MRGSEM-Sum: Unsupervised Multi-Doc Summarization

• MRGSEM-Sum is an unsupervised multi-document summarization framework that constructs a multi-relational sentence graph and minimizes structural entropy to adaptively cluster sentences.
• It employs a position-aware compression mechanism with K-shortest paths to extract salient summary units while effectively reducing redundancy.
• Empirical evaluations demonstrate that the method outperforms traditional unsupervised techniques and rivals supervised models and large LMs on benchmarks such as Multi-News and DUC-2004.

to=arxiv_search.search ￣影音先锋 {"query":"(Zhang et al., 31 Jul 2025) MRGSEM-Sum unsupervised multi-document summarization framework based on multi-relational graphs and structural entropy minimization", "max_results": 5} to=arxiv_search.search 天天爱彩票是json {"query":"title:\"MRGSEM-Sum\" OR (Zhang et al., 31 Jul 2025)", "max_results": 10} MRGSEM-Sum is an unsupervised multi-document summarization framework based on multi-relational graphs and structural entropy minimization. It is designed for multi-document summarization settings in which the input is a set of documents $D=\{d_1,d_2,\ldots,d_n\}$ discussing the same topic, and the objective is to generate a short summary that is both informative and non-redundant. The framework addresses two difficulties identified for multi-document summarization: the complexity of relationships among sentences across documents, and redundancy caused by repeated facts across multiple sources. Its method consists of three stages: construction of a multi-relational sentence graph, adaptive clustering by two-dimensional structural entropy minimization, and summary extraction by a position-aware compression mechanism (Zhang et al., 31 Jul 2025).

1. Definition and problem formulation

MRGSEM-Sum is situated in graph-based unsupervised multi-document summarization, where sentences are treated as the basic units of representation and selection. The framework is motivated by the observation that existing graph-clustering methods often model only a single type of relation and usually require the number of clusters to be preset. In the formulation associated with MRGSEM-Sum, these two limitations are treated jointly: sentence interactions are represented through multiple relation types, and sentence groups are partitioned adaptively rather than under a fixed cluster count (Zhang et al., 31 Jul 2025).

The input consists of a document cluster $D=\{d_1,d_2,\ldots,d_n\}$. The output is a concise summary intended to preserve coverage while reducing redundancy. The framework is fully unsupervised: no training on reference summaries is described. Instead, it relies on sentence embeddings from SBERT, TF-IDF cosine similarity, discourse relation extraction, structural entropy minimization, and shortest-path compression (Zhang et al., 31 Jul 2025).

A central design assumption is that redundancy reduction is best handled by grouping related sentences before compression. This suggests a two-level architecture: first discover coherent sentence groups, then distill each group into a compact summary unit. In MRGSEM-Sum, that architecture is implemented through clustering and cluster-level compression rather than through end-to-end neural generation (Zhang et al., 31 Jul 2025).

2. Multi-relational graph representation

The graph in MRGSEM-Sum is sentence-level. Each sentence in the document cluster is a node, and sentence representations are initialized using SBERT, yielding node embeddings $X$. The framework defines a multi-relational graph

$G=\{V,E_{r_1},E_{r_2}\},$

where $V$ is the set of sentence nodes, $E_{r_1}$ denotes semantic edges, and $E_{r_2}$ denotes discourse edges (Zhang et al., 31 Jul 2025).

Semantic relations $E_{r_1}$ are based on sentence content similarity. Sentences are represented using TF-IDF vectors, and edge weights are computed by cosine similarity between TF-IDF representations. This relation type captures topic overlap and lexical or content proximity among sentences (Zhang et al., 31 Jul 2025).

Discourse relations $E_{r_2}$ are based on discourse coherence cues following Christensen et al. (2013). The framework states that these relations consider discourse markers, coreference, and entity linking. These edges are intended to capture rhetorical connection, coherence structure, and cross-sentence logical linkage beyond surface-level semantic similarity (Zhang et al., 31 Jul 2025).

