Towards Automatic Evolution Tree Generation from Citation Graphs

# Towards Automatic Evolution Tree Generation from Citation Graphs
Source: [https://arxiv.org/html/2609.09561](https://arxiv.org/html/2609.09561)
Zexing ZhaoAffiliation:School of Mechanical Engineering, Georgia Institute of TechnologyEmail:[alfred\.zhao@gatech\.edu](mailto:[email protected])Yuntong HuLiang ZhaoEmail:[liang\.zhao@emory\.edu](mailto:)

###### Abstract

Surveys remain the primary way researchers grasp the lineage of methods within an AI subfield, but they scale poorly against the current rate of publication\. Existing taxonomy\-induction methods are largely leaf\-bound and time\-agnostic; they tend to force transitional papers into mature leaves and can create topological inversions between ancestors and descendants\. We propose EvoTree, a staged framework that decouples conceptual backbone learning from temporal refinement: a graph\-aware encoder with distribution\-based hierarchical clustering yields a stable taxonomy backbone; temporal fine\-tuning then re\-attaches marginal papers to internal nodes under monotonic\-path constraints; a final LLM pass labels concepts without altering the topology\. We release the first annotated benchmark for this task across 11 AI subfields\. EvoTree attains the highest NMI and citation\-direction accuracy among all baselines and the best concept purity on the annotated benchmark, and is the only method with non\-trivial marginal\-paper detection on the annotated set\.

†††Corresponding author\.## 1Introduction

The rapid growth of scientific literature has fundamentally challenged human\-centered knowledge organization and field understanding\. Open scholarly infrastructures such as OpenAlex[Priem et al\. \(2022\)](https://arxiv.org/html/2609.09561#bib.bib9)now index over 470 million scientific works together with continuously expanding citation networks\. As research fields evolve at an unprecedented pace, researchers increasingly struggle to efficiently understand the historical evolution, conceptual lineage, and paradigm transitions of rapidly developing domains[Fortunato et al\. \(2018\)](https://arxiv.org/html/2609.09561#bib.bib10), creating an increasing need for AI\-assisted methods to organize, synthesize, and understand scientific progress[Le et al\. \(2026\)](https://arxiv.org/html/2609.09561#bib.bib3);[Hu et al\. \(2025\)](https://arxiv.org/html/2609.09561#bib.bib2)\.

Among various forms of scientific organization, evolution trees and hierarchical lineage diagrams are particularly effective because they explicitly reveal conceptual inheritance, branching, and progressive refinement across generations of work\. Such structures are widely adopted in modern survey papers to summarize the evolution of research paradigms, model families, and emerging subfields[Zhang et al\. \(2018\)](https://arxiv.org/html/2609.09561#bib.bib17);[Wang et al\. \(2024\)](https://arxiv.org/html/2609.09561#bib.bib7);[Hu et al\. \(2024\)](https://arxiv.org/html/2609.09561#bib.bib5);[Liang et al\. \(2025\)](https://arxiv.org/html/2609.09561#bib.bib6)\. However, constructing these evolution trees remains largely manual, requiring substantial domain expertise and intensive literature analysis, while quickly becoming outdated as new papers continuously emerge[Wang et al\. \(2024\)](https://arxiv.org/html/2609.09561#bib.bib7);[Liang et al\. \(2025\)](https://arxiv.org/html/2609.09561#bib.bib6)\. This motivates a fundamental research question:

Can we automatically generate scientific evolution trees from citation graphs?

Addressing this problem is highly challenging due to several underexplored issues\. First, scientific evolution trees are hierarchical, temporal, and semantically structured objects, whereas citation graphs are large\-scale sparse relational networks\. Bridging these two fundamentally different structures requires learning evolution\-aware representations that preserve both citation dependencies and temporal scientific progression, which is not directly addressed by existing taxonomy induction methods[Zhang et al\. \(2018\)](https://arxiv.org/html/2609.09561#bib.bib17);[Shen et al\. \(2020\)](https://arxiv.org/html/2609.09561#bib.bib24);[Yu et al\. \(2020\)](https://arxiv.org/html/2609.09561#bib.bib23)or temporal topic modeling approaches[Blei and Lafferty \(2006\)](https://arxiv.org/html/2609.09561#bib.bib14);[Wang and McCallum \(2006\)](https://arxiv.org/html/2609.09561#bib.bib11);[Wang et al\. \(2008\)](https://arxiv.org/html/2609.09561#bib.bib13)\. Second, scientific evolution is inherently dynamic: research paradigms continuously branch, merge, and refine over time, making it difficult to construct stable and interpretable lineage structures from evolving citation graphs\. Existing citation and co\-citation analyses in science\-of\-science research primarily characterize global scientific trends rather than inducing explicit hierarchical evolutionary structures[Fortunato et al\. \(2018\)](https://arxiv.org/html/2609.09561#bib.bib10)\. Third, existing survey papers provide only limited supervision signals, requiring models to generalize from scarce high\-quality evolution annotations\. Moreover, marginal or transitional papers often lie between major paradigms, making them difficult to position within conventional taxonomy induction frameworks without introducing chronological inconsistencies\.

To address those challenges, we propose a structurally staged and temporally constrained framework that unifies taxonomy induction, temporal admissibility, and marginal\-paper re\-attachment into a cohesive pipeline\. Specifically, our framework first constructs a stable, time\-agnostic core taxonomy via distribution\-based hierarchical clustering on graph\-aware node embeddings\. Subsequently, it performs temporal refinement to model evolutionary dynamics and handle marginal papers by attaching them to broader internal concepts, while enforcing temporal consistency and structural legality constraints \(e\.g\., path monotonicity\)\. This staged approach ensures that the conceptual backbone remains robust while temporal dynamics are accurately and logically mapped\.

Our contributions are summarized as follows:

- •Novel Problem Formulation\.We formulate evolutionary tree construction from citation graphs, introducing a dynamic perspective for scientific literature mining\.
- •Staged & Constrained Framework\.We propose a staged framework that separates taxonomy initialization from temporal refinement, preserving citation\-aware structures while filtering peripheral papers from core trajectories\.
- •Evolutionary Dynamics Modeling\.We incorporate temporal and structural constraints with marginal\-paper detection and internal\-node reattachment, alleviating chronological distortions in traditional taxonomy generation\.
- •Comprehensive Benchmark\.We construct the first benchmark for this task across 11 AI subfields, where extensive experiments show consistent gains over taxonomy, citation\-based, and LLM baselines in evolution\-structure quality and annotated concept purity, together with the only non\-trivial marginal\-paper detection\.

## 2Related Work

### 2\.1Automatic Taxonomy Induction

Automatic taxonomy induction studies how to organize terms, entities, or topics into hierarchical structures such as trees or DAGs\. Prior work has shown that taxonomy quality requires more than isolated pairwise hypernym prediction[Snow et al\. \(2006\)](https://arxiv.org/html/2609.09561#bib.bib1);[Bansal et al\. \(2014\)](https://arxiv.org/html/2609.09561#bib.bib8);[Mao et al\. \(2018\)](https://arxiv.org/html/2609.09561#bib.bib16)\. Most existing approaches focus on taxonomy expansion or completion given an existing hierarchy[Shen et al\. \(2020\)](https://arxiv.org/html/2609.09561#bib.bib24);[Yu et al\. \(2020\)](https://arxiv.org/html/2609.09561#bib.bib23);[Mishra et al\. \(2025\)](https://arxiv.org/html/2609.09561#bib.bib22);[Jiang et al\. \(2022\)](https://arxiv.org/html/2609.09561#bib.bib20), or extend the hierarchy formalism itself[Lee et al\. \(2022\)](https://arxiv.org/html/2609.09561#bib.bib19);[Lu et al\. \(2024\)](https://arxiv.org/html/2609.09561#bib.bib18);[Kargupta et al\. \(2025\)](https://arxiv.org/html/2609.09561#bib.bib15)\. A smaller line of work constructs topic or concept hierarchies directly from corpora\. TaxoGen[Zhang et al\. \(2018\)](https://arxiv.org/html/2609.09561#bib.bib17)recursively builds topic taxonomies through adaptive spherical clustering and local embeddings, while HiExpan[Shen et al\. \(2018\)](https://arxiv.org/html/2609.09561#bib.bib21)expands user\-guided seed hierarchies using weakly supervised relation extraction\. A recent line of work applies language models to scholarly taxonomy construction\. TaxoAlign[Lahiri et al\. \(2025\)](https://arxiv.org/html/2609.09561#bib.bib44)generates taxonomies for scientific domains by aligning LM\-induced hierarchies to reference structures, and[Zhu et al\. \(2025\)](https://arxiv.org/html/2609.09561#bib.bib4)induce hierarchical taxonomies for scientific papers via LLM\-guided multi\-aspect clustering\. However, these methods are primarily designed for text corpora and cannot effectively model the structural dependencies\. Moreover, they generally assume static taxonomies and therefore fail to capture temporally constrained scientific evolution, including paradigm transitions and lineage progression across generations of work\.

### 2\.2Knowledge Evolution Modeling

Knowledge evolution modeling studies how scientific concepts, research topics, and paradigms emerge, evolve, and transition over time\. Early work primarily focused on temporal topic modeling, including Dynamic Topic Models[Blei and Lafferty \(2006\)](https://arxiv.org/html/2609.09561#bib.bib14);[Wang et al\. \(2008\)](https://arxiv.org/html/2609.09561#bib.bib13);[Bhadury et al\. \(2016\)](https://arxiv.org/html/2609.09561#bib.bib12)and Topics over Time[Wang and McCallum \(2006\)](https://arxiv.org/html/2609.09561#bib.bib11), which capture topic drift and temporal word distributions across document collections\. Another line of research investigates scientific evolution through citation and co\-citation analysis within the science\-of\-science community[Fortunato et al\. \(2018\)](https://arxiv.org/html/2609.09561#bib.bib10)\. More recently, LLM\-based survey systems such as AutoSurvey[Wang et al\. \(2024\)](https://arxiv.org/html/2609.09561#bib.bib7)and SurveyX[Liang et al\. \(2025\)](https://arxiv.org/html/2609.09561#bib.bib6)retrieve papers, construct outlines, and generate survey\-style text, but primarily optimize textual synthesis rather than explicit structural evolution modeling\. Although several recent works summarize papers into taxonomy\-like structures[Hu et al\. \(2024\)](https://arxiv.org/html/2609.09561#bib.bib5);[Zhu et al\. \(2025\)](https://arxiv.org/html/2609.09561#bib.bib4), none directly addresses scientific evolution tree generation\. Existing methods lack temporal constraints over evolutionary paths, and mechanisms for handling marginal papers or constructing survey\-style evolution structures\.

## 3Problem Formulation

##### Citation graph\.

Given a survey paper, let𝒢=\(𝒱,ℰ𝒢\)\\mathcal\{G\}=\(\\mathcal\{V\},\\mathcal\{E\}\_\{\\mathcal\{G\}\}\)denote the citation graph constructed from its reference set, where each nodevi∈𝒱v\_\{i\}\\in\\mathcal\{V\}is a referenced paper with text contentsis\_\{i\}\(title and abstract\) and publication yearτ⁡\(vi\)\\tau\(v\_\{i\}\)\. A directed edge\(vi,vj\)∈ℰ𝒢\(v\_\{i\},v\_\{j\}\)\\in\\mathcal\{E\}\_\{\\mathcal\{G\}\}indicates that paperviv\_\{i\}cites papervjv\_\{j\}\. For the main evaluation, the target survey itself is excluded from𝒢\\mathcal\{G\}\.

##### Taxonomy tree\.

A taxonomy tree organizes papers by conceptual inclusion\. We denote it as𝒯tax=\(𝒞tax,𝒱,ℰtax,ϕtax\)\\mathcal\{T\}^\{\\mathrm\{tax\}\}=\(\\mathcal\{C\}^\{\\mathrm\{tax\}\},\\mathcal\{V\},\\mathcal\{E\}^\{\\mathrm\{tax\}\},\\phi^\{\\mathrm\{tax\}\}\), where𝒞tax\\mathcal\{C\}^\{\\mathrm\{tax\}\}is the set of topic nodes,𝒱\\mathcal\{V\}is the set of paper nodes, andℰtax⊆𝒞tax×\(𝒞tax∪𝒱\)\\mathcal\{E\}^\{\\mathrm\{tax\}\}\\subseteq\\mathcal\{C\}^\{\\mathrm\{tax\}\}\\times\(\\mathcal\{C\}^\{\\mathrm\{tax\}\}\\cup\\mathcal\{V\}\)forms a rooted tree\. Each topic nodec∈𝒞taxc\\in\\mathcal\{C\}^\{\\mathrm\{tax\}\}represents a semantic concept with labelϕtax​\(c\)\\phi^\{\\mathrm\{tax\}\}\(c\), and each paper nodevi∈𝒱v\_\{i\}\\in\\mathcal\{V\}appears only as a terminal leaf \(i\.e\., for every paper node, its parent must be a concept node rather than another paper node, and this parent corresponds to the lowest\-level concept cluster that directly contains the paper\)\. Thus, edges in𝒯tax\\mathcal\{T\}^\{\\mathrm\{tax\}\}encode conceptual refinement only, with no temporal semantics\.

##### Evolutionary tree\.

An evolutionary tree𝒯=\(𝒞,𝒱,ℰC,ℰP,ϕ\)\\mathcal\{T\}=\(\\mathcal\{C\},\\mathcal\{V\},\\mathcal\{E\}\_\{C\},\\mathcal\{E\}\_\{P\},\\phi\)extends this organization with temporally admissible development relations\.ℰC\\mathcal\{E\}\_\{C\}forms a rooted tree over concepts𝒞\\mathcal\{C\}with labelsϕ\\phi, andℰP=\{\(a⁡\(vi\),vi\)\}\\mathcal\{E\}\_\{P\}=\\\{\(a\(v\_\{i\}\),v\_\{i\}\)\\\}attaches each paper to a concept via the attachment mapa:𝒱→𝒞a:\\mathcal\{V\}\\to\\mathcal\{C\}\. Unlike a taxonomy tree, papers may attach to internal concept nodes when better explained at a coarser abstraction level\.

For each conceptcc, let𝒱att​\(c\)=\{vi:a⁡\(vi\)=c\}\\mathcal\{V\}\_\{\\text\{att\}\}\(c\)=\\\{v\_\{i\}:a\(v\_\{i\}\)=c\\\}denote the papers attached directly tocc, and𝒱⁡\(c\)\\mathcal\{V\}\(c\)the papers in its full subtree\. We define two temporal statistics over publication yearsτ⁡\(⋅\)\\tau\(\\cdot\):

τatt​\(c\)=1\|𝒱att​\(c\)\|​∑v∈𝒱att​\(c\)τ⁡\(v\),τ¯​\(c\)=1\|𝒱⁡\(c\)\|​∑v∈𝒱⁡\(c\)τ⁡\(v\)\.\\tau^\{\\text\{att\}\}\(c\)=\\tfrac\{1\}\{\|\\mathcal\{V\}\_\{\\text\{att\}\}\(c\)\|\}\\\!\\\!\\\!\\sum\_\{v\\in\\mathcal\{V\}\_\{\\text\{att\}\}\(c\)\}\\\!\\\!\\\!\\tau\(v\),\\;\\bar\{\\tau\}\(c\)=\\tfrac\{1\}\{\|\\mathcal\{V\}\(c\)\|\}\\\!\\sum\_\{v\\in\\mathcal\{V\}\(c\)\}\\\!\\tau\(v\)\.\(1\)τatt\\tau^\{\\text\{att\}\}supports structural constraints: because the attachment sets of a parent and its children are disjoint, the constraint it induces is non\-trivial\.τ¯\\bar\{\\tau\}summarizes the full concept body and is used for path\-level evaluation\.

The tree must satisfy \(i\)Rooted Tree; \(ii\)Temporal Consistency, for each concept edge\(cp,cc\)∈ℰC\(c\_\{p\},c\_\{c\}\)\\in\\mathcal\{E\}\_\{C\}from parentcpc\_\{p\}to childccc\_\{c\},

τatt​\(cp\)≤τatt​\(cc\)\+ϵ;\\tau^\{\\text\{att\}\}\(c\_\{p\}\)\\leq\\tau^\{\\text\{att\}\}\(c\_\{c\}\)\+\\epsilon;\(2\)and \(iii\)Sibling Orderingby non\-decreasingτatt\\tau^\{\\text\{att\}\}\. Eq\.[2](https://arxiv.org/html/2609.09561#S3.E2)requires each root\-to\-leaf path to proceed from earlier, broader concepts to later, more specialized ones, with the slackϵ\\epsilonabsorbing noise in publication dates so that a single mis\-dated paper does not invalidate an otherwise valid edge\.

##### Marginal papers\.

A marginal paper has weak compatibility with all leaf\-level concepts\. Given a continuous compatibility scorem⁡\(vi,c\)∈\[0,1\]m\(v\_\{i\},c\)\\in\[0,1\]\(instantiated in §[4\.4\.3](https://arxiv.org/html/2609.09561#S4.SS4.SSS3)\), the marginal set is

ℳ=\{vi∈𝒱:maxℓ∈Leaves⁡\(𝒯\)⁡m⁡\(vi,ℓ\)<η\},\\mathcal\{M\}=\\\{v\_\{i\}\\in\\mathcal\{V\}:\\max\_\{\\ell\\in\\mathrm\{Leaves\}\(\\mathcal\{T\}\)\}m\(v\_\{i\},\\ell\)<\\eta\\\},\(3\)
whereη\\etais a threshold\. Marginal papers are not discarded; they may attach to internal nodes to represent isolated, transitional, or weakly continued contributions\.

##### Challenges and design overview\.

This formalism poses four challenges that shape our method\. \(C1\) The discrete structure\(𝒞,ℰC,a\)\(\\mathcal\{C\},\\mathcal\{E\}\_\{C\},a\)and continuous embeddings\{𝐞i\}\\\{\\mathbf\{e\}\_\{i\}\\\}cannot be jointly optimized end\-to\-end, motivating*alternating refinement*between structure and representation \(§[4\.4\.1](https://arxiv.org/html/2609.09561#S4.SS4.SSS1)\)\. \(C2\) Temporal consistency \(Eq\.[2](https://arxiv.org/html/2609.09561#S3.E2)\) cannot emerge from a time\-agnostic clustering loss, motivating a*temporal merge filter*onτatt\\tau^\{\\text\{att\}\}\(§[4\.4\.1](https://arxiv.org/html/2609.09561#S4.SS4.SSS1)\)\. \(C3\) Marginal papers fall outside leaf\-only partitions, motivating explicit*internal\-node re\-attachment*\(§[4\.4\.3](https://arxiv.org/html/2609.09561#S4.SS4.SSS3)\)\. \(C4\) Temporal refinement risks collapsing the conceptual organization, motivating a*staged design*that establishes a stable backbone𝒯tax\\mathcal\{T\}^\{\\mathrm\{tax\}\}\(§[4\.3](https://arxiv.org/html/2609.09561#S4.SS3)\) before applying temporal pressure \(§[4\.4](https://arxiv.org/html/2609.09561#S4.SS4)\)\.

