Relevant but Incomplete: Referential Dangling as a Paradigm-Level Failure Mode in Hard Prompt Compression

# Referential Dangling as a Paradigm-Level Failure Mode in Hard Prompt Compression
Source: [https://arxiv.org/html/2608.04569](https://arxiv.org/html/2608.04569)
Zhengpei Hu1\\equalcontrib, Kai Li2\\equalcontrib, Dapeng Fu3, Xuechao Zou2, Yuanhao Tang1, Yue Li1, Tengfei Cao1, Jianqiang Huang1\\corresponding

###### Abstract

Hard prompt compression reduces long\-context inference cost by scoring tokens, sentences, or chunks independently and retaining the highest\-scoring units under a budget\. We identify a structural failure in this procedure: independent selection can split dependent evidence pairs, retaining one member while deleting the other\. When the retained text span contains an answer but the deleted span defines the entity needed to interpret it, we call the result*referential dangling*\. At compression ratio0\.300\.30,Beaver, which ranks coherent chunks using Qwen3\-0\.6B embeddings, leaves the answer path incomplete in3434to54%54\\%of bridge examples across three multi\-hop question answering \(QA\) datasets\. The failure is not specific to that implementation: on a shared HotpotQA bridge set, all six hard compressors we test exhibit dangling at rates reaching60%60\\%, and every document in LongBench\-v2 Single\-Document QA contains at least one dangling reference\. We then test whether selecting different content at the same budget helps\. On dangling examples evaluated with Qwen3\-8B, reinserting the missing supporting paragraph and offsetting its tokens by removing paragraphs not annotated as supporting the answer improves accuracy by2929to3434points \(p<10−4p<10^\{\-4\}\), recovering at least88%88\\%of the gap to contexts that retain both annotated supporting paragraphs\. Stronger answer models do not absorb the loss: on MuSiQue, GPT\-5\.5 is8\.88\.8points less accurate on the compressed contexts than on contexts retaining both supporting paragraphs\. Finally, we train a compact classifier to rank sentences the compressor omitted by whether they are needed to interpret retained text, and reinsert the top\-ranked candidates without using support annotations at inference\. On HotpotQA with Qwen3\-8B as the downstream answer model, this automatic restoration improves accuracy by4\.74\.7points while changing the compression ratio only from0\.300\.30to0\.310\.31\. Hard compressors should optimize relevance and referential completeness\.

## 1Introduction

![Refer to caption](https://arxiv.org/html/2608.04569v1/x1.png)Figure 1:Referential dangling with a missing bridge\. Independent scoring retains the query subject and the answer string but removes the fact that Tim DuBois was born in Southwest City, leaving the inference chain incomplete\.In recent frontier models, the context windows of large language models \(LLMs\) have expanded from a few thousand tokens to the million\-token scale\. These expanded windows enable reasoning over entire documents and collections of documents\. Yet long contexts remain expensive: the quadratic cost of self\-attention inflates prefill latency, and models underuse relevant content when it appears away from prompt boundaries\(Liuet al\.[2024](https://arxiv.org/html/2608.04569#bib.bib1)\)\. Prompt compression addresses this tension by pruning the input before it reaches the target model while trying to preserve the information needed for the task\(Jianget al\.[2023b](https://arxiv.org/html/2608.04569#bib.bib4); Panet al\.[2024](https://arxiv.org/html/2608.04569#bib.bib5); Liet al\.[2023](https://arxiv.org/html/2608.04569#bib.bib7)\)\.

Many hard prompt compressors follow a common selection procedure: they score each token, sentence, or chunk for importance and retain the highest scoring fragments within a token budget\. These scores may reflect query relevance or perplexity\(Jianget al\.[2024](https://arxiv.org/html/2608.04569#bib.bib6)\), embedding similarity\(Huet al\.[2026](https://arxiv.org/html/2608.04569#bib.bib8)\), information content or learned classifier scores\(Liet al\.[2023](https://arxiv.org/html/2608.04569#bib.bib7); Panet al\.[2024](https://arxiv.org/html/2608.04569#bib.bib5)\), syntactic salience\(Maoet al\.[2025](https://arxiv.org/html/2608.04569#bib.bib9)\), or importance derived from attention\(Zhaoet al\.[2025](https://arxiv.org/html/2608.04569#bib.bib10)\)\. Although these methods differ in architecture and supervision, they share the objective of retaining fragments that appear important\. This objective assumes that the selected fragments collectively form a usable prompt\. However, an important fragment need not be self\-contained, because its meaning may depend on an earlier definition, an antecedent, or a bridge fact that the compressor removes independently\.

We call this failure*referential dangling*and formalize it in Section[3](https://arxiv.org/html/2608.04569#S3)\. A compressed prompt exhibits referential dangling when it retains a relevant fragment but omits a dependency required for its interpretation, leaving the fragment unusable to the target model\. Figure[1](https://arxiv.org/html/2608.04569#S1.F1)illustrates this mechanism\. The compressor retains one fragment mentioning Tim DuBois and another stating that Southwest City is in McDonald County, but deletes the bridge stating that DuBois was born in Southwest City\. Although the answer string remains in the compressed prompt, the retained fragments no longer support an inference from the query subject to the answer\. This example illustrates why relevance alone does not guarantee a usable compressed context\. It remains unclear whether dangling is systematic, fixed\-budget reselection recovers accuracy, or restoration can be automated\.

We first examine the official implementation ofBeaver\(Huet al\.[2026](https://arxiv.org/html/2608.04569#bib.bib8)\)\. At compression ratio0\.300\.30, it leaves answer paths incomplete in3434to54%54\\%of bridge examples across HotpotQA\(Yanget al\.[2018](https://arxiv.org/html/2608.04569#bib.bib22)\), 2WikiMultiHopQA\(Hoet al\.[2020](https://arxiv.org/html/2608.04569#bib.bib23)\), and MuSiQue\(Trivediet al\.[2022](https://arxiv.org/html/2608.04569#bib.bib24)\)\. A human audit finds95%95\\%precision\. The diagnosis extends beyond this setting: all six compressors tested exhibit dangling at rates from3232to60%60\\%on the shared bridge set, and all8080documents in LongBench\-v2 Single\-Document QA\(Baiet al\.[2025](https://arxiv.org/html/2608.04569#bib.bib25)\)contain at least one dangling reference\. We next conduct an annotation\-guided reselection experiment: the omitted supporting paragraph is reinserted, and its token count is offset by removing the lowest\-scoring paragraphs not annotated as supporting the answer\. On dangling examples evaluated with Qwen3\-8B, this intervention improves accuracy by2929to3434points without increasing the token budget \(p<10−4p<10^\{\-4\}\) and recovers at least88%88\\%of the accuracy gap between the original compressed contexts and contexts retaining both annotated supporting paragraphs\. Finally, we generate candidate sentences from the omitted text and train a compact classifier to rank them according to whether they are needed to interpret retained text\. Without using supporting paragraph annotations at inference, the method reinserts the highest ranked candidates\. On HotpotQA with Qwen3\-8B as the downstream answer model, this automatic restoration improves accuracy by4\.74\.7points while changing the compression ratio only from0\.300\.30to0\.310\.31\. We released the code, results for individual examples, and the trained model111https://cslikai\.cn/Referential\-Dangling/\.

## 2Related Work

#### Prompt and context compression\.

Prompt compression reduces long\-context inference cost by shortening the input before it reaches the target model\. It complements model\-side efficiency methods, including elastic subnetworks, compact discrete semantic tokens for multimodal inputs, and efficient encoder–decoder or state\-space architectures\(Li and Luo[2024](https://arxiv.org/html/2608.04569#bib.bib18); Liet al\.[2025b](https://arxiv.org/html/2608.04569#bib.bib21),[2022](https://arxiv.org/html/2608.04569#bib.bib19),[a](https://arxiv.org/html/2608.04569#bib.bib20)\)\. We study hard compression, which selects tokens, sentences, chunks, or parse nodes under a budget using self\-information or perplexity\(Liet al\.[2023](https://arxiv.org/html/2608.04569#bib.bib7); Jianget al\.[2024](https://arxiv.org/html/2608.04569#bib.bib6)\), learned token classifiers\(Jianget al\.[2023b](https://arxiv.org/html/2608.04569#bib.bib4); Panet al\.[2024](https://arxiv.org/html/2608.04569#bib.bib5)\), embedding similarity\(Huet al\.[2026](https://arxiv.org/html/2608.04569#bib.bib8)\), syntactic salience\(Maoet al\.[2025](https://arxiv.org/html/2608.04569#bib.bib9)\), attention\-based signals\(Zhaoet al\.[2025](https://arxiv.org/html/2608.04569#bib.bib10)\), or training\-free sentence and fragment selection\(Tanget al\.[2025](https://arxiv.org/html/2608.04569#bib.bib55)\)\. Task\-aware selectors add reinforcement\-learning rewards or key\-information density objectives\(Shandilyaet al\.[2025](https://arxiv.org/html/2608.04569#bib.bib44); Linet al\.[2025](https://arxiv.org/html/2608.04569#bib.bib45)\), whereas soft or latent approaches use gist tokens, autoencoders, semantic source coding, or learned special\-token representations\(Muet al\.[2023](https://arxiv.org/html/2608.04569#bib.bib14); Chevalieret al\.[2023](https://arxiv.org/html/2608.04569#bib.bib15); Geet al\.[2023](https://arxiv.org/html/2608.04569#bib.bib16); Feiet al\.[2024](https://arxiv.org/html/2608.04569#bib.bib43); Liet al\.[2025d](https://arxiv.org/html/2608.04569#bib.bib53)\)\. A further line of work compresses hidden activations or KV caches instead of source text\(Zhanget al\.[2025a](https://arxiv.org/html/2608.04569#bib.bib48),[2023](https://arxiv.org/html/2608.04569#bib.bib27)\); because these methods never produce a reduced text sequence, the failure we study does not arise in the same form and we do not evaluate them\. Hard methods differ in supervision, granularity, and query access but select fragments by salience or relevance\. Existing surveys organize prompt\-compression methods by hard versus soft strategies and discuss their downstream adaptations\(Liet al\.[2025c](https://arxiv.org/html/2608.04569#bib.bib17)\)\. Comparative studies further show that downstream performance and information preservation vary with the compression method, task, and compression setting\(Jhaet al\.[2024](https://arxiv.org/html/2608.04569#bib.bib46); Łajewskaet al\.[2025](https://arxiv.org/html/2608.04569#bib.bib54)\), while rate\-distortion analysis formalizes the budget–performance trade\-off and the role of query\-aware selection\(Nagleet al\.[2024](https://arxiv.org/html/2608.04569#bib.bib47)\)\. We study how independent hard selection can retain a fragment but remove its required definition or bridge\.

