← 研踪 PaperTrailarXiv:2610.34507 · v2
The Price of Scale in Proactive Memory Recall
首次提交 2026-10-26 03:07
版本更新 2026-10-29 13:14
雷达观测 2026-10-30 11:25
摘要
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, a similarity threshold tuned to 5% false alarms at N=8 reaches 84-100% at N=2048 across embedding models and cue types, and LoCoMo and LLM judges show it too. We prove that a gate which thresholds the best of N independent irrelevant scores at 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 regularly varying in N. A finite-pool form of this bound predicts the hit rate of a label-tuned threshold on held-out questions to within 6.1 points. At matched false alarms the deployed score recalls 14-26 points more than raw cosine. A cue-swap conformal gate, which ranks the current cue among other cues on the same store, has a finite-sample false-alarm guarantee under exchangeability. With a background drawn from the user's unfiltered history it keeps false alarms at 3-6% on LongMemEval at the hit rate of a label-tuned threshold; on LoCoMo it overshoots or turns conservative depending on where its reference cues come from. In a chronological replay with the user's own earlier messages as references, it speaks on 6-8% of session-opening turns, against 57% for the deployed gate at N=2048, at about 50 ms per decision on one CPU thread. A cross-encoder reranker pays the same price of scale, and on a prospective-memory benchmark, similarity gates recall at most 9% of constraints at controlled false alarms. One human and two LLM annotators judge most false alarms unhelpful for a response. Code and data: https://github.com/RiverChenStillCompiling/price-of-scale
作者备注：Code and data: https://github.com/RiverChenStillCompiling/price-of-scale
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v2 · 2026-10-29 13:14 · 最新观测版本
The Price of Scale in Proactive Memory Recall
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, a similarity threshold tuned to 5% false alarms at N=8 reaches 84-100% at N=2048 across embedding models and cue types, and LoCoMo and LLM judges show it too. We prove that a gate which thresholds the best of N independent irrelevant scores at 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 regularly varying in N. A finite-pool form of this bound predicts the hit rate of a label-tuned threshold on held-out questions to within 6.1 points. At matched false alarms the deployed score recalls 14-26 points more than raw cosine. A cue-swap conformal gate, which ranks the current cue among other cues on the same store, has a finite-sample false-alarm guarantee under exchangeability. With a background drawn from the user's unfiltered history it keeps false alarms at 3-6% on LongMemEval at the hit rate of a label-tuned threshold; on LoCoMo it overshoots or turns conservative depending on where its reference cues come from. In a chronological replay with the user's own earlier messages as references, it speaks on 6-8% of session-opening turns, against 57% for the deployed gate at N=2048, at about 50 ms per decision on one CPU thread. A cross-encoder reranker pays the same price of scale, and on a prospective-memory benchmark, similarity gates recall at most 9% of constraints at controlled false alarms. One human and two LLM annotators judge most false alarms unhelpful for a response. Code and data: https://github.com/RiverChenStillCompiling/price-of-scale
查看此版本解读 →查看此版本原文 ↗v1 · 2026-10-26 03:07
The Price of Scale in Proactive Memory Recall
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 $α$ operates at a per-item false-positive rate of about $-\ln(1-α)/N$, 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' $κ=0.63$) 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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