## 4Methodology

![Refer to caption](https://arxiv.org/html/2609.09561v1/frame.png)Figure 1:Overview of the EvoTree pipeline\.\(A\)Input citation graph encoded by SPECTER2\.\(B\)Shared backbone with graph\-aware encoder and distributional tree builder\.\(C\)Stage I taxonomy backbone learning underℒtax\\mathcal\{L\}^\{\\text\{tax\}\}\.\(D\)Stage II evolutionary refinement via alternating updates underℒevo\\mathcal\{L\}^\{\\text\{evo\}\}\.\(E\)Stage III few\-shot calibration\.\(F\)LLM concept labeling\.### 4\.1Overview

EvoTree \(Fig\.[1](https://arxiv.org/html/2609.09561#S4.F1)\) addresses challenges C1–C4 through three stages over a shared backbone\. The input of EvoTree \(Fig\.[1](https://arxiv.org/html/2609.09561#S4.F1)A\) is a citation graph in which each node carries paper text and a timestamp, encoded by SPECTER2\. The backbone \(§[4\.2](https://arxiv.org/html/2609.09561#S4.SS2)\) couples a graph\-aware encoder with a distributional tree builder that summarizes each cluster as a diagonal Gaussian\. Stage I \(§[4\.3](https://arxiv.org/html/2609.09561#S4.SS3)\) learns a time\-agnostic taxonomy backbone𝒯tax\\mathcal\{T\}^\{\\mathrm\{tax\}\}under section\-derived weak supervision\. Stage II \(§[4\.4](https://arxiv.org/html/2609.09561#S4.SS4)\) refines𝒯tax\\mathcal\{T\}^\{\\mathrm\{tax\}\}into the evolutionary tree𝒯\\mathcal\{T\}through alternating structure–representation updates with temporal admissibility and marginal\-paper handling\. Stage III \(§[4\.5](https://arxiv.org/html/2609.09561#S4.SS5)\) calibrates against reference trees via few\-shot metric learning, and a final LLM pass \(§[4\.6](https://arxiv.org/html/2609.09561#S4.SS6)\) verbalizes concept labels without altering topology\. The main text is self\-contained for the design rationale of each component; appendices provide derivations, loss formulations, and implementation details\.

### 4\.2Shared Backbone

The pipeline rests on two reusable modules: a*graph\-aware paper encoder*and a*distributional tree builder*\.

#### 4\.2\.1Graph\-aware Encoder

The encoder maps each paperviv\_\{i\}to a clustering embedding𝐞i∈ℝd\\mathbf\{e\}\_\{i\}\\in\\mathbb\{R\}^\{d\}from text and citation context\. A pretrained scientific encoder SPECTER2[Singh et al\. \(2022\)](https://arxiv.org/html/2609.09561#bib.bib27)produces a time\-agnostic vector𝐱i\\mathbf\{x\}\_\{i\}, from which a semantic stream𝐳isem=MLPsem​\(𝐱i\)\\mathbf\{z\}\_\{i\}^\{\\mathrm\{sem\}\}=\\mathrm\{MLP\}\_\{\\mathrm\{sem\}\}\(\\mathbf\{x\}\_\{i\}\)and a graph stream𝐡i\(0\)=MLPgraph​\(𝐱i\)\\mathbf\{h\}\_\{i\}^\{\(0\)\}=\\mathrm\{MLP\}\_\{\\mathrm\{graph\}\}\(\\mathbf\{x\}\_\{i\}\)are derived\. The graph stream propagates throughLLlayers with anchored residuals and PairNorm[Zhao and Akoglu \(2020\)](https://arxiv.org/html/2609.09561#bib.bib26):

𝐡i\(l\+1\)=\\displaystyle\\mathbf\{h\}\_\{i\}^\{\(l\+1\)\}=\(4\)PairNorm\\displaystyle\\mathrm\{PairNorm\}\(α​𝐱i\+\(1−α\)​\[β​𝐡i\(l\)\+\(1−β\)​𝐦i\(l\)\]\),\\displaystyle\\left\(\\alpha\\mathbf\{x\}\_\{i\}\+\(1\-\\alpha\)\\big\[\\beta\\mathbf\{h\}\_\{i\}^\{\(l\)\}\+\(1\-\\beta\)\\mathbf\{m\}\_\{i\}^\{\(l\)\}\\big\]\\right\),where𝐦i\(l\)\\mathbf\{m\}\_\{i\}^\{\(l\)\}aggregates messages from citation neighbors \(set to𝟎\\mathbf\{0\}for isolated nodes\)\. The anchored term mitigates over\-smoothing while PairNorm stabilizes propagation under uneven density\. The two streams fuse via a connectivity\-biased gate:

𝐳ifused=λi​𝐡i\(L\)\+\(1−λi\)​𝐳isem,\\displaystyle\\mathbf\{z\}\_\{i\}^\{\\mathrm\{fused\}\}=\\lambda\_\{i\}\\mathbf\{h\}\_\{i\}^\{\(L\)\}\+\(1\-\\lambda\_\{i\}\)\\mathbf\{z\}\_\{i\}^\{\\mathrm\{sem\}\},\(5\)λi=σ⁡\(𝐖g​\[⋅\]\+δ​1​\[iso⁡\(vi\)\]\),\\displaystyle\\quad\\lambda\_\{i\}\\\!=\\\!\\sigma\\\!\\big\(\\mathbf\{W\}\_\{g\}\[\\cdot\]\+\\delta\\,\\mathbb\{1\}\[\\mathrm\{iso\}\(v\_\{i\}\)\]\\big\),withδ<0\\delta<0biasing isolated nodes toward the semantic stream\. The final embedding is𝐞i=L2​Norm​\(𝐳ifused\)\\mathbf\{e\}\_\{i\}=\\mathrm\{L\_\{2\}Norm\}\(\\mathbf\{z\}\_\{i\}^\{\\mathrm\{fused\}\}\); a separate projection𝐩i\\mathbf\{p\}\_\{i\}is reserved for contrastive learning[Chen et al\. \(2020\)](https://arxiv.org/html/2609.09561#bib.bib28)\. Full details in Appendix[F](https://arxiv.org/html/2609.09561#A6)\.

#### 4\.2\.2Distributional Tree Builder

Given embeddings\{𝐞i\}\\\{\\mathbf\{e\}\_\{i\}\\\}, the builder constructs a hierarchical tree through distributional clustering\. HDBSCAN with soft membership[Campello et al\. \(2013\)](https://arxiv.org/html/2609.09561#bib.bib25)yields base clusters\{Ck\}k=1K\\\{C\_\{k\}\\\}\_\{k=1\}^\{K\}and weightswi​kw\_\{ik\}, each summarized asCk∼𝒩⁡\(𝝁k,diag⁡\(𝝈k2\)\)C\_\{k\}\\sim\\mathcal\{N\}\(\\boldsymbol\{\\mu\}\_\{k\},\\mathrm\{diag\}\(\\boldsymbol\{\\sigma\}\_\{k\}^\{2\}\)\)\. Higher\-level concepts arise from bottom\-up agglomeration under the closed\-form 2\-Wasserstein distance:

d2​\(Cp,Cq\)=‖𝝁p−𝝁q‖22\+‖𝝈p−𝝈q‖22\.d^\{2\}\(C\_\{p\},C\_\{q\}\)=\\\|\\boldsymbol\{\\mu\}\_\{p\}\-\\boldsymbol\{\\mu\}\_\{q\}\\\|\_\{2\}^\{2\}\+\\\|\\boldsymbol\{\\sigma\}\_\{p\}\-\\boldsymbol\{\\sigma\}\_\{q\}\\\|\_\{2\}^\{2\}\.\(6\)The parent Gaussian is re\-estimated from union members after each merge, reducing level\-wise drift\. The same builder is used in Stages I and II; what changes between them is the supervision and whether temporal admissibility is enforced\.

### 4\.3Stage I: Taxonomy Backbone Learning

Stage I learns a time\-agnostic backbone𝒯tax\\mathcal\{T\}^\{\\mathrm\{tax\}\}that captures conceptual inclusion\. Inputs are the citation graph, paper texts, and weak hierarchical labels derived from the survey section structure \(each paper inherits its section path\)\. We pre\-train the graph\-aware paper encoder \(§[4\.2\.1](https://arxiv.org/html/2609.09561#S4.SS2.SSS1)\) under three complementary signals:section supervision\(multi\-label classification and level prediction over the section hierarchy\),citation consistency\(link prediction and contrastive ranking on citation edges\), andcluster geometry\(centroid pulling for labeled papers\):

ℒtax=ℒsec\+ℒcite\+ℒgeo\.\\mathcal\{L\}^\{\\mathrm\{tax\}\}=\\mathcal\{L\}\_\{\\mathrm\{sec\}\}\+\\mathcal\{L\}\_\{\\mathrm\{cite\}\}\+\\mathcal\{L\}\_\{\\mathrm\{geo\}\}\.\(7\)Applying the distributional tree builder to the pre\-trained embeddings yields𝒯tax\\mathcal\{T\}^\{\\mathrm\{tax\}\}, which serves as the structural prior for Stage II\. Component formulations are given in Appendix[H](https://arxiv.org/html/2609.09561#A8)\.

We emphasize that section structures serve as weak supervision rather than ground\-truth concept hierarchies: headings reflect expository choices as much as conceptual organization, and their granularity varies across surveys\. Their influence is correspondingly bounded\. They contribute only one of the three terms in Eq\.[7](https://arxiv.org/html/2609.09561#S4.E7), shaping the initialization jointly with the citation and geometry objectives rather than acting as a direct optimization target, and are unavailable at inference\.

### 4\.4Stage II: Evolutionary Refinement

Stage II transforms𝒯tax\\mathcal\{T\}^\{\\mathrm\{tax\}\}into the evolutionary tree𝒯\\mathcal\{T\}, driven by three signals absent from Stage I:temporal admissibility\(Eq\.[2](https://arxiv.org/html/2609.09561#S3.E2)\),citation directionality\(citing papers attach deeper than cited ones\), andmarginal\-paper re\-attachment\. The heavy components \(SPECTER2, GNN weights\) remain frozen; only lightweight adapters \(projection MLP, fusion gate, marginal head, cluster Gaussians\) are fine\-tuned\.

#### 4\.4\.1EM\-style Refinement

Because discrete tree construction and continuous adapter updates cannot be jointly optimized end\-to\-end \(C1\), we adopt an alternating procedure inspired by EM\. We label the two phases as E\-step and M\-step for brevity, without claiming a strict EM optimization of a probabilistic likelihood\.

##### E\-step — structure update\.

With adapters fixed, we re\-apply the distributional tree builder to the current embeddings\. Unlike Stage I, agglomeration is filtered by temporal admissibility: a candidate merge producing parentcpc\_\{p\}from childrenca,cbc\_\{a\},c\_\{b\}is rejected if

τatt​\(cp\)\>min⁡\(τatt​\(ca\),τatt​\(cb\)\)\+ϵ,\\tau^\{\\text\{att\}\}\(c\_\{p\}\)\>\\min\\\!\\big\(\\tau^\{\\text\{att\}\}\(c\_\{a\}\),\\,\\tau^\{\\text\{att\}\}\(c\_\{b\}\)\\big\)\+\\epsilon,\(8\)which uses the sameτatt\\tau^\{\\text\{att\}\}statistic as the formal admissibility condition \(Eq\.[2](https://arxiv.org/html/2609.09561#S3.E2)\)\. This step yields an updated tree𝒯\(t\)\\mathcal\{T\}^\{\(t\)\}and a set of low\-membership marginal candidates\.

##### M\-step — representation update\.

With𝒯\(t\)\\mathcal\{T\}^\{\(t\)\}fixed, we update the adapters under three self\-supervised objectives:

ℒevo=ℒsem\+ℒtemp\+ℒmarg,\\mathcal\{L\}^\{\\mathrm\{evo\}\}=\\mathcal\{L\}\_\{\\mathrm\{sem\}\}\+\\mathcal\{L\}\_\{\\mathrm\{temp\}\}\+\\mathcal\{L\}\_\{\\mathrm\{marg\}\},\(9\)whereℒsem\\mathcal\{L\}\_\{\\mathrm\{sem\}\}preserves parent–child semantic coherence,ℒtemp\\mathcal\{L\}\_\{\\mathrm\{temp\}\}encourages temporal and citation\-direction consistency, andℒmarg\\mathcal\{L\}\_\{\\mathrm\{marg\}\}trains the marginal detector \(§[4\.4\.3](https://arxiv.org/html/2609.09561#S4.SS4.SSS3)\)\. Detailed formulations in Appendix[I](https://arxiv.org/html/2609.09561#A9)\.

#### 4\.4\.2Structural Admissibility Constraints

In addition to the differentiable objectives, the E\-step filters candidate trees using admissibility constraints\. These constraints prevent the evolutionary refinement from producing structures that are temporally invalid or that destroy the semantic backbone learned in Stage I\.

##### Temporal consistency\.

This constraint follows Eq\.[2](https://arxiv.org/html/2609.09561#S3.E2), directly rejecting violating merges\.

##### Backbone preservation\.

This retains the major branches of𝒯tax\\mathcal\{T\}^\{\\mathrm\{tax\}\}via the Major Branch Count:

MBC⁡\(𝒯\)=\|\{c∈children⁡\(r\):\|𝒱⁡\(c\)\|≥ρ​\|𝒱\|\}\|,\\mathrm\{MBC\}\(\\mathcal\{T\}\)=\\big\|\\\{c\\in\\mathrm\{children\}\(r\):\|\\mathcal\{V\}\(c\)\|\\geq\\rho\|\\mathcal\{V\}\|\\\}\\big\|,\(10\)requiringMBC⁡\(𝒯\)≥κ​MBC​\(𝒯tax\)\\mathrm\{MBC\}\(\\mathcal\{T\}\)\\geq\\kappa\\,\\mathrm\{MBC\}\(\\mathcal\{T\}^\{\\mathrm\{tax\}\}\)\.

##### Tree legality\.

The output must remain a valid rooted tree, with a single root, no cycles, and a unique parent for each non\-root concept node\. Detailed constraints are described in Appendix[J](https://arxiv.org/html/2609.09561#A10)\.

#### 4\.4\.3Marginal Paper Handling

Stage II explicitly handles*marginal papers*: papers poorly explained by all fine\-grained leaf concepts, which would blur concept boundaries and weaken temporal coherence if forced into leaves\. We separate handling into leaf\-level detection and all\-node re\-attachment\.

##### Detection\.

For each paperviv\_\{i\}, we compute its best leaf compatibilityAileaf=maxc∈Leaves⁡\(𝒯\(t\)\)⁡m⁡\(vi,c\)A\_\{i\}^\{\\mathrm\{leaf\}\}=\\max\_\{c\\in\\mathrm\{Leaves\}\(\\mathcal\{T\}^\{\(t\)\}\)\}m\(v\_\{i\},c\), wherem⁡\(vi,c\)∈\[0,1\]m\(v\_\{i\},c\)\\in\[0,1\]combines semantic similarity, citation\-neighbor overlap, and temporal compatibility \(Appendix[K](https://arxiv.org/html/2609.09561#A11)\)\. A paper is marginal whenAileaf<ηA\_\{i\}^\{\\mathrm\{leaf\}\}<\\eta, providing pseudo\-labels for a marginal classifier \(optionally reinforced by HDBSCAN low\-membership outliers\)\. Intuitively, a paper is marginal when it is not well explained by any single leaf: its compatibility with even its best\-matching concept falls belowη\\eta, typically because its citations span multiple sibling branches rather than concentrating in one\.

##### Re\-attachment\.

Each flagged marginal paper is re\-attached to the concept whose Gaussian best explains its embedding:

a⁡\(vm\)=arg⁡maxc∈𝒞\(t\)⁡log⁡𝒩⁡\(𝐞m,𝝁c,diag⁡\(𝝈c2\)\)\.a\(v\_\{m\}\)=\\arg\\\!\\max\_\{c\\in\\mathcal\{C\}^\{\(t\)\}\}\\log\\mathcal\{N\}\\\!\\left\(\\mathbf\{e\}\_\{m\};\\,\\boldsymbol\{\\mu\}\_\{c\},\\mathrm\{diag\}\(\\boldsymbol\{\\sigma\}\_\{c\}^\{2\}\)\\right\)\.\(11\)Unlike detection, re\-attachment searches over all concept nodes, allowing papers that fit no fine\-grained leaf to attach to broader internal concepts\.

### 4\.5Stage III: Few\-shot Metric Learning

To inject structural priors that self\-supervised signals alone cannot recover, we calibrate the model on a small set of reference evolutionary trees via few\-shot metric learning\. Only a lightweight adaptation layer \(∼\\sim17% of parameters\) is updated under a small learning rate \(5e\-6\) for 20 epochs over the reference trees \(10 per leave\-one\-domain\-out fold\) — orders of magnitude smaller than standard supervised fine\-tuning\. The calibration losses are purely metric\-learning: they shape embedding geometry to reflect concept clusters and evolution directions, without predicting discrete labels\.

ℒcal=ℒmargcal\+ℒconceptcal\+ℒedgecal\.\\mathcal\{L\}^\{\\mathrm\{cal\}\}=\\mathcal\{L\}^\{\\mathrm\{cal\}\}\_\{\\mathrm\{marg\}\}\+\\mathcal\{L\}^\{\\mathrm\{cal\}\}\_\{\\mathrm\{concept\}\}\+\\mathcal\{L\}^\{\\mathrm\{cal\}\}\_\{\\mathrm\{edge\}\}\.\(12\)Weight and learning\-rate choices ensure the reference signal refines rather than overrides earlier structure\. Full formulations in Appendix[L](https://arxiv.org/html/2609.09561#A12)\.

### 4\.6Concept Labeling

The tree𝒯\\mathcal\{T\}encodes structure but no human\-readable labels\. A single LLM pass traverses𝒯\\mathcal\{T\}bottom\-up:

ϕ⁡\(c\)=LLM⁡\(Π⁡\(c,𝒱⁡\(c\),\{ϕ⁡\(c′\):c′∈children⁡\(c\)\}\)\),\\phi\(c\)=\\mathrm\{LLM\}\\big\(\\Pi\(c,\\,\\mathcal\{V\}\(c\),\\,\\\{\\phi\(c^\{\\prime\}\):c^\{\\prime\}\\in\\mathrm\{children\}\(c\)\\\}\)\\big\),\(13\)whereΠ\\Piis a structured prompt\. Leaf prompts request a precise method name; internal\-node prompts require a more abstract noun phrase that generalizes over \(and does not repeat\) child labels\.The LLM is used only for concept verbalization and does not modify topology or paper attachments\.Prompt templates in Appendix[C](https://arxiv.org/html/2609.09561#A3)\.