#### Dependency\-preserving selection\.

Extractive summarization identified this dependency and built a constraint for it:Durrettet al\.\([2016](https://arxiv.org/html/2608.04569#bib.bib29)\)add anaphoricity constraints to the selection objective, so a sentence may not be extracted unless the text its pronouns depend on is extracted with it\. Hard prompt compressors inherit the selection problem without the constraint: they score units by salience or query relevance and keep the highest\-scoring units under a budget, with no term rewarding the joint retention of a unit and the text needed to interpret it\. Other work approaches the dependency from different angles\. Coreference resolution identifies anaphoric links\(Leeet al\.[2017](https://arxiv.org/html/2608.04569#bib.bib30)\), but on complete documents; resolving links in the source does not indicate whether the retained subset stays interpretable once the antecedent is deleted\. Faithfulness evaluation asks the converse question, whether a generated summary is supported by its source\(Maynezet al\.[2020](https://arxiv.org/html/2608.04569#bib.bib32)\), rather than whether the retained source is self\-contained\. Closest to our setting,Denget al\.\([2025](https://arxiv.org/html/2608.04569#bib.bib50)\)report boundary and information\-path failures under gist\-based compression\. Retrieval\-augmented generation retrieves, rewrites, or attends over evidence to favor passages that support generation\(Lewiset al\.[2020](https://arxiv.org/html/2608.04569#bib.bib35); Xuet al\.[2024](https://arxiv.org/html/2608.04569#bib.bib11); Liuet al\.[2023](https://arxiv.org/html/2608.04569#bib.bib42); Choiet al\.[2024](https://arxiv.org/html/2608.04569#bib.bib49)\), but scoring by answer support still lets a passage qualify while remaining uninterpretable once its definition is removed\. Long\-context studies show that accuracy also depends on where relevant information sits and on surrounding distractors\(Liuet al\.[2024](https://arxiv.org/html/2608.04569#bib.bib1); Shiet al\.[2023](https://arxiv.org/html/2608.04569#bib.bib2)\), factors that fixed\-budget reselection changes and that we therefore control\. We measure what the missing constraint costs: how often independent selection splits a dependency pair, and how much downstream accuracy is lost when it does\.

## 3Problem Formulation

#### Referential dangling\.

LetC=\(c1,…,c\|C\|\)C=\(c\_\{1\},\\ldots,c\_\{\|C\|\}\)denote a tokenized context,Q∈𝒬Q\\in\\mathcal\{Q\}a query, andτ∈ℕ\\tau\\in\\mathbb\{N\}a token budget\. We restrict the formal definition to extractive hard compressors\. For any extractive outputAA, letPosC⁡\(A\)⊆\{1,…,\|C\|\}\\operatorname\{Pos\}\_\{C\}\(A\)\\subseteq\\\{1,\\ldots,\|C\|\\\}denote the source\-token positions emitted inAA, each emitted at most once and in source order\. An extractive compressorffreturnsC~=f​\(C,Q,τ\)\\tilde\{C\}=f\(C,Q,\\tau\)with\|C~\|≤τ<\|C\|\|\\tilde\{C\}\|\\leq\\tau<\|C\|, where\|⋅\|\|\\cdot\|denotes the number of tokens\. A compressor that does not useQQis query agnostic\. The downstream LLM receivesQQandC~\\tilde\{C\}but notCC\.

A sentence relevant to the task may depend on explicit support elsewhere in the context, and several alternative support paths may be valid\. LetSent⁡\(C\)\\operatorname\{Sent\}\(C\)denote the indexed source\-sentence occurrences inCC\. For any indexed source fragmentyy, letℐ​\(y\)⊆\{1,…,\|C\|\}\\mathcal\{I\}\(y\)\\subseteq\\\{1,\\ldots,\|C\|\\\}contain its source\-token positions\. Let𝒯C,Q⊆Sent⁡\(C\)\\mathcal\{T\}\_\{C,Q\}\\subseteq\\operatorname\{Sent\}\(C\)contain the task\-relevant sentences whose interpretation or use in answeringQQmay require such support\. We define exact sentence retention by

RetC⁡\(A\)=\{s∈Sent⁡\(C\):ℐ​\(s\)⊆PosC⁡\(A\)\}\.\\operatorname\{Ret\}\_\{C\}\(A\)=\\left\\\{s\\in\\operatorname\{Sent\}\(C\):\\mathcal\{I\}\(s\)\\subseteq\\operatorname\{Pos\}\_\{C\}\(A\)\\right\\\}\.
Fors∈𝒯C,Qs\\in\\mathcal\{T\}\_\{C,Q\}andD⊆Sent⁡\(C\)∖\{s\}D\\subseteq\\operatorname\{Sent\}\(C\)\\setminus\\\{s\\\}, letSuffC,Q⁡\(s,D\)\\operatorname\{Suff\}\_\{C,Q\}\(s,D\)hold when the source\-ordered text formed byD∪\{s\}D\\cup\\\{s\\\}, together withQQ, contains all explicit information fromCCneeded to interpretssand use it in an evidence chain forQQ\. Sufficiency is assessed jointly onD∪\{s\}D\\cup\\\{s\\\}rather than one dependency edge at a time\. Define the complete family of inclusion\-minimal sufficient support sets

𝒟C,Q\(s\)=\{D:\\displaystyle\\mathcal\{D\}\_\{C,Q\}\(s\)=\\bigl\\\{D:D⊆Sent⁡\(C\)∖\{s\},SuffC,Q⁡\(s,D\),\\displaystyle D\\subseteq\\operatorname\{Sent\}\(C\)\\setminus\\\{s\\\},\\quad\\operatorname\{Suff\}\_\{C,Q\}\(s,D\),∄D′⊊DwithSuffC,Q\(s,D′\)\}\.\\displaystyle\\nexists D^\{\\prime\}\\subsetneq D\\ \\text\{with\}\\ \\operatorname\{Suff\}\_\{C,Q\}\(s,D^\{\\prime\}\)\\bigr\\\}\.For everys∈𝒯C,Qs\\in\\mathcal\{T\}\_\{C,Q\}, we assume𝒟C,Q​\(s\)≠∅\\mathcal\{D\}\_\{C,Q\}\(s\)\\neq\\varnothing\. BecauseSent⁡\(C\)\\operatorname\{Sent\}\(C\)is finite, every sufficientDDcontains an inclusion\-minimal sufficient subset, so retaining a sufficient support set is equivalent to retaining some member of this minimal family\. Ifssrequires no additional support, then∅∈𝒟C,Q​\(s\)\\varnothing\\in\\mathcal\{D\}\_\{C,Q\}\(s\)\. Following the notion of referential completeness in extractive summarization\(Durrettet al\.[2016](https://arxiv.org/html/2608.04569#bib.bib29)\), we consider only support stated explicitly inCCand exclude commonsense inferences, implicit temporal relations, and relations that require external information\. Writeℛ=RetC⁡\(C~\)\\mathcal\{R\}=\\operatorname\{Ret\}\_\{C\}\(\\tilde\{C\}\)\. The compressed contextC~\\tilde\{C\}exhibits referential dangling if it retains a sentence relevant to the task but retains no sufficient support set in full:

∃s∈ℛ∩𝒯C,Qsuch that∀D∈𝒟C,Q​\(s\),D⊈ℛ\.\\exists\\,s\\in\\mathcal\{R\}\\cap\\mathcal\{T\}\_\{C,Q\}\\quad\\text\{such that\}\\quad\\forall D\\in\\mathcal\{D\}\_\{C,Q\}\(s\),\\quad D\\nsubseteq\\mathcal\{R\}\.\(1\)This query\-dependent definition distinguishes support in the original context from support retained after compression\.

#### Additive fragment selection\.

We isolate the additive selection rule for hard compressors with nonoverlapping candidate units\. Letℱ=\{x1,…,xn\}\\mathcal\{F\}=\\\{x\_\{1\},\\ldots,x\_\{n\}\\\}be a finite collection of candidate fragments fromCC, with source\-token positionsℐ​\(x\)\\mathcal\{I\}\(x\)as above\. We assumeℐ​\(xi\)∩ℐ​\(xj\)=∅\\mathcal\{I\}\(x\_\{i\}\)\\cap\\mathcal\{I\}\(x\_\{j\}\)=\\varnothingfor alli≠ji\\neq j\. For any𝒮⊆ℱ\\mathcal\{S\}\\subseteq\\mathcal\{F\}, letOutC⁡\(𝒮\)\\operatorname\{Out\}\_\{C\}\(\\mathcal\{S\}\)be the text formed by emitting, once and in source order, the tokens in⋃x∈𝒮ℐ​\(x\)\\bigcup\_\{x\\in\\mathcal\{S\}\}\\mathcal\{I\}\(x\)\. Define

cost⁡\(𝒮\)\\displaystyle\\operatorname\{cost\}\(\\mathcal\{S\}\)=\|OutC⁡\(𝒮\)\|=∑x∈𝒮\|ℐ​\(x\)\|,\\displaystyle=\\big\|\\operatorname\{Out\}\_\{C\}\(\\mathcal\{S\}\)\\big\|=\\sum\_\{x\\in\\mathcal\{S\}\}\|\\mathcal\{I\}\(x\)\|,\(2\)ℛC​\(𝒮\)\\displaystyle\\mathcal\{R\}\_\{C\}\(\\mathcal\{S\}\)=RetC⁡\(OutC⁡\(𝒮\)\)\.\\displaystyle=\\operatorname\{Ret\}\_\{C\}\\\!\\left\(\\operatorname\{Out\}\_\{C\}\(\\mathcal\{S\}\)\\right\)\.This exact formulation covers token\-, sentence\-, and fixed\-chunk selectors with nonoverlapping candidate units whose final selection solves the stated global modular knapsack objective\. Selectors with overlapping or hierarchical candidates are not claimed to be exact instances of this objective and are evaluated empirically\. For fixed\(C,Q\)\(C,Q\), a scorer assigns each fragment a scalar utility

u​\(x\)=σ​\(x;C,Q\)∈ℝ,u\(x\)=\\sigma\(x;C,Q\)\\in\\mathbb\{R\},\(3\)whereσ\\sigmamay use the entire context and query\. The additive assumption concerns how the final selector combines fragment utilities rather than how those utilities are computed\. We model the selected set as a solution to

𝒦∈arg​max𝒮⊆ℱcost⁡\(𝒮\)≤τ​∑x∈𝒮u​\(x\)\.\\mathcal\{K\}\\in\\operatorname\*\{arg\\,max\}\_\{\\begin\{subarray\}\{c\}\\mathcal\{S\}\\subseteq\\mathcal\{F\}\\\\ \\operatorname\{cost\}\(\\mathcal\{S\}\)\\leq\\tau\\end\{subarray\}\}\\sum\_\{x\\in\\mathcal\{S\}\}u\(x\)\.\(4\)Ties are resolved by a fixed deterministic rule\. The resulting compressed text isC~=OutC⁡\(𝒦\)\\tilde\{C\}=\\operatorname\{Out\}\_\{C\}\(\\mathcal\{K\}\)\. It avoids referential dangling if and only if

∀s∈ℛC​\(𝒦\)∩𝒯C,Q,\\displaystyle\\forall s\\in\\mathcal\{R\}\_\{C\}\(\\mathcal\{K\}\)\\cap\\mathcal\{T\}\_\{C,Q\},∃D∈𝒟C,Q​\(s\)\\displaystyle\\exists D\\in\\mathcal\{D\}\_\{C,Q\}\(s\)\(5\)such thatD⊆ℛC​\(𝒦\)\.\\displaystyle\\text\{such that\}\\quad D\\subseteq\\mathcal\{R\}\_\{C\}\(\\mathcal\{K\}\)\.This condition is the complement of Equation \([1](https://arxiv.org/html/2608.04569#S3.E1)\) for the emitted text\. The additive objective contains no interaction term that enforces it\. The following construction shows that additive selection can omit required support even when the same budget admits a complete alternative\.

