Long-video question answering forces multimodal large language models to reason under strict visual-token budgets, creating a tradeoff between broad temporal coverage and fine-grained spatial detail. Uniform sampling preserves coverage but often obscures decisive local cues, while caption-based or frame-similarity retrieval operates over lossy proxies that can miss motion, state changes, and before-after relations. We recast long-video reasoning as a visual-token allocation problem: given a fixed budget, decide how much to spend on global context versus high-resolution local evidence, and where in the video to draw that local evidence from. We introduce AdaAlloc, a training-free inference framework that adaptively allocates visual tokens between a global video overview and localized visual detail. AdaAlloc first plans a global/local allocation policy, then uses temporal grounding to locate candidate evidence segments and refines them into a compact temporal memory. The selected policy controls both frame sampling density and resolution, combining sparse, lower-resolution global frames with denser, higher-resolution local frames drawn from the refined memory. The final answerer reasons over the allocated global context and refined local evidence. Across LVBench, MLVU, VideoMME, and LongVideoBench, AdaAlloc improves over budget-matched uniform sampling by up to 10.5 percentage points and outperforms the compared frame-selection and agentic methods on their reported benchmarks.

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