## 5Experiments

### 5\.1Datasets

##### Survey\-reference graph dataset\.

We construct 411 ego\-graphs from arXiv survey papers\. Hierarchical weak labels are derived from the survey section structure: a referenced paper inherits the section path in which it appears, e\.g\.,Chapter 2→\\rightarrow2\.2→\\rightarrow2\.2\.3\. We split graphs, rather than individual nodes, into train/validation/test sets with a 70/15/15 ratio\. Detailed statistics are shown in Table[6](https://arxiv.org/html/2609.09561#A2.T6)\.

##### Few\-shot \(FS\) calibration dataset\.

For direct evaluation against annotated labels, we curate 11 reference evolutionary trees spanning major AI subfields, including computer vision, natural language processing, graph learning, reinforcement learning, and large language models\. Each graph contains manual annotations for concept membership \(FS\_concept\), marginal\-paper labels \(FS\_is\_marginal\), evolution edges \(FS\_tree\_edges\), and node depth \(FS\_depth\)\. Detailed statistics are shown in Table[7](https://arxiv.org/html/2609.09561#A2.T7)\. Calibration follows an 11\-fold leave\-one\-domain\-out protocol \(Appendix[B\.3](https://arxiv.org/html/2609.09561#A2.SS3)\)\.

### 5\.2Clustering Semantic Quality and Evolution Structure Quality

#### 5\.2\.1Metrics & Baselines

We evaluate two aspects of tree quality\. For semantic clustering, we reportLeaf Purity \(LP\)andPath Purity \(PP\)to measure topic consistency at the leaf and root\-to\-leaf path levels, respectively, andNMIto measure agreement between the tree\-induced partition and topic labels\. For evolution structure, we reportCitation Direction Accuracy \(CDA\), which checks whether cited papers are placed at shallower depths than citing papers, andPath Monotonicity Rate \(PMR\), which measures whether publication years are non\-decreasing along root\-to\-leaf paths\.

We compare EvoTree with representative flat, hierarchical, citation\-aware, and taxonomy\-induction baselines, including HAC\-SPECTER2[Murtagh and Contreras \(2012\)](https://arxiv.org/html/2609.09561#bib.bib29), KMeans\-flat[Ahmed et al\. \(2020\)](https://arxiv.org/html/2609.09561#bib.bib30), HAC\-4level[Murtagh and Contreras \(2012\)](https://arxiv.org/html/2609.09561#bib.bib29), CitRank\+HAC[Woods \(2024\)](https://arxiv.org/html/2609.09561#bib.bib31), TaxoGen\-style[Zhang et al\. \(2018\)](https://arxiv.org/html/2609.09561#bib.bib17), Hu\-CiteTaxo[Hu et al\. \(2024\)](https://arxiv.org/html/2609.09561#bib.bib5), TaxoAlign[Lahiri et al\. \(2025\)](https://arxiv.org/html/2609.09561#bib.bib44), and Context\-Aware[Zhu et al\. \(2025\)](https://arxiv.org/html/2609.09561#bib.bib4)\. We also reportEvoTree \(Pre\-train\), which disables temporal fine\-tuning, to isolate the effect of representation–structure refinement\.

#### 5\.2\.2Results

Table 1:Clustering semantic quality and evolution structure quality\. Dashes indicate that the method does not produce the required output\. Results are mean±\\pmstandard deviation over 5 runs\. Best results are inbold\.MethodClusteringEvolutionLP↑\\uparrowPP↑\\uparrowNMI↑\\uparrowCDA↑\\uparrowPMR↑\\uparrowHAC\-SPECTER20\.526±\\pm0\.0080\.607±\\pm0\.0090\.399±\\pm0\.011––KMeans\-flat0\.524±\\pm0\.0100\.603±\\pm0\.0110\.392±\\pm0\.012––HAC\-4level0\.586±\\pm0\.0070\.665±\\pm0\.0080\.437±\\pm0\.0101\.0000\.293±\\pm0\.014CitRank\+HAC0\.498±\\pm0\.0110\.574±\\pm0\.0120\.346±\\pm0\.0131\.0000\.250±\\pm0\.015TaxoGen\-style0\.601±\\pm0\.0090\.674±\\pm0\.0080\.511±\\pm0\.0100\.892±\\pm0\.0130\.265±\\pm0\.013Hu\-CiteTaxo0\.664±\\pm0\.0060\.718±\\pm0\.0080\.519±\\pm0\.005–0\.322±\\pm0\.007TaxoAlign0\.650±\\pm0\.0070\.694±\\pm0\.0060\.480±\\pm0\.0090\.883±\\pm0\.0050\.305±\\pm0\.008Context\-Aware0\.713±\\pm0\.0050\.742±\\pm0\.0070\.512±\\pm0\.0060\.821±\\pm0\.0090\.318±\\pm0\.004EvoTree \(Pre\-train\)0\.591±\\pm0\.0080\.689±\\pm0\.0090\.494±\\pm0\.0110\.829±\\pm0\.0120\.284±\\pm0\.013EvoTree0\.653±\\pm0\.0070\.703±\\pm0\.0080\.526±\\pm0\.0090\.893±\\pm0\.0110\.312±\\pm0\.012##### Semantic clustering quality\.

Taxonomy\-generation methods remain competitive here: Context\-Aware leads on LP \(0\.713\) and PP \(0\.742\), exceeding EvoTree by 6\.0 and 3\.9 points\. EvoTree attains the highest NMI \(0\.526\)\. These metrics reward flat leaf coherence alone; EvoTree additionally constrains its hierarchy to be temporally admissible, trading some semantic compactness for evolution\-consistent structure\.

##### Citation\- and time\-consistent evolution structure\.

Hu\-CiteTaxo attains the highest PMR \(0\.322\); its CDA is not comparable, as its output does not expose the directional edges the metric evaluates\. The more informative distinction is structural: none of the three taxonomy\-generation baselines emits evolution edges or marginal scores, so they are not evaluated on the FS\-aligned metrics \(§[5\.3](https://arxiv.org/html/2609.09561#S5.SS3)\)\. The indirect metrics above cover only the semantic objective that taxonomy generation shares with evolution\-tree induction\.

##### Effect of temporal fine\-tuning\.

Comparing EvoTree with EvoTree \(Pre\-train\) isolates the effect of the temporal fine\-tuning stage\. Full EvoTree improves LP and CDA, showing that joint representation–structure refinement improves both semantic coherence and citation\-direction consistency\.

### 5\.3Evaluation on Few\-shot Test

#### 5\.3\.1Metrics & Baselines

We evaluate against the annotated few\-shot dataset using three metrics:FS\-CP, which measures concept purity within predicted leaf nodes;FS\-EDA, which measures whether annotated evolutionary descendants are placed deeper than their predecessors; andFS\-Mar, which evaluates marginal\-paper detection by AUROC\.

We compare EvoTree with clustering baselines from §[5\.2](https://arxiv.org/html/2609.09561#S5.SS2)and LLM\-based baselines that prompt GPT\-4o to generate hierarchies from titles, titles plus years, or titles plus citation\-graph context\. We again include EvoTree \(Pre\-train\) to measure the effect of temporal fine\-tuning\.

#### 5\.3\.2Results

Table 2:Evaluation on the few\-shot benchmark\. Results are mean±\\pmstandard deviation over 5 runs\. Best results are inbold\.MethodFS\-CP↑\\uparrowFS\-EDA↑\\uparrowFS\-Mar↑\\uparrowHAC\-SPECTER20\.600±\\pm0\.0110\.838±\\pm0\.013–CitRank\+HAC0\.739±\\pm0\.0101\.000–TaxoGen\-style0\.661±\\pm0\.0110\.929±\\pm0\.012–LLM \(title\)0\.767±\\pm0\.0090\.964±\\pm0\.010–LLM \(title \+ year\)0\.759±\\pm0\.0100\.937±\\pm0\.011–LLM \(citation graphs\)0\.769±\\pm0\.0090\.952±\\pm0\.010–EvoTree \(Pre\-train\)0\.653±\\pm0\.0110\.904±\\pm0\.0120\.662±\\pm0\.013EvoTree0\.775±\\pm0\.0080\.949±\\pm0\.0100\.726±\\pm0\.011##### Alignment with annotated concepts\.

On the few\-shot dataset, EvoTree achieves the highest FS\-CP, though the gap is narrow\. Its improvement over the strongest LLM baseline is modest, but it consistently outperforms clustering\-based baselines and substantially improves over EvoTree \(Pre\-train\), indicating that temporal fine\-tuning and tree refinement help align predicted clusters with ground\-truth concepts\.

##### Evolution\-direction accuracy\.

EvoTree is on par with the strongest LLM baseline on FS\-EDA\. The strong performance of LLM\-title suggests that large language models can often infer local predecessor–successor relations from method names alone\. However, LLM\-only methods do not provide explicit structure\-level constraints or marginality estimates, which are required for controlled, audit\-friendly tree construction\.

##### Marginal\-paper detection\.

FS\-Mar reflects a structural capability that, to our knowledge, no other method evaluated in this work exposes: standard clustering and LLM baselines produce only hard assignments and therefore admit no continuous marginality score, while EvoTree directly outputs marginality scores from its hierarchical structure\. EvoTree obtains a non\-trivial FS\-Mar AUROC and improves over its pre\-training\-only variant, supporting the value of modeling boundary papers rather than forcing every paper into a fine\-grained leaf cluster\.

### 5\.4Ablation Studies

#### 5\.4\.1Contribution of Each Training Stage

EvoTree is trained in three stages:Pre\-train only\(Stage I\) uses multi\-task supervision with section structure as weak labels;\+ Post\-train\(Stage II\) adds self\-supervised evolutionary losses;\+ FS\-correction\(Stage III few\-shot calibration; our full model\) injects structural priors via few\-shot metric learning on the reference trees\. We evaluate on test graphs and on the FS dataset \(Table[3](https://arxiv.org/html/2609.09561#S5.T3)\) to verify that gains generalize beyond the FS\-correction training set\.

Table 3:Ablation study on the contribution of each training stage\. Left: clustering and evolution\-structure metrics on test graphs; right: FS\-aligned metrics on the 11 annotated domains\. Results are mean±\\pmstandard deviation over 5 runs\. Best results are inbold\.VariantClusteringEvolutionFS\-alignedLP↑\\uparrowPP↑\\uparrowNMI↑\\uparrowCDA↑\\uparrowPMR↑\\uparrowFS\-CP↑\\uparrowFS\-EDA↑\\uparrowFS\-Mar↑\\uparrowPre\-train only0\.541±\\pm0\.0100\.629±\\pm0\.0110\.530±\\pm0\.0110\.829±\\pm0\.0130\.240±\\pm0\.0140\.553±\\pm0\.0110\.954±\\pm0\.0120\.662±\\pm0\.013\+ Post\-train0\.598±\\pm0\.0090\.665±\\pm0\.0090\.455±\\pm0\.0110\.857±\\pm0\.0120\.270±\\pm0\.0130\.657±\\pm0\.0100\.880±\\pm0\.0120\.750±\\pm0\.012\+ FS\-correction0\.653±\\pm0\.0070\.703±\\pm0\.0080\.526±\\pm0\.0090\.893±\\pm0\.0110\.312±\\pm0\.0120\.775±\\pm0\.0080\.949±\\pm0\.0100\.726±\\pm0\.011Both later stages deliver substantial gains in leaf purity and concept\-level alignment \(FS\-CP\+0\.104\+0\.104after post\-training and a further\+0\.118\+0\.118after FS\-correction\), consistent with the self\-supervised evolutionary losses injecting temporal structure that label supervision cannot capture, and with the few\-shot priors sharpening concept boundaries\. Post\-training yields the largest gain in marginal\-paper recognition \(FS\-Mar0\.662→0\.7500\.662\\rightarrow 0\.750\), most of which FS\-correction preserves \(0\.7260\.726\)\. These gains also transfer to test graphs unseen during FS\-correction training, mitigating concerns about overfitting to the reference trees\. The dip in FS\-EDA after post\-training reflects the tension between self\-supervised temporal refinement and strict depth ordering; FS\-correction recovers most of it \(0\.880→0\.9490\.880\\rightarrow 0\.949\)\.

#### 5\.4\.2Necessity of Graph Structure

To verify that the GNN exploits the citation graph rather than merely propagating SPECTER2 embeddings, we constructPre\-train \(MLP\)— identical toPre\-train \(GNN\)in hyperparameters and training objective but with the citation edge set replaced by an empty set, so any gap is attributable solely to the citation graph\.

Table 4:Ablation study on the necessity of the citation graph\. “Val\. score” is the validation score during training\. Best inbold\. Mean±\\pmstd over 5 runs\.VariantLP↑\\uparrowPP↑\\uparrowNMI↑\\uparrowPMR↑\\uparrowVal\. score↑\\uparrowPre\-train \(MLP, no graph\)0\.450±\\pm0\.0120\.536±\\pm0\.0130\.363±\\pm0\.0130\.306±\\pm0\.0130\.514±\\pm0\.014Pre\-train \(GNN, with graph\)0\.541±\\pm0\.0100\.629±\\pm0\.0110\.464±\\pm0\.0110\.240±\\pm0\.0140\.780±\\pm0\.010Table 5:Generation\-quality evaluation on the FS domains under two independent protocols, LLM\-as\-a\-Judge and Human evaluation\. Scores are on a 1–10 scale \(mean±\\pmstandard deviation over LLM runs or human evaluators\)\. Best results are inbold\.LLM\-as\-a\-JudgeHuman evaluationMethodConceptEvolutionTransitionalOverallConceptEvolutionTransitionalOverallCitRank\+HAC4\.21±\\pm0\.123\.57±\\pm0\.142\.82±\\pm0\.064\.08±\\pm0\.044\.77±\\pm0\.074\.38±\\pm0\.054\.90±\\pm0\.094\.21±\\pm0\.09Hu\-CiteTaxo4\.55±\\pm0\.114\.73±\\pm0\.073\.57±\\pm0\.134\.64±\\pm0\.146\.65±\\pm0\.155\.87±\\pm0\.105\.82±\\pm0\.016\.19±\\pm0\.05TaxoAlign5\.44±\\pm0\.054\.89±\\pm0\.114\.22±\\pm0\.054\.67±\\pm0\.065\.94±\\pm0\.055\.61±\\pm0\.085\.26±\\pm0\.056\.44±\\pm0\.04Context\-Aware5\.60±\\pm0\.145\.20±\\pm0\.044\.40±\\pm0\.075\.10±\\pm0\.126\.81±\\pm0\.046\.32±\\pm0\.145\.97±\\pm0\.016\.67±\\pm0\.09TaxoGen\-style7\.14±\\pm0\.055\.66±\\pm0\.114\.97±\\pm0\.046\.27±\\pm0\.128\.64±\\pm0\.056\.18±\\pm0\.035\.93±\\pm0\.137\.40±\\pm0\.12EvoTree6\.03±\\pm0\.137\.51±\\pm0\.046\.85±\\pm0\.106\.82±\\pm0\.057\.16±\\pm0\.088\.65±\\pm0\.156\.47±\\pm0\.118\.05±\\pm0\.03Removing the citation graph causes an even larger gap in validation score than at inference, indicating that the graph contributes signal throughout optimization\. The MLP variant’s slightly higher PMR is a degenerate artifact: without citation constraints, tree construction relies on the temporal distribution of embeddings alone, trivially producing monotonic paths — mirroring the CDA artifact for HAC\-4level in §[5\.2](https://arxiv.org/html/2609.09561#S5.SS2)\. Together with the training\-stage ablation \(§[5\.4\.1](https://arxiv.org/html/2609.09561#S5.SS4.SSS1)\), these results confirm that EvoTree relies jointly on the citation graph as a structural backbone and on the staged training framework that progressively injects supervised, self\-supervised, and correction signals\.

### 5\.5Generation Quality

The metrics in Tables[1](https://arxiv.org/html/2609.09561#S5.T1)and[2](https://arxiv.org/html/2609.09561#S5.T2)measure agreement with reference partitions and citation ordering, but not whether a structure reads as a coherent account of how a field developed\. We therefore evaluate the generated structures directly under two independent protocols: an LLM judge, instantiated with the same model as concept labeling \(§[4\.6](https://arxiv.org/html/2609.09561#S4.SS6)\) and run multiple times per structure, and three CS graduate students distinct from the FS annotators, scoring independently\. Both apply the same four criteria—conceptual organization, scientific evolution, transitional\-paper placement, and overall quality—to anonymized structures in randomized order\. Protocol details are in Appendix[N](https://arxiv.org/html/2609.09561#A14)\.

Both protocols rank EvoTree first on overall quality and produce the same overall ordering of all six methods \(Table[5](https://arxiv.org/html/2609.09561#S5.T5)\)\. EvoTree leads on scientific evolution and transitional\-paper placement, the two dimensions taxonomy induction does not target, while TaxoGen\-style leads on conceptual organization\. The latter follows from temporal admissibility: when a method family develops over a long span, enforcing Eq\.[2](https://arxiv.org/html/2609.09561#S3.E2)separates papers that are semantically adjacent but temporally distant, at some cost to leaf\-level compactness—the same trade\-off behind EvoTree’s lower LP and PP\. The rubric is generic across hierarchy\-generation methods and does not reward EvoTree\-specific mechanisms such as temporal constraints or internal\-node re\-attachment\.

## 6Conclusion

We introduced EvoTree, the first framework for automatically inducing scientific evolution trees from citation graphs, and formalized the task with an annotated benchmark covering 11 AI subfields\. By decoupling conceptual backbone learning from temporal refinement, EvoTree first constructs a stable taxonomy via graph\-aware encoding and distribution\-based hierarchical clustering, then re\-attaches marginal papers to internal nodes under monotonic\-path constraints, and finally invokes an LLM solely for concept verbalization without altering topology\. Against taxonomy\-induction, citation\-only, and LLM\-based baselines, EvoTree attains the best NMI, citation\-direction accuracy, and annotated concept purity, is preferred by both LLM and human judges on overall quality, and is the only method that recovers transitional papers with non\-trivial accuracy; ablations confirm that both the citation graph and the staged training framework are jointly necessary\. We view evolution\-tree induction as a step toward scalable, temporally faithful organization of scientific literature\.

## Limitations

##### Scope of domains\.

Our 411 ego\-graphs and 11 reference trees are drawn from AI surveys\. We have not verified transfer to disciplines whose citation conventions and paradigm cadences differ substantially from AI\.

