone.

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