Text summarization via global structure awareness
Authors: Jiaquan Zhang
Chaoning Zhang
Shuxu Chen
Yibei Liu
Chenghao Li
Qigan Sun
Shuai Yuan
Fachrina Dewi Puspitasari
Dongshen Han
Guoqing Wang
Sung-Ho Bae
Yang Yang
Venue: ICLR 2026 Poster (2026)
Keywords: Text summarization
Topological Data Analysis
natural language processing
Primary area: foundation or frontier models, including LLMs

Abstract: With the explosive growth of information, the volume of long documents has surged, and the cost of processing them continues to rise, making text summarization increasingly important. Existing studies primarily focus on model enhancements and sentence-level pruning based on contextual dependencies and semantic patterns. Although some approaches leverage large language models (LLMs) for text summarization and achieve higher accuracy, they incur substantial computational costs and often overlook global structural modeling. Consequently, summarized texts may lose critical logical chains, disrupting coherence and weakening downstream task performance. To address these issues, we propose GloSA-Sum, a novel text summarization framework that performs global structural analysis of texts via topological data analysis (TDA), enabling efficient summarization while preserving semantic cores and logical dependencies. Specifically, we construct a semantic-weighted graph from sentence embeddings, where persistent homology identifies core semantics and logical structures, preserved in a ``protection pool'' as the backbone for summarization. We design a topology-guided iterative strategy, where lightweight proxy metrics approximate sentence importance to avoid repeated high-cost computations, thus preserving structural integrity while improving efficiency. To further enhance long-text processing, we propose a hierarchical strategy that integrates segment-level and global summarization. Experiments on multiple datasets demonstrate that GloSA-sum reduces redundancy while preserving semantic and logical integrity, striking a balance between accuracy and efficiency, and further benefits LLM downstream tasks by shortening contexts while retaining essential reasoning chains.

Published as a conference paper at ICLR 2026
TEXT SUMMARIZATION VIA GLOBAL STRUCTURE AWARENESS
Jiaquan Zhang', Chaoning Zhang",, Shuxu Chen', Yibei Liu', Chenghao Li', Qigan Sun! Shuai Yuan', Fachrina Dewi Puspitasari', Dongshen Han', Guoqing Wang', Sung-HH Ho Bae?, Yang Yang'
I 'University of Electronic Science and Technology of China "Kyung Hee University
ABSTRACT
With the explosive growth of information, the volume of long documents has surged, and the cost of processing them continues rise, making text summariza- tion increasingly important. Existing studies primarily focus on model enhance- ments and sentence-level pruning based contextual dependencies and semantic patterns. Although some approaches leverage large language models (LLMs) for text summarization and achieve higher accuracy, they incur substantial computa- tional costs and often overlook global structural modeling. Consequently, summa- rized texts may lose critical logical chains, disrupting coherence and weakening downstream task performance. To address these issues, we propose GloSA-Sun) novel text summarization framework that performs global structural analysis of texts via topological data analysis (TDA), enabling efficient summarization while preserving semantic cores and logical dependencies. Specifically, we construct a semantic-weighte graph from sentence embeddings, where persistent homology identifies core semantics and logical structures, preserved in a "protection pool" as the backbone for summarization. We design a topology-guice where lightweight proxy metrics approximate sentence importance to avoid re- peated high-cost computations, thus preserving structural integrity while improv- ing efficiency. To further enhance long-text processing, we propose a hierarchical strategy that integrates segment-level and global summarization. Experiments multiple datasets demonstrate that GloSA-sum reduces redundancy while preserv- ing semantic and logical integrity, striking a balance between accuracy and effi- ciency, and further benefits LLM downstream tasks by shortening contexts while retaining essential reasoning chains.
iterative strategy,
INTRODUCTION
With the explosive growth of digital information Zheng al. (2025bla). human society generates massive volumes long documents daily. Directly processing such lengthy texts creates effi- ciency and accuracy bottlenecks for downstream NLP tasks. In particular, when LLMs LLMs/Zheg al. b) are required to handle long contexts, redundant information quickly exhausts the con- text window, increases computational cost, and distracts the model from focusing on core content. Therefore, effectively summarizing long texts without losing key information and logical chains has become central challenge in NLP.
Existing methods aim to improve summarization performance from different perspectives. A straightforward and widely adopted approach is sentence-level pruning based local semantic similarity or statistical features. A typical example models MMhhaleaa & Tarau (2004); Erkan & Radev (2004) document a graph of sentence similarities and then applies graph ranking to
** Corresponding Author: Contact: chwonningghaagg 990e 990@gaa1111111
Additional contact:: siaquannhhngg2005@gm.... com, coccsx3228gma1l.. com,
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20240909090118std.. weste. edut...edu.ccm en,
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select salient sentences. This idea is also extended to multi multi-document summarization by incorporat- ing document-level weights to better capture cross-documen importance Wan (2008). Other works formulate sentence selection
optimization problem to balance content coverage and redun- dancy [Clarke & Lapata (2008); Lin & Bilmes (011). These methods are efficient and intuitive, yet their reliance on local similarity shallow features often limits their ability capture global semantic structures and long-range logical dependencies, Some studies focus on improving model architectures enhance summarization. BERTSum Liu & Lapata (2019) employs BERT-based encoders with sentence-level classifiers to strengthen contextual representations, while MatchSum Zhong et al. (2020) reformulates the task as a candidate summary docummet matching problem to ensure holistic consistency. TexShape Kale et al. (2024) combines pretrained language mod- els with a neural module to construct information-theoreete sentence embeddings based on mutual information, enabling controllable summarization while preserving useful content and filtering sen- sitive information. Although these approaches improve representational power and accuracy, they often face scalability and efficiency bottlenecks when applied to very long documents. Another line of research leverages LLMs for summarization Zhang et al. (2024); ) AAzher et al. (2024). Despite their strong performance, LLM-based methods incur substantial inference costs and computational overhead, which limit their applicability in large-scale long-text scenarios.
To address these issues, explore whether it is possible to reduce excessive resource consumption while maintaining summarization quality. TDA [Chhedu & Le (2024); Wasserman (2018) provides global perspective for capturing semantic structures and logical dependencies, enabling the extrac- tion of key reasoning chains and thus preserving the overall skeleton of a document during summa- rization. Based on this insight, we propose a Global Structure-Aware TDA-based Summarization Framework (GloSA-sum). Specifically, we encode sentences into high-dimensional semantic em- beddings and construct a weighted undirected graph where edge weights jointly reflect semantic similarity and positional distance, thereby balancing global semantic relations with local discourse coherence, We then apply persistent homology to track the birth and death of semantic structures across scales, distinguishing short-lived noise from persistent structural features. Zero-dimensional homology (HO) corresponds to semantic clusters that reveal the document's 's core themes, while one-dimensional homology (H1) captures loop structures that reflect cross-paragraph logical de- pendencies. By selecting persistent topological features, we extract a robust semantic and logical backbone that is preserved throughout the summarization process. However, directly applying TDA to long-text summarization introduces efficiency challenges: repeatedly computing persistent ho- mology during iterative summarization computationally prohibitive. Consequently, we propose Protected Pool mechanism, which performs a one-time topological analysis to identify and fix the document's semantic and logical backbone. Persistent homology is computed only once, while subsequent iterations rely on lightweight proxy metrics to evaluate and filter non-critical sentences, achieving efficient iterative summarization. Furthermore, handle ultra-long texts, we design a hierarchical summarization strategy. The document is first partitioned into paragraphs semantic segments, within which local TDA-based summarization is executed in parallel; the locally sum- marized results are then globally integrated and refined with a lightweight topological constraint to ensure cross cross-paragrapy paragraphh logical consistency.
The contributions of this work are follows:
We introduce TDA into text summarization for the first time, offering a novel global struc- tural perspective that explicitly models and preserves both semantic clusters and cross- paragraph logical dependencies.
We propose one-time topological analysis and proxy-based iterative summarization strat- egy, where the Protected Pool mechanism avoids repeated persistent homology computa- tions and achieves an effective balance between efficiency and semantic integrity.
We design a hierarchical summarization framework that enables coordinated local summa- rization and global integration, thereby significantly enhancing scalability and robustness in long-text scenarios.
Extensive experiments show that GloSA-sum outperforms strong baselines in summariza- tion while also enhancing LLM downstream tasks by reducing context length and preserv- ing essential reasoning chains.
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2
RELATED WORK
2.1 TEXT SUMMARIZATION METHOD
Text summarization methods can be broadly categorized into two lines: model-level improvements and sentence-level pruning. which exploit contextual dependencies and semantic patterns. Early text compression and summarization approaches primarily relied on sentence-level pruning, treating sentences as atomic units be selected or discarded based estimated importance. Graph-based methods such as TextRank Mihalcea & Tarau (2004) and LexRank EErkan & Radev (2004) construct sentence similarity graphs and apply centrality-baut -based ranking to identify core sentences, demon- strating the effectiveness of unsupervised approaches across diverse corpora, but offering limited modeling of global discourse structure and cross- poossppargggph dependencies. To alleviate these limita- tions, integer linear programming frameworks Clarke & Lapata (2008) formulate sentence selection as an optimization problem that balances content coverage and redundancy. More recent unsuper- vised methods further extend sentence-level pruning. RankSum [Joshi et al. (2022) fuses multiple ranking signals to estimate sentence importance without annotated data, while Jie et al. (2024) in- troduces a differentiable knapsack module to enable learnable length control in extractive summa- rization. Despite their efficiency and simplicity, sentence-level pruning methods often fail to capture fine-grained semantic coherence and global logical flow due their coarse granularity. From the model-level perspective, Gu et al.] (2022) employs memory networks to iteratively track selected content and reduce redundancy, and Goyal et al. (2019) combines recurrent neural networks with arithmetic coding for lossless semantic compression. With the emergence of large language models, recent work explores their potential for lossless semantic compression, including fine-tuning LLMs toward the Shannon limit Mittu et al. (2024) and leveraging next-token predictive distributions for entropy coding Mao al. (2025).