##### Scale of the few\-shot reference set\.

The FS dataset comprises 11 curated reference trees and 352 papers, sufficient to demonstrate the few\-shot regime but limiting fine\-grained per\-domain analyses; a larger curated set would strengthen alignment evaluation\.

##### Reliance on survey section structure\.

Stage I assumes that section organization reflects a coherent conceptual taxonomy\. Surveys organized by application area or chronology may provide weaker supervision than those organized by methodology\.

##### Temporal signal noise\.

Publication years conflate arXiv preprint, conference, and journal dates, introducing noise into the temporal\-admissibility constraint and PMR\. This contributes to the modest absolute PMR values observed in our experiments\.

##### External LLM dependence\.

Concept labels are generated by GPT\-4\.1\-mini\. Although the LLM is used only for verbalization and does not alter topology, this introduces a dependency on a closed\-source model; substituting an open\-source LLM is straightforward but may change labeling style\.

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## Appendix ACase Study: Evolution Tree on Adversarial Attacks on Text\-to\-Image Diffusion Models

### A\.1Setup

We instantiate EvoTree on the reference corpus of*Adversarial Attacks and Defenses on Text\-to\-Image Diffusion Models: A Survey*[Zhang et al\. \(2025\)](https://arxiv.org/html/2609.09561#bib.bib32)111arXiv:2407\.15861\., which serves as both the ego node and the topical anchor of the resulting tree\. The survey was selected because \(i\) it provides a recent, curated, and topically coherent snapshot of an actively evolving subfield, \(ii\) it spans both attack\-side and defense\-side work, allowing the tree to surface convergent research lines, and \(iii\) the ego node itself appears as paper \[20\] in the corpus, providing a natural reference point for the green branch\. Unlike the experiments setting, we retain the survey node in this case\-study visualization to anchor the visual layout and to illustrate how the ego work would be positioned by EvoTree in its own subfield\.

After deduplication and minor filtering of off\-topic citations, the corpus contains6161papers published between 2021 and 2024\. EvoTree organizes them into1212leaf clusters grouped under44top\-level branches, as visualized in Figure[2](https://arxiv.org/html/2609.09561#A1.F2)\. The bracketed indices\[1\]\[1\]–\[61\]\[61\]refer exclusively to the corpus entries and are independent of the bibliography numbering in the main paper\.

![Refer to caption](https://arxiv.org/html/2609.09561v1/diffusion_adv_clean.png)Figure 2:Evolution tree generated by EvoTree for the topic*Adversarial Attacks on Text\-to\-Image Diffusion Models*, instantiated on the reference corpus of the survey by[Zhang et al\. \(2025\)](https://arxiv.org/html/2609.09561#bib.bib32)\. Cluster labels are produced by an LLM; the layout is rendered from the induced tree\.
### A\.2Branch and Cluster Overview

The four top\-level branches partition the corpus along complementary dimensions of the research landscape:

- •Adversarial Threats and Defenses in Generative Models\(19 papers, blue\) — work targeting T2I diffusion models with adversarial prompts, red\-teaming protocols, and safety filter evaluation\.
- •Adversarial Robustness and Defense Methods\(3 papers, green\) — robustness evaluation studies and the ego survey itself\.
- •Text\-Conditioned Image Diffusion Models\(19 papers, red\) — the foundation\-model lineage on which downstream attack/defense work depends, from unconditional DDPM\-class models through latent and spatially conditioned T2I systems\.
- •Concept Manipulation and Optimization\(20 papers, purple\) — concept erasure, model editing, and pruning techniques that intersect heavily with the safety agenda\.

### A\.3Analysis and Discussion

EvoTree recovers three structural properties of the subfield\. \(i\) A clear*foundation–application*stratification: the red branch \(DiT \[24\][Peebles and Xie \(2023\)](https://arxiv.org/html/2609.09561#bib.bib33), latent diffusion \[31\][Rombach et al\. \(2022\)](https://arxiv.org/html/2609.09561#bib.bib34), GLIDE \[32\][Nichol et al\. \(2021\)](https://arxiv.org/html/2609.09561#bib.bib35), SDXL \[27\][Podell et al\. \(2024\)](https://arxiv.org/html/2609.09561#bib.bib36), and spatially conditioned variants \[38\]–\[41\][Couairon et al\. \(2023\)](https://arxiv.org/html/2609.09561#bib.bib37);[Chefer et al\. \(2023\)](https://arxiv.org/html/2609.09561#bib.bib38);[Avrahami et al\. \(2023\)](https://arxiv.org/html/2609.09561#bib.bib39);[Balaji et al\. \(2022\)](https://arxiv.org/html/2609.09561#bib.bib40)\) temporally and conceptually precedes the attack and editing work in the blue and purple branches\. \(ii\) The concept\-erasure cluster \(entries \[42\]–\[55\][Wu et al\. \(2025\)](https://arxiv.org/html/2609.09561#bib.bib41);[Zhang et al\. \(2024\)](https://arxiv.org/html/2609.09561#bib.bib42)\) is the densest single thematic block, marking it as the dominant defense paradigm in this timeframe—ahead of input\-side filtering or output\-side detection\. \(iii\) The blue branch is essentially confined to 2023 and later, placing adversarial\-attack research on T2I[Yang et al\. \(2024\)](https://arxiv.org/html/2609.09561#bib.bib43)roughly two years behind the foundation work\.

## Appendix BDetails of Datasets

### B\.1Main Dataset

We construct 411 ego\-graphs from arXiv survey papers\. Each graph is centered on one survey paper: its references form the graph nodes, and citations among these references form the directed edges\. The survey node itself is excluded\. Each paper node carries a title, an abstract, a publication year, and a 768\-dimensional SPECTER2[Singh et al\. \(2022\)](https://arxiv.org/html/2609.09561#bib.bib27)embedding\. Weak hierarchical labels are inherited from the survey’s section structure: a referenced paper takes on the section path in which it appears, e\.g\.,Chapter 2→\\rightarrow2\.2→\\rightarrow2\.2\.3\. We split at the graph level, rather than the node level, into train/validation/test sets with a 70/15/15 ratio\.

Table 6:Statistics of the survey\-reference graph dataset\.StatisticValueGraphs411Paper nodes44,812Citation edges205,725Avg\. nodes / graph109\.0Avg\. edges / graph500\.5Node embedding dim\.768
### B\.2Few\-shot Dataset

Table 7:Statistics of the FS dataset\.StatisticValueDomains11Paper nodes352FS evolution edges90FS marginal papers24Avg\. nodes / domain32\.0##### Annotation schema\.

Each domain graph contains four types of annotations: \(i\)FS\_concept, which assigns each paper to a defined method concept; \(ii\)FS\_is\_marginal, which marks papers that lie on topic boundaries or cannot be confidently assigned to a fine\-grained concept; \(iii\)FS\_tree\_edges, which records directed method\-evolution relations, each typed asextends,improves, or \(cross\-domain\)adapts, where the source paper is regarded as an extension or improvement of the target paper; and \(iv\)FS\_depth, which indicates the depth of a paper in the evolution structure\.

##### Domain coverage\.

The FS dataset contains 11 high\-quality annotated AI subfields\. We retain domains with sufficiently informative annotations for concept membership, evolution relations, and marginal\-paper evaluation, and exclude domains whose evolution\-edge annotations are too sparse for reliable FS\-based comparison\. Table[8](https://arxiv.org/html/2609.09561#A2.T8)reports the per\-domain statistics\.

Table 8:Per\-domain statistics of the annotated FS dataset\.NNdenotes the number of papers in each domain\. “Concepts” denotes the number of annotated method concepts\. “FS edges” denotes the number of annotated method\-evolution edges\. “Marginal” denotes the number of papers annotated as marginal or boundary papers\.DomainNNConceptsFS edgesMarginal3D Vision255114CV ConvNets40741Vision Transformers27423GAN Image Synthesis236103LLM Alignment555121Meta / Few\-shot275132NLP Transformers35632Object Detection38631Self\-supervised Learning295112Semantic Segmentation375142Video Understanding16673Total352609024Average32\.05\.58\.22\.2
##### FS evaluation protocol\.

The FS benchmark participates in Stage III calibration under an 11\-fold leave\-one\-domain\-out protocol\. In each fold, calibration uses the 10 remaining domains and evaluation is performed on the held\-out domain; the held\-out domain’s concept labels, marginal\-paper labels, evolution edges, and depth annotations are used neither for calibration nor for validation, threshold selection, or hyperparameter tuning\. Each of the 11 domains serves once as the held\-out domain; FS\-aligned metrics are averaged over the 11 held\-out evaluations, and we report the mean and standard deviation of this average over 5 runs\.

### B\.3FS Cross\-domain Overlap

The leave\-one\-domain\-out protocol assumes that the held\-out domain is genuinely unseen during calibration\. Because the 11 FS domains are drawn from surveys within a single broad field, this assumption could be weakened if the same papers recur across domains: a paper appearing in both the calibration and held\-out sets would leak its annotation indirectly\. We therefore quantify paper\-level overlap across all domain pairs\.

Table[9](https://arxiv.org/html/2609.09561#A2.T9)reports the number of papers shared by each pair of domains, with domain sizes on the diagonal\. Overlap is sparse throughout: the largest shared count is 3 papers, or 8\.6% when normalized by the smaller domain in the pair, and most pairs share at most one or two papers\. The non\-negligible overlaps concentrate between semantically adjacent domains \(D2/D6/D8: CV ConvNets, Object Detection, and Semantic Segmentation; D10/D11: NLP Transformers and LLM Alignment\), which is expected since neighboring subfields cite a common set of foundational works\. Under this level of overlap, a held\-out domain’s evaluation set is composed almost entirely of papers absent from the corresponding calibration folds, so the FS\-aligned results are unlikely to reflect within\-set memorization\.

D1D2D3D4D5D6D7D8D9D10D11D1251100101000D2140212323200D3122711121121D4011230010000D5021027100100D6131013813200D7022101291000D8131003137100D9021012011600D10002000000353D11001000000355Table 9:Pairwise paper\-level overlap across the 11 FS domains\. Diagonal entries \(bold\) give domain sizes; off\-diagonal entries give the number of papers shared by the two domains\.We note that overlap counts alone do not exclude all forms of information sharing—semantically similar papers may appear under different identifiers across surveys\. The reported figures bound direct duplication, not conceptual proximity between domains\.

### B\.4FS Benchmark Construction and Annotation

The 11 reference evolution trees were curated from survey papers that explicitly present evolution diagrams or method\-lineage organizations, rather than topic\-only taxonomies\. This requirement restricts the candidate pool but ensures each reference tree reflects an author\-endorsed account of how the field developed, which we standardize into a unified annotation format\.

Three graduate students annotated four aspects independently, following a shared guideline: concept membership \(which concept node each paper belongs to\), evolution edges \(directed development relations between concepts\), marginal\-paper labels \(whether a paper is better explained at a coarser abstraction level\), and paper depth\. Annotators worked from paper titles, abstracts, publication years, and the citation graph, and had access to the source survey\.

## Appendix CConcept\-Labeling Prompt Templates

This appendix provides the full prompt templates used in the bottom\-up concept generation pass described in §[4\.6](https://arxiv.org/html/2609.09561#S4.SS6)\. Both templates are instantiated per node and consumed by GPT\-4\.1\-mini at temperature0\.10\.1\.

### C\.1Leaf Prompt

A leaf node represents a specific research micro\-topic\. The prompt supplies all paper titles with publication years and instructs the model to produce a precise 3–6 word noun phrase naming the shared method or technique, explicitly discouraging generic openers \(e\.g\.,*Advanced*,*Large*\)\.

### C\.2Internal\-Node Prompt

An internal node must generalize over its children\. The prompt provides the already\-assigned child concept names \(bottom\-up guarantee\) and a sample of representative papers\. The model is explicitly required to produce a label that \(i\) is more abstract than any single child, and \(ii\) does not repeat any child label verbatim\.

Leaf\-node promptYou are assigning a precise concept label to a leaf cluster in an academic evolutionary taxonomy\. The cluster groups closely related papers that share a specific research method, task, or technique\.Papers in this cluster:\[list of titles with years\]Note: these papers spanYYYY\-\-YYYY\. Reflect the temporal focus if it is distinctive\.Requirements:1\.Use 3–6 words; noun phrase, no verbs\.2\.Be specific — prefer method/technique names over broad area names\.3\.Do NOT start with ‘Advanced’, ‘Large’, or ‘Modern’\.Reply with ONLY the concept name, nothing else\.

Internal\-node promptYou are assigning a concept label to an internal node in an academic evolutionary taxonomy\. This node is the common parent of several sub\-topics and must be named at a higher level of abstraction than its children\.Child sub\-topics:\[• child\_label\_1, • child\_label\_2, …\]This subtree coversYYYY\-\-YYYY\.Representative papers from this subtree \(sample\):\[up to 5 titles with years\]Requirements:1\.Use 3–6 words; noun phrase, no verbs\.2\.The name must generalize over ALL child sub\-topics listed above\.3\.It must be more abstract than any single child concept\.4\.Do NOT repeat a child concept name verbatim\.Reply with ONLY the concept name, nothing else\.

## Appendix DEvaluation Metrics

This appendix specifies the eight evaluation metrics used in §[5](https://arxiv.org/html/2609.09561#S5)\. We organize them into two parts:*indirect metrics*computed on citation graphs without annotation, and*few\-shot metrics*computed on the 11 annotated graphs\. Table[10](https://arxiv.org/html/2609.09561#A4.T10)summarizes the role of each metric\.

Table 10:Summary of evaluation metrics\. “FS” indicates whether the metric requires annotation\.MetricWhat it measuresSignal sourceEq\.StageFS?LPLeaf\-cluster topic homogeneitySection labelsEq\.[15](https://arxiv.org/html/2609.09561#A4.E15)1—PPLeaf\-cluster path consistencySection pathsEq\.[16](https://arxiv.org/html/2609.09561#A4.E16)1—NMICluster–class agreement at depth 2Section labelsEq\.[17](https://arxiv.org/html/2609.09561#A4.E17)1—CDACitation direction vs\. tree depthCitation graphEq\.[18](https://arxiv.org/html/2609.09561#A4.E18)2—PMRWhole\-path temporal monotonicityPublication yearsEq\.[20](https://arxiv.org/html/2609.09561#A4.E20)2—FS\-CPLeaf vs\. conceptConceptsEq\.[21](https://arxiv.org/html/2609.09561#A4.E21)3✓FS\-EDAEvolution direction vs\. tree depthEvolution edgesEq\.[22](https://arxiv.org/html/2609.09561#A4.E22)3✓FS\-MarMarginal\-paper detection \(AUROC\)Marginal flagsEq\.[23](https://arxiv.org/html/2609.09561#A4.E23)3✓Throughout this appendix,𝒯\\mathcal\{T\}denotes a predicted evolutionary tree with leaf setLeaves⁡\(𝒯\)=\{L1,…,LK\}\\mathrm\{Leaves\}\(\\mathcal\{T\}\)=\\\{L\_\{1\},\\ldots,L\_\{K\}\\\}\. For each leafLkL\_\{k\},ℳk\\mathcal\{M\}\_\{k\}denotes the set of papers attached toLkL\_\{k\}\(i\.e\.,𝒱⁡\(Lk\)\\mathcal\{V\}\(L\_\{k\}\)restricted to direct attachment\)\. Each paperviv\_\{i\}carries a publication yearτ⁡\(vi\)\\tau\(v\_\{i\}\), a section\-label set𝐲i⊆𝒴\\mathbf\{y\}\_\{i\}\\subseteq\\mathcal\{Y\}\(multi\-hot weak labels from the survey vocabulary\), and a section\-path set𝐡i⊆ℋ\\mathbf\{h\}\_\{i\}\\subseteq\\mathcal\{H\}from the pretrained section taxonomy\. For papers in the annotated set𝒱fs\\mathcal\{V\}^\{\\mathrm\{fs\}\}, additional labels include a conceptgi∈𝒢fsg\_\{i\}\\in\\mathcal\{G\}^\{\\mathrm\{fs\}\}\(single\-label, deterministic\), a marginal flagyim,fs∈\{0,1\}y\_\{i\}^\{\\mathrm\{m,fs\}\}\\in\\\{0,1\\\}, and an evolution edge setℰevo\\mathcal\{E\}^\{\\mathrm\{evo\}\}over papers\. We writeδ⁡\(vi\)\\delta\(v\_\{i\}\)for the depth of the concept node to whichviv\_\{i\}is attached — whether that node is a leaf or an internal node \(root depth=0=0\)\. For methods that produce only leaf\-level partitions \(all baselines in this work\),δ⁡\(vi\)\\delta\(v\_\{i\}\)is trivially the depth of the assigned leaf\.

### D\.1Indirect metrics on held\-out test graphs

##### LP — Leaf Label Purity\.

The label purity of a leafLkL\_\{k\}is the fraction of its labeled papers covered by its single most frequent section label:

Purity\(Lk\)=maxℓ∈𝒴⁡\|\{vi∈ℳk:ℓ∈𝐲i\}\|\|\{vi∈ℳk:𝐲i≠∅\}\|\.\\mathrm\{Purity\}\(L\_\{k\}\)=\\frac\{\\displaystyle\\max\_\{\\ell\\in\\mathcal\{Y\}\}\\big\|\\\{v\_\{i\}\\in\\mathcal\{M\}\_\{k\}:\\ell\\in\\mathbf\{y\}\_\{i\}\\\}\\big\|\}\{\\big\|\\\{v\_\{i\}\\in\\mathcal\{M\}\_\{k\}:\\mathbf\{y\}\_\{i\}\\neq\\emptyset\\\}\\big\|\}\.\(14\)LP averages this across leaves:

LP=1K​∑k=1KPurity⁡\(Lk\)\.\\mathrm\{LP\}=\\frac\{1\}\{K\}\\sum\_\{k=1\}^\{K\}\\mathrm\{Purity\}\(L\_\{k\}\)\.\(15\)LP measures topic homogeneity within each leaf cluster\.

##### PP — Leaf Path Purity\.

PP applies the same definition but operates over section\-path labels𝐡i\\mathbf\{h\}\_\{i\}instead of label sets𝐲i\\mathbf\{y\}\_\{i\}:

PP=1K∑k=1Kmaxh∈ℋ⁡\|\{vi∈ℳk:h∈𝐡i\}\|\|\{vi∈ℳk:𝐡i≠∅\}\|\.\\mathrm\{PP\}=\\frac\{1\}\{K\}\\sum\_\{k=1\}^\{K\}\\frac\{\\displaystyle\\max\_\{h\\in\\mathcal\{H\}\}\\big\|\\\{v\_\{i\}\\in\\mathcal\{M\}\_\{k\}:h\\in\\mathbf\{h\}\_\{i\}\\\}\\big\|\}\{\\big\|\\\{v\_\{i\}\\in\\mathcal\{M\}\_\{k\}:\\mathbf\{h\}\_\{i\}\\neq\\emptyset\\\}\\big\|\}\.\(16\)PP is stricter than LP: papers grouped in the same leaf must agree not only on labels but on the full hierarchical path leading to them in the survey taxonomy\.