Because the clustering stage operates on a single graph, the multi-relational graph is merged into an integrated graph

$G'=\{V,E\}$

with adjacency matrix $D=\{d_1,d_2,\ldots,d_n\}$0. The merge rule is defined so that if either relation yields a nonzero edge between two sentences, the integrated edge weight is the maximum of the two relation-specific weights; otherwise it is zero. In effect, the integrated graph preserves the strongest available evidence of connection between two sentences (Zhang et al., 31 Jul 2025).

This graph design is one of the framework’s defining characteristics. Rather than treating sentence affinity as a single scalar derived from one feature family, MRGSEM-Sum combines semantic and discourse signals into a common graph substrate. A plausible implication is that cluster formation is influenced not only by lexical similarity but also by coherence-inducing links that connect sentences across documents even when their surface overlap is limited.

3. Structural entropy minimization and adaptive clustering

The clustering mechanism is based on two-dimensional structural entropy minimization. Its role is not only to partition the graph, but also to determine the number of clusters automatically. This directly contrasts with graph-clustering approaches that require a predefined number of clusters (Zhang et al., 31 Jul 2025).

The method constructs an encoding tree $D=\{d_1,d_2,\ldots,d_n\}$1 over $D=\{d_1,d_2,\ldots,d_n\}$2. Each node $D=\{d_1,d_2,\ldots,d_n\}$3 in the encoding tree corresponds to a subset $D=\{d_1,d_2,\ldots,d_n\}$4. The root node is $D=\{d_1,d_2,\ldots,d_n\}$5, with

$D=\{d_1,d_2,\ldots,d_n\}$6

and a leaf node $D=\{d_1,d_2,\ldots,d_n\}$7 corresponds to a single sentence,

$D=\{d_1,d_2,\ldots,d_n\}$8

Children of a node form a partition of that node’s sentence set. Leaf height is zero, and parent height is one more than child height (Zhang et al., 31 Jul 2025).

The first-level entropy term is defined as

$D=\{d_1,d_2,\ldots,d_n\}$9

where $X$0 is the degree of node $X$1, and $X$2 is the sum of degrees of all nodes in the root set $X$3. The structural entropy of node $X$4 is written as

$X$5

with $X$6 denoting the total weight of cut edges by $X$7, and $X$8 the volume of cluster $X$9 (Zhang et al., 31 Jul 2025).

Clustering proceeds through greedy merging. For two nodes or clusters $G=\{V,E_{r_1},E_{r_2}\},$0 and $G=\{V,E_{r_1},E_{r_2}\},$1, the change in structural entropy is defined by

$G=\{V,E_{r_1},E_{r_2}\},$2

with the explicit expression given in the framework for the merge-induced entropy variation. The merge operation $G=\{V,E_{r_1},E_{r_2}\},$3 creates a new node $G=\{V,E_{r_1},E_{r_2}\},$4, removes $G=\{V,E_{r_1},E_{r_2}\},$5, sets the children of $G=\{V,E_{r_1},E_{r_2}\},$6 to the union of the children of $G=\{V,E_{r_1},E_{r_2}\},$7 and $G=\{V,E_{r_1},E_{r_2}\},$8, and assigns $G=\{V,E_{r_1},E_{r_2}\},$9’s parent to the root $V$0 (Zhang et al., 31 Jul 2025).

The greedy policy repeatedly merges the pair with the largest decrease in structural entropy, that is, the most negative $V$1, until no negative merge remains. The algorithm starts with every sentence as its own cluster and stops when no merge reduces entropy. In this way, the final cluster count is the one that yields minimum structural entropy under the greedy procedure (Zhang et al., 31 Jul 2025).

The paper also describes a batching strategy: clusters are grouped into subsets of size $V$2, and if no merges occur in any subset, $V$3 is doubled so that larger merge candidates can be considered. The final leaf nodes of the subtrees under the root define the sentence clusters

$V$4

This suggests that the method treats cluster cardinality as an emergent structural property of the integrated graph rather than as a user-specified hyperparameter.

4. Position-aware compression and summary construction

After clustering, MRGSEM-Sum does not output clusters directly. It applies a position-aware compression mechanism to convert selected clusters into concise summary units (Zhang et al., 31 Jul 2025).

