The Price of Scale in Proactive Memory Recall

arXiv:2610.34507v1 Announce Type: cross Abstract: A long-lived assistant that brings up memories without being asked must decide at every turn whether anything in its store is worth an interruption. We show that this decision is a multiple-testing problem whose difficulty grows with the store size N. On streaming replays of LongMemEval and LoCoMo, a similarity threshold tuned to 5% false alarms at N=8 reaches 87-100% at N=2048, across embedding models and for explicit and implicit cues; LLM judges show the same growth from a lower base. We prove that a gate with false-alarm rate alpha operates at a per-item false-positive rate of about -ln(1-alpha)/N, which pins its hit rate to the far left of the single-comparison ROC curve and, under regular variation, makes it decay as a power of N with an explicit constant. The resulting prediction matches the hit rate of a per-N oracle threshold to within one percentage point. The analysis explains why lexical and semantic channels need thresholds growing like ln N and sqrt{ln N}, and why per-cue normalisation roughly doubles the hit rate at matched false alarms. A cue-swap conformal gate, which compares the current cue with the user's other cues on the same store, needs no labels and has a finite-sample false-alarm guarantee under exchangeability; on LongMemEval it holds false alarms near 5% at the hit rate of a label-tuned threshold. Three annotators (Fleiss' kappa=0.63) find that about nine in ten false alarms are genuine interruptions. Code and data: https://github.com/RiverChenStillCompiling/price-of-scale

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Source: arXiv cs.AI | 2026-10-27