##### NMI — Normalized Mutual Information\.

To compare predicted trees against flat\-clustering baselines under equal granularity, we truncate𝒯\\mathcal\{T\}at depth22, obtaining a per\-paper cluster assignmentc^i∈\{1,…,K′\}\\hat\{c\}\_\{i\}\\in\\\{1,\\ldots,K^\{\\prime\}\\\}\. The reference class for paperviv\_\{i\}is its lexicographically smallest labelyi=min⁡\(𝐲i\)y\_\{i\}=\\min\(\\mathbf\{y\}\_\{i\}\)\. Restricting to papers with𝐲i≠∅\\mathbf\{y\}\_\{i\}\\neq\\emptysetandc^i\\hat\{c\}\_\{i\}defined,

NMI=2​I​\(C^,Y\)H⁡\(C^\)\+H⁡\(Y\),\\mathrm\{NMI\}=\\frac\{2\\,I\(\\hat\{C\};Y\)\}\{H\(\\hat\{C\}\)\+H\(Y\)\},\(17\)whereI⁡\(⋅,⋅\)I\(\\cdot;\\cdot\)is mutual information andH⁡\(⋅\)H\(\\cdot\)is entropy, following the arithmetic\-mean normalization in scikit\-learn\.

##### CDA — Citation Direction Accuracy\.

For a citation edge\(vs,vd\)∈ℰ𝒢\(v\_\{s\},v\_\{d\}\)\\in\\mathcal\{E\}\_\{\\mathcal\{G\}\}in whichvsv\_\{s\}citesvdv\_\{d\},vsv\_\{s\}is typically the more recent work building onvdv\_\{d\}\. We expectvsv\_\{s\}to attach at a depth no shallower thanvdv\_\{d\}\. To suppress citations within the same year \(which carry weak directional information\), we restrict to edges with year gapτ⁡\(vs\)−τ⁡\(vd\)≥1\\tau\(v\_\{s\}\)\-\\tau\(v\_\{d\}\)\\geq 1:

CDA=\\displaystyle\\mathrm\{CDA\}=\(18\)\|\{\(vs,vd\)∈ℰ𝒢:δ\(vs\)≥δ\(vd\),τ\(vs\)−τ\(vd\)≥1\}\|\|\{\(vs,vd\)∈ℰ𝒢:τ⁡\(vs\)−τ⁡\(vd\)≥1\}\|\\displaystyle\\frac\{\\big\|\\\{\(v\_\{s\},v\_\{d\}\)\\in\\mathcal\{E\}\_\{\\mathcal\{G\}\}:\\delta\(v\_\{s\}\)\\geq\\delta\(v\_\{d\}\),\\;\\tau\(v\_\{s\}\)\-\\tau\(v\_\{d\}\)\\geq 1\\\}\\big\|\}\{\\big\|\\\{\(v\_\{s\},v\_\{d\}\)\\in\\mathcal\{E\}\_\{\\mathcal\{G\}\}:\\tau\(v\_\{s\}\)\-\\tau\(v\_\{d\}\)\\geq 1\\\}\\big\|\}\\displaystyle\.CDA assesses whether the predicted depth structure aligns with the directionality of citations\.

##### PMR — Path Monotonicity Rate\.

PMR evaluates whether root\-to\-leaf paths reflect a temporally forward\-progressing trajectory at the level of the entire concept body, including descendants\. For each concept nodecc, we use the*subtree\-mean time*τ¯𝒯​\(c\)=1\|𝒱⁡\(c\)\|​∑vi∈𝒱⁡\(c\)τ⁡\(vi\)\\bar\{\\tau\}\_\{\\mathcal\{T\}\}\(c\)=\\tfrac\{1\}\{\|\\mathcal\{V\}\(c\)\|\}\\sum\_\{v\_\{i\}\\in\\mathcal\{V\}\(c\)\}\\tau\(v\_\{i\}\)as the path statistic \(Eq\.[1](https://arxiv.org/html/2609.09561#S3.E1)\)\. LetΠ\\Pibe the set of root\-to\-leaf paths in𝒯\\mathcal\{T\}containing at least two nodes with validτ¯\\bar\{\\tau\}\. A pathπ=\(c0,c1,…,cL\)∈Π\\pi=\(c\_\{0\},c\_\{1\},\\ldots,c\_\{L\}\)\\in\\Piis temporally monotone if

τ¯𝒯​\(c0\)≤τ¯𝒯​\(c1\)≤⋯≤τ¯𝒯​\(cL\)\.\\bar\{\\tau\}\_\{\\mathcal\{T\}\}\(c\_\{0\}\)\\leq\\bar\{\\tau\}\_\{\\mathcal\{T\}\}\(c\_\{1\}\)\\leq\\cdots\\leq\\bar\{\\tau\}\_\{\\mathcal\{T\}\}\(c\_\{L\}\)\.\(19\)PMR is the fraction of monotone paths:

PMR=\|\{π∈Π:π​is temporally monotone\}\|\|Π\|\.\\text\{PMR\}=\\frac\{\\bigl\|\\\{\\pi\\in\\Pi:\\pi\\text\{ is temporally monotone\}\\\}\\bigr\|\}\{\|\\Pi\|\}\.\(20\)

### D\.2Few\-shot metrics on annotated graphs

##### FS\-CP — FS Concept Purity\.

FS\-CP replicates LP using single\-label conceptsgig\_\{i\}in place of multi\-label section labels:

FS\-CP=1K∑k=1Kmaxg∈𝒢fs⁡\|\{vi∈ℳk:gi=g\}\|\|ℳk\|\.\\mathrm\{FS\\text\{\-\}CP\}=\\frac\{1\}\{K\}\\sum\_\{k=1\}^\{K\}\\frac\{\\displaystyle\\max\_\{g\\in\\mathcal\{G\}^\{\\mathrm\{fs\}\}\}\\big\|\\\{v\_\{i\}\\in\\mathcal\{M\}\_\{k\}:g\_\{i\}=g\\\}\\big\|\}\{\|\\mathcal\{M\}\_\{k\}\|\}\.\(21\)FS\-CP directly measures how well the predicted leaf clusters align with research concepts and is the primary structural\-alignment metric in our evaluation\.

##### FS\-EDA — FS Evolutionary Direction Accuracy\.

FS\-EDA mirrors CDA but uses annotated evolution edgesℰevo\\mathcal\{E\}^\{\\mathrm\{evo\}\}, in which\(vs,vd\)\(v\_\{s\},v\_\{d\}\)indicates thatvsv\_\{s\}is an evolutionary descendant \(typically more recent\) ofvdv\_\{d\}:

FS\-EDA=\|\{\(vs,vd\)∈ℰevo:δ⁡\(vs\)≥δ⁡\(vd\)\}\|\|ℰevo\|\.\\mathrm\{FS\\text\{\-\}EDA\}=\\frac\{\\big\|\\\{\(v\_\{s\},v\_\{d\}\)\\in\\mathcal\{E\}^\{\\mathrm\{evo\}\}:\\delta\(v\_\{s\}\)\\geq\\delta\(v\_\{d\}\)\\\}\\big\|\}\{\|\\mathcal\{E\}^\{\\mathrm\{evo\}\}\|\}\.\(22\)Compared with CDA, FS\-EDA replaces the noisy citation graph with a clean signal: an edge inℰevo\\mathcal\{E\}^\{\\mathrm\{evo\}\}reflects “vsv\_\{s\}extends/improvesvdv\_\{d\}”, whereas a citation inℰ𝒢\\mathcal\{E\}\_\{\\mathcal\{G\}\}may indicate any of comparison, background, or methodological reuse\.

##### FS\-Mar — FS Marginal AUROC\.

Our model produces a per\-paper marginality scorehi∈\[0,1\]h\_\{i\}\\in\[0,1\]\(the marginal\-head output from Eq\.[53](https://arxiv.org/html/2609.09561#A9.E53)\)\. Withyim,fs∈\{0,1\}y\_\{i\}^\{\\mathrm\{m,fs\}\}\\in\\\{0,1\\\}as ground truth,

FS\-Mar=\|\{\(vi,vj\):yim,fs=1,yjm,fs=0,hi\>hj\}\|\|\{\(vi,vj\):yim,fs=1,yjm,fs=0\}\|,\\displaystyle\\mathrm\{FS\\text\{\-\}Mar\}=\\frac\{\\big\|\\\{\(v\_\{i\},v\_\{j\}\):y\_\{i\}^\{\\mathrm\{m,fs\}\}=1,\\;y\_\{j\}^\{\\mathrm\{m,fs\}\}=0,\\;h\_\{i\}\>h\_\{j\}\\\}\\big\|\}\{\\big\|\\\{\(v\_\{i\},v\_\{j\}\):y\_\{i\}^\{\\mathrm\{m,fs\}\}=1,\\;y\_\{j\}^\{\\mathrm\{m,fs\}\}=0\\\}\\big\|\},\(23\)which equals the standard AUROC ofhhagainstym,fsy^\{\\mathrm\{m,fs\}\}\. Marginal papers are those occupying domain boundaries: relevant by topic, but whose research focus deviates from the core methodological lineage\. FS\-Mar evaluates a capability unique to our framework—neither standard clustering baselines nor LLM baselines produce a marginality score \(reported as “–” in Table[2](https://arxiv.org/html/2609.09561#S5.T2); a constant score would give the trivial AUROC of0\.5000\.500\)\.

## Appendix ENotation Summary

Table[11](https://arxiv.org/html/2609.09561#A5.T11)summarizes the notation used throughout the paper\. Symbols are grouped by category for ease of reference\.

Table 11:Notation summary\. Symbols introduced in the problem formulation \(§[3](https://arxiv.org/html/2609.09561#S3)\) are used consistently across the Methodology and Appendix\.SymbolMeaningIntroduced*Input citation graph*𝒢=\(𝒱,ℰ𝒢\)\\mathcal\{G\}=\(\\mathcal\{V\},\\mathcal\{E\}\_\{\\mathcal\{G\}\}\)Citation graph from survey reference set§[3](https://arxiv.org/html/2609.09561#S3)vi∈𝒱v\_\{i\}\\in\\mathcal\{V\}A paper node§[3](https://arxiv.org/html/2609.09561#S3)sis\_\{i\}Title and abstract text of paperviv\_\{i\}§[3](https://arxiv.org/html/2609.09561#S3)τ⁡\(vi\)\\tau\(v\_\{i\}\)Publication year of paperviv\_\{i\}§[3](https://arxiv.org/html/2609.09561#S3)𝒩𝒢​\(vi\)\\mathcal\{N\}\_\{\\mathcal\{G\}\}\(v\_\{i\}\)Citation neighborhood ofviv\_\{i\}App\.[F](https://arxiv.org/html/2609.09561#A6)*Trees and concepts*𝒯tax\\mathcal\{T\}^\{\\mathrm\{tax\}\}Time\-agnostic taxonomy backbone§[3](https://arxiv.org/html/2609.09561#S3)𝒯\\mathcal\{T\}Target evolutionary tree§[3](https://arxiv.org/html/2609.09561#S3)𝒯\(t\),𝒞\(t\)\\mathcal\{T\}^\{\(t\)\},\\mathcal\{C\}^\{\(t\)\}Tree and concept set at EM iterationtt§[4\.4\.1](https://arxiv.org/html/2609.09561#S4.SS4.SSS1)c∈𝒞c\\in\\mathcal\{C\}Concept node \(also indexes a cluster\)§[3](https://arxiv.org/html/2609.09561#S3)rrRoot concept node§[4\.4\.2](https://arxiv.org/html/2609.09561#S4.SS4.SSS2)ℰC,ℰP\\mathcal\{E\}\_\{C\},\\mathcal\{E\}\_\{P\}Concept edges, paper\-attachment edges§[3](https://arxiv.org/html/2609.09561#S3)𝒱⁡\(c\)\\mathcal\{V\}\(c\)Papers attached toccor its descendants§[3](https://arxiv.org/html/2609.09561#S3)children⁡\(c\)\\mathrm\{children\}\(c\)Direct children ofccin𝒯\\mathcal\{T\}§[4\.6](https://arxiv.org/html/2609.09561#S4.SS6)Leaves⁡\(𝒯\)\\mathrm\{Leaves\}\(\\mathcal\{T\}\)Leaf concept nodes of𝒯\\mathcal\{T\}§[4\.4\.3](https://arxiv.org/html/2609.09561#S4.SS4.SSS3)ϕ⁡\(c\)\\phi\(c\)Concept label ofcc§[3](https://arxiv.org/html/2609.09561#S3)τatt​\(c\),τ¯​\(c\)\\tau^\{\\text\{att\}\}\(c\),\\bar\{\\tau\}\(c\)Attached\-mean / subtree\-mean publication year ofcc§[3](https://arxiv.org/html/2609.09561#S3)ϵ\\epsilonTemporal tolerance margin§[3](https://arxiv.org/html/2609.09561#S3)*Representations*𝐱i\\mathbf\{x\}\_\{i\}Pretrained LM embedding ofsis\_\{i\}§[4\.2\.1](https://arxiv.org/html/2609.09561#S4.SS2.SSS1)𝐳isem,𝐳igraph\(=𝐡i\(L\)\)\\mathbf\{z\}\_\{i\}^\{\\mathrm\{sem\}\},\\mathbf\{z\}\_\{i\}^\{\\mathrm\{graph\}\}\\,\(=\\mathbf\{h\}\_\{i\}^\{\(L\)\}\)Semantic / graph stream output§[4\.2\.1](https://arxiv.org/html/2609.09561#S4.SS2.SSS1)𝐞i\\mathbf\{e\}\_\{i\}Fused clustering embedding§[4\.2\.1](https://arxiv.org/html/2609.09561#S4.SS2.SSS1)𝐩i\\mathbf\{p\}\_\{i\}Projection representation \(contrastive only\)§[4\.2\.1](https://arxiv.org/html/2609.09561#S4.SS2.SSS1)𝝁c,𝝈c2\\boldsymbol\{\\mu\}\_\{c\},\\boldsymbol\{\\sigma\}\_\{c\}^\{2\}Diagonal Gaussian parameters of conceptcc§[4\.2\.2](https://arxiv.org/html/2609.09561#S4.SS2.SSS2)wi​cw\_\{ic\}Soft membershipp⁡\(vi∈Cc\)p\(v\_\{i\}\\in C\_\{c\}\)App\.[G](https://arxiv.org/html/2609.09561#A7)*Marginal mechanism*ℳ\\mathcal\{M\}Marginal paper set§[3](https://arxiv.org/html/2609.09561#S3)m⁡\(vi,c\)m\(v\_\{i\},c\)Paper\-to\-concept compatibility score§[3](https://arxiv.org/html/2609.09561#S3)AileafA\_\{i\}^\{\\mathrm\{leaf\}\}Maximum leaf compatibility forviv\_\{i\}§[4\.4\.3](https://arxiv.org/html/2609.09561#S4.SS4.SSS3)η\\etaMarginal threshold§[3](https://arxiv.org/html/2609.09561#S3)ssem,sgraph,stimes\_\{\\mathrm\{sem\}\},s\_\{\\mathrm\{graph\}\},s\_\{\\mathrm\{time\}\}Compatibility\-score componentsApp\.[K](https://arxiv.org/html/2609.09561#A11)γ1,γ2,γ3\\gamma\_\{1\},\\gamma\_\{2\},\\gamma\_\{3\}Compatibility\-score weightsApp\.[K](https://arxiv.org/html/2609.09561#A11)*Constraints and constants*ρ\\rhoMajor\-branch minimum size ratio§[4\.4\.2](https://arxiv.org/html/2609.09561#S4.SS4.SSS2)MBC⁡\(𝒯\)\\mathrm\{MBC\}\(\\mathcal\{T\}\)Major Branch Count of𝒯\\mathcal\{T\}§[4\.4\.2](https://arxiv.org/html/2609.09561#S4.SS4.SSS2)\[dmin,dmax\]\[d\_\{\\min\},d\_\{\\max\}\]Drift\-window boundsApp\.[I](https://arxiv.org/html/2609.09561#A9)
## Appendix FGraph\-Aware Paper Encoder

This appendix expands the abstract encoderfθf\_\{\\theta\}introduced in §[4\.2\.1](https://arxiv.org/html/2609.09561#S4.SS2.SSS1)into concrete forward computations and justifies the three design choices discussed in the main text\.

### F\.1Forward computation

A pretrained scientific encoder \(SPECTER2[Singh et al\. \(2022\)](https://arxiv.org/html/2609.09561#bib.bib27)\) produces a fixed semantic representation

𝐱i=fLM​\(si\)∈ℝdLM,\\mathbf\{x\}\_\{i\}=f\_\{\\mathrm\{LM\}\}\(s\_\{i\}\)\\in\\mathbb\{R\}^\{d\_\{\\mathrm\{LM\}\}\},\(24\)which is then passed through two parallel branches\.

##### Semantic branch\.

A lightweight two\-layer MLP produces the semantic stream

𝐳isem=𝐖2​GELU​\(𝐖1​𝐱i\),\\mathbf\{z\}\_\{i\}^\{\\mathrm\{sem\}\}=\\mathbf\{W\}\_\{2\}\\,\\mathrm\{GELU\}\(\\mathbf\{W\}\_\{1\}\\mathbf\{x\}\_\{i\}\),\(25\)where𝐖1∈ℝd×dLM\\mathbf\{W\}\_\{1\}\\in\\mathbb\{R\}^\{d\\times d\_\{\\mathrm\{LM\}\}\}and𝐖2∈ℝd×d\\mathbf\{W\}\_\{2\}\\in\\mathbb\{R\}^\{d\\times d\}\.