###### Proposition 1\(No guarantee of complete support\)

Letℱ=Sent⁡\(C\)=\{x,d,z\}\\mathcal\{F\}=\\operatorname\{Sent\}\(C\)=\\\{x,d,z\\\}consist of three disjoint fragments with equal costm∈ℕ\>0m\\in\\mathbb\{N\}\_\{\>0\}, and assumeℛC​\(𝒮\)=𝒮\\mathcal\{R\}\_\{C\}\(\\mathcal\{S\}\)=\\mathcal\{S\}for every𝒮⊆ℱ\\mathcal\{S\}\\subseteq\\mathcal\{F\}\. Letτ=2​m\\tau=2m,𝒯C,Q=\{x\}\\mathcal\{T\}\_\{C,Q\}=\\\{x\\\}, and𝒟C,Q​\(x\)=\{\{d\}\}\\mathcal\{D\}\_\{C,Q\}\(x\)=\\\{\\\{d\\\}\\\}\. Ifu​\(x\)\>u​\(z\)\>u​\(d\)≥0u\(x\)\>u\(z\)\>u\(d\)\\geq 0, then the unique additive maximizer is𝒦=\{x,z\}\\mathcal\{K\}=\\\{x,z\\\}, whose output dangles even though the feasible selection\{x,d\}\\\{x,d\\\}has complete support\.

*Proof\.*The two largest utilities belong toxxandzz, so the unique maximizer under the budget is\{x,z\}\\\{x,z\\\}\. Its retained sentencexxhas the sole sufficient support set\{d\}\\\{d\\\}, which is absent\. The alternative\{x,d\}\\\{x,d\\\}has cost2​m2mand retains this support set, so it is feasible and complete\.□\\square

The proposition is an existence result\. It shows that the additive objective alone provides no guarantee for arbitrary utilities, but it does not claim that every compressed context will dangle or that a complete alternative always fits the same budget\. The exact class includes context\-aware\(Liskavetset al\.[2025](https://arxiv.org/html/2608.04569#bib.bib13)\)or reinforcement\-learned scores\(Jung and Kim[2024](https://arxiv.org/html/2608.04569#bib.bib12)\)only when the final selector solves the stated fixed modular objective without a support constraint\. Section[4](https://arxiv.org/html/2608.04569#S4)evaluates recurrence empirically for selectors both inside and outside this class\.

## 4Empirical Diagnosis of Referential Dangling

The formulation in Section[3](https://arxiv.org/html/2608.04569#S3)motivates two empirical analyses\. We first useBeaverto measure the prevalence of referential dangling and its variation with compression ratio, annotated hop count, and reference distance\. We then compare six compressors to test whether the diagnostic recurs across scoring signals and output granularities\.

#### Measurement protocol\.

Because support annotations are incomplete and exact sentence retention is not uniformly available, we use directional content\-word coverage\. LetCW⁡\(y\)\\operatorname\{CW\}\(y\)be the normalized content\-word multiset of unityy, and let𝒰​\(A\)\\mathcal\{U\}\(A\)contain the retained output units\. When\|CW⁡\(v\)\|\>0\|\\operatorname\{CW\}\(v\)\|\>0and𝒰​\(A\)≠∅\\mathcal\{U\}\(A\)\\neq\\varnothing, define

cov⁡\(v,A\)=maxa∈𝒰​\(A\)⁡\|CW⁡\(v\)∩CW⁡\(a\)\|\|CW⁡\(v\)\|\.\\operatorname\{cov\}\(v,A\)=\\max\_\{a\\in\\mathcal\{U\}\(A\)\}\\frac\{\|\\operatorname\{CW\}\(v\)\\cap\\operatorname\{CW\}\(a\)\|\}\{\|\\operatorname\{CW\}\(v\)\|\}\.Setcov⁡\(v,A\)=0\\operatorname\{cov\}\(v,A\)=0when\|CW⁡\(v\)\|=0\|\\operatorname\{CW\}\(v\)\|=0or𝒰​\(A\)=∅\\mathcal\{U\}\(A\)=\\varnothing\. Span\-, sentence\-, and chunk\-level outputs use native retained units; token\-level outputs regroup retained tokens by source sentence\. Intersections count multiplicity, and the maximum is per output unit, not over their union\. Forθ∈\(0,1\]\\theta\\in\(0,1\], writeKeepθ⁡\(v,A\)\\operatorname\{Keep\}\_\{\\theta\}\(v,A\)whencov⁡\(v,A\)≥θ\\operatorname\{cov\}\(v,A\)\\geq\\theta\. We useθ=0\.5\\theta=0\.5, with a sweep in Appendix[A](https://arxiv.org/html/2608.04569#A1)\. This protocol approximates Equation \([1](https://arxiv.org/html/2608.04569#S3.E1)\) rather than evaluating it exactly\.

In bridge questions, the definition paragraph introduces a bridge entity and the answer paragraph refers to it\. At each evaluation granularity, we apply the same directional event to the paired answer and definition units: an example is answer\-path dangling whenKeepθ\\operatorname\{Keep\}\_\{\\theta\}holds for the answer unit but not for the definition unit\. The prevalence analysis uses paragraphs, whereas the cross\-compressor analysis uses the corresponding source sentences\. This test does not enumerate alternative support paths\.

Among bridge examples whose answer paragraph satisfiesKeepθ\\operatorname\{Keep\}\_\{\\theta\},ρd\\rho\_\{\\mathrm\{d\}\}is the fraction whose paired definition paragraph does not satisfyKeepθ\\operatorname\{Keep\}\_\{\\theta\}\. The complete evidence retention rateρe\\rho\_\{\\mathrm\{e\}\}is the fraction of all evaluated examples retaining every annotated evidence paragraph\. LongBench\-v2 Single\-Document QA uses a separate first\-mention diagnostic\.

### 4\.1Referential Dangling underBeaver

![Refer to caption](https://arxiv.org/html/2608.04569v1/x2.png)Figure 2:Referential dangling underBeaver\. Panel \(a\) reportsρd\\rho\_\{\\mathrm\{d\}\}across compression ratios on HotpotQA \(n=269n\{=\}269to300300per point, including partial paragraph retention\)\. Panel \(b\) reportsρd\\rho\_\{\\mathrm\{d\}\}by annotated hop count on HotpotQA \(n=234n\{=\}234\), 2WikiMultiHopQA \(n=241n\{=\}241\), and MuSiQue \(n=286n\{=\}286\)\. Panel \(c\) reports dangling rates for4,6494\{,\}649reference pairs in LongBench\-v2 Single\-Document QA by sentence distance from first mention to later reference\. Error bars are bootstrap95%95\\%confidence intervals\.#### Setup\.

We use the officialBeaverimplementation\(Huet al\.[2026](https://arxiv.org/html/2608.04569#bib.bib8)\)with Qwen3\-0\.6B embeddings\(Yanget al\.[2025](https://arxiv.org/html/2608.04569#bib.bib37); Zhanget al\.[2025b](https://arxiv.org/html/2608.04569#bib.bib40)\)\. We evaluate HotpotQA\(Yanget al\.[2018](https://arxiv.org/html/2608.04569#bib.bib22)\), 2WikiMultiHopQA\(Hoet al\.[2020](https://arxiv.org/html/2608.04569#bib.bib23)\), and MuSiQue\(Trivediet al\.[2022](https://arxiv.org/html/2608.04569#bib.bib24)\)\. HotpotQA and 2WikiMultiHopQA use contexts of about4040paragraphs and5\.75\.7k tokens, formed by mixing annotated supporting paragraphs with sampled distractors; MuSiQue uses its native2020\-paragraph contexts\. We definer=\|C~\|/\|C\|r=\|\\tilde\{C\}\|/\|C\|and use binary search to reach each target ratio\.

#### Prevalence\.

Atr=0\.30r=0\.30,ρd\\rho\_\{\\mathrm\{d\}\}ranges from34\.2%34\.2\\%to54\.2%54\.2\\%across the three datasets, whileρe\\rho\_\{\\mathrm\{e\}\}ranges from27\.0%27\.0\\%to61\.0%61\.0\\%\(Table[1](https://arxiv.org/html/2608.04569#S4.T1)\)\. MuSiQue has the highestρd\\rho\_\{\\mathrm\{d\}\}and the lowestρe\\rho\_\{\\mathrm\{e\}\}\. Figure[2](https://arxiv.org/html/2608.04569#S4.F2)a uses a broader HotpotQA sample that includes partial paragraph retention \(n=293n\{=\}293atr=0\.30r=0\.30\) and reports31\.1%31\.1\\%, compared with34\.2%34\.2\\%for the234234\-example table sample\. In a manual audit, the omitted paragraph was required in3838of4040flagged examples, yielding95%95\\%precision\. Appendix[B](https://arxiv.org/html/2608.04569#A2)reports the dependency categories, false positives, and qualitative examples\.

DatasetHopsρd\\rho\_\{\\mathrm\{d\}\}\(%\)ρe\\rho\_\{\\mathrm\{e\}\}\(%\)HotpotQA234\.261\.02WikiMultiHopQA253\.530\.7MuSiQue2 to 454\.227\.0Table 1:Referential dangling and complete evidence retention underBeaveratr=0\.30r=0\.30\.
#### Long documents\.

LongBench\-v2 Single\-Document QA\(Baiet al\.[2025](https://arxiv.org/html/2608.04569#bib.bib25)\)lacks annotations of supporting evidence and multi\-hop structure, so we use a separate first\-mention diagnostic\. A later reference dangles when its entity’s first\-mention sentence is omitted while the reference sentence survives\. Across8080documents atr=0\.30r=0\.30, the mean per\-document rate is30\.5%30\.5\\%, and every document contains at least one dangling reference\. Rates range from25%25\\%to37%37\\%across seven subdomains \(Appendix[C](https://arxiv.org/html/2608.04569#A3)\)\. Because this diagnostic uses retained sentences as its denominator rather than bridge examples with a retained answer paragraph, it is not directly comparable withρd\\rho\_\{\\mathrm\{d\}\}\.

#### Variation across measured conditions\.

On the broader HotpotQA sample in Figure[2](https://arxiv.org/html/2608.04569#S4.F2)a,ρd\\rho\_\{\\mathrm\{d\}\}rises from6\.3%6\.3\\%atr=0\.70r=0\.70to53\.5%53\.5\\%atr=0\.20r=0\.20, with nonoverlapping bootstrap95%95\\%confidence intervals between adjacent operating points\. This endpoint is distinct from the53\.5%53\.5\\%reported for 2WikiMultiHopQA in Table[1](https://arxiv.org/html/2608.04569#S4.T1)\. Dataset groups with larger annotated hop counts also have largerρd\\rho\_\{\\mathrm\{d\}\}values \(Figure[2](https://arxiv.org/html/2608.04569#S4.F2)b\), but dataset construction differs, so this comparison does not isolate reasoning depth\. On LongBench\-v2 Single\-Document QA, the pair\-level dangling rate is51\.7%51\.7\\%for distances of11to1010sentences,67\.0%67\.0\\%for7171to150150, and64\.2%64\.2\\%beyond150150\. Dangling pairs have a mean distance of8989sentences, compared with7373for complete pairs\.

### 4\.2Comparison Across Six Scoring Signals

The comparison includes six hard compressors that assign importance using different signals: embedding similarity withBeaver\(Huet al\.[2026](https://arxiv.org/html/2608.04569#bib.bib8)\), syntactic parse structure with PartPrompt\(Maoet al\.[2025](https://arxiv.org/html/2608.04569#bib.bib9)\), self\-information with Selective\-Context\(Liet al\.[2023](https://arxiv.org/html/2608.04569#bib.bib7)\), a learned token classifier with LLMLingua\-2\(Panet al\.[2024](https://arxiv.org/html/2608.04569#bib.bib5)\), perplexity with LongLLMLingua\(Jianget al\.[2024](https://arxiv.org/html/2608.04569#bib.bib6)\), and importance derived from attention with DAC\(Zhaoet al\.[2025](https://arxiv.org/html/2608.04569#bib.bib10)\)\. These methods span chunk, parse node, sentence, and token outputs\.Beaverand LongLLMLingua use the query, whereas the other four methods do not\. The procedures differ, but none explicitly constrains joint dependency retention\.