2.2 TOPOLOGICAL DATA ANALYSIS IN NLP
TDA offers a systematic framework to capture global structures in nigh-dimensional and complex data. Wu et al. (2022) integrates persistent homology features over embeddings into deep learn- ing models to detect multiple types of textual contradictions. Their results show that topological features significantly outperform standard baselines in contradiction detection. Recent research fur- ther extends TDA to interpretability and discourse-level analysis. For example, [Proskurina et al.) (2023) applies TDA to linguistic acceptability judgments. By designing new topological features such as chordality and matching number on attention graphs, they achieve performance gains over fine-tuning baselines in both English and Russian, and further reveal correspondences between spe- cific attention heads and linguistic phenomena. In parallel, Jain et al. (2024) investigates discourse coherence through TDA in Beyond Words and shows that topological signatures capture semantic flow and logical structure within documents. Despite these advances, existing works focus primarily on interpretability or classification tasks, while the systematic integration of TDA into large-scale text compression and summarization frameworks remains underexplored. Our work addresses this gap by leveraging persistent homology Edelsbrunner et al. (2008) to identify and preserve robust topological features for summarization, thereby ensuring both semantic coherence and logical con- sistency in the output.
3 METHODOLOGY
3.1 PRELIMINARY KNOWLEDGE OF TDA AND HOMOLOGY GROUPS
TDA is a framework originating from algebraic topology that captures the intrinsic structural pat- terns of complex data. It represents a dataset as collection of points a high-dimensional space (a point cloud) and examines how these points are connected. To extract meaningful structures, TDA employs persistent homology, which tracks how topological features emerge and disappear as the observation scale changes. Intuitively, this process is akin to gradually increasing the resolution for observing data, much like continuously zooming in and out. Features that vanish quickly are usually seen noise, while those that persist across wide range of scales are regarded as meaningful and robust patterns. Through this multi-scabe view, TDA can reveal fundamental elements of structure, such connected clusters, loops, and higner-dimensional cavities that are otherwise difficult to cap-
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Perdedence Diagrant
Non Protected Pool
Output
Affroe RerAAe The peli oport
Babhediing
Comitratiion
Protected Pool
She wAp Zhngg'
Daop FNn viy
Mudia dhe
TootLenghh
Compraaaton
Good
pauarn eNy swakdn,, lus pritas GIBAy pRIAAS
Figure I: Overall of GloSA-sum
ture. Formally, these topological features are characterized by homology groups, which summarize the structure of simplicial complex at different dimensions. In essence, homology groups provide the algebraic foundation of TDA by formally characterizing topological features such as connected components and cycles, while TDA operationalizes these concepts through persistent homology to analyze complex datasets across multiple scales. The k-th homology group is defined as
ker Ōj im 1m+11
H₂(K)=
(1)
where θ denotes the boundary operator mapping k-chains to (k- - 1-hchainss and H₂ intuitively captures k-dimensional "holes" that cannot be expressed as the boundary of higher-dimensional ob- jects. In particular, Ho (zero-dimensional homology) corresponds to connected components, which in the context of text analysis can be interpreted as core semantic themes or independent clusters of meaning that form the backbone of the discourse. Meanwhile, H1 (one-dimensional homology) corresponds to non-trivial loops or cycles, which often manifest in text as logical loops recurrent argumentative structures that link different parts of the document. Although higher-order homology groups such as H2 describe voids or cavities in data, They are less relevant for sequence-like data such text. Therefore, in this work, primarily focus on Ho and H1, as they directly correspond to the preservation of semantic themes and logical structures, which are crucial for maintaining coherence in compressed text representations.
3.2 OVERVIEW OF GLOSA-SUM
As shown in Figure D GloSA-sum global structure-aware summarization framework. It per- forms one-time persistent homology analysis extract core semantic clusters (H0) and logical cycles (HI), preserved in Protected Pool as the document backbone. Guided by lightweight proxy metrics and hierarchical compression strategy, the method progressively removes redun- dancy while ensuring semantic fidelity and logical consistency for long texts.
3.3 SEMANTIC GRAPH CONSTRUCTION
To enable the application of TDA, we first transform the input document D into a representation suitable for topological analysis. Each sentence is then encoded using pretrained sentence encoder into a semantic embedding e; To climinate scale discrepancies across sentences, we apply normal- ization all e;, enabling stable similarity computations. Based the sentence embeddings, construct a weighted undirected graph:
G (V. E)
where the node set V corresponds to the sentence set S, and the edge set encodes the semantic and sequential relations between sentences. To capture global semantic relations while maintaining graph sparsity, we adopt a mutual k-nearest neighbor strategy Baoli et al. (2004) with an adaptively determined neighborhood size. The value of k grows logarithmically with the document length, ensuring that shorter texts are not over-connected while longer texts preserve sufficient structural connectivity. An undirected edge (i.j) E established if and only if sentence 8; lies within the adaptive neighborhood of sj and vice versa. Each edge is further assigned hybrid weight way:
Wij = a dem + a) eexp
(3)
T

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where 4:3" = cos(e,, eÿ) denotes the semantic distance derived from cosine similarity between sentence embeddingg, and j represents the absolute positional distance between two sentences in the original sequence. The coefficient a E [0. 1] serves as a fusion parameter that balances the contributions of semantic similarity and sequential adjacency. At the same time, the temporal decay factor т controls the sensitivity of the sequential proximity term, ensuring that adjacent sentences exert stronger influence than distant ones. The wij scheme encodes both semantic proximity and sequential coherence, thus preserving argumentative continuity, Notably, the semantic distance dij also retained as the primary metric for subsequent TDA.
3.4 PROTECTED POOL INITIALIZATION FROM TOPOLOGICAL ANALYSIS
Unlike prior iterative graph-based summarization methods, GloSA-sum performs persistent homol- ogy computation only once at the beginning, to identify the document's semantic and logical back- bone. This one-time topological analysis permanently fixes the global structure, thereby avoiding repeated high-cost TDA computations and ensuring scalability to long documents. Concretely, we compute persistent homology over the point cloud "1,....,,,, where each sentence embedding is treated as a discrete point a high-dimensional semantic space. To approximate the underlying sim- plicial complex efficiently, we employ the Lazy Witness Complex |rafat al. (2019) with fixed proportion of landmark points. Persistent homology is computed up to dimension one, yielding persistence diagrams (00) and (11) corresponding to Hu and H1, respectively. Each topological feature, whether a connected component or cycle, is quantified by its persistence length:
- b,
(4)
where b and d denote the birth and death scales within the filtration. Then, we initialize the Protected Pool P to preserve the document's s essential structural backbone permanently. The Protected Pool consists of complementary components derived from different homological dimensions:
Core themes (Ho): We select the top-K longest-living Ho features (i.e., the connected components with the greatest persistence), and collect the sentences associated with their landmark points into Pho. This guarantees that the primary semantic clusters of the docu- ment are retained while keeping the pool size controllable.
Critical logical cycles (H1): We select the top-M most persistent H1 cycles and aggregate all sentences participating in these cycles into PH1- This ensures that essential logical dependencies and discourse-level cycles are preserved.
Finally, the Protected Pool is defined as:
P Pho U PHr
(5)
which jointly safeguards the document's 's semantic themes and logical structures throughout the com- pression process.
3.5 TOPOL.OGY-GUIDED ITERATIVE COMPRESSION
Since the Protected Pool has already secured the global semantic backbone through single persis- tent homology analysis, the subsequent compression process no longer requires recomputing TDA. Instead, redundant sentences are progressively removed using lightweight proxy metrics that ap- proximate topological importance. This design preserves the global semantic and logical structure identified by the Protected Pool while avoiding the prohibitive cost repeated persistent homology computations.
Specifically, each iteration, every sentence 8; E P outside the Protected Pool is assigned a composite deletion priority score that jointly considers topological connectivity and task relevance. Sentences with lower scores are deleted earlier, ensuring that structurally important sentences remain protected. This scoring mechanism balances structural preservation with adaptability to downstream queries, making the compression process both computationally efficient and faithful to the global semantic structure.
Score(s:)
A TopoSSore(s:) + A): (TssSSooees:));
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where À E [0, 1] controls the relative weight of the two components.
TopoScore Computation. The topological proxy score TopoScoro(s:) quantifies the structural im- portance of a sentence with respect to the semantic backbone captured by the Protected Pool. We adopt Dijkstra's 's algorithm to obtain the shortest-palte length SPL(s,, sj) from node 8; to each pro- tected node sj P. The semantic graph G' is constructed via --nearest-neighhor strategy, resulting in a sparse topology that allows fast shortest-pane path calculations even for long documents. The score computed as:
TopoScore(s)) = Σ SPL(s;; 83),
PJEP
Because of the negative sign, TopoScore(ss) values closer to zero indicate stronger connectivity to the structural skeleton (thus higher importance), whereas more negative values indicate weaker connectivity. For nodes that are not connected to any protected node (i.e., SPI.(s,, 8j) = co for all s,), we assign a large negative penalty to TopoScore(ss). This ensures that semantically peripheral and structurally isolated sentences are removed early in the process, consistent with the overall design objective of preserving the document's 's core logical structure. In the rare case of ties, we adopt the original sentence index as a secondary criterion and preferentially retain later sentences. Since TopoScore already captures structural importance, this tie- tre-breaking mechanism prevents spurious preference toward introductory sentences and helps eliminate potentially redundant lead material without compromising global coherence.
TaskScore Computation. When a downstream query is available, an additional task relevance score TaskScore s;) is incorporated to bias compression toward sentences more relevant to the query. This is computed as a weighted combination of semantic similarity and classical retrieval metrics:
TaskScore(s; = (o, 02y) + (1 - 3002MM25 9)
where e,, is the embedding of the query and 3 E [0, 1] balances the two terms. Here, BM25 is well- established retrieval function that scores keyword relevance by combining term frequency, inverse document freeuuecy, and length normalization, thereby complementing the semantic similarity term with lcxical-level matching.