For a sentence $V$5 in document $V$6, the positional importance is defined as

$V$7

where $V$8 is the sentence position in the original document and $V$9 is the number of sentences in the document. Under this definition, earlier sentences receive higher weights, with the first sentence assigned weight $E_{r_1}$0 (Zhang et al., 31 Jul 2025).

For each cluster $E_{r_1}$1, the positional importance score is

$E_{r_1}$2

Clusters are ranked by this score, and only the top $E_{r_1}$3 clusters are retained. This filtering stage is intended to privilege clusters that contain positionally salient sentences, especially in news-like settings where leading sentences often carry core information (Zhang et al., 31 Jul 2025).

Compression within each retained cluster follows Boudin and Morin (2013). The framework uses the K-shortest paths algorithm to generate $E_{r_1}$4 shortest-path compression candidates

$E_{r_1}$5

scores them using keyphrases, and selects the Top-1 compression candidate from each cluster. The selected candidates are concatenated to form the final summary (Zhang et al., 31 Jul 2025).

Within the architecture of MRGSEM-Sum, compression serves two roles. First, it suppresses redundancy inside a cluster by eliminating repeated or less essential material. Second, it turns a sentence cluster into a shorter discourse unit that can be concatenated with outputs from other clusters. The framework therefore separates content organization from sentence-level surface realization: clustering determines thematic structure, while compression determines local expression.

5. Empirical evaluation and reported performance

MRGSEM-Sum is evaluated on four benchmark datasets: Multi-News, DUC-2004, PubMed, and WikiSum (Zhang et al., 31 Jul 2025). The datasets reported in the framework are summarized below.

Dataset	Test examples	Average document length
Multi-News	5,622	2103.49
DUC-2004	50	5978.2
PubMed	5,025	3224.5
WikiSum	2,000	2238.2

The paper further reports docs per cluster and average summary length: Multi-News has docs per cluster $E_{r_1}$6 and average summary length $E_{r_1}$7; DUC-2004 has docs per cluster $E_{r_1}$8 and average summary length $E_{r_1}$9; PubMed has docs per cluster $E_{r_2}$0 and average summary length $E_{r_2}$1; WikiSum has docs per cluster $E_{r_2}$2 and average summary length $E_{r_2}$3 (Zhang et al., 31 Jul 2025).

Evaluation uses ROUGE-1, ROUGE-2, and ROUGE-SU. The unsupervised baselines are LexRank, TextRank, MMR, Centroid, and SummPip. The supervised baselines are PG-Original, PG-MMR, Copy-Transformer, and Hi-MAP. The LLM baselines are GPT-3.5-turbo-16k and GPT-4-32k, prompted with “Summarize the above article:” (Zhang et al., 31 Jul 2025).

MRGSEM-Sum is reported as the best among unsupervised methods on all four datasets. On Multi-News, it achieves ROUGE-1 $E_{r_2}$4, ROUGE-2 $E_{r_2}$5, and ROUGE-SU $E_{r_2}$6, compared with SummPip at $E_{r_2}$7. On DUC-2004, it achieves $E_{r_2}$8, compared with SummPip at $E_{r_2}$9 and LexRank at $E_{r_1}$0. On PubMed, it achieves $E_{r_1}$1, compared with SummPip at $E_{r_1}$2. On WikiSum, it achieves $E_{r_1}$3, compared with SummPip at $E_{r_1}$4 (Zhang et al., 31 Jul 2025).

The paper states that the method consistently outperforms previous unsupervised methods and, in several cases, achieves performance comparable to supervised models and LLMs. It also notes that on WikiSum, MRGSEM-Sum exceeds GPT-4-32k on ROUGE-1 by $E_{r_1}$5 according to the paper’s discussion (Zhang et al., 31 Jul 2025).

Human evaluation was conducted by three graduate students on 100 random summaries from the Multi-News test set. The systems compared were TextRank, Centroid, SummPip, GPT-3.5-turbo-16k, GPT-4-32k, and MRGSEM-Sum. The criteria were Fluency, Consistency, and Coverage on a 1-to-5-star scale. The reported outcome is that MRGSEM-Sum has much higher 5-star ratings for Consistency and Coverage than other methods and is comparable to LLMs in Fluency (Zhang et al., 31 Jul 2025).

