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A memory threshold tuned for eight items produced 87 to 100 percent false alarms at 2,048, and the maths says why

AspireAI community · arXiv
An assistant that surfaces memories unprompted has to decide at every turn whether anything in its store is worth interrupting the user for, and the authors show this is a multiple-testing problem whose difficulty grows with store size N. On streaming replays of LongMemEval and LoCoMo, a similarity threshold tuned for a 5 percent false-alarm rate at N=8 rose to 87 to 100 percent at N=2048, across embedding models and for both explicit and implicit cues. They derive that such a gate operates at a per-item false-positive rate of roughly -ln(1-alpha)/N, which pins its hit rate far to the left of the single-comparison ROC curve and explains why thresholds must grow like ln N, and they release a label-free cue-swap conformal gate that holds false alarms near 5 percent at the hit rate of a label-tuned threshold. Code and data are published with the paper.
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