At each iteration, the sentence with the lowest Score(s;) is deleted from both the sentence set and the graph G. The node corresponding to the deleted sentence, along with all its incident edges, is removed, and the graph is updated accordingly. Importantly, is required during the iterative process, since the Protected Pool P has already secured the global semantic backbone. This procedure is repeated until the compressed text reaches the predefined target compression ratio.
additional TDA computation
3.6 HIERARCHICAL COMPRESSION STRATEGY
To further enhance scalability while preserving both local and global semantic structures, we design hierarchical compression strategy. Before any graph construction, the document is first segmented into sentences using the widely adopted NLTK sentence boundary. We intentionally operate at the sentence level, as finer- grained units (e.g., clauses) would drastically increase the number of nodes and dramatically raise the computational burden of persistent homology. For hierarchical decomposition, the input docu- ment D is first divided into T segments {C1, ......, Cr either based on natural boundaries such as chapters or by fixed-lena ixed-length partitioning. Each segment then processed independently and in parallel by applying the procedures described in Sections t. resulting in set of locally com- This parallelization significantly reduces computational cost and allows the method to scale to long-form documents without sacrificing efficiency. After local compression, the compressed segments are concatenated in their original order to form an interme- diate summary document D', which preserves the global discourse flow. A final global compression stage is then applied to D' to remove cross-segment redundancy and enforce document- coher- ence. This two-level design ensures that both intra-segment semantic integrity and inter-segment logical structure are jointly preserved in the final compressed summary, enabling GloSA-sum to maintain high accuracy even under extreme compression ratios.
ee tool, which provides a consistent
and
pressed segments {C), Ch,...,C%,,

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4 EXPERIMENT
In this section, we conduct extensive experiments to evaluate the effectiveness of our proposed model. Specifically, we aim address the following research questions:
Q1: Does GloSA-sum demonstrate strong performance on text summarization?
Q2: How competitive is GloSA-sum in terms of computational efficiency compared with existing approaches?
Q3: Can GloSA-sum preserve logical coherence and readability while achieving high com- pression rates?
Q4: Are the individual components of GloSA-sum effective and necessary?
Q5: Are the text summarizations produced by GloSA-sum equally effective when applied to LLMs downstream tasks?
Q6: How do different hyperparameter settings affect model performance, and what config- urations are most suitable for Assm?
4.1 IMPLEMENTATION DETAILS
We evaluate GloSA-sum using ROUGE, BERTScore, QAFactEval, and human evaluation metrics. ROUGE evaluates summaries from word-level coverage global structure. Specifically, ROUGE-1 measures unigram overlap to capture basic content coverage, ROUGE-2 focuses on bigram overlap to reflect local fluency, and ROUGE-L relies on the longest common subsequence assess global structural similarity. BERTScore uses pretrained language models to measure semantic similarity between system and reference summaries. QAFactEval checks factual consistency by generating questions from the reference and verifying answers from the summary. The detailed definitions are provided in the Appendix A. To improve the reproducibility the experiment, the experimental details and parameter settings provided in the Appendix A.2
4.2 BASELINE MODELS
To comprchensively evaluate GloSA-sum. compare it with ten baselines that reflect two major search directions in text compression: sentence-level pruning and model-imp modellimppoveemett approaches.
The baseline models include TextRank Mihalceaa & Tarau 2004), LexRank Erkan & Radev 2004).
Lead-3, BERTSum Liu & Lapata 2019). MatchSum Zhong et al. (2020), MemSum Gu et al. 2022
BART Lewis al. PEGASUS Zhang al. (2020), BIGBIRD Zaheer et al. (2020) and DANCER
Gidiotis & Tsoumakas 2020)) with details provided in the Appendix A.3
4.3 DATASETS
We evaluate GloSA-sum on five long-text datasets: GovReport Huang et al. (2021) 1, ArXiv Clement al. (2019). PubMed Jin et al. (2019), and CNN//ailyMail (CNN/DM) See al. (2017) from diverse domains, each posing distinct structural challenges for compression. The specific datasets description shown in the Appendix A.4
4.4 PERFORMANCE EVALUATION
Answer Q1: As shown in Table GloSA-sum achieves clear improvements on ROUGE-L. Specifically, on ArXiv, it surpasses BART by +2.14, and on PubMed, it achieves the highest score of 44.5, exceeding MemSum by +0.17 and BigBird by +2.17. These results highlight our enhanced ability to preserve logical structure in long-document scenarios. For ROUGE-2, GloSA-sum im- proves over Bir by +1.19 on GovReport, achieves 20.0 on ArXiv, outperforms BART by +3.45, surpasses BART by +3.13, and demonstrates superior capability in capturing fine-grained depen- dencies. Regarding ROUGE-1, GloSA-sun reaches 47.5 on ArXiv, clearly surpassing BART and PEGASUS, which shows its strength in capturing essential content coverage in scientific texts. On PubMed, it further achieves 49.5, highlighting its ability to retain key biomedical information. Rel- ative to pretrained abstractive models such as BART and PEGASUS, which perform well short

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texts but often lose global coherence on long documents, GloSA-sum achieves substantial gain of +2.14 ROUGE-L on ArXiv, showing a stronger ability to maintain logical flow in scientific texts. Compared to long-text optimized models such as BigBird and DANCER, which process extended contexts but struggle with fine-grained dependencies, GloSA-sum delivers higher scores, including +1.19 ROUGE-2 on GovReport and +2.17 ROUGE-L on PubMed. We report the additional result and analysis on the BERTScore and QAFactEval metrics in the Appendix A.5
Table 1: Automatic evaluation results (ROUGE scores) across datasets.
CNN/DMI
GovReport
ArXiv
PubMed
Method
R-1
R-2
R-L
R-1
R-2
R-L
R-1
R-2
R-L
R-1
R-2
R-L
TextRank
33.10
12.20
29.70
53.19
23.12
49.86
33.10
8.80
30.05
38.66
15.87
34.53
Lead-3
39.94
17.46
36.06
50.94
19.53
48.45
25.53
5.98
15.22
26.38
8.73
16.60
BERTSum
41.63
19.44
40.13
47.10
18,20
20.80
49.10
24.30
25.70
MatchSum
44.41
20.86
40.55
41.21
14.91
36.75
MemSum
49.14
22.92
44.33
48.23
20.17
42.31
49.14
22.92
44,33
BART
44.16
21.28
40.09
52.24
22.09
49.99
43.84
16.55
39.86
44.61
19.37
41.01
PEGASUS
44.17
21.47
41.11
54,29
20.80
51.35
43.27
19.70
34,79
44.70
17.27
25.80
BigBird
43.83
21.11
40.74
60.64
24.81
50.01
46.63
19.02
41.77
46.32
20.65
42.33
DANCER
45.01
17.60
40,56
46.34
19.97
42.42
GloSA-sum (Ours)
44.05
21.22
41.06
55,50
26.00
51.00
47.50
20.00
42,00
49.50
22.50
44.50
Overall, these results demonstrate that introducing global structure awareness is key to achieving consistent improvements across metrics and datasets, particularly long-document compression, where both local dependencies and global backbones must be preserved.
We analyze the computational efficiency of different summarization methods in terms of time and memory complexity well parallelizability. Here, N denotes the input length, L the output length, the hidden size, K the number of candidates, and M the number of iterations. Table 2 presents the efficiency comparison across different summarization methods. Extractive ap- proaches such as TextRank and Lead-3 are lightweight and highly parallelizable, serving as effi- ciency baselines but lacking the ability to model complex structures in long texts. BERTSum, BART, and PEGASUS incur a quadratic complexity of ( due to attention, and BART/PEGASUS fur- ther suffer from autoregressive decoding, leading to 10-20x slower runtime than TextRank. Long- document optimizers such as BigBird and DANCER reduce the encoder complexity to nearly linear time through sparse attention or segmentation, yet still require 7-12x runtime. MatchSum and MemSum face additional inefficiency due to candidate explosion or reinforcement Marning-basee sequential selection, which limits parallelism. In contrast, GloSA-sum performs one-time topo- logical analysis to construct protected pool, after which compression proceeds through lightweight proxy metrics with a per-iteration cost of approximately O(Me e logn). With its hierarchical design, GloSA-sum enables both intra-and inter-tegment parallelization and scales nearly linearly to very long documents. In practice, it runs only 6-8x x slower than TextRank, substantially faster than gen- erative models, and competitive with BigBird and DANCER. These results confirm that GloSA-sum achieves a favorable balance between accuracy and efficiency, making it particularly suitable for long-document summarization where both scalability and structural fidelity are essential.
Answer to Q2:
Table 2: Theoretical efficiency comparison of summarization methods.
Method
Complexity (Time / Memory)
Parallclizability
TextRank
Graph O(a²), iteration O(E I)
Graph iteration parallelizable
LEAD-3
Oin) Encoding O(
Fully parallelizable
BERTSum
Encoder parallelizable
MatchSum
Encoding O(N2) candidates K- K-O(m²)
Candidate-lewe parallelizable
McmSum
O(N) x selection steps
Encoder parallelizable, sequential selection
BART
Encoding O(N*), devoding O(Ld)
Encoder purallel, decoder sequential
PEGASUS
Encoding O(N2), decoding O(L)
Encoder parallel, decoder sequential
BigBird
Spurse attention O(N)
Encoder parallelizable
DANCER
Segmentation ( logn), global merge O(k)
Segment- parallel, merge sequential
GloSA-sum (ours)
Graph O(n log ni (one-time), iteration OLM log m)
Matra-iiter-seemmen parallelizable
Answer to Q3: Table 4 rreports human evaluation results on coherence, informativeness, and con-
ciseness. Traditional extractive methods such as TextRank and Lead-3 obtain the lowest average
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Table 3: Relative runtime of different methods compared TextRank.
Method
Relative to TextRank
TextRank
1x
LEAD-3
0.17-0.33x
BERTSum
2-3.3x
MatchSum
2.7-4x
MemSum
4-5x
BART
10-15x
PEGASUS
10-20x
BigBird
8-12x
DANCER
7-10x
GloSA Slom (ours)
6-8x
scores, reflecting their limitations in capturing discourse structure and ensuring content coverage. BERTSum, MatchSum, and MemSum perform better, with MemSum achieving the highest among them, but still lag behind generative models in conciseness and overall readability. BART and PE- GASUS further improve informativeness and conciseness, while long-document optimizers such as BigBird and DANCER reach higher averages by balancing coherence and completeness. In contrast, proposed GloSA-sum achieves the best overall performance, with notable gains in coherence and informativeness while also maintaining strong conciseness. These results confirm that incorporating global structure awareness enables GloSA-sum to better preserve discourse coherence and infor- mation completeness. We include a comprehensive comparison against several strong LLM-bbsed summarization baselines in the Appendix A.6
Table 4: Human evaluation results coherence, informativeness, and conciseness (1-5 scale).
