The Price of Scale in Proactive Memory Recall
Organizations: School of Art and Design, Zhejiang Sci-Tech University, Hangzhou 310018, China
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 . On streaming replays of LongMemEval and LoCoMo, a similarity threshold tuned to 5% false alarms at reaches 87-100% at , 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 operates at a per-item false-positive rate of about , 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 with an explicit constant. The resulting prediction matches the hit rate of a per- oracle threshold to within one percentage point. The analysis explains why lexical and semantic channels need thresholds growing like and , 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' ) find that about nine in ten false alarms are genuine interruptions. Code and data: https://github.com/RiverChenStillCompiling/price-of-scale
Figures & tables
| cues, embedding | cosine, oracle | -score, oracle | cue-swap | |
|---|---|---|---|---|
| explicit, bge-small | 8 | .70 (.05) | .84 (.05) | .83 (.05) |
| 128 | .36 (.06) | .56 (.05) | .54 (.04) | |
| 2048 | .08 (.07) | .18 (.03) | .22 (.05) | |
| explicit, bge-large | 8 | .80 (.06) | .88 (.07) | .86 (.05) |
| 128 | .38 (.06) | .58 (.05) | .55 (.05) | |
| 2048 | .10 (.05) | .16 (.02) | .21 (.04) |
Appendix figures & tables1 asset
Supplementary material from the paper’s appendix.
Appendix
| max FA | hit, | hit, | hit, | hit, | ||
|---|---|---|---|---|---|---|
| 0.01 | 19 | .000 (.000) | .00 | .00 | .00 | .00 |
| 49 | .000 (.000) | .00 | .00 | .00 | .00 | |
| 99 | .015 (.023) | .59 | .35 | .15 | .06 | |
| 199 | .014 (.023) | .64 | .36 | .15 | .06 | |
| 399 | .017 (.026) | .67 | .39 | .16 | .07 | |
| 0.05 | 19 | .067 (.084) | .77 | .56 | .30 | .18 |
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