Eviction as Estimation: A Fixed-Lag Smoothing View of Test-Time Memory, and When Measuring Beats Accumulating

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Eviction as Estimation: A Fixed-Lag Smoothing View of Test-Time Memory, and When Measuring Beats Accumulating

A language model with a bounded working memory must repeatedly decide which stored items to keep. Every deployed method decides the moment an item arrives, from the past (StreamingLLM, H2O) or from a guess about the future (SnapKV). We recast the choice as an estimation problem on a hidden signal, whether an item will be reused, placing existing methods on one axis, the commit lag $H$: online filters and learned predictors commit at $H=0$, while Belady's offline optimum sits where the whole futu


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