Method
Coherence Informativeness
Conciseness
Avg. Score
TextRank
3,6
2.8
3.2
3.20
LEAD-3
3.0
3.2
3.4
3.20
BERTSum
3.5
3.6
3.3
3.47
MatchSum
3.6
3.8
3.5
3.63
MemSum
3.7
3.9
3.6
3.73
BART
3.8
4.0
4.0
3.93
PEGASUS
3.9
4.1
4.1
4.03
BigBird
4.1
4.2
4.0
4.10
DANCER
4.2
4.1
4.0
4.10
GloSA-sum (ours)
4.4
4.3
4.2
4.30
To further ensure that the improvements of GloSA-sum not due random variation, duct a paired bootstrap significance test. For each dataset, we perform 1,000 bootstrap resamples and compute the mean difference in ROUGE-L between GloSA-sum and the strongest baseline, DANCER. Across all datasets, including CNN/DM, GovReport, ArXiv, and PubMed, the resulting p-values are consistently below 0.01, indicating strong statistical significance. These results confirm that the gains achieved by GloSA-sun are both reliable and robust rather than arising from stochastic fluctuations.
Furthermore, common concern is whether the protected pool P behaves similarly to positional heuristics such as Lead-3. However, TDA operates on high-dimensional semantic geometry rather than surface-level positional cues. To verify this. we analyze the sentence- sentence-position distribution of protected sentences on GovReport in Appendix A.10
4.5 ABLATION EXPERIMENT
Answer to Q4: We conduct comprehensive ablation study to examine the contribution of each major component in the GloSA-sum framework. As shown in Table removing the protected pool leads the most severe degradation, with ROUGE scores dropping by more than 5 points,

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firming that the TDA-identified backbone is essential for preserving global structure. Replacing the topological proxy score with random selection also results a clear decline of around points, indi- cating that TopoScore provides meaningful guidance during iterative compression. To further isolate the role of topological features, we compare using only Hn clusters with the full model that incor- porates both Hg and H1- The gains from including H1 cycles, particularly in ROUGE-L, show that persistent one-dimensional structures capture cross-paragraph logical dependencies beyond simple thematic grouping. We also evaluate whether the global backbone can be constructed without TDA by replacing persistent homology with Louvain community detection. The Louvain-basee variant performs substantially worse, indicating that multi-scale topological persistence provides a more re- liable structural signal than conventional graph clustering. Finally, we further verify the effect of the hierarchical strategy on short documents by comparing variants on the CNN/DM dataset. The differ- ences between hierarchical and non-hierarchice versions are negligible (j0.2 ROUGE), confirming that the strategy is safe for shorter texts while being indispensable for long-documenn processing on GovReport, where removing it makes the model unable run. Collectively, these results demon- strate that the protected pool, TopoScore, topological features (Hn and H1). and hierarchical design form complementary set of components, each contributing to the structural fidelity, stability, and scalability of GloSA-sum
Table 5: Ablation experiments on the GovReport dataset and effect of hierarchical compression on short documents (CNN/DM).
Dataset
Ablation Variant
ROUGE-1 ROUGE-2
ROUGE-L
GloSA-sum (ours)
55.5
26.0
51.0
w/o Protected Pool w/o TopoScore (Random)
50.2
22.1
45,8
52.4
23.3
47.0
GovReport
w/o H1 Cycle (HO only)
54.1
24.8
49.8
Louvain Communities w/o Hierarchical
52.9
24.1
48.3
Hierarchical (Full) w/o Hierarchical
44.1
21.2
41.1
CNN/DM
44.0
21.1
40.9
Beyond the core ablations, further examine the robustness of GloSA-sum with respect dif- is intentional: it provides a ferent sentence encoders. Our choice of all-mpnet-base isolate the contribution of TDA lightweight and context-local representation that allows without conflating with the global reasoning implicitly embedded in larger contextual en- coders. This ensures that the observed performance gains indeed arise from the topological mech- anism rather than from the encoder's s own long-range capacity. To assess the potential perfor- mance ceiling, we additionally evaluate GloSA-sun with stronger embedding models, including text-embedding - sma 1 large, with results shown in Appendix A.9
CONCLUSION
We present GloSA-sum, global structure- summarization framework that integrates TDA to preserve semantic clusters and logical dependencies in long texts explicitly. Through a one-time persistent homology analysis and a Protected Pool mechanism, GloSA-sum secures the semantic backbone while avoiding repeated high-cost computations. Combined with a topology-guides iter- ative strategy and hierarchical design, the method achieves both scalability and structural fidelity. Experiments across multiple long-text datasets demonstrate consistent improvements over strong baselines in ROUGE and human evaluation, with notable efficiency advantages. Furthermore, eval- uations on downstream LLM tasks show that GloS S-sm effectively reduces context length while retaining essential reasoning chains, making it broadly beneficial beyond summarization.
ACKNOWLEDGMENTS
This work was partially supported by the National Natural Science Foundation of China under grants 62572104, and 62220106008.
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A APPENDIX A: EXPERIMENTS
A.1 EVALUATION METRICS
We evaluate GloSA-sum using both ROUGE and human evaluation metrics. ROUGE (Recall- Oriented Understudy for Gisting Evaluation) Chin- Yew (2004) is the most widely adopted metric for text summarization and compression. We report Precision, Recall, and F1 scores.
ROUGE-1: Measures unigram (word-level) overlap between system output and reference, which captures basic content coverage and indicates whether key information units are retained.
Measures bigram (two-word sequence) overlap, which evaluates local fluency and short-range dependencies. It is more strict than ROUGE-1, reflecting sentence-level quality.
ROUGE-2:
ROUGE-L:
Based on the Longest Common Subsequence (LCS), this metric captures global sequence similarity and reflects whether overall sentence structure and order preserved.
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Since automatic metrics cannot fully reflect linguistic quality, further conduct human evaluation. Each dimension is rated on a 5- 5-point Likert scale (1 = poor, 5 = excellent). Three graduate-leve an- notators with backgrounds in natural language processing computational linguistics participated in the evaluation, all possessing sufficient English proficiency for academic-level text reading. For each dataset, 50 documents were randomly sampled, and the corresponding system outputs were independently scored by the three annotators. To ensure reliability, Cohen's 's K was employed to measure inter-annotator agreement, yielding an overall value of 0.71, which indicates substantial consistency. The evaluation was conducted in blind setting, where annotators were not informed of system identities avoid subjective bias.
Coherence: Evaluates whether the compressed text preserves logical flow and semantic consistency, where high scores mean no abrupt jumps or incoherent transitions.
Informativeness: Assesses whether the essential information, arguments, and key facts from the original text are preserved, with high scores indicating comprehensive content coverage.
Conciseness:
Measures whether redundant or repetitive content is removed, where high scores reflect compact yet readable summaries.
A.2 INPLEMENTATION DETAILS
All experiments are conducted on a single NVIDIA RTX 4090 GPU (24GB) with an Intel Xeon Gold 6330 CPU (16 cores) and 256GB RAM. All experiments are run in a single-GPU setting, with a batch size of (document-level processing) and maximum document length of 8, 8,192 tokens.
To ensure reproducibility, we adopt unified default configurations across all experiments. For data preprocessing, we employ the Sentence TentenceTrrasffrman model all-mpnet-bag baseet- as the encoder, pro- ducing -08-dimessional sentence embeddings that are L2- 1-2normalized before similarity computation and graph construction. The document graph is built using mutual k-nearest neighbor strategy, where grows logarithmically with the number of sentences and bounded between and 20. Similarity search is implemented with FAISS using the HNSW index (with M 32). Edge weights combine semantic distance and positional decay, with default parameters a = 0.5 and
10.
For topological data analysis, we adopt the Lazy Witness Complex with maximum edge length of 3, and compute homology up to dimension 1 (i.e., Hu and H1) over the coefficient field Zz. The importance of each sentence is further quantified by a TopoScore that integrates persistence-basee gain and bridge centrality, where the default weights are 0.7 and 0.3, and persistence gain assigns weight 1.0 to Ho features and 2.0 to H1 features. All experiments
conducted with fixed random seed of 42 for NumPy, PyToorc,, and FAISS. For interpretability and reproducibility. barcodes and persistence diagrams are saved every 10 epochs during training and evaluation.
A.3 BASELINE MODELS
TextRank Mihalcea & Tarau (2044) is an unsupervised graph-based method that builds a sentence similarity graph and applies PageRank to select important sentences.
LexRank Erkan & Radev (2004) measures sentence salience through eigenvector centrality within a similarity graph.
Lead-3 is heuristic extractive summarization method that selects the first three sentences of a document as the summary.
BERTSum Liu & Lapata| (2019) fine-tunes the BERT encoder in a supervised framework to perform extractive summarization.
MatchSum Zhong et al. (2020) formulates summarization as candidate matching problem and achieves strong performance among extractive models.
MemSum Gu et al. (022) is an extractive summarization method that formulates the task multi- step Markov decision process, using reinforcement learning to iteratively select sentences with awareness of local content, global context, and extraction history, thereby producing concise and high-quality summaries.
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BART et al. combines bidirectional encoding with autoregressive decoding, enabling fluent abstractive summarization.
PEGASUS Zhang et al. (2200) is pre-trained abstractive summarization model that lever-
ages a gap-sentence generation objective, masking salient sentences during pre-training to align closely with the summarization task.
BIGBIRD Zaheer et al. 2020 utilizes sparse attention mechanisms to handle long docu-
ments in summarization tasks efficiently.
DANCER Gidiotis & Tsoumakas (2020) integrates dynamic aligmment with contrastive
learning, thereby improving semantic consistency in generated summaries.
