← 研踪 PaperTrailarXiv:2610.34682 · v2
Beyond Multiplicity Correction: Sharp Retrieval Thresholds for Attention with Correlated Distractors
首次提交 2026-10-26 09:19
版本更新 2026-10-28 16:29
雷达观测 2026-10-30 10:22
摘要
Redundant context affects attention in two distinct ways: multiplicity adds normalization mass, while score variation within correlated groups can produce extreme individual scores. We separate these effects in a planted retrieval model with exponentially many Gaussian distractors organized into supplied clusters whose number and size both grow exponentially with dimension. The model is a two-level generalized random energy model, whose classical free energy yields exact retrieval thresholds. Gaussian interpolation further shows that increasing positive correlation at fixed token count lowers the distractor free energy, unlike adding duplicates. Our main result establishes a sharp limitation of count correction, which subtracts the log cluster size from pre-softmax scores: this correction removes multiplicity but retains within-cluster extremes. Even when the inverse temperature is chosen after observing all scores, count correction requires a signal at least $\sqrt{2α_1}$, where $α_1$ is the exponential growth rate of the number of clusters. By contrast, averaging scores before exponentiation suppresses token-level fluctuations and lowers the optimal signal threshold to $\sqrt{2ρα_1}$, where $ρ$ is the within-cluster correlation. This gap persists after adding exponentially many singleton distractors, so group size alone does not identify the target, and extends, under explicit cumulant regularity assumptions, to fixed finite hierarchies of independent-increment scores. Finite-sample, stability, and participation results complement the asymptotic analysis. A controlled retrieval experiment with frozen sentence embeddings illustrates both sides of the distinction: averaging helps when the relevant item is a singleton, but can discard useful evidence when a relevant group contains multiple matching items.
作者备注：42 pages, 2 figures, 3 tables
观测到的版本
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v2 · 2026-10-28 16:29 · 最新观测版本
Beyond Multiplicity Correction: Sharp Retrieval Thresholds for Attention with Correlated Distractors
Redundant context affects attention in two distinct ways: multiplicity adds normalization mass, while score variation within correlated groups can produce extreme individual scores. We separate these effects in a planted retrieval model with exponentially many Gaussian distractors organized into supplied clusters whose number and size both grow exponentially with dimension. The model is a two-level generalized random energy model, whose classical free energy yields exact retrieval thresholds. Gaussian interpolation further shows that increasing positive correlation at fixed token count lowers the distractor free energy, unlike adding duplicates. Our main result establishes a sharp limitation of count correction, which subtracts the log cluster size from pre-softmax scores: this correction removes multiplicity but retains within-cluster extremes. Even when the inverse temperature is chosen after observing all scores, count correction requires a signal at least $\sqrt{2α_1}$, where $α_1$ is the exponential growth rate of the number of clusters. By contrast, averaging scores before exponentiation suppresses token-level fluctuations and lowers the optimal signal threshold to $\sqrt{2ρα_1}$, where $ρ$ is the within-cluster correlation. This gap persists after adding exponentially many singleton distractors, so group size alone does not identify the target, and extends, under explicit cumulant regularity assumptions, to fixed finite hierarchies of independent-increment scores. Finite-sample, stability, and participation results complement the asymptotic analysis. A controlled retrieval experiment with frozen sentence embeddings illustrates both sides of the distinction: averaging helps when the relevant item is a singleton, but can discard useful evidence when a relevant group contains multiple matching items.
查看此版本解读 →查看此版本原文 ↗v1 · 2026-10-26 09:19
Beyond Deduplication: Sharp Retrieval Limits for Attention with Correlated Distractors
Redundant context affects attention through two distinct mechanisms: repeated items add normalization mass, while score variation within correlated groups can produce extreme individual scores. We separate these effects in a planted retrieval model with exponentially many Gaussian distractors arranged in known, exponentially large clusters. The model is a two-level generalized random energy model, whose classical free energy yields exact retrieval thresholds. Gaussian interpolation further shows that increasing positive correlation at fixed token count lowers the distractor free energy, unlike adding duplicates. Our main result identifies a sharp limitation of subtracting log cluster size from pre-softmax scores: this correction removes multiplicity but retains within-cluster extremes. Even a temperature chosen after observing all scores cannot lower the required signal below $\sqrt{2α_1}$, where $α_1$ is the exponential rate of the number of clusters. Averaging scores before exponentiation instead suppresses these fluctuations and achieves $\sqrt{2ρα_1}$, where $ρ$ is the within-cluster correlation. The gap persists after adding exponentially many singleton distractors, so group size alone does not identify the target, and extends to fixed finite hierarchies of light-tailed independent-increment scores. Finite-sample, stability, and participation results complement the asymptotic analysis. A controlled retrieval experiment with frozen sentence embeddings supports this distinction while delineating its scope: averaging helps when the relevant item is a singleton, but can discard useful evidence when a relevant group contains multiple matching items.
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