##### Graph branch\.

A stack ofLLcontrolled propagation blocks computes the graph stream\. With𝐡i\(0\)=MLPgraph​\(𝐱i\)\\mathbf\{h\}\_\{i\}^\{\(0\)\}=\\mathrm\{MLP\}\_\{\\mathrm\{graph\}\}\(\\mathbf\{x\}\_\{i\}\), each layerl=0,…,L−1l=0,\\ldots,L\-1updates

𝐦i\(l\)\\displaystyle\\mathbf\{m\}\_\{i\}^\{\(l\)\}=1\|𝒩𝒢​\(vi\)\|​∑j∈𝒩𝒢​\(vi\)𝐖msg​𝐡j\(l\),\\displaystyle=\\frac\{1\}\{\|\\mathcal\{N\}\_\{\\mathcal\{G\}\}\(v\_\{i\}\)\|\}\\\!\\\!\\sum\_\{j\\in\\mathcal\{N\}\_\{\\mathcal\{G\}\}\(v\_\{i\}\)\}\\\!\\\!\\mathbf\{W\}\_\{\\mathrm\{msg\}\}\\,\\mathbf\{h\}\_\{j\}^\{\(l\)\},\(26\)𝐮i\(l\)\\displaystyle\\mathbf\{u\}\_\{i\}^\{\(l\)\}=β​𝐡i\(l\)\+\(1−β\)​𝐦i\(l\),\\displaystyle=\\beta\\,\\mathbf\{h\}\_\{i\}^\{\(l\)\}\+\(1\-\\beta\)\\,\\mathbf\{m\}\_\{i\}^\{\(l\)\},\(27\)𝐡i\(l\+1\)\\displaystyle\\mathbf\{h\}\_\{i\}^\{\(l\+1\)\}=PairNorm⁡\(α​𝐱i\+\(1−α\)​𝐮i\(l\)\)\.\\displaystyle=\\mathrm\{PairNorm\}\\\!\\left\(\\alpha\\,\\mathbf\{x\}\_\{i\}\+\(1\-\\alpha\)\\,\\mathbf\{u\}\_\{i\}^\{\(l\)\}\\right\)\.\(28\)For isolated nodesvi∈𝒱ov\_\{i\}\\in\\mathcal\{V\}\_\{o\}where\|𝒩𝒢​\(vi\)\|=0\|\\mathcal\{N\}\_\{\\mathcal\{G\}\}\(v\_\{i\}\)\|=0, neighborhood aggregation is undefined; we set𝐦i\(l\)=𝟎\\mathbf\{m\}\_\{i\}^\{\(l\)\}=\\mathbf\{0\}so that the propagation reduces to𝐡i\(l\+1\)=PairNorm⁡\(α​𝐱i\+\(1−α\)​β​𝐡i\(l\)\)\\mathbf\{h\}\_\{i\}^\{\(l\+1\)\}=\\mathrm\{PairNorm\}\(\\alpha\\mathbf\{x\}\_\{i\}\+\(1\-\\alpha\)\\beta\\mathbf\{h\}\_\{i\}^\{\(l\)\}\), i\.e\., a pure semantic residual\. The final graph\-stream output is𝐳igraph=𝐡i\(L\)\\mathbf\{z\}\_\{i\}^\{\\mathrm\{graph\}\}=\\mathbf\{h\}\_\{i\}^\{\(L\)\}\.

##### Adaptive fusion gate\.

The two streams are combined through a learnable connectivity\-biased gate:

λi\\displaystyle\\lambda\_\{i\}=σ\(𝐖g\[𝐳igraph∥𝐳isem\]\+δ1\[iso\(vi\)\]\),\\displaystyle=\\sigma\\\!\\left\(\\mathbf\{W\}\_\{g\}\[\\mathbf\{z\}\_\{i\}^\{\\mathrm\{graph\}\}\\,\\\|\\,\\mathbf\{z\}\_\{i\}^\{\\mathrm\{sem\}\}\]\+\\delta\\,\\mathbb\{1\}\[\\mathrm\{iso\}\(v\_\{i\}\)\]\\right\),\(29\)𝐳ifused\\displaystyle\\mathbf\{z\}\_\{i\}^\{\\mathrm\{fused\}\}=λi​𝐳igraph\+\(1−λi\)​𝐳isem\.\\displaystyle=\\lambda\_\{i\}\\,\\mathbf\{z\}\_\{i\}^\{\\mathrm\{graph\}\}\+\(1\-\\lambda\_\{i\}\)\\,\\mathbf\{z\}\_\{i\}^\{\\mathrm\{sem\}\}\.\(30\)The clustering embedding is𝐞i=L2​Norm​\(𝐳ifused\)\\mathbf\{e\}\_\{i\}=\\mathrm\{L\_\{2\}Norm\}\(\\mathbf\{z\}\_\{i\}^\{\\mathrm\{fused\}\}\)\. An independent two\-layer MLP produces the projection representation𝐩i=MLPproj​\(𝐳ifused\)\\mathbf\{p\}\_\{i\}=\\mathrm\{MLP\}\_\{\\mathrm\{proj\}\}\(\\mathbf\{z\}\_\{i\}^\{\\mathrm\{fused\}\}\), used exclusively by the contrastive objective in §[4\.3](https://arxiv.org/html/2609.09561#S4.SS3)and never as input to clustering or downstream attachment\.

The three design choices flagged in the main text correspond to specific equations above:

- •Anchored residual:theα​𝐱i\\alpha\\mathbf\{x\}\_\{i\}term in Eq\.[28](https://arxiv.org/html/2609.09561#A6.E28)preserves the original semantic vector at every layer, preventing the propagation from collapsing distinct papers to similar representations in shallow citation graphs\.
- •Density\-aware normalization:PairNorm\\mathrm\{PairNorm\}in Eq\.[28](https://arxiv.org/html/2609.09561#A6.E28)centers features and rescales pairwise distances, accommodating the highly uneven cluster densities induced by hub papers\.
- •Connectivity\-biased fusion gate:the termδ​𝟙​\[iso⁡\(vi\)\]\\delta\\mathbb\{1\}\[\\mathrm\{iso\}\(v\_\{i\}\)\]in Eq\.[29](https://arxiv.org/html/2609.09561#A6.E29), withδ\\deltainitialized to−2\.0\-2\.0, drivesλi\\lambda\_\{i\}toward00for isolated nodes so that𝐳ifused≈𝐳isem\\mathbf\{z\}\_\{i\}^\{\\mathrm\{fused\}\}\\approx\\mathbf\{z\}\_\{i\}^\{\\mathrm\{sem\}\}at initialization, while remaining learnable\.

## Appendix GDistributional Tree Builder

### G\.1Base clustering with soft membership

HDBSCAN is applied to the L2\-normalized embeddings\{𝐞i\}\\\{\\mathbf\{e\}\_\{i\}\\\}to identify dense regions\. To obtain soft membership, we use the algorithm’s native extension based on the mutual reachability tree\([Campello et al\., 2013](https://arxiv.org/html/2609.09561#bib.bib25)\), which yields

wi​c=p\(vi∈Cc\)∈\[0,1\],c=1,…,K,w\_\{ic\}=p\(v\_\{i\}\\in C\_\{c\}\)\\in\[0,1\],\\quad c=1,\\ldots,K,\(31\)whereKKis the number of discovered base clusters\. Each cluster’s diagonal Gaussian is fitted by weighted maximum likelihood:

𝝁c\\displaystyle\\boldsymbol\{\\mu\}\_\{c\}=∑iwi​c​𝐞i∑iwi​c,\\displaystyle=\\frac\{\\sum\_\{i\}w\_\{ic\}\\,\\mathbf\{e\}\_\{i\}\}\{\\sum\_\{i\}w\_\{ic\}\},\(32\)σc,d2\\displaystyle\\sigma\_\{c,d\}^\{2\}=max⁡\(∑iwi​c​\(ei,d−μc,d\)2∑iwi​c,σmin2\),\\displaystyle=\\max\\\!\\left\(\\frac\{\\sum\_\{i\}w\_\{ic\}\\,\(e\_\{i,d\}\-\\mu\_\{c,d\}\)^\{2\}\}\{\\sum\_\{i\}w\_\{ic\}\},\\;\\sigma\_\{\\min\}^\{2\}\\right\),\(33\)whereddindexes embedding dimensions andσmin2\\sigma\_\{\\min\}^\{2\}is a numerical floor preventing degenerate Gaussians\.

### G\.22\-Wasserstein distance between diagonal Gaussians

For two diagonal GaussiansCp∼𝒩⁡\(𝝁p,diag⁡\(𝝈p2\)\)C\_\{p\}\\sim\\mathcal\{N\}\(\\boldsymbol\{\\mu\}\_\{p\},\\mathrm\{diag\}\(\\boldsymbol\{\\sigma\}\_\{p\}^\{2\}\)\)andCq∼𝒩⁡\(𝝁q,diag⁡\(𝝈q2\)\)C\_\{q\}\\sim\\mathcal\{N\}\(\\boldsymbol\{\\mu\}\_\{q\},\\mathrm\{diag\}\(\\boldsymbol\{\\sigma\}\_\{q\}^\{2\}\)\), the squared 2\-Wasserstein distance has a closed form:

𝒲22​\(Cp,Cq\)=‖𝝁p−𝝁q‖22\+∑d\(σp,d−σq,d\)2\.\\mathcal\{W\}\_\{2\}^\{2\}\(C\_\{p\},C\_\{q\}\)=\\\|\\boldsymbol\{\\mu\}\_\{p\}\-\\boldsymbol\{\\mu\}\_\{q\}\\\|\_\{2\}^\{2\}\+\\sum\_\{d\}\(\\sigma\_\{p,d\}\-\\sigma\_\{q,d\}\)^\{2\}\.\(34\)

### G\.3Bottom\-up agglomeration

Starting from theKKbase clusters, we greedily merge the pair\(Cp⋆,Cq⋆\)=arg⁡minp≠q​𝒲2​\(Cp,Cq\)\(C\_\{p\}^\{\\star\},C\_\{q\}^\{\\star\}\)=\\arg\\min\_\{p\\neq q\}\\mathcal\{W\}\_\{2\}\(C\_\{p\},C\_\{q\}\)at each step\. The merged parent’s Gaussian is re\-estimated from the union of member papersM=members⁡\(Cp⋆\)∪members⁡\(Cq⋆\)M=\\mathrm\{members\}\(C\_\{p\}^\{\\star\}\)\\cup\\mathrm\{members\}\(C\_\{q\}^\{\\star\}\)via unweighted maximum likelihood:

𝝁parent\\displaystyle\\boldsymbol\{\\mu\}\_\{\\mathrm\{parent\}\}=1\|M\|​∑i∈M𝐞i,\\displaystyle=\\frac\{1\}\{\|M\|\}\\sum\_\{i\\in M\}\\mathbf\{e\}\_\{i\},\(35\)σparent,d2\\displaystyle\\sigma\_\{\\mathrm\{parent\},d\}^\{2\}=\\displaystyle=max\\displaystyle\\max\(1\|M\|​∑i∈M\(ei,d−μparent,d\)2,σmin2\)\.\\displaystyle\\left\(\\frac\{1\}\{\|M\|\}\\sum\_\{i\\in M\}\(e\_\{i,d\}\-\\mu\_\{\\mathrm\{parent\},d\}\)^\{2\},\\;\\sigma\_\{\\min\}^\{2\}\\right\)\.Re\-estimation relies only on running sums∑i∈M𝐞i\\sum\_\{i\\in M\}\\mathbf\{e\}\_\{i\}and sum of squares∑i∈M𝐞i⊙2\\sum\_\{i\\in M\}\\mathbf\{e\}\_\{i\}^\{\\odot 2\}, which can be incrementally maintained as sufficient statistics during agglomeration\. The procedure terminates when a single root cluster remains\. Algorithm[1](https://arxiv.org/html/2609.09561#alg1)summarizes the full builder\.

Algorithm 1Distributional tree builder\.0:Embeddings

\{𝐞i\}\\\{\\mathbf\{e\}\_\{i\}\\\}; HDBSCAN parameters; \(optional\) temporal admissibility filter

ℱϵ\\mathcal\{F\}\_\{\\epsilon\}\.

1:

\{wi​c\},K←HDBSCAN​\_​SoftMembership​\(\{𝐞i\}\)\\\{w\_\{ic\}\\\},K\\leftarrow\\mathrm\{HDBSCAN\\\_SoftMembership\}\(\\\{\\mathbf\{e\}\_\{i\}\\\}\)
2:for

c=1,…,Kc=1,\\ldots,Kdo

3:Compute

𝝁c,𝝈c2\\boldsymbol\{\\mu\}\_\{c\},\\boldsymbol\{\\sigma\}\_\{c\}^\{2\}via Eq\.[32](https://arxiv.org/html/2609.09561#A7.E32)–[33](https://arxiv.org/html/2609.09561#A7.E33)\.

4:endfor

5:

𝒞←\{C1,…,CK\}\\mathcal\{C\}\\leftarrow\\\{C\_\{1\},\\ldots,C\_\{K\}\\\}; record member papers per cluster\.

6:while

\|𝒞\|\>1\|\\mathcal\{C\}\|\>1do

7:Compute

𝒲2​\(Cp,Cq\)\\mathcal\{W\}\_\{2\}\(C\_\{p\},C\_\{q\}\)for all pairs \(Eq\.[34](https://arxiv.org/html/2609.09561#A7.E34)\)\.

8:Select

\(Cp⋆,Cq⋆\)←arg⁡min⁡𝒲2\(C\_\{p\}^\{\\star\},C\_\{q\}^\{\\star\}\)\\leftarrow\\arg\\min\\mathcal\{W\}\_\{2\}satisfyingℱϵ\\mathcal\{F\}\_\{\\epsilon\}if provided\.

9:Re\-estimate parent via Eq\.[35](https://arxiv.org/html/2609.09561#A7.E35); remove children, add parent\.

10:endwhile

11:returnHierarchical tree with

\(𝝁c,𝝈c2\)\(\\boldsymbol\{\\mu\}\_\{c\},\\boldsymbol\{\\sigma\}\_\{c\}^\{2\}\)at every node\.

## Appendix HStage I Loss Details

This appendix expands the three pre\-training loss groups summarized in §[4\.3](https://arxiv.org/html/2609.09561#S4.SS3):

ℒtax=ℒsec\+ℒcite\+ℒgeo\.\\mathcal\{L\}^\{\\mathrm\{tax\}\}=\\mathcal\{L\}\_\{\\mathrm\{sec\}\}\+\\mathcal\{L\}\_\{\\mathrm\{cite\}\}\+\\mathcal\{L\}\_\{\\mathrm\{geo\}\}\.
### H\.1Section supervisionℒsec\\mathcal\{L\}\_\{\\mathrm\{sec\}\}

Survey section structure supplies weak labels: each paperviv\_\{i\}inherits a multi\-hot section vector𝐲ilbl∈\{0,1\}\|𝒮\|\\mathbf\{y\}\_\{i\}^\{\\mathrm\{lbl\}\}\\in\\\{0,1\\\}^\{\|\\mathcal\{S\}\|\}over the union of section labels𝒮\\mathcal\{S\}, plus a hierarchical levelyilvl∈\{1,…,Lmax\}y\_\{i\}^\{\\mathrm\{lvl\}\}\\in\\\{1,\\ldots,L\_\{\\max\}\\\}\. Let𝐲^ilbl=sigmoid⁡\(𝐖lbl​𝐞i\)\\hat\{\\mathbf\{y\}\}\_\{i\}^\{\\mathrm\{lbl\}\}=\\mathrm\{sigmoid\}\(\\mathbf\{W\}\_\{\\mathrm\{lbl\}\}\\mathbf\{e\}\_\{i\}\)and𝐲^ilvl=softmax⁡\(𝐖lvl​𝐞i\)\\hat\{\\mathbf\{y\}\}\_\{i\}^\{\\mathrm\{lvl\}\}=\\mathrm\{softmax\}\(\\mathbf\{W\}\_\{\\mathrm\{lvl\}\}\\mathbf\{e\}\_\{i\}\)\. We use masked binary cross\-entropy and categorical cross\-entropy over labeled nodes𝒱lbl⊆𝒱\\mathcal\{V\}\_\{\\mathrm\{lbl\}\}\\subseteq\\mathcal\{V\}:

ℒlabel\\displaystyle\\mathcal\{L\}\_\{\\mathrm\{label\}\}=−1\|𝒱lbl\|∑i∈𝒱lblBCE\(𝐲^ilbl,𝐲ilbl\),\\displaystyle=\-\\frac\{1\}\{\|\\mathcal\{V\}\_\{\\mathrm\{lbl\}\}\|\}\\\!\\\!\\sum\_\{i\\in\\mathcal\{V\}\_\{\\mathrm\{lbl\}\}\}\\\!\\\!\\mathrm\{BCE\}\\\!\\left\(\\hat\{\\mathbf\{y\}\}\_\{i\}^\{\\mathrm\{lbl\}\},\\mathbf\{y\}\_\{i\}^\{\\mathrm\{lbl\}\}\\right\),\(36\)ℒlevel\\displaystyle\\mathcal\{L\}\_\{\\mathrm\{level\}\}=−1\|𝒱lbl\|∑i∈𝒱lbllogy^i,yilvllvl,\\displaystyle=\-\\frac\{1\}\{\|\\mathcal\{V\}\_\{\\mathrm\{lbl\}\}\|\}\\\!\\\!\\sum\_\{i\\in\\mathcal\{V\}\_\{\\mathrm\{lbl\}\}\}\\\!\\\!\\log\\hat\{y\}\_\{i,y\_\{i\}^\{\\mathrm\{lvl\}\}\}^\{\\mathrm\{lvl\}\},\(37\)ℒsec\\displaystyle\\mathcal\{L\}\_\{\\mathrm\{sec\}\}=wlbl​ℒlabel\+wlvl​ℒlevel\.\\displaystyle=w\_\{\\mathrm\{lbl\}\}\\mathcal\{L\}\_\{\\mathrm\{label\}\}\+w\_\{\\mathrm\{lvl\}\}\\mathcal\{L\}\_\{\\mathrm\{level\}\}\.\(38\)

### H\.2Citation consistencyℒcite\\mathcal\{L\}\_\{\\mathrm\{cite\}\}

Two terms preserve citation structure: link prediction on𝐞i\\mathbf\{e\}\_\{i\}and contrastive ranking on𝐩i\\mathbf\{p\}\_\{i\}\.

##### Link prediction\.

For each observed edge\(vi,vj\)∈ℰ𝒢\(v\_\{i\},v\_\{j\}\)\\in\\mathcal\{E\}\_\{\\mathcal\{G\}\}\(positive\) and randomly sampled non\-edge\(vi,vj−\)\(v\_\{i\},v\_\{j^\{\-\}\}\)\(negative\), define the logity^i​j=τlnk​𝐞i⊤​𝐞j\\hat\{y\}\_\{ij\}=\\tau\_\{\\mathrm\{lnk\}\}\\,\\mathbf\{e\}\_\{i\}^\{\\top\}\\mathbf\{e\}\_\{j\}with temperatureτlnk\\tau\_\{\\mathrm\{lnk\}\}\(we use1010to scale cosine similarities into a useful logit range\):

ℒlink=BCE⁡\(sigmoid⁡\(y^i​j\),yi​j\),\\mathcal\{L\}\_\{\\mathrm\{link\}\}=\\mathrm\{BCE\}\\\!\\left\(\\mathrm\{sigmoid\}\(\\hat\{y\}\_\{ij\}\),\\,y\_\{ij\}\\right\),\(39\)whereyi​j∈\{0,1\}y\_\{ij\}\\in\\\{0,1\\\}indicates edge existence\. We use one negative per positive\.