A.4 DATASETS
GovReport Huang et al. 2 is a large-scale dataset of government reports containing nearly 9,500 long documents, which require models to preserve structural coherence across ultra-long contexts.
ArXiv Clement et (2019) consists of about 5,000 scientific papers, challenging models to maintain complex logical chains and argumentative flow.
DebateSum Roush & Balaji (020)) includes roughly 1,500 debate transcripts, where the key difficulty lies in capturing argumentative structures and preserving central claims.
Pib et al. (2019) (long-answer) contains around 2,000 biomedical question-answer pairs with long textual answers, emphasizing the need for factual accuracy and consistent referential grounding.
CNNi (CNN/DM) See et al. (0177) is large-scale news summarization dataset containing long news articles paired with concise human-written highlights.
A.5 PERFORMANCE EVALUATION
Answer to Q1: We further verify the performance of GloSA-sum the BERTScore and QAFactE- val metrics. The specific results are shown in Table
BERTScore goes beyond surface word overlap by leveraging contextual embeddings from pretrained language models such as BERT. Instead of only matching tokens, aligns words in the candidate and reference summaries in the embedding space and computes precision, recall, and Fl based on cosine similarity. This allows to capture subtle semantic equiv- alence even when different surface forms are used, making it more robust indicator of semantic preservation.
QAFactEval focuses on factual consistency. It first generates a set of questions from the source or reference text that cover key information, then attempts to answer these questions summary. The predicted answers compared against ground-
using the wystem-generaae truth answers to determine whether the summary retains and conveys the essential facts correctly. In this way, QAFactEval provides direct measure of whether summary is not only fluent and coherent, but also factually reliable.
The evaluation on BERTScore and QAFactEval demonstrates that GloSA-sum consistently pre- serves both semantic equivalence and factual accuracy across domains and document lengths. Com- pared with extractive basclines such as TextRank, which achieves only 0.73/0.58 on CNN/DM, GloSA-sum reaches 0.88/0.78, showing clear advantage capturing deeper semantic meaning rather than surface token overlap. Against strong abstractive models like BART and PEGASUS, which obtain around 0.79-0.83 on ArXiv and PubMed. GloSA-sum maintains higher factual consis- tency, reaching 0.83/0.75 on ArXiv and 0.86/0.76 76 PubMed. The latter is particularly noteworthy, as GloSA-sum surpasses all baselines this biomedical domain where factual reliability is essen- tial. Overall, these results confirm that GloSA-sum effectively balances the global logical structure of long texts with the fidelity local details, making especially robust in information-denn and fact-sensitive scenarios.
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Table 6: Evaluation results with BERTScore and QAFactEval across datasets.
Method
CNN/DM
GovReport
ArXiv
PubMed
BERTScore
QAFactEvval
QAFaciEval
QAFaciFival
QAFactEval
TextRank
0.73
0.58
0.91
0.81
0.73
0.58
0.80
0.70
LEAD-3
0.79
BERTSum
0.87
0.77
0.80
0.70
0.85
0.75
MatchSum
0.78
0.82
MemSam
0.88
0.78
0.83
0.75
0.85
0.75
PEGASUS
0,89
0.79
0.91
0.81
0.80
0.72
0.83
0.72
BIGBIRD
0.87
0.78
0.92
0.82
0.82
0.74
0.85
DANCER
0.81
0.73
0.85
0.75
GloSA-sum (ours)
0.78
0.81
0.75
A.6 HUMAN EVALUATION COMPARED TO LLMS-BASED BASELINE MODELS
We further compare against LLM baselines commonly used in text summarization research, as shown in Table 7
GPT-4 et al. (2023) Prompt-based Summarization: Zero-/few-shot prompting with
GPT-4, a strong commercial baseline.
Claude-3 Anthropic (024) Summarization: Strong long-context summarization with high alignment.
Fine-tuned ILLaMA-233 Touvron al. (2023) vised on summarization datasets.
Summarizer: Open-source models super-
RAG-enhanced Summarization Lewis et 2020) Retriever-augmentee LLMS to improve
long-document handling and factual consistency.
Compared with these LLM baselines, GloSA-sum achieves the same highest average score 4.30 as GPT-4 while surpassing it in coherence, scoring 4.4 compared to 4.3. This highlights the advantage of explicitly modeling global semantic and logical structures, which enables our method to maintain discourse flow and structural integrity that even oate-of-thhearr LLMs struggle with. At the same time, A-sum attains balanced performance across coherence, informativeness, and conciseness, offering more efficient and controllable alternative resource-intensive LLM summarization.
Table 7: Human evaluation results on LLM-based baselines and GloSA-sum
Method
Coherence
Informativeness Conciseness
Avg. Score
GPT-4 Prompt-Sum
4.3
4.4
4,2
4.30
Claude-3 Sum
4.2
4.3
4.1
4.20
Fine-tuned LLaMA
4.0
4.1
4.0
4.03
RAG LLM Sum
4.1
4.2
4.1
4.13
GloSA-sum (ours)
4.4
4.3
4.2
4.30
Moreover, report ROUGE-1/2/L, BeRTScore, and QAFactEval across all four datasets mea- sure fluency, semantic similarity, and factual consistency. As shown in Table S GloSA-sum con- sistently outperforms strong LLM summarization baselines across all four datasets. The gains are substantial in both ROUGE-L and BERTScore, demonstrating superior global discourse preserva- tion and richer semantic fidelity. Notably, GloSA-sum achieves the highest QAFactEval scores, indicating stronger factual consistency than modern LLMs, which remain prone to hallucination in fact-dense scientific and governmental documents. On ultra-long datasets such as GovReport, LLM performance degrades significantly due to context-length and reasoning limitations, while GloSA- sum retains stable and qugh-tuality summaries thanks to its topology-guidee structural backbone. These results collectively highlight that GloSA-sum is not only computationally efficient but also highly competitive with tfate-of-the-a LLMs, particularly in scenarios where global structure re- tention, factual accuracy, and long-range logical coherence essential.
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Table 8: Comparison with state-of-the-art LLM summarization baselines on four datasets.
Dataset
Encoder
R-1
R-2
R-L
BERTScore
QAFactEval
GPT-4 Prompt-Sum
37.91
15,42
34.83
0.858
0.762
Claude-3 Sum
38.66
16.01
35.24
0.863
0.771
CNN/DM
FI-LLLMA-3 8B
39.14
17.94
36.10
0.870
0.776
GloSA-sum
44.05
21.22
41.06
0.880
0.780
GPT-4 Prompt-Sum
33.21
12.67
30.14
0.847
0.785
Claude-3 Sum
34.88
13.54
31.66
0.855
0.793
GovReport
FT-LLaMA-3 8B
23.01
8.72
21.87
0.803
0.731
GloSA-sum
55.50
26.00
51.00
0.910
0.810
GPT-4 Prompt-Sum
36.86
14.92
33.05
0,801
0.705
Claude-3 Sum
39.74
16.22
35.44
0.812
0.721
ArXiv
FI-L-LaMA-3 8B
43.61
17.41
38.27
0.821
0.734
GloSA-sum
47.50
20.00
42.00
0.830
0.750
GPT-4 Prompt-Sum
41.25
18.11
38.09
0.839
0.742
Claude-3 Sum
44.02
19.55
41.44
0.850
0.760
PubMed
FT-LLaMA-3 8B
42.94
18.64
39.72
0.846
0.751
GloSA-sum
49.50
22.50
44.50
0.860
0.760
A.7 ADDITIONAL. LLMS DOWNSTREAM EXPERIMENTS
To further evaluate the practical utility our method, we test whether the summaries produced by GloSA-sum remain effective for downstream tasks. Specifically, conduct experiments the SQuAD 2.0 machine reading comprehension benchmark, which requires models to extract spans from context passages predict that no answer is available. Following standard practice, tok- enize the input using BERT or TS tokenizers, fine-tune models with contexi-question pairs as input, and evaluate predictions with F1 and EM scores. We compare three summarization strategies: the ETC Pipeline, where contexts are explicitly summarized before being fed into the QA model; the ITC Joint approach, where summarization and QA are trained jointly an end-to-end manner; and our TDA-based Summarization, which applies peaccurre-reservingg semantic summarization to re- tain core themes and logical cycles while reducing context length. As shown in Table P GloSA-sum achieves the highest performance (91. 1.55 F1 88.50 EM the test set), surpassing both pipeline and joint summarization baselines across BERT, ALBERT, and GPT-4 variants. These results demon- strate that TDA-bases summarization not only reduces computational cost but also preserves essen- tial semantic and logical information, enabling models to answer questions as effectively as andand in some cases better than using the original uncompressed text.
Table Performance on the SQuAD 2.0 question answering task.
Model
Dev F1
Test F1
Dev EM
Test EM
BERT Baseline
81.84
83,06
78.57
80.00
BERT ETC Pipeline
82.59
83.23
79.33
80.00
BERT ITC Joint
82.94
83.54
79.62
80.00
ALBERT Baseline
90.15
90.90
87.00
88.10
ALBERT + ETC Pipeline
90.50
90.97
87.50
88.10
ALBBRT + ITC Joint
90.85
91.00
87.75
88.10
GPT-4o-mini Baseline
84.50
85.20
81.10
82.00
GloSA-sum (ours)
91.20
91.50
88.00
88.50
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A.8 HYPERPARAMETER EXPERIMENT
We further examine the impact of key hyperparameters GloSA-sum using the GovReport dataset, with ROUGE scores as evaluation metries. For the fusion coefficient a that balances semantic and temporal signals, performance improves steadily when increasing a from 0.0 (temporal only) to 0.5, where ROUGE-I/2/L reach the best results 557.3/2688522.44 This in- dicates that balanced integration of semantic and temporal information is essential, while relying solely on either component degrades performance. For the topological proxy weight X, which con- trols the trade-off between TopoScore and TaskScore, the best results are obtained at À 0.7 (57.1/26.9/52.1 showing that structural signals should carry higher weight but still need to be combined with task objectives. For the size of the protected pool K, performance increases as K grows from 1 to 3 and peaks at K = 3 (57.2/26.8/52..1 after which further enlargement introduces redundancy and slightly reduces performance. Overall, these results demonstrate that GloSA-sun benefits most from balanced fusion of semantic and temporal cues, a higher but not exclusive weight on topological information, and moderately sized protected pool that preserves essential structures without redundancy.