All six compressors process the same184184HotpotQA bridge examples at compression ratio0\.300\.30\. We apply the sentence\-level predicateKeep0\.5\\operatorname\{Keep\}\_\{0\.5\}defined above to outputs at every granularity\. Under this criterion,Beaverhas a dangling rate of32\.1%32\.1\\%on the shared set\. Table[1](https://arxiv.org/html/2608.04569#S4.T1)reports34\.2%34\.2\\%under the paragraph\-level predicate on a different234234\-example sample, so the two values are not a controlled comparison of the predicates\. Appendix[A](https://arxiv.org/html/2608.04569#A1)sweeps the threshold from0\.30\.3to0\.70\.7; Appendix[E](https://arxiv.org/html/2608.04569#A5)details each compressor’s implementation\.

![Refer to caption](https://arxiv.org/html/2608.04569v1/x3.png)Figure 3:Dangling rates for six compressors on the shared HotpotQA bridge set \(n=184n\{=\}184\) at compression ratio0\.300\.30\. PartPr\. denotes PartPrompt, Sel\.\-Ctx denotes Selective\-Context, LLML\-2 denotes LLMLingua\-2, and LongLL denotes LongLLMLingua\. All outputs are evaluated using the content\-word overlap criterion with threshold0\.50\.5\. Light bars denote methods that use the query, and darker bars denote methods that do not\.#### Results across scoring signals\.

Figure[3](https://arxiv.org/html/2608.04569#S4.F3)reports rates from32\.1%32\.1\\%forBeaverto59\.8%59\.8\\%for LongLLMLingua\. Referential dangling is therefore observed beyond selection based on embeddings\. The two methods that use the query,Beaverand LongLLMLingua, have rates at opposite ends of the measured range, so query access alone does not remove the diagnostic event\. PartPrompt has a rate of47\.8%47\.8\\%on the shared set, indicating that the event also occurs under hierarchical syntactic selection in this setting\. These comparisons extend the diagnosis beyond the exact additive model without implying that every evaluated selector instantiates it\.

#### Definition salience\.

We next examine whether omitted definitions simply receive low importance scores\. For each bridge example, we measure the isolated salience percentile of the answer sentence and the definition sentence among all sentences usingBeaversentence similarity, which uses the query, and self\-information, which does not\. Figure[4](https://arxiv.org/html/2608.04569#S4.F4)reports the results for180180examples\. UnderBeaversimilarity, the mean percentile is92\.8%92\.8\\%for definitions and84\.1%84\.1\\%for answer sentences\. Under self\-information, the corresponding values are46\.7%46\.7\\%and54\.3%54\.3\\%\. Low isolated salience is therefore insufficient to explain the omitted definitions, although these measurements do not identify the reason for each individual selection decision\.

![Refer to caption](https://arxiv.org/html/2608.04569v1/x4.png)Figure 4:Mean salience percentiles \(%\) for answer and definition sentences among all sentences in180180bridge examples\.Beaversimilarity is query\-aware; self\-information is not\.
#### Overlap of affected examples\.

We compare the dangling case sets using Jaccard similarity to determine whether the compressors fail on the same examples\. Table[2](https://arxiv.org/html/2608.04569#S4.T2)reports a mean pairwise similarity of0\.380\.38, compared with0\.340\.34expected under independent occurrence at the observed rates\. Only5\.4%5\.4\\%of examples dangle under all six compressors, whereas95%95\\%dangle under at least one\. The affected sets therefore vary across scoring methods, a pattern consistent with selection that varies by method rather than a single fixed pool of difficult examples\. These measurements quantify prevalence under the diagnostic but do not determine whether changing the selected content at the same budget improves downstream accuracy, which we evaluate next\.

BEAVERPartPr\.Sel\.\-CtxLLML\-2DACLongLLDanglingrate \(%\)32\.147\.851\.656\.058\.759\.8BEAVERN/A0\.360\.230\.300\.290\.32PartPr\.0\.36N/A0\.360\.440\.440\.37Sel\.\-Ctx0\.230\.36N/A0\.390\.350\.51LLML\-20\.300\.440\.39N/A0\.470\.45DAC0\.290\.440\.350\.47N/A0\.48LongLL0\.320\.370\.510\.450\.48N/ATable 2:Pairwise Jaccard similarities between dangling case sets on the shared HotpotQA bridge set \(n=184n\{=\}184\) at compression ratio0\.300\.30\. The first row reports the dangling rate of each compressor\. Abbreviations match Figure[3](https://arxiv.org/html/2608.04569#S4.F3)\.

## 5Fixed\-Budget Content Reselection

The preceding diagnostics show that compression often separates annotated support pairs, but prevalence alone does not determine whether selecting different content improves downstream accuracy without increasing the token budget\. We test this by restoring the omitted supporting paragraph and removing at least as many tokens from paragraphs that are not annotated as supporting the answer\.

#### Comparison protocol\.

Panel 1 of Table[3](https://arxiv.org/html/2608.04569#S5.T3)evaluates three content conditions on the dangling subsets\. Base is the original compressed context\. Reselected reinserts the omitted supporting paragraph and removes the lowest scoring paragraphs not annotated as supporting the answer until at least the same number of tokens has been removed\. Full support retains both annotated supporting paragraphs and provides a reference for complete evidence retention\. Base and Reselected form the fixed\-budget comparison, while Full support provides the reference used to quantify the accuracy recovered through reselection\. Panel 2 separately compares Base with Full support on200200HotpotQA examples and does not evaluate Reselected\. We conduct these comparisons withBeaverbecause its coherent chunk output permits paragraph replacement while leaving the remaining retained text unchanged\. Applying the same operation to token\-level output would require inserting whole paragraphs into fragmented text and would not yield a directly comparable setting\. Appendix D specifies the construction for each dataset\.

*Panel 1: dangling subsets evaluated with Qwen3\-8B*DatasetDownstream LLMBaseReselectedFull supportMcNemarppHotpotQAQwen3\-8B0\.2870\.2870\.5750\.5750\.6000\.6001\.6×10−61\.6\\times 10^\{\-6\}2WikiMultiHopQAQwen3\-8B0\.0970\.0970\.4030\.4030\.4440\.4441\.1×10−51\.1\\times 10^\{\-5\}MuSiQueQwen3\-8B0\.1470\.1470\.4900\.4900\.4710\.4713\.1×10−83\.1\\times 10^\{\-8\}*Panel 2: a200200example HotpotQA evaluation set with four downstream LLMs*DatasetDownstream LLMBaseFull supportMcNemarppHotpotQAQwen3\-8B0\.5350\.5350\.6150\.6150\.0010\.001Qwen3\-4B0\.5000\.5000\.5850\.5850\.0020\.002Llama\-3\.1\-8B0\.5750\.5750\.6600\.6600\.0040\.004Mistral\-7B0\.4550\.4550\.5450\.5450\.00050\.0005Table 3:Answer accuracy with base contexts produced byBeaverat target compression ratio0\.300\.30\. Panel 1 uses the dangling subsets of HotpotQA \(n=80n\{=\}80\), 2WikiMultiHopQA \(n=72n\{=\}72\), and MuSiQue \(n=102n\{=\}102\), with McNemarppvalues comparing Base and Reselected\. Panel 2 uses a separate set of200200HotpotQA examples, with McNemarppvalues comparing Base and Full support\.We evaluate GPT\-5\.5\(OpenAI[2026](https://arxiv.org/html/2608.04569#bib.bib60)\)and GLM\-5\.2\(Zhipu AI[2026](https://arxiv.org/html/2608.04569#bib.bib61)\)as proprietary downstream models\. Their API identifiers are listed in Table[9](https://arxiv.org/html/2608.04569#A5.T9)\.

ModelDatasetnnBaseFull supportMcNemarppGPT\-5\.5HotpotQA1841840\.9130\.9130\.9130\.9131\.01\.0GPT\-5\.5MuSiQue1021020\.7750\.7750\.8630\.8630\.0110\.011GLM\-5\.2MuSiQue95950\.6950\.6950\.9370\.9372\.4×10−72\.4\\times 10^\{\-7\}Table 4:Answer accuracy of proprietary models under Base and Full support, with base contexts produced byBeaverat target compression ratio0\.300\.30\. HotpotQA uses the full shared bridge set, while MuSiQue uses the dangling subset\. GLM\-5\.2 returned answers for9595of the102102MuSiQue contexts because of API timeouts\.
#### Accuracy on dangling examples\.

The dangling subsets are defined by paragraph retention and do not depend on whether the downstream model answers correctly\. Panel 1 of Table[3](https://arxiv.org/html/2608.04569#S5.T3)shows that Reselected improves accuracy over Base by28\.828\.8to34\.334\.3points, withp<10−4p<10^\{\-4\}on all three datasets\. It recovers92%92\\%and88%88\\%of the difference between Base and Full support on HotpotQA and 2WikiMultiHopQA, respectively, and exceeds Full support by1\.91\.9points on MuSiQue\. Because Reselected and Full support remove different paragraphs that are not annotated as supporting the answer, these comparisons measure the joint change in retained content rather than the isolated contribution of the reinserted paragraph\. The reselected contexts are shorter than the base contexts on average, as reported in Appendix D, so their gains cannot be explained by a larger token budget\. The protocol relies on annotated supporting paragraphs, and we apply it to all three multi\-hop QA datasets used in the prevalence analysis\.

#### Results across downstream models\.

We next compare Base and Full support across Qwen3, Llama\-3\.1, and Mistral models\(Yanget al\.[2025](https://arxiv.org/html/2608.04569#bib.bib37); Grattafioriet al\.[2024](https://arxiv.org/html/2608.04569#bib.bib36); Jianget al\.[2023a](https://arxiv.org/html/2608.04569#bib.bib38)\)\. Exact checkpoint and API identifiers are listed in Table[9](https://arxiv.org/html/2608.04569#A5.T9)\. Panel 2 of Table[3](https://arxiv.org/html/2608.04569#S5.T3)reports gains of8\.08\.0to9\.09\.0accuracy points for Full support, withp<0\.01p<0\.01for all four models\. These comparisons remain significant after Holm correction atα=0\.05\\alpha\{=\}0\.05\. The gains for Qwen3\-4B and Qwen3\-8B are similar, at8\.58\.5and8\.08\.0points, respectively\. Additional comparisons with proprietary models are reported in Table[4](https://arxiv.org/html/2608.04569#S5.T4)\. On HotpotQA, GPT\-5\.5 has the same aggregate accuracy under both conditions because restoring both supporting paragraphs produces four fixes and four breaks\. On MuSiQue, Full support improves accuracy by8\.88\.8points for GPT\-5\.5 and24\.224\.2points for GLM\-5\.2\. Full support improves accuracy for all four evaluated open\-weight models on HotpotQA and both proprietary models on MuSiQue, while GPT\-5\.5 shows no aggregate difference on HotpotQA\.

## 6Automatic Context Restoration

The fixed\-budget comparison relies on annotated supporting paragraphs to determine which content to restore\. We therefore test whether omitted supporting sentences can be selected automatically at inference with only a small increase in the token budget\. We treat the resulting pipeline as a diagnostic of targeted sentence restoration rather than a complete compression system\. We evaluate it onBeaveroutputs because their coherent blocks containing multiple sentences permit controlled insertion at sentence boundaries while leaving the remaining compressed context unchanged\.