6. Ablations, interpretation, and relation to prior paradigms

The ablation study isolates the contribution of each major component. Replacing the multi-relation graph with the approximate discourse graph from SummPip yields a substantial decline; on Multi-News, ROUGE-1 drops from $E_{r_1}$6 to $E_{r_1}$7. Replacing two-dimensional structural entropy clustering with spectral clustering and a preset cluster number also causes a marked decline; on Multi-News, ROUGE-1 drops from $E_{r_1}$8 to $E_{r_1}$9. Replacing position-aware compression with the generic compression method from Boudin and Morin (2013) produces a moderate drop on Multi-News and a very large drop on PubMed; on PubMed, ROUGE-1 drops from $E_{r_2}$0 to $E_{r_2}$1 (Zhang et al., 31 Jul 2025).

These results identify the framework’s main technical dependencies. The multi-relation graph is the mechanism for richer sentence representation; two-dimensional structural entropy minimization is the mechanism for adaptive cluster discovery; and position-aware compression is the mechanism for salience-sensitive reduction within clusters. The large ablation loss on PubMed suggests that positional information is especially useful for long documents, which is explicitly stated in the framework (Zhang et al., 31 Jul 2025).

The case study reported for the method emphasizes improved coverage and relevance. The summary generated by MRGSEM-Sum is described as closer to the reference than the baselines, capturing details such as “A 6.5-magnitude earthquake struck eureka at around 4:30 p.m. saturday,” “without power,” “around 30 seconds,” and “as of 5:30 p.m.” The comparison with SummPip is used to illustrate that the latter missed key facts and included irrelevant content (Zhang et al., 31 Jul 2025).

In methodological terms, MRGSEM-Sum belongs to a graph-clustering lineage in unsupervised summarization, but it extends that lineage in two explicit ways: the graph is multi-relational rather than single-relational, and clustering is entropy-minimizing and adaptive rather than based on a preset number of groups. A plausible implication is that the framework treats redundancy reduction as a graph partitioning problem whose optimal granularity should be inferred from sentence interactions rather than fixed a priori.

7. Significance and scope

The framework’s reported contribution is an equivalence between richer sentence-relationship modeling and adaptive redundancy control in unsupervised multi-document summarization. Its three-stage pipeline can be summarized as follows: represent sentences with semantic and discourse signals in a multi-relational graph; discover sentence clusters by minimizing structural entropy; rank and compress selected clusters using sentence position and shortest-path compression; and concatenate the resulting compressed units into a final summary (Zhang et al., 31 Jul 2025).

Within the reported experiments, MRGSEM-Sum is presented as effective on news summarization, long-document summarization, and non-news summarization, as represented by Multi-News, DUC-2004, PubMed, and WikiSum. The framework is also described as competitive with supervised systems and LLMs while remaining unsupervised (Zhang et al., 31 Jul 2025).

The paper does not provide a formal complexity analysis, but it does specify several implementation-relevant elements: sentence nodes are initialized with SBERT embeddings, semantic edges use TF-IDF cosine similarity, discourse edges follow Christensen et al. (2013), clustering is greedy and subset-based, subset size is increased when no merges are possible, and compression uses K-shortest paths with keyphrase scoring (Zhang et al., 31 Jul 2025). This suggests that the framework is best understood not as a monolithic model, but as a deterministic summarization pipeline whose effectiveness depends on the interaction among graph construction, entropy-based clustering, and compression.

In that sense, MRGSEM-Sum represents a structurally explicit approach to multi-document summarization. Rather than learning summary generation from paired examples, it organizes sentence relations into a graph, derives coherent groups by entropy minimization, and compresses those groups into summary units. Its reported empirical profile indicates that, for the evaluated benchmarks, this combination is sufficient to outperform prior unsupervised methods and to approach or match stronger supervised and large-model baselines in several settings (Zhang et al., 31 Jul 2025).