Answer to Q6:
60 Sensthvity Analysls Coefidint C
Sensiiiity Analysis Topology Agent Weight A 50
Sensiivity Analysia Pool
5
ROUGE Score
ROUGE ROUGE-
ROUGE-T 1
5
PRO
40
RoUGE-2 ROUGELL
RouGs
85
8
8
20
/Semantio Temporal)
AToopBBoore vs. TaskSoore)
K(PProtction Pool Bize)
Figure 2: Hyperparameter Experiment
A.9 ENCODER ROBUSTNESS ANALYSIS
To further evaluate the stability and generality of GloSA-sum, we conduct an additional ablation study using multiple sentence encoders of varying capacity. By relying on a compact and locally contextualized embedding model all-mpnet-base formation into the representation itself, ensuring that improvements can be attributed directly to TDA. This design choice confirms that TDA alone capable of constructing long-range semantic and logical structures even under limited contextual input.
we avoid leaking global discourse
To assess potential headroom and robustness, we replace mpnet with stronger encoders, including all-roberre rta- wwweeerraararrglaeeeee large-vl and text -ext--emeedding--- 3 11 / /la arge from OpenAL. Results across all four datasets are summarized in Table We observe a clear and monotonic improvement encoder capacity increases. Importantly, the gains smooth rather than volatile, demonstrating that the topological backbone construction operates consistently regardless of the underlying em- bedding model. Meanwhile, the competitive performance obtained even with lightweight encoders verifies that GloSA-sum maintains strong structural awareness in resource-limine settings. These findings confirm that GloSA-sum is not only encoder-agnostic but also highly plug-and-play, al- lowing practitioners to select encoders based on computational budget, accuracy requirements, or latency constraints.
A. POSITION DISTRIBUTION ANALYSIS OF THE PROTECTED POOL
To examine whether the protected pool P is influenced by positional heuristics, analyze the relative sentence- posittion distribution on the GovReport dataset. Unlike extractive baselines such as Lead-3, which inherently select the first three sentences and therefore exhibit fully front-loaded distribution, TDA-based selection in GloSA-sum depends solely on the high-dimensiona geometric structure of the semantic space. Table I1 summarizes the comparative distribution patterns.
As shown in the table, more than 70% of sentences in P originate from the middle and end sections of GovReport documents. This sharply contrasts with Lead-3 and confirms that GloSA-sum does
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Table 10: Encoder robustness and plug-and-play evaluation of GloSA-sum across four datasets.
Dataset
Encoder
R-1
R-2
R-L
BERTScore
QAFactEval
all-mpu 1ll-mpett-baee-22
44.05
21.22
41.06
0.880
0.78
I1-roberta-llrge--e
45.12
22.04
42.18
0.890
0.80
CNN/DM
axt-embbedding----mmae
45.78
22.63
42.71
0.895
0.81
text-embedding-3-BBll
46.41
23.12
43.29
0.903
0.82
all-mpnet-base-v2
55,50
26.00
51.00
0,910
0,81
all-roberta- large--v
56.92
27.18
52.41
0.920
0.83
GovReport
text-embeddingg---e 3-maall
57.64
27.92
53.34
0.924
0.84
eexteembedding---lare
58.43
28.57
54.12
0.931
0.86
all-mppet-base-v2
47.50
20.00
42.00
0.830
0.75
all-roberta-aarge-v
49.38
21.46
44.02
0.850
0.77
ArXiv
(ext-embedddig----smmee
50.23
22.11
45.03
0.861
0.78
(ext-embedddin----largg
51.07
22.76
45.84
0.871
0.80
all-mpnet-hase-v2
49.50
22.50
44.50
0.860
0.76
all-roberta-aarge-vl
51.21
23.78
46.12
0,880
0.78
PubMed
text-embeddingg---mmee 3-mmal
51.97
24.35
47.02
0.887
0.80
(ext-embedding-3-lare
52.74
25.14
47.81
0.896
0.82
Table 11: Relative sentence-position distribution of the Protected Pool (P) on GovReport compared with the Lead-3 baseline.
Document Segment
Lead-3 Sentence Share
GloSA-sum Protected Pool Share
Beginning (0%-10%)
100%
28%
Middle (10%-80%)
0%
52%
End (80%-100%)
0%
20%
not rely positional heuristics. Instead, the protected pool captures sentences that exhibit per- sistent topological importance, reflecting long-range semantic themes and cross-paragraph logical dependencies. These findings provide strong evidence that GloSA-sum successfully overcomes the positional rigidity inherent to many extractive summarization methods and operates based on global structural information encoded in the semantic manifold.
B APPENDIX B: CASE STUDY
To further illustrate the effectiveness of our proposed method, we provide qualitative case studies from different domains GovReport dataset and ArXiv dataset. These examples demonstrate how the one-time TDA-based analysis and the Protected Pool mechanism preserve core semantic clusters (H0) and logical loops (HI), while effectively compressing redundant content.
B. CASE 1: GOVREPORT DATASET (POLICY OVERSIGHT AND HEALTH PROTECTION)
This report discusses the Department of Defense's (DOD) force health protection and surveillance policies for deployed federal civilian personnel. Over recent years, with the expansion of the Global War on Terrorism, the role of DOD's 's federal civilians has grown to include critical functions such as intelligence collection, criminal investigations, and weapons systems acquisition in the theater of operations. To ensure these personnel can carry out essential tasks, the DOD established the Emergency Essential Program 1985, designating civilian positions as "emmergency-essentaa" for deployment to combat zones. Although DOD has implemented range of health protection poli- cies, there are significant implementation issues. The DOD lacks a centralized system to track the health status and movements of deployed civilians. Notably, the deployment records for personnel in Afghanistan and Iraq show gaps, with some federal civilians missing required pre-deployment health assessments and immunizations, compromising the effectiveness of health monitoring. The
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report further highlights that DOD policies do not require the collection of location-specifie data for deployed personnel, hindering the assessment of health risks in the operational theater. In the absence of such data, DOD is unable to effectively monitor and ensure comprehensive health pro- tection for federal civilian personnel. Moreover, the DOD's force health protection and surveillance policies lack effective oversight mechanism. While DOD has introduced revised policies to im- prove record management and health monitoring, it has not established quality control system to ensure full compliance across all components. These gaps in policy enforcement may jeopardize the health and readiness of federal civilian personnel, impacting their ability to support contingency operations effectively.
This report mainly discusses DOD's deployment health protection and monitor- ing policies for federal civilian personnel. It focuses how DOD ensures that these personnel receive appropriate health assessments, immunizations, and monitoring before, during, and after de- ployment. Despite existing policies, multiple implementation problems highlighted, particularly regarding data tracking and health monitoring.
Original Theme:
Topo Protected Pool:
HO (Core Themes):
--Bergency-Esseeeeeeee Essenntia Program: DOD established the program to ensure that key civilian positions can support combat operations, designating these positions as peeergencc-essenntiinn for deployment.
Health Protection and Monitoring Policies: The report discusses DOD's policies such as pre-deployment health assessments, immunizations, and post-deployment health checks.
Gaps Deployment Health Monitoring: The lack of a centralized data system pre- vents effective tracking of civilian personnel's 's health status and movements.
H1 (Logical Loops):
Health Protection Challenge Cycle: Recurring problems of missing centralized data, incomplete assessments, and ineffective monitoring.
Link Between Data Gaps and Policy Gaps: Without sufficient records, DOD cannot enforce its health protection policies effectively. leading systemic weaknesses.
Summarization Effect: Applying our proposed method, which performs a one-time TDA-based analysis and constructs Protected Pool to preserve core semantic clusters and logical cycles, the summary successfully retained the report's essential themes and reasoning chains. Key elements preserved, while logical loops clearly highlighted. At the same time, redundant back- ground information and detailed statistics were effectively pruned, resulting in a concise yet struc- turally faithful summary.
Overall Evaluation:
1. Structural Preservation:
Our method ensures that the report's global structure is pre- served. By analyzing semantic clusters and logical relations once and fixing them in the Protected Pool, the summary remains concise while maintaining logical integrity.
2. Information Condensation: Core information such as DOD's 's health protection policies, the emergency-esseenial program, and implementation challenges retained, while irrel- evant details are discarded for conciseness.
3. Logical Consistency: The one-time TDA analysis highlights logical relations (e.g., health monitoring and data gaps), preventing fragmented or inconsistent summaries and ensuring overall coherence.
B.2 CASE GOVREPORT DATASET (FINANCIAL OVERSIGHT ACCOUNTABILITY LOOP)
This example comes from government financial oversight report discussing budget allocation, evaluation metrics, and accountability mechanisms. The following four sentences form persistent and semantically stable H, cycle:
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Sg: The total budget appropriated for the Department's modernization initiative reached $850 million in the current fiscal year. Function: Resource allocation (funding input)
Ss: However, our analysis revealed lack of clear performance metrics for evaluating the long-term return on investment (ROI) from this expenditure. Function: Oversight gap (first hop: lack of measurement)
Se: Consequently, the Department spent over 30% of the funds vendor contracts that were not explicitly tied to the initiative core objectives. Function: Spending consequence (second hop: misaligned expenditure)
Sa: The oversight committee formally recommends freezing all future capital appropriation until the new ROI tracking standards are implemented and proven effective. Function: Accountability feedback (third hop: corrective action)
Identified H1 Logical Loop:
S. + Sb - S. Sa + Sa
This loop reflects the argumentative structure of the report: funding allocation oversight deficiency + misaligned spending + accountability correction. By fixing all nodes in this Hi cycle within the Protected Pool, GloSA-sum ensures that the final summary preserves the complete chain of responsibility and avoids producing an incomplete narrative (e.g., only mentioning the budget but omitting the oversight conclusion).
Summarization Effect: Our method successfully retains the full accountability chain, eliminating financial table details and secondary commentary while preserving the causal logic.