#### Restoration pipeline and training\.

A candidate generator first collects sentences from the omitted context that may support retained text\. Abert\-base\-uncasedclassifier\(Devlinet al\.[2019](https://arxiv.org/html/2608.04569#bib.bib39)\)then ranks the candidates using a retained sentence, a candidate sentence, and the question, separated by\[SEP\]tokens\. Training pairs are constructed from the HotpotQA training split\. Positive pairs consist of a retained sentence and an omitted annotated supporting sentence that share an entity\. Pairs that share an entity but do not meet this positive criterion serve as hard negatives, whereas pairs without a shared entity serve as easy negatives\. After negative downsampling, the training set contains7,5657\{,\}565pairs, of which40%40\\%are positive\. Pairs are split by example identifier into classifier training and development partitions, and the source contexts are disjoint from the downstream evaluation contexts\. We fine\-tune the classifier for three epochs with AdamW using a learning rate of2×10−52\\times 10^\{\-5\}, a batch size of3232, and a maximum sequence length of256256, and retain the checkpoint with the highest development F1\. At inference, theKKcandidates with the highest classifier scores are reinserted\. We useK=3K\{=\}3in the main analyses; Appendix[F](https://arxiv.org/html/2608.04569#A6)reports theKKsweep and remaining implementation details\.

#### Downstream accuracy\.

With first\-mention candidates, the restoration pipeline improves Qwen3\-8B accuracy by4\.74\.7points \(p=0\.022p\{=\}0\.022\) while changing the compression ratio from0\.300\.30to0\.310\.31\. The same procedure improves Mistral\-7B accuracy by6\.56\.5points \(p=0\.012p\{=\}0\.012\)\. On Llama\-3\.1\-8B, the gain ranges from1\.31\.3to2\.32\.3points across candidate sources and is not statistically significant\. Subsequent analyses use Qwen3\-8B; Appendix G reports all downstream\-model results\.

#### Candidate sources\.

Table[5](https://arxiv.org/html/2608.04569#S6.T5)compares candidate sources while holding the classifier fixed\. First\-mention candidates yield a gain of4\.74\.7points on HotpotQA but only0\.50\.5points on 2WikiMultiHopQA\. Combining first\-mention candidates with embedding retrieval gives point estimates of4\.54\.5and5\.55\.5points, respectively\. In a diagnostic condition that includes the annotated supporting sentence in the candidate set, the gain reaches8\.08\.0points \(p=0\.008p\{=\}0\.008\) while adding only0\.40\.4sentences on average\. The larger point estimate suggests that candidate construction limits the current pipeline\. Appendix G further compares cases with successful and unsuccessful restoration\.

Candidate sourceHotpotQA2WikiMultiHopQAFirst mention\+4\.7 \(p=0\.022p\{=\}0\.022\)\+0\.5\(not significant\)All mentions\+4\.5 \(p=0\.15p\{=\}0\.15\)\+4\.0 \(p=0\.20p\{=\}0\.20\)Hybrid\+4\.5 \(p=0\.12p\{=\}0\.12\)\+5\.5 \(p=0\.063p\{=\}0\.063\)Annotated support included\+8\.0\(p=0\.008p\{=\}0\.008\)N/ATable 5:Changes in answer accuracy, in percentage points relative to Base, for candidate sources with a fixed classifier and Qwen3\-8B \(K=3K\{=\}3\)\. Hybrid augments first\-mention candidates with embedding retrieval, and the final row includes the annotated supporting sentence in the candidate set\.
#### Matched addition control\.

Adding the same number of randomly selected sentences improves accuracy by2\.02\.0points, compared with4\.74\.7points for targeted restoration \(Appendix G\)\. The direct contrast is suggestive but not significant at this sample size \(p=0\.15p\{=\}0\.15\); it therefore does not establish an advantage over random insertion\.

#### Transfer across compressors\.

Applying the same restoration configuration to three additional compressor outputs yields smaller gains that are not statistically significant\. Because the configuration is calibrated onBeaverand HotpotQA and output granularity varies, transfer to other compressors remains unresolved \(Appendix H\)\.

## 7Conclusion

We identify referential dangling, in which independent hard compression retains task\-relevant text but removes support required for interpretation\. Atr=0\.30r=0\.30, paragraph\-level dangling occurs in34%34\\%to54%54\\%of bridge examples with a retained answer paragraph underBeaveracross three multi\-hop QA datasets\. The event also recurs across six compressors on HotpotQA, and a separate LongBench\-v2 Single\-Document QA diagnostic flags every evaluated document\. On affectedBeaverexamples, fixed\-budget reselection improves Qwen3\-8B accuracy by2929to3434points, and automatic restoration adds4\.74\.7points on HotpotQA while changing the compression ratio from0\.300\.30to0\.310\.31\. These findings motivate dependency\-preserving selection, although transfer beyondBeaverand annotated\-support QA remains unresolved\.