##### Contrastive ranking on𝐩i\\mathbf\{p\}\_\{i\}\.

For two papersvi,vjv\_\{i\},v\_\{j\}sharing a section label, they form a positive pair\. Hard negativesvk−v\_\{k^\{\-\}\}are mined as the most similar paper toviv\_\{i\}not sharing any label ofviv\_\{i\}\. With cosine similaritysim⁡\(a,b\)=𝐩a⊤​𝐩b/\(‖𝐩a‖​‖𝐩b‖\)\\mathrm\{sim\}\(a,b\)=\\mathbf\{p\}\_\{a\}^\{\\top\}\\mathbf\{p\}\_\{b\}/\(\\\|\\mathbf\{p\}\_\{a\}\\\|\\\|\\mathbf\{p\}\_\{b\}\\\|\)and temperatureτctr\\tau\_\{\\mathrm\{ctr\}\}:

ℒcontrast=\\displaystyle\\mathcal\{L\}\_\{\\mathrm\{contrast\}\}=\(40\)−log\\displaystyle\-\\logexp⁡\(sim⁡\(vi,vj\)/τctr\)∑k∈\{j\}∪𝒦i−exp⁡\(sim⁡\(vi,vk\)/τctr\),\\displaystyle\\frac\{\\exp\(\\mathrm\{sim\}\(v\_\{i\},v\_\{j\}\)/\\tau\_\{\\mathrm\{ctr\}\}\)\}\{\\sum\_\{k\\in\\\{j\\\}\\cup\\mathcal\{K\}^\{\-\}\_\{i\}\}\\exp\(\\mathrm\{sim\}\(v\_\{i\},v\_\{k\}\)/\\tau\_\{\\mathrm\{ctr\}\}\)\},with𝒦i−\\mathcal\{K\}^\{\-\}\_\{i\}the hard\-negative set \(\|𝒦i−\|=8\|\\mathcal\{K\}^\{\-\}\_\{i\}\|=8\)\. Note thatℒcontrast\\mathcal\{L\}\_\{\\mathrm\{contrast\}\}acts on𝐩i\\mathbf\{p\}\_\{i\}and never on𝐞i\\mathbf\{e\}\_\{i\}, keeping the clustering geometry untouched\.

##### Combination\.

ℒcite=wlnk​ℒlink\+wctr​ℒcontrast\.\\mathcal\{L\}\_\{\\mathrm\{cite\}\}=w\_\{\\mathrm\{lnk\}\}\\mathcal\{L\}\_\{\\mathrm\{link\}\}\+w\_\{\\mathrm\{ctr\}\}\\mathcal\{L\}\_\{\\mathrm\{contrast\}\}\.\(41\)

### H\.3Cluster geometryℒgeo\\mathcal\{L\}\_\{\\mathrm\{geo\}\}

A prototype\-anchoring term pulls each labeled node toward its class centroid\. For each labels∈𝒮s\\in\\mathcal\{S\}, let𝒱s=\{vi:s∈𝐲ilbl\}\\mathcal\{V\}\_\{s\}=\\\{v\_\{i\}:s\\in\\mathbf\{y\}\_\{i\}^\{\\mathrm\{lbl\}\}\\\}and define the stop\-gradient centroid

𝐞¯s=sg⁡\(1\|𝒱s\|​∑i∈𝒱s𝐞i\)\.\\bar\{\\mathbf\{e\}\}\_\{s\}=\\mathrm\{sg\}\\\!\\left\(\\frac\{1\}\{\|\\mathcal\{V\}\_\{s\}\|\}\\\!\\sum\_\{i\\in\\mathcal\{V\}\_\{s\}\}\\\!\\\!\\mathbf\{e\}\_\{i\}\\right\)\.\(42\)The anchor loss is:

ℒanchor=1\|𝒮\|​∑s∈𝒮1\|𝒱s\|​∑i∈𝒱s\(1−𝐞i⊤​𝐞¯s\)\.\\mathcal\{L\}\_\{\\mathrm\{anchor\}\}=\\frac\{1\}\{\|\\mathcal\{S\}\|\}\\\!\\sum\_\{s\\in\\mathcal\{S\}\}\\\!\\frac\{1\}\{\|\\mathcal\{V\}\_\{s\}\|\}\\\!\\sum\_\{i\\in\\mathcal\{V\}\_\{s\}\}\\\!\\\!\\left\(1\-\\mathbf\{e\}\_\{i\}^\{\\top\}\\bar\{\\mathbf\{e\}\}\_\{s\}\\right\)\.\(43\)ℒgeo=wanc​ℒanchor\\mathcal\{L\}\_\{\\mathrm\{geo\}\}=w\_\{\\mathrm\{anc\}\}\\mathcal\{L\}\_\{\\mathrm\{anchor\}\}\.

## Appendix IStage II Loss Details

This appendix expands the three evolution loss groups summarized in §[4\.4\.1](https://arxiv.org/html/2609.09561#S4.SS4.SSS1):

ℒevo=ℒsem\+ℒtemp\+ℒmarg\.\\mathcal\{L\}^\{\\mathrm\{evo\}\}=\\mathcal\{L\}\_\{\\mathrm\{sem\}\}\+\\mathcal\{L\}\_\{\\mathrm\{temp\}\}\+\\mathcal\{L\}\_\{\\mathrm\{marg\}\}\.All terms operate on the current tree𝒯\(t\)\\mathcal\{T\}^\{\(t\)\}with concept Gaussians\{\(𝝁c,𝝈c2\)\}c∈𝒞\(t\)\\\{\(\\boldsymbol\{\\mu\}\_\{c\},\\boldsymbol\{\\sigma\}\_\{c\}^\{2\}\)\\\}\_\{c\\in\\mathcal\{C\}^\{\(t\)\}\}\. Letp⁡\(c\)p\(c\)denote the parent of conceptccandp⁡\(i\)p\(i\)the parent concept of paperviv\_\{i\}under attachmentaa\.

### I\.1Semantic evolution consistencyℒsem\\mathcal\{L\}\_\{\\mathrm\{sem\}\}

Three sub\-terms enforce parent–child semantic coherence\.

##### Node\-to\-parent pull\.

Each paper is pulled toward the centroid of its parent concept:

ℒsem​\-​n=1\|𝒱\|​∑i∈𝒱\(1−cos⁡\(𝐞i,𝝁p⁡\(i\)\)\)\.\\mathcal\{L\}\_\{\\mathrm\{sem\\text\{\-\}n\}\}=\\frac\{1\}\{\|\\mathcal\{V\}\|\}\\sum\_\{i\\in\\mathcal\{V\}\}\\\!\\left\(1\-\\cos\(\\mathbf\{e\}\_\{i\},\\boldsymbol\{\\mu\}\_\{p\(i\)\}\)\\right\)\.\(44\)

##### Cluster\-to\-parent pull\.

Each concept is pulled toward the centroid of its parent concept:

ℒsem​\-​c=\\displaystyle\\mathcal\{L\}\_\{\\mathrm\{sem\\text\{\-\}c\}\}=\(45\)1\|𝒞\(t\)∖\{r\}\|\\displaystyle\\frac\{1\}\{\|\\mathcal\{C\}^\{\(t\)\}\\setminus\\\{r\\\}\|\}∑c∈𝒞\(t\)∖\{r\}\(1−cos⁡\(𝝁c,𝝁p⁡\(c\)\)\)\.\\displaystyle\\sum\_\{c\\in\\mathcal\{C\}^\{\(t\)\}\\setminus\\\{r\\\}\}\\\!\\\!\\\!\\left\(1\-\\cos\(\\boldsymbol\{\\mu\}\_\{c\},\\boldsymbol\{\\mu\}\_\{p\(c\)\}\)\\right\)\.

##### Drift window\.

Letδc=‖𝝁c−𝝁p⁡\(c\)‖2\\delta\_\{c\}=\\\|\\boldsymbol\{\\mu\}\_\{c\}\-\\boldsymbol\{\\mu\}\_\{p\(c\)\}\\\|\_\{2\}\. A two\-sided hinge confinesδc\\delta\_\{c\}to\[dmin,dmax\]\[d\_\{\\min\},d\_\{\\max\}\]:

ℒdrift=\\displaystyle\\mathcal\{L\}\_\{\\mathrm\{drift\}\}=\(46\)∑c∈𝒞\(t\)∖\{r\}\\displaystyle\\\!\\\!\\sum\_\{c\\in\\mathcal\{C\}^\{\(t\)\}\\setminus\\\{r\\\}\}\[max⁡\(0,dmin−δc\)\+max⁡\(0,δc−dmax\)\]\.\\displaystyle\\big\[\\max\(0,d\_\{\\min\}\-\\delta\_\{c\}\)\+\\max\(0,\\delta\_\{c\}\-d\_\{\\max\}\)\\big\]\.

##### Combination\.

ℒsem=wsemn​ℒsem​\-​n\+wsemc​ℒsem​\-​c\+wdrift​ℒdrift\.\\mathcal\{L\}\_\{\\mathrm\{sem\}\}=w\_\{\\mathrm\{semn\}\}\\mathcal\{L\}\_\{\\mathrm\{sem\\text\{\-\}n\}\}\+w\_\{\\mathrm\{semc\}\}\\mathcal\{L\}\_\{\\mathrm\{sem\\text\{\-\}c\}\}\+w\_\{\\mathrm\{drift\}\}\\mathcal\{L\}\_\{\\mathrm\{drift\}\}\.\(47\)

### I\.2Temporal coherenceℒtemp\\mathcal\{L\}\_\{\\mathrm\{temp\}\}

Three sub\-terms enforce forward\-progressing evolution\.

##### Path smoothness\.

For a root\-to\-leaf concept pathP=\(c0,c1,…,cL\)P=\(c\_\{0\},c\_\{1\},\\ldots,c\_\{L\}\), define velocityΔl=𝝁cl−𝝁cl−1\\Delta\_\{l\}=\\boldsymbol\{\\mu\}\_\{c\_\{l\}\}\-\\boldsymbol\{\\mu\}\_\{c\_\{l\-1\}\}\. We penalize second\-order changes:

ℒsmooth=1\|𝒫\|​∑P∈𝒫1L−1​∑l=2L‖Δl−Δl−1‖22,\\mathcal\{L\}\_\{\\mathrm\{smooth\}\}=\\frac\{1\}\{\|\\mathcal\{P\}\|\}\\\!\\sum\_\{P\\in\\mathcal\{P\}\}\\\!\\frac\{1\}\{L\-1\}\\\!\\sum\_\{l=2\}^\{L\}\\\!\\\|\\Delta\_\{l\}\-\\Delta\_\{l\-1\}\\\|\_\{2\}^\{2\},\(48\)where𝒫\\mathcal\{P\}is the set of root\-to\-leaf paths in𝒯\(t\)\\mathcal\{T\}^\{\(t\)\}\.

##### Path monotonicity\.

LetτT​\(c\)=minv∈𝒱⁡\(c\)⁡τ⁡\(v\)\\tau\_\{T\}\(c\)=\\min\_\{v\\in\\mathcal\{V\}\(c\)\}\\tau\(v\)denote the earliest publication year in the subtree ofcc\(also used in Appendix[J](https://arxiv.org/html/2609.09561#A10)\)\. A hinge encourages child concepts to be no earlier than parents:

ℒpath​\-​mono=∑\(cp,cc\)∈ℰCmax⁡\(0,τT​\(cp\)−τT​\(cc\)−ϵ\)\.\\mathcal\{L\}\_\{\\mathrm\{path\\text\{\-\}mono\}\}=\\\!\\\!\\\!\\\!\\\!\\sum\_\{\(c\_\{p\},c\_\{c\}\)\\in\\mathcal\{E\}\_\{C\}\}\\\!\\\!\\\!\\\!\\\!\\max\(0,\\,\\tau\_\{T\}\(c\_\{p\}\)\-\\tau\_\{T\}\(c\_\{c\}\)\-\\epsilon\)\.\(49\)

##### Citation directionality\.

For each citation\(vi,vj\)∈ℰ𝒢\(v\_\{i\},v\_\{j\}\)\\in\\mathcal\{E\}\_\{\\mathcal\{G\}\}withviv\_\{i\}citingvjv\_\{j\}, the citing paper should attach to a deeper node\. Letqi,cq\_\{i,c\}be the soft attachment probability ofviv\_\{i\}to conceptcc:

qi,c=exp\(−∥𝐞i−𝝁c∥22/τatt\)∑c′∈𝒞\(t\)exp\(−∥𝐞i−𝝁c′∥22/τatt\)\.q\_\{i,c\}=\\frac\{\\exp\\\!\\left\(\-\\\|\\mathbf\{e\}\_\{i\}\-\\boldsymbol\{\\mu\}\_\{c\}\\\|\_\{2\}^\{2\}/\\tau\_\{\\mathrm\{att\}\}\\right\)\}\{\\sum\_\{c^\{\\prime\}\\in\\mathcal\{C\}^\{\(t\)\}\}\\\!\\exp\\\!\\left\(\-\\\|\\mathbf\{e\}\_\{i\}\-\\boldsymbol\{\\mu\}\_\{c^\{\\prime\}\}\\\|\_\{2\}^\{2\}/\\tau\_\{\\mathrm\{att\}\}\\right\)\}\.\(50\)Define the expected depthd¯​\(vi\)=∑cqi,c​depth​\(c\)\\bar\{d\}\(v\_\{i\}\)=\\sum\_\{c\}q\_\{i,c\}\\,\\mathrm\{depth\}\(c\)\. The citation directionality loss is:

ℒcite​\-​dir=∑\(vi,vj\)∈ℰ𝒢max⁡\(0,d¯​\(vj\)−d¯​\(vi\)\+ξ\),\\mathcal\{L\}\_\{\\mathrm\{cite\\text\{\-\}dir\}\}=\\\!\\\!\\\!\\\!\\\!\\sum\_\{\(v\_\{i\},v\_\{j\}\)\\in\\mathcal\{E\}\_\{\\mathcal\{G\}\}\}\\\!\\\!\\\!\\\!\\\!\\max\(0,\\,\\bar\{d\}\(v\_\{j\}\)\-\\bar\{d\}\(v\_\{i\}\)\+\\xi\),\(51\)penalizing cases where the cited papervjv\_\{j\}ends up at leastξ\\xilevels deeper than the citingviv\_\{i\}\.

##### Combination\.

ℒtemp=ℒsmooth\+ℒpath​\-​mono\+ℒcite​\-​dir\.\\mathcal\{L\}\_\{\\mathrm\{temp\}\}=\\mathcal\{L\}\_\{\\mathrm\{smooth\}\}\+\\mathcal\{L\}\_\{\\mathrm\{path\\text\{\-\}mono\}\}\+\\mathcal\{L\}\_\{\\mathrm\{cite\\text\{\-\}dir\}\}\.\(52\)

### I\.3Marginal identification and re\-attachmentℒmarg\\mathcal\{L\}\_\{\\mathrm\{marg\}\}

Lethi=MLPmar​\(𝐞i\)∈\[0,1\]h\_\{i\}=\\mathrm\{MLP\}\_\{\\mathrm\{mar\}\}\(\\mathbf\{e\}\_\{i\}\)\\in\[0,1\]be the marginal\-head output\. Pseudo\-labels arey~im=𝟙\[Aileaf<η\]\\tilde\{y\}\_\{i\}^\{\\mathrm\{m\}\}=\\mathbb\{1\}\[A\_\{i\}^\{\\mathrm\{leaf\}\}<\\eta\]\.

##### Marginal classification\.

ℒmar=−1\|𝒱\|∑i∈𝒱\[y~imloghi\+\(1−y~im\)log\(1−hi\)\]\.\\mathcal\{L\}\_\{\\mathrm\{mar\}\}=\-\\frac\{1\}\{\|\\mathcal\{V\}\|\}\\\!\\sum\_\{i\\in\\mathcal\{V\}\}\\\!\\big\[\\tilde\{y\}\_\{i\}^\{\\mathrm\{m\}\}\\log h\_\{i\}\+\(1\-\\tilde\{y\}\_\{i\}^\{\\mathrm\{m\}\}\)\\log\(1\-h\_\{i\}\)\\big\]\.\(53\)

##### Attachment ranking\.

For each flagged marginal papervm∈ℳ\(t\)v\_\{m\}\\in\\mathcal\{M\}^\{\(t\)\}, letcm\+=a⁡\(vm\)c^\{\+\}\_\{m\}=a\(v\_\{m\}\)\(the optimal attachment from Eq\.[11](https://arxiv.org/html/2609.09561#S4.E11)\) andc−c^\{\-\}a candidate concept that fails the temporal admissibility check\. With score

satt​\(c,m\)=log⁡𝒩⁡\(𝐞m,𝝁c,diag⁡\(𝝈c2\)\),s\_\{\\mathrm\{att\}\}\(c,m\)=\\log\\mathcal\{N\}\\\!\\left\(\\mathbf\{e\}\_\{m\};\\,\\boldsymbol\{\\mu\}\_\{c\},\\mathrm\{diag\}\(\\boldsymbol\{\\sigma\}\_\{c\}^\{2\}\)\\right\),ℒattrank=\\displaystyle\\mathcal\{L\}\_\{\\mathrm\{att\}\}^\{\\mathrm\{rank\}\}=\(54\)∑vm∈ℳ\(t\)∑c−\\displaystyle\\\!\\\!\\sum\_\{v\_\{m\}\\in\\mathcal\{M\}^\{\(t\)\}\}\\\!\\\!\\\!\\sum\_\{c^\{\-\}\}max⁡\(0,satt​\(c−,m\)−satt​\(cm\+,m\)\+ζ\),\\displaystyle\\max\\\!\\big\(0,\\,s\_\{\\mathrm\{att\}\}\(c^\{\-\},m\)\-s\_\{\\mathrm\{att\}\}\(c^\{\+\}\_\{m\},m\)\+\\zeta\\big\),with marginζ\\zeta\.

##### Centroid repulsion\.

To prevent internal concept centroids from collapsing, sibling concepts are encouraged to maintain pairwise separation\. For each internal conceptccwith childrenchildren⁡\(c\)\\mathrm\{children\}\(c\):

ℒrepulsion=\\displaystyle\\mathcal\{L\}\_\{\\mathrm\{repulsion\}\}=\(55\)∑c∑ca,cb∈children⁡\(c\)a≠b\\displaystyle\\\!\\\!\\sum\_\{c\}\\\!\\\!\\sum\_\{\\begin\{subarray\}\{c\}c\_\{a\},c\_\{b\}\\in\\mathrm\{children\}\(c\)\\\\ a\\neq b\\end\{subarray\}\}max⁡\(0,ζr−‖𝝁ca−𝝁cb‖2\),\\displaystyle\\max\\\!\\big\(0,\\,\\zeta\_\{r\}\-\\\|\\boldsymbol\{\\mu\}\_\{c\_\{a\}\}\-\\boldsymbol\{\\mu\}\_\{c\_\{b\}\}\\\|\_\{2\}\\big\),with separation marginζr\\zeta\_\{r\}\.