Overall Evaluation:
1. Structural Preservation: The H1 cycle ensures that the financial logic is preserved across multiple paragraphs.
2. Information Condensation: Only the key retained.
www.eeeenceeeeeeeeeeeeeee action path is
3. Logical Consistency: The feedback loop structure remains intact, supporting coherent policy narrative.
B.3 CASE ARXIV DATASET (ADDITIVE KERNEL SVM MODEL)
Additive models are powerful family of tools for semiparametric regression and classification. Compared to linear or generalized linear models, additive models offer greater flexibility, and they more interpretable than fully nonparametric models. By using regularized kemnel methods, es- pecially Support Vector Machines (SVMs), additive models can perform better in high-dimensional data, reducing the curse of dimensionality. SVMs with additive kernels outperform traditional Gaus- sian RBF kernels in high- high-dimensional spaces, especially in quantile regression problems, where the of the Pinball loss function offers significant advantages. Additive models decompose the in- put space, allowing learning algorithms to efficiently fit data with lower complexity. This paper discusses the application of additive kernel SVMs in high-dimensional spaces, highlighting their superior learning performance compared to traditional kernels when the additive model assumption satisfied, particularly in quantile regression.
Original Theme:
This paper introduces machine learning model, covering the model design, experimental validation, and related discussion. It emphasizes the theoretical foundation, empiri- cal effectiveness, and potential directions for future research. The paper evaluates the model with multiple metrics, analyzes experimental results, and discusses both limitations and opportunities.
Topo Protected Pool:
HO (Core Themes):
Model Proposal: The paper presents the design principles and algorithmic framework of the proposed machine learning model, highlighting its innovations and advantages over traditional approaches.
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Experimental Results: A series of experiments validates the model's effectiveness and compares its performance with baseline methods.
Academic Contribution: The paper demonstrates the model's superiority in specific tasks and discusses future directions for optimization.
H1 (Logical Loops):
Work Loop: The paper shows experimental evidence of the model's advantages, acknowledges existing limitations, and proposes future research directions, forming a coherent loop between experiments, discussions, and outlook.
Snpperieen-Discusioo--ie-
Using proposed method, which performs one-time TDA-based anal- ysis and constructs a Protected Pool to preserve the semantic backbone, the summary retained the main content of the paper. Essential aspects such the model proposal, experimental validation, and academic contributions were preserved, while the logical loop linking experiments, discussion, and future work was also maintained. Redundant experimental details and lengthy technical derivations were pruned, resulting in a concise and focused summary.
Summarization Effect:
Overall Evaluation:
1. Structural Preservation:
The one-time TDA analysis ensures that the paper's 's global struc- ture preserved, maintaining the integrity of theoretical, experimental, and discussion components.
2. Information Condensation: Core information such as the model framework, empirical validation, and contributions is retained, while non-essential details are removed for brevity.
3. Logical Consistency: The Protected Pool effectively captures the logical cycle (exper- iment- sinnt-ddccusioo-ffuee work), preventing fragmentation and ensuring a coherent sum- mary.
B.4 CASE 4: ARXIV DATASET (ITERATIVE METHODOLOGICAL REFINEMENT LOOP)
This case illustrates a typical scientific reasoning cycle in a model development paper. Four sen- tences form a persistent and meaningful H, loop:
Sp: We propose a novel attention mechanism, the Gated Spatial Encoder (GSE), designed to capture non-local dependencies. Function: Method proposal (new model component)
Sy: However, the initial ablation study revealed that the GSE struggled to maintain high accuracy when sequence lengths exceeded 512 tokens. Function: Experimental limitation (first hop: structural weakness)
Sz: To mitigate this scalability issue, we introduced a cascaded hierarchical pooling layer after the initial GSE pass. Function: Method refinement (second hop: solution proposal)
Sr: The final results in Table 5 confirm that the cascaded pooling structure successfully solves the uen-seeueenc degradation problem, validating our structural refinement. Func- tion: Empirical validation (closing hop: resolution)
Identified H1 Logical Loop:
Sp Sp + S. St +
This loop corresponds canonical scientific reasoning pattern: method proposal limitation discovery + architectural fix + validated improvement. Removing any sentence disrupts the causal chain and produces an incoherent summary. Fixing the loop Protected Pool preserves the full methodological refinement cycle.
Summarization Effect: Our method preserves both the introduction of the model component and the key insight that the method requires refinement to achieve its final performance.
Overall Evaluation:
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1. Structural Preservation:
The full methodological iteration is maintained.
2. Information Condensation: Detailed ablation numbers are removed while the causal structure is preserved.
3. Logical Consisteney:
The summary maintains the problem-sohutioo--vllddannn loop sential to scientific argumentation.
B.5 CASE 5: CNN/DM DATASET (THEMATICALLY SCATTERED NEWS LEADING TO TDA FAILURE)
This case illustrates failure scenario commonly observed in CNNDM news articles. Many news reports- especially those involving mixed viewpoints, citizen quotes, historical side notes, and po- inverted peeetedd-yramiid style: the core fact appears early, but the narra-
litical commenntay--ddonn tive quickly diverges into loosely connected background elements. This produces a semantically "scattered" embedding space with weak cross-sentence coherence, causing TDA-based structural extraction to fail.
Example Sentences:
S₁ (Core Event) The City Council voted 4-3 Tuesday approve the controversial down- town rezoning measure, effective immediately.
S2 (Peripheral Emotional Testimony) Resident Sarah Chen, holding a sign, testified that the traffic disruption would make her commute living nightmare' every morning.
Sa (Historical Background) The last major rezoning debute in the city, held decade ago, focused primarily on historical preservation laws, a factor largely absent this year.
S4 (High-Leve Political Commentary) Mayor Johnson released a statement later saying the council's 's decision represented 'a difficult but necessary step forward for community growth.'
TDA Failure Analysis:
Ho (Semantic Clusters) Failure - All Clusters Are Short-Lived. The four sentences span distinct semantic categories-pooliieee fact (S1). emotional testimony (S2), historical background (Sa), and high-level commentary (S4). They far apart the embedding space and lack persistent support. During multiscale filtration, all candidate clusters quickly dissolve, creating only short-lived Ho components with low persistence.
2. H1 (Logical Loops) Failure- -
No Recurring Argumentation. Unlike structured docu- ments such GovReport scientific papers, these news articles do not contain a consistent "problem - consequence - resolution" loop. As a result, no stable H1 cycles appear in the persistence diagram.
Because both Ho and H, fail to produce persistent features, the resulting Protected Pool P nearly empty. Without a detectable semantic or logical backbone, GloS A-sum struggles to identify stable topological core, and the summary quality naturally degrades. This failure case reinforces the fact that TDA operates on geometric robustness rather than surface-level heuristics: when the underlying discourse lacks stable structure, the topological analysis correctly reflects that lack of coherence.
C ACKNOWLEDGMENT
This article used large language models (such as ChatGPT) as an auxiliary tool in the language polishing process, but did not use them in research conception and academic content generation.
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Reviews:
[{"review_id": "wMRm0ZCV9s", "reviewer": "Reviewer_zufN", "summary": "This paper proposes GloSA-sum, a text summarization method that applies topological data analysis (TDA) to preserve the global semantic and logical structure of long documents during compression. The approach constructs a semantic graph from sentence embeddings and uses persistent homology to identify robust topological features. Such features are collected in a \"Protected Pool\" that guides subsequent compression through lightweight proxy metrics, avoiding repeated expensive TDA computations. A hierarchical strategy enables scalable processing of long documents.", "questions": "1. Could the authors describe the sentence splitting procedure in detail? Which tools or methods are used to determine sentence boundaries, and how might different splitting strategies affect the resulting topological features?\n2. Have the authors analyzed whether sentences in the Protected Pool exhibit systematic patterns with respect to their position in the original document (e.g., beginning, middle, end)? Such analysis would help validate that TDA captures semantic structure rather than positional biases.\n3. How are shortest paths computed in the weighted graph when calculating TopoScore (Equation 7)? Specifically, how does the algorithm handle potentially disconnected components, and how are ties broken when multiple sentences have identical scores?", "limitations": "", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 2, "contribution": 3, "strengths": "- The paper is among the first to employ topological data analysis for text summarization, explicitly modeling and preserving semantic clusters and logical dependencies.\n- Tables 2 and 3 provide a thorough analysis of computational complexity and runtime, demonstrating efficiency gains from the proposed one-time Protected Pool mechanism and hierarchical pipeline. The method achieves a favorable balance between computational cost and performance, which is particularly valuable for long-document scenarios.\n- The paper presents a thorough empirical validation. The downstream experiments particularly enhance the practical relevance of the approach. Additional experiments demonstrate that GloSA-sum summaries provide effective context for LLM-based downstream tasks, indicating practical relevance beyond the summarization task itself and suggesting broader applicability of the method.", "weaknesses": "1. **Unclear presentation and interpretation of main results:** The results in Table 1 demonstrate competitive performance, but do not clearly establish consistent advantages over strong baselines across all datasets and metrics. The improvements are often modest and inconsistently distributed across evaluation metrics. The paper would be strengthened by statistical significance testing to confirm that observed gains are reliable rather than artifacts of random variation. Moreover, the interpretation does not address cases where baselines perform comparably or better. A more nuanced interpretation would help readers better understand the method's contributions and limitations.\n\n2. **Potential limitation in semantic representation through independent sentence encoding:** The paper employs sentence-level encoding where each sentence is embedded independently. This design choice raises a concern: cross-reference information, such as pronouns, anaphora, and other referential expressions, is encoded without their antecedents, potentially resulting in semantically incomplete representations. Moreover, sentence-level encoding may not fully capture document-level phenomena such as topic progression, rhetorical structure, or long-range dependencies. Since TDA operates on these independent local embeddings, the method might miss some genuine semantic relationships that require broader discourse context. This limitation warrants discussion, particularly given that the method's core claim is to preserve \"global structure\" through operations on what are fundamentally local representations.