## References

- Longbench v2: towards deeper understanding and reasoning on realistic long\-context multitasks\.InProceedings of the 63rd Annual Meeting of the Association for Computational Linguistics \(Volume 1: Long Papers\),pp\. 3639–3664\.Cited by:[§1](https://arxiv.org/html/2608.04569#S1.p4.14),[§4\.1](https://arxiv.org/html/2608.04569#S4.SS1.SSS0.Px3.p1.6)\.
- A\. Chevalier, A\. Wettig, A\. Ajith, and D\. Chen \(2023\)Adapting language models to compress contexts\.InProceedings of the 2023 Conference on Empirical Methods in Natural Language Processing,pp\. 3829–3846\.Cited by:[§2](https://arxiv.org/html/2608.04569#S2.SS0.SSS0.Px1.p1.1)\.
- E\. Choi, S\. Lee, M\. Choi, J\. Park, and J\. Lee \(2024\)From reading to compressing: exploring the multi\-document reader for prompt compression\.InFindings of the Association for Computational Linguistics: EMNLP 2024,pp\. 14734–14754\.Cited by:[§2](https://arxiv.org/html/2608.04569#S2.SS0.SSS0.Px2.p1.1)\.
- C\. Deng, Z\. Zhang, K\. Mao, S\. Li, X\. Huang, D\. Yu, and Z\. Dou \(2025\)A silver bullet or a compromise for full attention? a comprehensive study of gist token\-based context compression\.InProceedings of the 63rd Annual Meeting of the Association for Computational Linguistics \(Volume 1: Long Papers\),pp\. 4861–4879\.Cited by:[§2](https://arxiv.org/html/2608.04569#S2.SS0.SSS0.Px2.p1.1)\.
- J\. Devlin, M\. Chang, K\. Lee, and K\. Toutanova \(2019\)Bert: pre\-training of deep bidirectional transformers for language understanding\.InProceedings of the 2019 conference of the North American chapter of the association for computational linguistics: human language technologies, volume 1 \(long and short papers\),pp\. 4171–4186\.Cited by:[§6](https://arxiv.org/html/2608.04569#S6.SS0.SSS0.Px1.p1.8)\.
- G\. Durrett, T\. Berg\-Kirkpatrick, and D\. Klein \(2016\)Learning\-based single\-document summarization with compression and anaphoricity constraints\.InProceedings of the 54th Annual Meeting of the Association for Computational Linguistics \(Volume 1: Long Papers\),pp\. 1998–2008\.Cited by:[§2](https://arxiv.org/html/2608.04569#S2.SS0.SSS0.Px2.p1.1),[§3](https://arxiv.org/html/2608.04569#S3.SS0.SSS0.Px1.p3.18)\.
- W\. Fei, X\. Niu, P\. Zhou, L\. Hou, B\. Bai, L\. Deng, and W\. Han \(2024\)Extending context window of large language models via semantic compression\.InFindings of the Association for Computational Linguistics: ACL 2024,pp\. 5169–5181\.Cited by:[§2](https://arxiv.org/html/2608.04569#S2.SS0.SSS0.Px1.p1.1)\.
- T\. Ge, J\. Hu, L\. Wang, X\. Wang, S\. Chen, and F\. Wei \(2023\)In\-context autoencoder for context compression in a large language model\.Cited by:[§2](https://arxiv.org/html/2608.04569#S2.SS0.SSS0.Px1.p1.1)\.
- A\. Grattafiori, A\. Dubey, A\. Jauhri, A\. Pandey, A\. Kadian, A\. Al\-Dahle, A\. Letman, A\. Mathur, A\. Schelten, A\. Vaughan,et al\.\(2024\)The llama 3 herd of models\.Cited by:[§5](https://arxiv.org/html/2608.04569#S5.SS0.SSS0.Px3.p1.8)\.
- X\. Ho, A\. D\. Nguyen, S\. Sugawara, and A\. Aizawa \(2020\)Constructing a multi\-hop qa dataset for comprehensive evaluation of reasoning steps\.InProceedings of the 28th International Conference on Computational Linguistics,pp\. 6609–6625\.Cited by:[§1](https://arxiv.org/html/2608.04569#S1.p4.14),[§4\.1](https://arxiv.org/html/2608.04569#S4.SS1.SSS0.Px1.p1.4)\.
- Z\. Hu, K\. Li, D\. Fu, C\. Zeng, Y\. Li, Y\. Tang, and J\. Huang \(2026\)BEAVER: a training\-free hierarchical prompt compression method via structure\-aware page selection\.Cited by:[§1](https://arxiv.org/html/2608.04569#S1.p2.1),[§1](https://arxiv.org/html/2608.04569#S1.p4.14),[§2](https://arxiv.org/html/2608.04569#S2.SS0.SSS0.Px1.p1.1),[§4\.1](https://arxiv.org/html/2608.04569#S4.SS1.SSS0.Px1.p1.4),[§4\.2](https://arxiv.org/html/2608.04569#S4.SS2.p1.1)\.
- S\. Jha, L\. E\. Erdogan, S\. Kim, K\. Keutzer, and A\. Gholami \(2024\)Characterizing prompt compression methods for long context inference\.Cited by:[§2](https://arxiv.org/html/2608.04569#S2.SS0.SSS0.Px1.p1.1)\.
- A\. Q\. Jiang, A\. Sablayrolles, A\. Mensch, C\. Bamford, D\. S\. Chaplot, D\. de las Casas, F\. Bressand, G\. Lengyel, G\. Lample, L\. Saulnier, L\. R\. Lavaud, M\. Lachaux, P\. Stock, T\. L\. Scao, T\. Lavril, T\. Wang, T\. Lacroix, and W\. E\. Sayed \(2023a\)Mistral 7b\.External Links:2310\.06825,[Link](https://arxiv.org/abs/2310.06825)Cited by:[§5](https://arxiv.org/html/2608.04569#S5.SS0.SSS0.Px3.p1.8)\.
- H\. Jiang, Q\. Wu, C\. Lin, Y\. Yang, and L\. Qiu \(2023b\)Llmlingua: compressing prompts for accelerated inference of large language models\.InProceedings of the 2023 conference on empirical methods in natural language processing,pp\. 13358–13376\.Cited by:[§1](https://arxiv.org/html/2608.04569#S1.p1.1),[§2](https://arxiv.org/html/2608.04569#S2.SS0.SSS0.Px1.p1.1)\.
- H\. Jiang, Q\. Wu, X\. Luo, D\. Li, C\. Lin, Y\. Yang, and L\. Qiu \(2024\)Longllmlingua: accelerating and enhancing llms in long context scenarios via prompt compression\.InProceedings of the 62nd Annual Meeting of the Association for Computational Linguistics \(Volume 1: Long Papers\),pp\. 1658–1677\.Cited by:[§1](https://arxiv.org/html/2608.04569#S1.p2.1),[§2](https://arxiv.org/html/2608.04569#S2.SS0.SSS0.Px1.p1.1),[§4\.2](https://arxiv.org/html/2608.04569#S4.SS2.p1.1)\.
- H\. Jung and K\. Kim \(2024\)Discrete prompt compression with reinforcement learning\.IEEE Access12,pp\. 72578–72587\.Cited by:[§3](https://arxiv.org/html/2608.04569#S3.SS0.SSS0.Px2.p3.1)\.
- W\. Łajewska, M\. Hardalov, L\. Aina, N\. A\. John, H\. Su, and L\. Màrquez \(2025\)Understanding and improving information preservation in prompt compression for llms\.Cited by:[§2](https://arxiv.org/html/2608.04569#S2.SS0.SSS0.Px1.p1.1)\.
- K\. Lee, L\. He, M\. Lewis, and L\. Zettlemoyer \(2017\)End\-to\-end neural coreference resolution\.InProceedings of the 2017 conference on empirical methods in natural language processing,pp\. 188–197\.Cited by:[§2](https://arxiv.org/html/2608.04569#S2.SS0.SSS0.Px2.p1.1)\.
- P\. Lewis, E\. Perez, A\. Piktus, F\. Petroni, V\. Karpukhin, N\. Goyal, H\. Küttler, M\. Lewis, W\. Yih, T\. Rocktäschel,et al\.\(2020\)Retrieval\-augmented generation for knowledge\-intensive nlp tasks\.Advances in neural information processing systems33,pp\. 9459–9474\.Cited by:[§2](https://arxiv.org/html/2608.04569#S2.SS0.SSS0.Px2.p1.1)\.
- K\. Li, G\. Chen, R\. Yang, and X\. Hu \(2025a\)SPMamba: leveraging long\-sequence modeling with state space models for speech separation\.In2025 IEEE International Conference on Multimedia and Expo \(ICME\),pp\. 1–6\.Cited by:[§2](https://arxiv.org/html/2608.04569#S2.SS0.SSS0.Px1.p1.1)\.
- K\. Li, K\. Gao, and X\. Hu \(2025b\)Efficient audio\-visual speech separation with discrete lip semantics and multi\-scale global\-local attention\.Cited by:[§2](https://arxiv.org/html/2608.04569#S2.SS0.SSS0.Px1.p1.1)\.
- K\. Li and Y\. Luo \(2024\)Subnetwork\-to\-go: elastic neural network with dynamic training and customizable inference\.InICASSP 2024\-2024 IEEE International Conference on Acoustics, Speech and Signal Processing \(ICASSP\),pp\. 6775–6779\.Cited by:[§2](https://arxiv.org/html/2608.04569#S2.SS0.SSS0.Px1.p1.1)\.
- K\. Li, R\. Yang, and X\. Hu \(2022\)An efficient encoder\-decoder architecture with top\-down attention for speech separation\.Cited by:[§2](https://arxiv.org/html/2608.04569#S2.SS0.SSS0.Px1.p1.1)\.
- Y\. Li, B\. Dong, F\. Guerin, and C\. Lin \(2023\)Compressing context to enhance inference efficiency of large language models\.InProceedings of the 2023 conference on empirical methods in natural language processing,pp\. 6342–6353\.Cited by:[Appendix E](https://arxiv.org/html/2608.04569#A5.SS0.SSS0.Px3.p1.1),[§1](https://arxiv.org/html/2608.04569#S1.p1.1),[§1](https://arxiv.org/html/2608.04569#S1.p2.1),[§2](https://arxiv.org/html/2608.04569#S2.SS0.SSS0.Px1.p1.1),[§4\.2](https://arxiv.org/html/2608.04569#S4.SS2.p1.1)\.
- Z\. Li, Y\. Liu, Y\. Su, and N\. Collier \(2025c\)Prompt compression for large language models: a survey\.InProceedings of the 2025 Conference of the Nations of the Americas Chapter of the Association for Computational Linguistics: Human Language Technologies \(Volume 1: Long Papers\),pp\. 7182–7195\.Cited by:[§2](https://arxiv.org/html/2608.04569#S2.SS0.SSS0.Px1.p1.1)\.
- Z\. Li, Y\. Su, and N\. Collier \(2025d\)500xcompressor: generalized prompt compression for large language models\.InProceedings of the 63rd Annual Meeting of the Association for Computational Linguistics \(Volume 1: Long Papers\),pp\. 25081–25091\.Cited by:[§2](https://arxiv.org/html/2608.04569#S2.SS0.SSS0.Px1.p1.1)\.
- Y\. Lin, W\. Guo, Y\. Zhang, C\. Yang, and Z\. Li \(2025\)Prompt compression based on key\-information density\.Expert Systems with Applications284,pp\. 127738\.Cited by:[§2](https://arxiv.org/html/2608.04569#S2.SS0.SSS0.Px1.p1.1)\.
- B\. Liskavets, M\. Ushakov, S\. Roy, M\. Klibanov, A\. Etemad, and S\. K\. Luke \(2025\)Prompt compression with context\-aware sentence encoding for fast and improved llm inference\.InProceedings of the AAAI Conference on Artificial Intelligence,Vol\.39,pp\. 24595–24604\.Cited by:[§3](https://arxiv.org/html/2608.04569#S3.SS0.SSS0.Px2.p3.1)\.
- J\. Liu, L\. Li, T\. Xiang, B\. Wang, and Y\. Qian \(2023\)Tcra\-llm: token compression retrieval augmented large language model for inference cost reduction\.InFindings of the association for computational linguistics: EMNLP 2023,pp\. 9796–9810\.Cited by:[§2](https://arxiv.org/html/2608.04569#S2.SS0.SSS0.Px2.p1.1)\.
- N\. F\. Liu, K\. Lin, J\. Hewitt, A\. Paranjape, M\. Bevilacqua, F\. Petroni, and P\. Liang \(2024\)Lost in the middle: how language models use long contexts\.Transactions of the association for computational linguistics12,pp\. 157–173\.Cited by:[§1](https://arxiv.org/html/2608.04569#S1.p1.1),[§2](https://arxiv.org/html/2608.04569#S2.SS0.SSS0.Px2.p1.1)\.
- W\. Mao, C\. Hou, T\. Zhang, X\. Lin, K\. Tang, and H\. Lv \(2025\)Parse trees guided llm prompt compression\.IEEE Transactions on Pattern Analysis and Machine Intelligence\.Cited by:[§1](https://arxiv.org/html/2608.04569#S1.p2.1),[§2](https://arxiv.org/html/2608.04569#S2.SS0.SSS0.Px1.p1.1),[§4\.2](https://arxiv.org/html/2608.04569#S4.SS2.p1.1)\.
- J\. Maynez, S\. Narayan, B\. Bohnet, and R\. McDonald \(2020\)On faithfulness and factuality in abstractive summarization\.InProceedings of the 58th annual meeting of the association for computational linguistics,pp\. 1906–1919\.Cited by:[§2](https://arxiv.org/html/2608.04569#S2.SS0.SSS0.Px2.p1.1)\.
- J\. Mu, X\. Li, and N\. Goodman \(2023\)Learning to compress prompts with gist tokens\.Advances in Neural Information Processing Systems36,pp\. 19327–19352\.Cited by:[§2](https://arxiv.org/html/2608.04569#S2.SS0.SSS0.Px1.p1.1)\.
- A\. Nagle, A\. Girish, M\. Bondaschi, M\. Gastpar, A\. V\. Makkuva, and H\. Kim \(2024\)Fundamental limits of prompt compression: a rate\-distortion framework for black\-box language models\.Advances in Neural Information Processing Systems37,pp\. 94934–94970\.Cited by:[§2](https://arxiv.org/html/2608.04569#S2.SS0.SSS0.Px1.p1.1)\.
- OpenAI \(2026\)Models\.Note:OpenAI API documentationAccessed July 18, 2026\. Available athttps://developers\.openai\.com/api/docs/modelsCited by:[§5](https://arxiv.org/html/2608.04569#S5.SS0.SSS0.Px1.p2.1)\.
- Z\. Pan, Q\. Wu, H\. Jiang, M\. Xia, X\. Luo, J\. Zhang, Q\. Lin, V\. Rühle, Y\. Yang, C\. Lin,et al\.\(2024\)Llmlingua\-2: data distillation for efficient and faithful task\-agnostic prompt compression\.InFindings of the Association for Computational Linguistics: ACL 2024,pp\. 963–981\.Cited by:[§1](https://arxiv.org/html/2608.04569#S1.p1.1),[§1](https://arxiv.org/html/2608.04569#S1.p2.1),[§2](https://arxiv.org/html/2608.04569#S2.SS0.SSS0.Px1.p1.1),[§4\.2](https://arxiv.org/html/2608.04569#S4.SS2.p1.1)\.
- A\. Radford, J\. Wu, R\. Child, D\. Luan, D\. Amodei, I\. Sutskever,et al\.\(2019\)Language models are unsupervised multitask learners\.OpenAI blog1\(8\),pp\. 9\.Cited by:[Appendix A](https://arxiv.org/html/2608.04569#A1.SS0.SSS0.Px1.p1.4)\.
- S\. Shandilya, M\. Xia, S\. Ghosh, H\. Jiang, J\. Zhang, Q\. Wu, V\. Rühle, and S\. Rajmohan \(2025\)Taco\-rl: task aware prompt compression optimization with reinforcement learning\.InFindings of the Association for Computational Linguistics: ACL 2025,pp\. 1582–1597\.Cited by:[§2](https://arxiv.org/html/2608.04569#S2.SS0.SSS0.Px1.p1.1)\.
- F\. Shi, X\. Chen, K\. Misra, N\. Scales, D\. Dohan, E\. H\. Chi, N\. Schärli, and D\. Zhou \(2023\)Large language models can be easily distracted by irrelevant context\.InInternational Conference on Machine Learning,pp\. 31210–31227\.Cited by:[§2](https://arxiv.org/html/2608.04569#S2.SS0.SSS0.Px2.p1.1)\.
- J\. Tang, J\. Xu, T\. Lu, Z\. Zhang, Y\. YimingZhao, L\. LinHai, and H\. Zheng \(2025\)Perception compressor: a training\-free prompt compression framework in long context scenarios\.InFindings of the Association for Computational Linguistics: NAACL 2025,pp\. 4093–4108\.Cited by:[§2](https://arxiv.org/html/2608.04569#S2.SS0.SSS0.Px1.p1.1)\.
- H\. Touvron, L\. Martin, K\. Stone, P\. Albert, A\. Almahairi, Y\. Babaei, N\. Bashlykov, S\. Batra, P\. Bhargava, S\. Bhosale,et al\.\(2023\)Llama 2: open foundation and fine\-tuned chat models\.Cited by:[Appendix E](https://arxiv.org/html/2608.04569#A5.SS0.SSS0.Px3.p1.1),[Appendix E](https://arxiv.org/html/2608.04569#A5.SS0.SSS0.Px5.p1.1)\.
- H\. Trivedi, N\. Balasubramanian, T\. Khot, and A\. Sabharwal \(2022\)MuSiQue: multihop questions via single\-hop question composition\.Transactions of the Association for Computational Linguistics10,pp\. 539–554\.Cited by:[§1](https://arxiv.org/html/2608.04569#S1.p4.14),[§4\.1](https://arxiv.org/html/2608.04569#S4.SS1.SSS0.Px1.p1.4)\.
- F\. Xu, W\. Shi, and E\. Choi \(2024\)Recomp: improving retrieval\-augmented lms with context compression and selective augmentation\.InInternational Conference on Learning Representations,Vol\.2024,pp\. 43478–43502\.Cited by:[§2](https://arxiv.org/html/2608.04569#S2.SS0.SSS0.Px2.p1.1)\.
- A\. Yang, A\. Li, B\. Yang, B\. Zhang, B\. Hui, B\. Zheng, B\. Yu, C\. Gao, C\. Huang, C\. Lv,et al\.\(2025\)Qwen3 technical report\.Cited by:[Appendix E](https://arxiv.org/html/2608.04569#A5.SS0.SSS0.Px6.p1.4),[§4\.1](https://arxiv.org/html/2608.04569#S4.SS1.SSS0.Px1.p1.4),[§5](https://arxiv.org/html/2608.04569#S5.SS0.SSS0.Px3.p1.8)\.
- Z\. Yang, P\. Qi, S\. Zhang, Y\. Bengio, W\. Cohen, R\. Salakhutdinov, and C\. D\. Manning \(2018\)HotpotQA: a dataset for diverse, explainable multi\-hop question answering\.InProceedings of the 2018 conference on empirical methods in natural language processing,pp\. 2369–2380\.Cited by:[§1](https://arxiv.org/html/2608.04569#S1.p4.14),[§4\.1](https://arxiv.org/html/2608.04569#S4.SS1.SSS0.Px1.p1.4)\.
- P\. Zhang, Z\. Liu, S\. Xiao, N\. Shao, Q\. Ye, and Z\. Dou \(2025a\)Long context compression with activation beacon\.InInternational Conference on Learning Representations,Vol\.2025,pp\. 101932–101948\.Cited by:[§2](https://arxiv.org/html/2608.04569#S2.SS0.SSS0.Px1.p1.1)\.
- Y\. Zhang, M\. Li, D\. Long, X\. Zhang, H\. Lin, B\. Yang, P\. Xie, A\. Yang, D\. Liu, J\. Lin,et al\.\(2025b\)Qwen3 embedding: advancing text embedding and reranking through foundation models\.Cited by:[§4\.1](https://arxiv.org/html/2608.04569#S4.SS1.SSS0.Px1.p1.4)\.
- Z\. Zhang, Y\. Sheng, T\. Zhou, T\. Chen, L\. Zheng, R\. Cai, Z\. Song, Y\. Tian, C\. Ré, C\. Barrett,et al\.\(2023\)H2o: heavy\-hitter oracle for efficient generative inference of large language models\.Advances in Neural Information Processing Systems36,pp\. 34661–34710\.Cited by:[§2](https://arxiv.org/html/2608.04569#S2.SS0.SSS0.Px1.p1.1)\.
- Y\. Zhao, Z\. Li, H\. Zhao, B\. Qi, and L\. Guoming \(2025\)DAC: a dynamic attention\-aware approach for task\-agnostic prompt compression\.InProceedings of the 63rd Annual Meeting of the Association for Computational Linguistics \(Volume 1: Long Papers\),pp\. 19395–19407\.Cited by:[§1](https://arxiv.org/html/2608.04569#S1.p2.1),[§2](https://arxiv.org/html/2608.04569#S2.SS0.SSS0.Px1.p1.1),[§4\.2](https://arxiv.org/html/2608.04569#S4.SS2.p1.1)\.
- Zhipu AI \(2026\)GLM\-5\.2\.Note:Zhipu AI open documentationAccessed July 18, 2026\. Available athttps://docs\.bigmodel\.cn/cn/guide/models/text/glm\-5\.2Cited by:[§5](https://arxiv.org/html/2608.04569#S5.SS0.SSS0.Px1.p2.1)\.