##### Combination\.

ℒmarg=ℒmar\+ℒattrank\+ℒrepulsion\.\\mathcal\{L\}\_\{\\mathrm\{marg\}\}=\\mathcal\{L\}\_\{\\mathrm\{mar\}\}\+\\mathcal\{L\}\_\{\\mathrm\{att\}\}^\{\\mathrm\{rank\}\}\+\\mathcal\{L\}\_\{\\mathrm\{repulsion\}\}\.\(56\)

## Appendix JStructural Constraints

The main text describes the three most consequential constraints \(temporal consistency, backbone preservation, tree legality\)\. Here we formalize the two remaining constraints deferred from §[4\.4\.2](https://arxiv.org/html/2609.09561#S4.SS4.SSS2)\.

### J\.1Path temporal consistency

For every root\-to\-leaf concept path\(c0,c1,…,cL\)\(c\_\{0\},c\_\{1\},\\ldots,c\_\{L\}\)in𝒯\\mathcal\{T\},

τT​\(c0\)≤τT​\(c1\)\+ϵ≤⋯≤τT​\(cL\)\+L​ϵ,\\tau\_\{T\}\(c\_\{0\}\)\\leq\\tau\_\{T\}\(c\_\{1\}\)\+\\epsilon\\leq\\cdots\\leq\\tau\_\{T\}\(c\_\{L\}\)\+L\\epsilon,\(57\)whereτT​\(c\)=minv∈𝒱⁡\(c\)⁡τ⁡\(v\)\\tau\_\{T\}\(c\)=\\min\_\{v\\in\\mathcal\{V\}\(c\)\}\\tau\(v\)andϵ\\epsilonis the per\-edge tolerance margin\. This rules out global temporal inversions in which local pairs satisfy the temporal order but the path as a whole accumulates a violation\.

### J\.2Path membership coherence

For every conceptc∈𝒞c\\in\\mathcal\{C\}, its evolutionary ancestor chainancevo​\(c\)=\(c,p⁡\(c\),p⁡\(p⁡\(c\)\),…,r\)\\mathrm\{anc\}^\{\\mathrm\{evo\}\}\(c\)=\(c,p\(c\),p\(p\(c\)\),\\ldots,r\)must retain non\-trivial distributional overlap with its taxonomy\-ancestor chainanctax​\(c\)\\mathrm\{anc\}^\{\\mathrm\{tax\}\}\(c\)\. Formally, defining overlap as the maximum normalized intersection between any ancestor in the two chains,

Ω⁡\(c\)=maxce∈ancevo​\(c\),ct∈anctax​\(c\)⁡\|𝒱⁡\(ce\)∩𝒱⁡\(ct\)\|min⁡\(\|𝒱⁡\(ce\)\|,\|𝒱⁡\(ct\)\|\),\\\!\\\!\\\!\\Omega\(c\)=\\max\_\{c\_\{e\}\\in\\mathrm\{anc\}^\{\\mathrm\{evo\}\}\(c\),\\,c\_\{t\}\\in\\mathrm\{anc\}^\{\\mathrm\{tax\}\}\(c\)\}\\frac\{\|\\mathcal\{V\}\(c\_\{e\}\)\\cap\\mathcal\{V\}\(c\_\{t\}\)\|\}\{\\min\(\|\\mathcal\{V\}\(c\_\{e\}\)\|,\|\\mathcal\{V\}\(c\_\{t\}\)\|\)\},\(58\)and requiringΩ⁡\(c\)≥θov\\Omega\(c\)\\geq\\theta\_\{\\mathrm\{ov\}\}\. We useθov=0\.3\\theta\_\{\\mathrm\{ov\}\}=0\.3\. This constraint prevents the temporal reorientation in Stage II from rewiring a concept into a semantically unrelated branch\.

## Appendix KMarginal Compatibility Score

This appendix specifies the compatibility scorem⁡\(vi,c\)m\(v\_\{i\},c\)in §[4\.4\.3](https://arxiv.org/html/2609.09561#S4.SS4.SSS3)\.

For paperviv\_\{i\}and conceptccwith Gaussian\(𝝁c,𝝈c2\)\(\\boldsymbol\{\\mu\}\_\{c\},\\boldsymbol\{\\sigma\}\_\{c\}^\{2\}\)and member set𝒱⁡\(c\)\\mathcal\{V\}\(c\):

##### Semantic similarity\.

ssem​\(i,c\)=12​\(1\+cos⁡\(𝐞i,𝝁c\)\)∈\[0,1\]\.s\_\{\\mathrm\{sem\}\}\(i,c\)=\\frac\{1\}\{2\}\\\!\\left\(1\+\\cos\(\\mathbf\{e\}\_\{i\},\\boldsymbol\{\\mu\}\_\{c\}\)\\right\)\\in\[0,1\]\.\(59\)

##### Citation\-neighborhood overlap\.

sgraph​\(i,c\)=\|𝒩𝒢​\(vi\)∩𝒱⁡\(c\)\|max⁡\(\|𝒩𝒢​\(vi\)\|,1\)∈\[0,1\]\.s\_\{\\mathrm\{graph\}\}\(i,c\)=\\frac\{\|\\mathcal\{N\}\_\{\\mathcal\{G\}\}\(v\_\{i\}\)\\cap\\mathcal\{V\}\(c\)\|\}\{\\max\(\|\\mathcal\{N\}\_\{\\mathcal\{G\}\}\(v\_\{i\}\)\|,1\)\}\\in\[0,1\]\.\(60\)

##### Temporal compatibility\.

Letτ¯c=\|𝒱⁡\(c\)\|−1​∑v∈𝒱⁡\(c\)τ⁡\(v\)\\bar\{\\tau\}\_\{c\}=\|\\mathcal\{V\}\(c\)\|^\{\-1\}\\\!\\sum\_\{v\\in\\mathcal\{V\}\(c\)\}\\tau\(v\)be the nominal time ofcc\. With time\-scaleσt\\sigma\_\{t\}:

stime​\(i,c\)=exp⁡\(−\|τ⁡\(vi\)−τ¯c\|σt\)∈\(0,1\]\.s\_\{\\mathrm\{time\}\}\(i,c\)=\\exp\\\!\\left\(\-\\frac\{\|\\tau\(v\_\{i\}\)\-\\bar\{\\tau\}\_\{c\}\|\}\{\\sigma\_\{t\}\}\\right\)\\in\(0,1\]\.\(61\)

##### Combined compatibility\.

m⁡\(vi,c\)=\\displaystyle m\(v\_\{i\},c\)=\(62\)γ1​ssem​\(i,c\)\\displaystyle\\gamma\_\{1\}\\,s\_\{\\mathrm\{sem\}\}\(i,c\)\+γ2​sgraph​\(i,c\)\+γ3​stime​\(i,c\),\\displaystyle\+\\gamma\_\{2\}\\,s\_\{\\mathrm\{graph\}\}\(i,c\)\+\\gamma\_\{3\}\\,s\_\{\\mathrm\{time\}\}\(i,c\),withγ1\+γ2\+γ3=1\\gamma\_\{1\}\+\\gamma\_\{2\}\+\\gamma\_\{3\}=1andm⁡\(vi,c\)∈\[0,1\]m\(v\_\{i\},c\)\\in\[0,1\]\.

## Appendix LStage III Calibration Loss Details

This appendix expands the three calibration loss terms summarized in §[4\.5](https://arxiv.org/html/2609.09561#S4.SS5):

ℒcal=ℒmargcal\+ℒconceptcal\+ℒedgecal\.\\mathcal\{L\}^\{\\mathrm\{cal\}\}=\\mathcal\{L\}^\{\\mathrm\{cal\}\}\_\{\\mathrm\{marg\}\}\+\\mathcal\{L\}^\{\\mathrm\{cal\}\}\_\{\\mathrm\{concept\}\}\+\\mathcal\{L\}^\{\\mathrm\{cal\}\}\_\{\\mathrm\{edge\}\}\.The FS dataset \(§[5\.1](https://arxiv.org/html/2609.09561#S5.SS1)\) provides per\-paper labelsyim,fs∈\{0,1\}y\_\{i\}^\{\\mathrm\{m,fs\}\}\\in\\\{0,1\\\}\(marginal\),gi∈𝒢fsg\_\{i\}\\in\\mathcal\{G\}^\{\\mathrm\{fs\}\}\(concept\), and the evolution edge setℰevo\\mathcal\{E\}^\{\\mathrm\{evo\}\}over papers \(Appendix[D](https://arxiv.org/html/2609.09561#A4)\)\.

### L\.1FS marginal classification

Class\-weighted BCE to handle the imbalance between core and marginal papers:

ℒcalmarg=−1\|𝒱fs\|∑i∈𝒱fs\\displaystyle\\mathcal\{L\}^\{\\mathrm\{cal\}\}\_\{\\mathrm\{marg\}\}=\-\\frac\{1\}\{\|\\mathcal\{V\}^\{\\mathrm\{fs\}\}\|\}\\\!\\\!\\sum\_\{i\\in\\mathcal\{V\}^\{\\mathrm\{fs\}\}\}\[w\+yim,fsloghi\\displaystyle\\big\[w^\{\+\}y\_\{i\}^\{\\mathrm\{m,fs\}\}\\log h\_\{i\}\(63\)\+w−\(1−yim,fs\)log\(1−hi\)\],\\displaystyle\+w^\{\-\}\(1\-y\_\{i\}^\{\\mathrm\{m,fs\}\}\)\\log\(1\-h\_\{i\}\)\\big\],withw\+=\(1−y¯m\)/y¯mw^\{\+\}=\(1\-\\bar\{y\}^\{\\mathrm\{m\}\}\)/\\bar\{y\}^\{\\mathrm\{m\}\},w−=1w^\{\-\}=1, andy¯m\\bar\{y\}^\{\\mathrm\{m\}\}the marginal fraction in the FS set\.

### L\.2FS concept alignment

For each FS conceptg∈𝒢fsg\\in\\mathcal\{G\}^\{\\mathrm\{fs\}\}, define its empirical centroid

𝐞¯g=sg⁡\(1\|𝒱gfs\|​∑i∈𝒱gfs𝐞i\),\\bar\{\\mathbf\{e\}\}\_\{g\}=\\mathrm\{sg\}\\\!\\left\(\\frac\{1\}\{\|\\mathcal\{V\}\_\{g\}^\{\\mathrm\{fs\}\}\|\}\\\!\\\!\\sum\_\{i\\in\\mathcal\{V\}\_\{g\}^\{\\mathrm\{fs\}\}\}\\\!\\\!\\mathbf\{e\}\_\{i\}\\right\),\(64\)with𝒱gfs=\{vi:gi=g\}\\mathcal\{V\}\_\{g\}^\{\\mathrm\{fs\}\}=\\\{v\_\{i\}:g\_\{i\}=g\\\}\. An InfoNCE objective aligns each paper with its FS centroid:

ℒcalconcept=−1\|𝒱fs\|∑i∈𝒱fslogexp⁡\(𝐞i⊤​𝐞¯gi/τic\)∑g′∈𝒢fsexp⁡\(𝐞i⊤​𝐞¯g′/τic\)\.\\mathcal\{L\}^\{\\mathrm\{cal\}\}\_\{\\mathrm\{concept\}\}=\-\\frac\{1\}\{\|\\mathcal\{V\}^\{\\mathrm\{fs\}\}\|\}\\\!\\\!\\sum\_\{i\\in\\mathcal\{V\}^\{\\mathrm\{fs\}\}\}\\\!\\\!\\log\\frac\{\\exp\(\\mathbf\{e\}\_\{i\}^\{\\top\}\\bar\{\\mathbf\{e\}\}\_\{g\_\{i\}\}/\\tau\_\{\\mathrm\{ic\}\}\)\}\{\\sum\_\{g^\{\\prime\}\\in\\mathcal\{G\}^\{\\mathrm\{fs\}\}\}\\\!\\exp\(\\mathbf\{e\}\_\{i\}^\{\\top\}\\bar\{\\mathbf\{e\}\}\_\{g^\{\\prime\}\}/\\tau\_\{\\mathrm\{ic\}\}\)\}\.\(65\)

### L\.3FS edge directionality

For each annotated edge\(vs,vd\)∈ℰevo\(v\_\{s\},v\_\{d\}\)\\in\\mathcal\{E\}^\{\\mathrm\{evo\}\},vsv\_\{s\}is the evolutionary descendant ofvdv\_\{d\}\. A triplet\-margin loss requires the predicted depth ofvsv\_\{s\}to exceed that ofvdv\_\{d\}, with cross\-domainadaptsrelations receiving a smaller margin:

ℒedgecal=∑\(vs,vd\)∈ℰevomax⁡\(0,d¯​\(vd\)−d¯​\(vs\)\+μ⁡\(vs,vd\)\),\\mathcal\{L\}^\{\\mathrm\{cal\}\}\_\{\\mathrm\{edge\}\}=\\\!\\\!\\\!\\\!\\\!\\\!\\\!\\sum\_\{\(v\_\{s\},v\_\{d\}\)\\in\\mathcal\{E\}^\{\\mathrm\{evo\}\}\}\\\!\\\!\\\!\\\!\\\!\\\!\\\!\\max\\\!\\big\(0,\\,\\bar\{d\}\(v\_\{d\}\)\-\\bar\{d\}\(v\_\{s\}\)\+\\mu\(v\_\{s\},v\_\{d\}\)\\big\),\(66\)whered¯​\(⋅\)\\bar\{d\}\(\\cdot\)is the expected depth from Eq\.[50](https://arxiv.org/html/2609.09561#A9.E50), and

μ⁡\(vs,vd\)=\{μstrictextends/improves,μrelaxadapts\.\\mu\(v\_\{s\},v\_\{d\}\)=\\begin\{cases\}\\mu\_\{\\mathrm\{strict\}\}&\\text\{\{extends\} / \{improves\}\},\\\\ \\mu\_\{\\mathrm\{relax\}\}&\\text\{\{adapts\}\}\.\\end\{cases\}

## Appendix MEM\-style Optimization

This appendix details the E\-step / M\-step alternation summarized in §[4\.4\.1](https://arxiv.org/html/2609.09561#S4.SS4.SSS1)\.

Algorithm 2Stage II EM\-style optimization\.0:Pre\-trained encoder

fθf\_\{\\theta\}with adapters

θa\\theta\_\{a\}; taxonomy backbone

𝒯tax\\mathcal\{T\}^\{\\mathrm\{tax\}\}; epochs

TT\.

1:Initialize

𝒯\(0\)←𝒯tax\\mathcal\{T\}^\{\(0\)\}\\leftarrow\\mathcal\{T\}^\{\\mathrm\{tax\}\}\.

2:for

t=1,…,Tt=1,\\ldots,Tdo

3:E\-step:

4:Freeze

θa\\theta\_\{a\}; compute

\{𝐞i\}\\\{\\mathbf\{e\}\_\{i\}\\\}via current encoder\.

5:Run Algorithm[1](https://arxiv.org/html/2609.09561#alg1)with temporal admissibility filter

ℱϵ\\mathcal\{F\}\_\{\\epsilon\}\.

6:Obtain

𝒯\(t\),𝒞\(t\)\\mathcal\{T\}^\{\(t\)\},\\mathcal\{C\}^\{\(t\)\}and identify marginal candidates

ℳ\(t\)\\mathcal\{M\}^\{\(t\)\}\.

7:Generate pseudo\-labels

\{y~im\}\\\{\\tilde\{y\}\_\{i\}^\{\\mathrm\{m\}\}\\\}via Eq\.[3](https://arxiv.org/html/2609.09561#S3.E3)\.

8:M\-step:

9:Freeze

𝒯\(t\)\\mathcal\{T\}^\{\(t\)\}; update

θa\\theta\_\{a\}by one epoch of SGD on

ℒevo\\mathcal\{L\}^\{\\mathrm\{evo\}\}\.

10:endfor

11:returnAdapters

θa\\theta\_\{a\}, final tree

𝒯=𝒯\(T\)\\mathcal\{T\}=\\mathcal\{T\}^\{\(T\)\}\.

##### E\-step frequency\.

In practice we run the E\-step once per epoch\. Running it more frequently \(e\.g\., every 100 steps\) did not improve performance and increased compute by∼3×\\sim 3\\times\.

##### Temporal admissibility filterℱϵ\\mathcal\{F\}\_\{\\epsilon\}\.

A candidate merge of clustersCp,CqC\_\{p\},C\_\{q\}is admissible if for each subsequent merging step the resulting parent does not violate parental temporal ordering by more thanϵ=1\\epsilon=1year, where the nominal time of a cluster isτatt\\tau^\{\\text\{att\}\}\(Eq\.[1](https://arxiv.org/html/2609.09561#S3.E1)\), the mean publication year of its directly attached papers, as in Eq\.[8](https://arxiv.org/html/2609.09561#S4.E8)\.

## Appendix NGeneration\-quality Evaluation Protocol

### N\.1Evaluation Setup

Both protocols receive identical supporting information: paper titles, publication years, citation relations, and the anonymized generated hierarchy\. Method names, model descriptions, and metric results are withheld\. To reduce presentation bias, structures are assigned randomized anonymous identifiers and presented in randomized order\. The LLM judge is the same model used for concept labeling, evaluating each structure over multiple independent runs under a fixed prompt and decoding configuration\. Human evaluation is conducted by three CS graduate students who did not participate in constructing the FS annotations; they evaluate each structure independently and do not discuss individual cases before submitting their judgments\.

### N\.2Criteria and Aggregation

Both protocols score four dimensions—conceptual organization, scientific evolution, transitional\-paper placement, and overall explanatory quality—on a 1–10 scale under the same rubric, each accompanied by a brief evidence\-based justification\. Scores are averaged over evaluation runs \(LLM\) or evaluators \(human\), then over the FS domains, and we report the mean and standard deviation per method and dimension in Table[5](https://arxiv.org/html/2609.09561#S5.T5)\.

The following prompt is given to the LLM judge; human evaluators receive the same criteria in written form\.

Generation\-quality evaluation promptYou are an expert researcher\. Given a citation graph and a generated hierarchy, evaluate the hierarchy on the following aspects\.Citation graph:\[titles, publication years, citation relations\]Generated hierarchy:\[anonymized structure\]Aspects:1\.Conceptual Organization— Are papers grouped into semantically coherent concepts? Are concept names accurate?2\.Scientific Evolution— Does the hierarchy reflect the historical development of the field? Are parent–child relationships reasonable?3\.Transitional Papers— Are transitional / bridge papers attached at an appropriate position?4\.Overall Quality— How well does the hierarchy explain the organization and evolution of this research field?Give a score from 1–10 for each aspect and provide a brief explanation\.