\nAn ablative analysis examining different text granularities—such as clause-level, sentence-level, and multi-sentence chunks—would provide more insightful details about the method's robustness to encoding choices. Such an analysis would also help address the problem of short and isolated sentence embeddings by revealing whether coarser or finer granularities better capture semantic structure for TDA-based analysis. Additionally, the choice of `all-mpnet-base-v2` as the sentence encoder is concerning, as this relatively modest model may not provide sufficiently rich semantic representations for a method whose effectiveness critically depends on the quality of the initial embeddings—particularly when identifying nuanced topological structures that distinguish genuine semantic relationships from spurious patterns.\n\n3. **Incomplete empirical validation of H₁ cycles' contribution:** While H₁ cycles are described as essential for preserving logical flow, their actual contribution could be more thoroughly validated. The ablation study in Table 5 evaluates the removal of the Protected Pool, TopoScore, and hierarchical components, but does not isolate the differential impact of H₀ versus H₁ features within the Protected Pool itself. Specifically, a comparison between P = P_H₀ only versus P = P_H₀ ∪ P_H₁ would directly test whether incorporating H₁ cycles meaningfully improves performance beyond semantic clusters alone.\n\n\n4. **Limited analysis of hierarchical segmentation strategy:** The hierarchical compression strategy is described as partitioning documents into segments that are processed independently; however, a systematic comparison of segmentation methods (semantic versus fixed-length versus paragraph-based) would strengthen the paper. The sensitivity of summary quality to segmentation choices and the method's robustness to documents with non-standard structure remain unexplored. Such analysis would help clarify whether the hierarchical design genuinely contributes to performance improvements.\n\n\n5. **Miss related work:** Lack of pertinent literature for graph construction to retain only important sentences:\n    - Graph-based Abstractive Summarization of Extracted Essential Knowledge for Low-Resource Scenario (ECAI 2023)\n    - Cross-Document Distillation via Graph-based Summarization of Extracted Essential Knowledge (IEEE TASLP 2025)", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "KpwVWEbSEh", "reviewer": "Reviewer_rLwA", "summary": "This paper presents GloSA-sum, a new method for summarizing long documents by preserving their overall structure. Its core idea is to use Topological Data Analysis (TDA), a mathematical technique, to create a high-level map of the document's main topics and logical connections. The most important sentences that form this structural \"backbone\" are placed in a \"Protected Pool\" and are never deleted. The system then iteratively removes less important sentences from around this core. For extremely long texts, it uses a divide-and-conquer strategy. Experiments show that GloSA-sum produces more coherent summaries and is more computationally efficient than strong existing methods, especially on long and complex documents.", "questions": "1. Regarding the interpretation of H1 features: Could you provide more examples from your experiments where H1 cycles clearly map to specific reasoning chains or logical dependencies? Is it possible that some of these cycles are artifacts of the embedding space rather than true semantic structures?\n2. In the ablation study (Table 5), the result for \"w/o Hierarchical\" is missing. Could you run this ablation on a shorter-document dataset like CNNDM to quantify how the hierarchical approach affects ROUGE scores compared to a non-hierarchical global analysis?\n3. How does the method handle documents with very flat or simple structures, where there might be few persistent H1 cycles? Does the performance rely heavily on the presence of these complex features, or does the H0 backbone suffice for good performance?", "limitations": "", "rating": 8, "confidence": 3, "soundness": 4, "presentation": 3, "contribution": 3, "strengths": "1. The paper’s primary strength is its novel use of Topological Data Analysis (TDA) to formally model a document's global structure. This allows the method to identify core semantic themes and logical connections in a principled way, moving beyond traditional local similarity graphs.\n2. The framework is cleverly designed to be both highly effective and computationally efficient. The one-time TDA analysis and \"Protected Pool\" mechanism avoid costly repeated calculations, making the method scalable for summarizing very long documents.\n3. The method is supported by comprehensive experiments against numerous strong baselines across multiple challenging datasets. The rigorous evaluation, including a detailed ablation study, provides convincing evidence that each component of the framework is essential for its success.", "weaknesses": "1. The paper posits that H1 cycles correspond to \"logical loops\" or \"recurrent argumentative structures.\" While this is a compelling intuition, the connection is not explicitly demonstrated. The work would be significantly strengthened by a qualitative analysis that visualizes a few high-persistence H1 cycles from the data and shows the exact sentences that form them, explaining how they constitute a logical loop. Without this, the interpretation remains a plausible but unproven claim.\n2. The entire analysis is highly dependent on the quality of the initial sentence embeddings. The paper does not investigate the model's sensitivity to different sentence encoders, making it unclear how robust the identified structures are across various embedding spaces.\n3. The \"Protected Pool\" mechanism, while efficient, may be too rigid. It unconditionally preserves sentences based on an initial analysis, which could lead to keeping structurally important but contextually redundant information without any way to reconsider them.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "vnwsoqfEeH", "reviewer": "Reviewer_Ezky", "summary": "The paper proposes GloSA-sum, a global-structure-aware framework for long document summarization that uses Topological Data Analysis (TDA) to identify and preserve the semantic and logical backbone of a document. Experiments on GovReport, ArXiv, PubMed and CNN/DailyMail show higher ROUGE-L than several extractive and long-context baselines, and the authors claim that the structure-preserving summaries help LLM downstream tasks.", "questions": "- Have you compared GloSA-sum against a variant that uses non-TDA global structure detection (e.g., Louvain clustering for H₀, dependency parsing or RST for H₁)? Is TDA truly necessary, or is the gain from the Protected Pool concept alone?\n\n- Have you explored using GloSA-sum as a preprocessing step for LLMs in a retrieval-augmented generation (RAG) pipeline? Does it reduce hallucination?", "limitations": "", "rating": 2, "confidence": 4, "soundness": 2, "presentation": 2, "contribution": 2, "strengths": "- First work to apply TDA to summarization.\n\n- The Protected Pool + proxy scoring design avoids repeated TDA, this enables scalability\n\n- High QAFactEval scores suggest better factual consistency than many abstractive models.", "weaknesses": "- The paper says it is the first to bring TDA into summarization. That might be acceptable wording, but a lot of what is actually done after the TDA step looks like a graph based extractive summarizer with a protected set plus shortest-path based importance.\n\n- The ablation study removes the Protected Pool but does not compare against alternative global-structure-aware summarizers (e.g., graph-based methods with community detection, discourse parsers, or transformer-based long-range attention proxies).\n\n- Is the performance gain due to TDA specifically, or just the idea of preserving a global backbone? Could a non-TDA method (e.g., spectral clustering + cycle detection) achieve similar results more cheaply?\n\n- There is no point in comparing the performance gains if the latest baseline is 6 years old. Please provide baselines from newer LLMs ( at least LLMs with <8B parameters )", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "fdNd3bv9uE", "reviewer": "Reviewer_U95Z", "summary": "The paper proposes GloSA-sum, a novel extractive text summarization framework that leverages Topological Data Analysis (TDA), specifically persistent homology, to preserve global semantic structures and logical dependencies in long documents. The core idea is to perform a one-time TDA computation on a semantic-weighted graph built from sentence embeddings, identifying persistent features (H0 for semantic clusters/themes, H1 for logical cycles/loops) that form a \"Protected Pool\" as the document's backbone. Subsequent iterative compression uses lightweight proxy metrics (topological connectivity and task relevance) to remove redundancy without recomputing TDA, ensuring efficiency. For ultra-long texts, a hierarchical strategy segments the document for parallel local summarization followed by global integration. Experiments on datasets like GovReport, ArXiv, PubMed, and CNN/DailyMail show improvements over baselines (e.g., TextRank, BART, BigBird) in ROUGE, BERTScore, QAFactEval, and human evaluations for coherence, informativeness, and conciseness. The method also enhances downstream LLM tasks by shortening contexts while retaining reasoning chains.", "questions": "Please check the comments in the Weaknesses Section", "limitations": "", "rating": 2, "confidence": 4, "soundness": 2, "presentation": 2, "contribution": 2, "strengths": "Technical Soundness:  Integrating TDA into text summarization, providing a fresh global perspective that explicitly models semantic clusters (H0) and cross-paragraph logical dependencies (H1) is novel and original. Prior TDA applications in NLP (e.g., contradiction detection, discourse coherence) are classification-focused, making this a meaningful extension to generation/compression tasks. The \"Protected Pool\" and proxy-based iteration cleverly address TDA's computational overhead, differentiating it from graph-based methods like TextRank or optimization-based approaches.", "weaknesses": "1- Limited Justification for H1 in Text Data: While H0 (clusters) intuitively maps to themes, H1 (loops) is less straightforward for linear text. The paper claims it captures \"cross-paragraph logical dependencies,\" but examples (e.g., case studies) are vague.  How do loops manifest in sentences? Empirical evidence (e.g., ablation on H1 alone) is missing, and higher dimensions (H2+) are dismissed without deeper analysis.\n\n2- Scalability Concerns: TDA is computed once, but for ultra-long docs (e.g., >10k sentences), even one-time persistent homology on high-dimensional embeddings could be prohibitive (O(n log n) graph + complex homology). The paper's max length (8,192 tokens in A.2) is modest; tests on book-length texts would strengthen claims. Hierarchical segmentation is \"fixed-length or semantic,\" but details (e.g., how semantic segments are detected) are underspecified.\n\n3- Baseline Gaps and Evaluation Choices: Some baselines (e.g., BERTSum, MatchSum) are absent from certain datasets (e.g., GovReport), potentially biasing comparisons. LLM baselines (A.6) rely only on human eval, no ROUGE/BERTScore, limiting objectivity. QAFactEval is useful for factuality, but its question generation could be biased toward extractive methods. No analysis of failure cases (e.g., noisy embeddings) or robustness to embedding models beyond all-mpnet-base-v2.\n\n4- Potential Overfitting to Datasets: Gains are strongest on scientific/long docs (ArXiv, PubMed), but modest on news (CNNDM). Hyperparameters (e.g., α=0.5, λ=0.7) are tuned on GovReportm; cross-dataset generalization isn't explicitly tested.\n\n5- Extensive Experiment is required: In the era of LLMs (decoder only), summarization is quite a simple task. Please emphasize the motivation and the comparison of traditional methods, like this study, compared with LLM-based methods.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Decision: Accept (Poster)