## Appendix ARobustness to Experimental Choices

The main diagnostic depends on theBeaverembedding model, the content\-word\-overlap threshold, and the compression ratio\. This appendix varies each choice and shows that the diagnosis remains stable across all variations\.

#### Embedding scorer\.

Beaverscores chunks by cosine similarity to the query under an embedding model; the main text uses the released Qwen3\-0\.6B embeddings configuration\. Substituting the GPT\-2 checkpoint\(Radfordet al\.[2019](https://arxiv.org/html/2608.04569#bib.bib59)\)leaves the HotpotQA dangling rate essentially unchanged \(Table[7](https://arxiv.org/html/2608.04569#A1.T7),n=300n\{=\}300, ratio0\.300\.30\)\. The GPT\-2 encoder changesρd\\rho\_\{\\mathrm\{d\}\}by at most0\.90\.9percentage points\. The diagnosis is therefore robust across bothBeaverembedding encoders\.

#### Overlap threshold\.

The unified cross\-compressor metric uses the sentence\-level predicateKeepθ\\operatorname\{Keep\}\_\{\\theta\}defined in Section[4](https://arxiv.org/html/2608.04569#S4); paragraph\-level prevalence uses the separate paragraph instantiation described there\. Sweepingθ\\thetafrom0\.30\.3to0\.70\.7\(Figure[5](https://arxiv.org/html/2608.04569#A1.F5), Table[6](https://arxiv.org/html/2608.04569#A1.T6)\) keeps dangling substantial for both a chunk\-level and a token\-level compressor across the entire range, and at every threshold up to0\.60\.6, including the setting most lenient to token fragments, LLMLingua\-2 dangles at least as much asBeaver, whereas a metric biased against fragments would show the reverse\. So the cross\-signal agreement in Section[4\.2](https://arxiv.org/html/2608.04569#S4.SS2)is not an artifact of one lenient cutoff\. The token\-level curve is nonmonotonic by construction: at strict thresholds a partially retained supporting sentence fails the overlap test and the case moves from dangling to full evidence loss rather than to safety, whereasBeaver’s coherent blocks keep clearing the bar\.

Overlap threshold0\.30\.30\.40\.40\.50\.50\.60\.60\.70\.7LLMLingua\-2 \(token\)28\.328\.343\.543\.556\.056\.057\.657\.636\.436\.4Beaver\(chunk\)19\.619\.625\.025\.032\.132\.136\.436\.440\.240\.2Table 6:Dangling rate \(%\) across content\-word overlap retention thresholds on the same184184bridge examples as Figure[3](https://arxiv.org/html/2608.04569#S4.F3)at compression ratio0\.300\.30\. The0\.50\.5column matches Figure[3](https://arxiv.org/html/2608.04569#S4.F3)\.CheckVariationOutcomeEmbedding scorerQwen3\-0\.6B embeddings→\\toGPT\-2\+0\.9\+0\.9pointsOverlap threshold0\.30\.3to0\.70\.7substantial throughoutCompression ratio0\.700\.70to0\.200\.20monotonic increaseTable 7:Robustness of the dangling diagnostic to its three main free choices \(HotpotQA,n=300n\{=\}300, ratio0\.300\.30unless swept\)\. Embedding shifts are measured in percentage points relative to the released Qwen3\-0\.6B embedding setup\.![Refer to caption](https://arxiv.org/html/2608.04569v1/x5.png)Figure 5:Dangling rate across content\-word\-overlap thresholds for184184bridge examples \(Figure[3](https://arxiv.org/html/2608.04569#S4.F3); ratio0\.300\.30\)\.![Refer to caption](https://arxiv.org/html/2608.04569v1/x6.png)Figure 6:Referential dangling examples from HotpotQA, 2WikiMultiHopQA, MuSiQue, and LongBench\-v2 Single\-Document QA\. Each panel shows the original context and the compressed output\.
#### Compression ratio\.

The compression ratio analysis \(Figure[2](https://arxiv.org/html/2608.04569#S4.F2)a\) sweeps the ratio from0\.700\.70to0\.200\.20and finds the HotpotQA dangling rate rising monotonically with no qualitative threshold or reversal\. The finding is therefore not limited to a single operating ratio\. Table[7](https://arxiv.org/html/2608.04569#A1.T7)summarizes all three checks\.

## Appendix BManual Audit and Qualitative Examples

We present one representative dangling case from each dataset to illustrate the “answer present but bridge deleted” mechanism\. All examples are real cases from the experimental data\. Each panel shows the original context and the compressed output with referential dangling\. Among the3838confirmed cases in the manual audit, the omitted paragraph contained the dataset answer string in2626, the entity definition in1010, and another dependency in22\. The two false positives involved an answer paragraph that was sufficient on its own and an omitted paragraph that supplied only a generic modifier\.

## Appendix CLong\-Document Dangling by Subdomain

Table[8](https://arxiv.org/html/2608.04569#A3.T8)breaks down the LongBench\-v2 Single\-Document QA diagnostic \(Section[4](https://arxiv.org/html/2608.04569#S4),n=80n\{=\}80, ratio0\.300\.30\) by subdomain\. The per\-kept\-sentence dangling rate is consistent across all seven subdomains \(25\.1%25\.1\\%to36\.5%36\.5\\%\), and every document in every subdomain has at least one dangling reference\. Academic text has the highest rate and also contains dense terminology, frequent cross\-section references, and the longest retained\-sentence counts\. This pattern is consistent with the association between dependency span and dangling reported in Section[4](https://arxiv.org/html/2608.04569#S4)\. No subdomain falls below25%25\\%, suggesting that the phenomenon is not confined to a single document type\.

SubdomainnnMean rateAffected docsAcademic131336\.5%36\.5\\%100%100\\%Literary121234\.4%34\.4\\%100%100\\%Financial121232\.3%32\.3\\%100%100\\%Legal8829\.1%29\.1\\%100%100\\%Detective151527\.3%27\.3\\%100%100\\%Event ordering111127\.0%27\.0\\%100%100\\%Governmental9925\.1%25\.1\\%100%100\\%All808030\.5%\\mathbf\{30\.5\\%\}𝟏𝟎𝟎%\\mathbf\{100\\%\}Table 8:Referential dangling on LongBench\-v2 Single\-Document QA by subdomain \(Beaver, ratio0\.300\.30,n=80n\{=\}80documents\)\. “Mean rate” is the per\-document average fraction of retained sentences that are dangling, macro\-averaged over documents\. “Affected docs” is the fraction of documents with at least one dangling reference\.
## Appendix DProtocol for Fixed\-Budget Content Reselection

The comparison in Section[5](https://arxiv.org/html/2608.04569#S5)measures the accuracy change when a missing supporting paragraph replaces lower scoring paragraphs that are not annotated as supporting the answer, without increasing the token budget\.

#### Three conditions\.

Each dangling example is evaluated under three conditions\. Base is the compressor’s original dangling output at target compression ratio0\.300\.30\. Reselected reinserts one omitted supporting paragraph and removes paragraphs not annotated as supporting the answer whose combined length is at least as large\. Full support retains both annotated supporting paragraphs while removing two paragraphs not annotated as supporting the answer\. We use Base and Reselected for the fixed\-budget comparison, while Full support provides a reference for complete evidence retention\.

#### Token budget enforcement\.

We tokenize all paragraphs with spaCy, which is also used during compressor preprocessing, and track cumulative token counts\. For Reselected, we rank omitted supporting paragraphs by their isolated salience score under the compressor and select the highest scoring paragraph\. We then remove the lowest scoring paragraphs not annotated as supporting the answer until their combined token count matches or exceeds that of the reinserted paragraph\. Contexts under Reselected are shorter than those under Base on average by1\.5%1\.5\\%on HotpotQA,1\.6%1\.6\\%on 2WikiMultiHopQA, and9\.6%9\.6\\%on MuSiQue\.

#### Dataset specifics\.

HotpotQA uses bridge examples with two annotated supporting paragraphs\. Panel 1 uses a dangling subset of8080examples, while Panel 2 uses a separate evaluation set of200200examples\. 2WikiMultiHopQA uses compositional examples with exactly two annotated supporting paragraphs and a dangling subset of7272examples\. MuSiQue uses paragraph\-level supporting facts with exactly two annotated supporting paragraphs per example in the first200200examples of the development split, yielding a dangling subset of102102examples\. The dangling subset uses directional content\-word overlap at threshold0\.50\.5\(Section[4](https://arxiv.org/html/2608.04569#S4)\): the answer paragraph survives but its paired definition paragraph does not\.

#### Statistical test\.

Significance is assessed with the two\-sided exact McNemar test on the2×22\{\\times\}2contingency table of fixes, where the answer under Base is incorrect and the comparison answer is correct, and breaks, where the answer under Base is correct and the comparison answer is incorrect\. All three datasets yieldp<10−4p<10^\{\-4\}for the comparison between Base and Reselected on the dangling subset\. Base versus Full support yieldsp<0\.01p<0\.01for all four downstream LLMs on the200200\-example HotpotQA set\.

## Appendix ECompressor Configurations

The six compressors of Section[4\.2](https://arxiv.org/html/2608.04569#S4.SS2)all compress the same184184HotpotQA bridge examples to ratio0\.300\.30\(keep30%30\\%of tokens\)\. We use official implementations where available; training\-free methods require no adaptation\.

Role and reported nameOfficial checkpoint or API identifierBeaver scorerQwen3\-0\.6B embeddingsQwen/Qwen3\-0\.6BRobustness scorerGPT\-2openai\-community/gpt2DAC proxyQwen3 0\.6BQwen/Qwen3\-0\.6BDownstream QAQwen3 4B; Qwen3 8BQwen/Qwen3\-4B;Qwen/Qwen3\-8BDownstream QALlama 3\.1 8B; Mistral 7Bmeta\-llama/Llama\-3\.1\-8B\-Instructmistralai/Mistral\-7B\-Instruct\-v0\.3Self\-information /perplexity proxyLlama 2 7Bmeta\-llama/Llama\-2\-7b\-hfCompression /restoration classifiersmicrosoft/llmlingua\-2\-xlm\-roberta\-large\-meetingbank;google\-bert/bert\-base\-uncasedProprietary downstream QAGPT\-5\.5; GLM\-5\.2API IDs:gpt\-5\.5;glm\-5\.2Table 9:Official checkpoint and API identifiers\. Display names are the shorthand used in the paper; exact identifiers are shown for reproducibility\.#### Beaver\(embedding similarity, query\-aware\)\.

Official repositorygithub\.com/JusperLee/BEAVER, coherent\-block selection\. We use the released configuration with theQwen/Qwen3\-0\.6Bcheckpoint as the embedding scorer\. Each document is segmented into6464\-token pages; the compressor scores pages by cosine similarity between the query embedding and the page’s inverse document frequency weighted token embedding average, then selects top\-kkpages to meet the target ratio\. Hardware: NVIDIA A100 80GB\.

#### LLMLingua\-2 \(trained token classifier, query\-agnostic\)\.

Official repositoryhttps://github\.com/microsoft/LLMLingua, checkpointmicrosoft/llmlingua\-2\-xlm\-roberta\-large\-meetingbank\. Token\-level binary classifier over a sliding512512\-token window; tokens are kept if the classifier score exceeds a threshold calibrated to the target ratio\. No query input\.

#### Selective\-Context \(self\-information, query\-agnostic\)\.

Reproduced fromLiet al\.\([2023](https://arxiv.org/html/2608.04569#bib.bib7)\)\. Each token’s self\-information is computed as−log⁡p​\(token∣prefix\)\-\\log p\(\\text\{token\}\\mid\\text\{prefix\}\)under themeta\-llama/Llama\-2\-7b\-hfproxy model\(Touvronet al\.[2023](https://arxiv.org/html/2608.04569#bib.bib41)\); tokens with self\-information below a calibrated threshold are dropped\. No query input\.

#### PartPrompt \(syntactic parse tree, query\-agnostic\)\.

Official repository\. Constituency parse tree built with Berkeley Neural Parser; each node \(phrase\) scores by syntactic salience \(depth and span\); a knapsack solver based on dynamic programming selects a subset of nodes covering the target ratio\. The selected nodes’ token spans are concatenated in document order\. No query input\.

#### LongLLMLingua \(perplexity, query\-aware\)\.

Official repositorymicrosoft/LLMLingua\. Scores sentences by perplexity under the proxy model conditioned on the query and preceding context; keeps lowest\-perplexity \(most “expected”\) sentences up to the budget\. Uses themeta\-llama/Llama\-2\-7b\-hfproxy model\(Touvronet al\.[2023](https://arxiv.org/html/2608.04569#bib.bib41)\)\.

#### DAC \(attention, query\-agnostic\)\.

Official implementation, methoddynamic\_attn\_ppl, fusionadditivewithα=0\.8\\alpha\{=\}0\.8\. Token\-level importance derived from attention weights during a single forward pass of theQwen/Qwen3\-0\.6Bproxy model\(Yanget al\.[2025](https://arxiv.org/html/2608.04569#bib.bib37)\)over the context; tokens below the importance threshold are dropped\. Parametercompress\_ratio\(the drop fraction\) set to0\.700\.70to keep30%30\\%\. We run DAC with a memory\-efficient attention accumulator that is numerically identical to its original scoring, allowing the full184184\-example bridge set to fit in memory\.

All compressors run single\-threaded on an A100 80GB for consistency\.

## Appendix FImplementation Details for Automatic Context Restoration

The following engineering details document the automatic restoration pipeline of Section[6](https://arxiv.org/html/2608.04569#S6)for reproducibility\.

Downstream LLMCandidatesourceBaseRestoredppQwen3\-8BFirst mention0\.5670\.6130\.022Mistral\-7BFirst mention0\.4550\.5200\.012Llama\-3\.1\-8BFirst mention0\.5870\.6000\.60Llama\-3\.1\-8BHybrid0\.5870\.6100\.17Table 10:Automatic restoration results with the classifier fixed atK=3K\{=\}3\. The evaluation uses300300HotpotQA examples, except for Mistral\-7B, which uses200200\. Base isBeaverat compression ratio0\.300\.30, and Restored has an average ratio of0\.310\.31\. The reportedppvalues use paired McNemar tests\.![Refer to caption](https://arxiv.org/html/2608.04569v1/x7.png)Figure 7:Accuracy gains from full support and first\-mention automatic restoration on HotpotQA \(Beaverat ratio0\.300\.30,K=3K\{=\}3\)\. Full support uses200200examples; restoration uses300300for Qwen3\-8B and Llama\-3\.1\-8B and200200for Mistral\-7B\.FeatureFixed \(23\)Failed \(107\)Sentences added, mean±\\pmSD2\.13±\\pm1\.081\.79±\\pm1\.17Sentences added, median3\.02\.0McNemar: 23 fixes, 9 breaks,p=0\.022p=0\.022Table 11:Restoration statistics when theBeaverbaseline was incorrect \(HotpotQA,n=300n\{=\}300, compression ratio0\.300\.30; downstream Qwen3\-8B\)\. SD denotes standard deviation\.ConditionAccuracy \[95% CI\]Δ\\DeltaBase compressor0\.5670\.567\[\.51,\.62\]N/ARandom insertion,mmsentences0\.5870\.587\[\.53,\.64\]\+2\.0\+2\.0Targeted restoration,mmsentences0\.613\\mathbf\{0\.613\}\[\.55,\.67\]\+4\.7\+4\.7Table 12:Matched addition control on HotpotQA with Qwen3\-8B \(n=300n\{=\}300\)\. Random insertion and targeted restoration add the same number of sentences per example \(mm: mean1\.811\.81, median22, interquartile range\[1,3\]\[1,3\]; approximately4040tokens; compression ratio0\.300\.30to0\.310\.31;K=3K\{=\}3\)\. Brackets report bootstrap95%95\\%confidence intervals\.Compressor \(output type\)GainMcNemarppBeaver\(coherent chunks\)\+4\.7\+4\.7p=0\.022p\{=\}0\.022PartPrompt \(parse tree spans\)\+3\.2\+3\.20\.300\.30Selective\-Context \(self\-information\)\+1\.0\+1\.00\.800\.80LLMLingua\-2 \(token fragments\)\+1\.0\+1\.00\.750\.75Table 13:Transfer of one restoration configuration across four compressor outputs on HotpotQA with downstream Qwen3\-8B \(n≈150n\{\\approx\}150to300300\)\.#### Output granularity\.

We evaluate automatic restoration onBeaverbecause its coherent multi\-sentence blocks permit controlled changes at sentence boundaries and keep restored sentences interpretable\. Compressors with token\-level outputs produce fragmented text in which inserting complete supporting sentences may alter the original selection objective and complicate comparison\. Appendix H reports transfer across four compressor outputs, including LLMLingua\-2\. The classifier does not take compressor scores or identities as input, although its training distribution and integration strategy may affect transfer across output granularities\.

#### Classifier architecture and training\.

The classifier isbert\-base\-uncased\(about110110M parameters\) with a binary classification head over a retained sentence, a candidate sentence, and the question, separated by\[SEP\]tokens\. The maximum sequence length is256256\. We fine\-tune the classifier for three epochs with AdamW using a learning rate of2×10−52\\times 10^\{\-5\}, a batch size of3232, a linear schedule with10%10\\%warmup, and fp16, and retain the checkpoint with the highest development F1\. The resulting development F1 is0\.820\.82, with a precision of0\.840\.84\.

#### Training pair construction\.

Positive pairs consist of a retained sentence and an omitted annotated supporting sentence that share an entity\. Hard negatives also share an entity but do not satisfy this positive\-pair rule, while easy negatives share no entity\. Positive pairs account for1\.9%1\.9\\%of all candidate pairs \(3026/1578873026/157887\), so we downsample negatives to1\.5×1\.5\\timesthe number of positives, yielding7,5657\{,\}565rebalanced pairs with40%40\\%positives\. Pairs are split by example identifier so that no example crosses the training and development boundary\. The source contexts come from the HotpotQA training split and are disjoint from the evaluation contexts used in all downstream experiments\.

#### Number of restored sentences \(KK\)\.

At inference, we add the top\-KKcandidates by classifier confidence\. In the Qwen3\-8B sweep,K=2K\{=\}2gives\+3\.7\+3\.7points \(p=0\.08p\{=\}0\.08\),K=3K\{=\}3gives\+4\.7\+4\.7points \(p=0\.02p\{=\}0\.02\), and adding all candidates gives\+4\.3\+4\.3points \(p=0\.03p\{=\}0\.03\)\. We useK=3K\{=\}3, the setting with the largest observed gain, which adds about1\.81\.8sentences per example\.

## Appendix GAutomatic Context Restoration Results and Controls

#### Downstream results\.

Table[10](https://arxiv.org/html/2608.04569#A6.T10)reports the accuracies and significance tests for automatic restoration, and Figure[7](https://arxiv.org/html/2608.04569#A6.F7)compares the restoration gain with the gain obtained when both supporting paragraphs are retained\.

#### Restoration outcomes\.

Table[11](https://arxiv.org/html/2608.04569#A6.T11)compares cases corrected by automatic restoration with those that remain incorrect among the130130examples for which theBeaverbaseline is incorrect\. The two groups receive similar numbers of restored sentences\. These measurements show that restoration size alone does not distinguish the outcomes\.

#### Matched addition control\.

Table[12](https://arxiv.org/html/2608.04569#A6.T12)reports the control experiment of Section[6](https://arxiv.org/html/2608.04569#S6)\. Random insertion and targeted restoration add the same number of sentences per example\.

## Appendix HTransfer Across Compressor Outputs

Table[13](https://arxiv.org/html/2608.04569#A6.T13)applies the same restoration configuration to each compressor output with Qwen3\-8B as the downstream model on HotpotQA\. The classifier and candidate generator are calibrated onBeaver’s retained sentence distribution and HotpotQA first\-mention structure, so the experiment evaluates transfer of one fixed configuration rather than configurations optimized separately for each compressor\.