BERTilda: Explainable Topic Lifecycle Tracking with Split/Merge Detection via Similarity-and-Flow Temporal Graphs

# BERTilda: Explainable Topic Lifecycle Tracking with Split/Merge Detection via Similarity-and-Flow Temporal Graphs
Source: [https://arxiv.org/html/2608.18101](https://arxiv.org/html/2608.18101)
11institutetext:Faculty of Sciences, University of Porto, Portugal
11email:arfiguei@fc\.up\.pt22institutetext:INESCTEC, Porto, Portugal###### Abstract

Longitudinal text streams exhibit topic birth and death, but also discrete structural reorganizations in which themes*split*into subtopics or*merge*into broader narratives\. Many dynamic topic models emphasize smooth drift, while snapshot topic models \(fit independently per time window\) leave temporal correspondence underspecified\. We present*BERTilda*, an explainable framework that discovers topics independently in each window \(using an embedding\-based topic model\) and then constructs a*temporal topic graph*linking topics across adjacent windows\. Links are supported by two complementary signals: \(i\) semantic similarity between topic representations and \(ii\) a*bidirectional coverage*signal that estimates document outflow \(where a topic goes\) and inflow \(where a topic comes from\) via cross\-window tweet\-to\-topic attribution\. Graph\-based rules label continuations, splits, merges, disappearances, and unclear transitions\. We evaluate BERTilda on political corpora, including U\.S\. congressional tweets and historical speech datasets, report topic\-quality and temporal\-stability diagnostics, and validate lifecycle labels on a gold\-standard subset annotated by three independent annotators\. On the annotated subset, BERTilda reaches majority agreement rates up to 87% and attains the highest macro\-average agreement across the compared methods, with particularly strong disappearance detection relative to similarity\-only and forward\-only baselines\.

## 1Introduction

Topic modeling is a standard tool for exploring large text collections, yet many real\-world corpora are inherently longitudinal\. In political communication on social media and in institutional speeches, themes do not only drift gradually: topics are born and die, but also fragment into competing sub\-narratives \(splits\) or converge when previously separate debates become tightly coupled \(merges\)\. Explicitly identifying such structural events is useful for summarizing how attention shifts and reorganizes over time\.

Methodologically, split/merge detection is difficult because the concept of a*topic*depends on the modeling family\. Classical probabilistic topic models such as LDA\[[6](https://arxiv.org/html/2608.18101#bib.bib2)\]and many dynamic extensions \(e\.g\., DTM\[[5](https://arxiv.org/html/2608.18101#bib.bib6)\], Topics over Time\[[33](https://arxiv.org/html/2608.18101#bib.bib7)\], and continuous\-time variants\[[32](https://arxiv.org/html/2608.18101#bib.bib13)\]\) define topics as distributions over words and often assume relatively smooth evolution\. Neural dynamic models \(e\.g\., DETM\[[11](https://arxiv.org/html/2608.18101#bib.bib18)\]\) instead evolve latent representations\. These formulations provide valuable temporal regularization, but they do not naturally yield discrete, auditable split/merge events\. Conversely, snapshot topic models, including embedding\-based approaches effective for short texts \(e\.g\., Top2Vec\[[3](https://arxiv.org/html/2608.18101#bib.bib17)\], BERTopic\[[13](https://arxiv.org/html/2608.18101#bib.bib1)\], and embedding\-space topic models\[[12](https://arxiv.org/html/2608.18101#bib.bib27)\]\), avoid imposing continuity but leave topic correspondence across windows ambiguous\.

We propose BERTilda, "BERT\-based Temporal Identification, Lifecycle Detection and Analysis", which treats temporal topic modeling as an alignment\-and\-event\-labeling problem on an explicit graph\. Topics are discovered independently within each window using a snapshot topic model \(we instantiate with BERTopic\[[13](https://arxiv.org/html/2608.18101#bib.bib1)\], but the framework is model\-agnostic\)\. We then link topics across adjacent windows using two signals\. The first is semantic similarity between topic representations in a shared embedding space\. The second is*bidirectional coverage*, an interpretable flow signal that estimates \(i\) document*outflow*from a source topic and \(ii\) document*inflow*into a target topic via cross\-window document\-to\-topic attribution\. Together, we use these signals and apply transparent rules to label continuations, splits, merges, disappearances, and unclear transitions, which are then used to construct a temporal topic graph\.

Empirically, we evaluate BERTilda on a corpus of 357,896 tweets authored by 544 members of the 119th U\.S\. Congress, and on historical political speech corpora used in prior dynamic topic modeling work\. We report topic quality and temporal stability diagnostics and validate lifecycle labels on a gold\-standard subset annotated by three independent annotators\.

This paper makes three contributions: \(i\) bidirectional coverage as an interpretable flow signal for temporal topic alignment that complements embedding\-based similarity; \(ii\) a graph\-based labeling scheme that operationalizes topic lifecycles and split/merge events without assuming smooth evolution; and \(iii\) an evaluation protocol that combines quantitative diagnostics with human validation on political corpora\.

The remainder of this paper is organized as follows\. Section[2](https://arxiv.org/html/2608.18101#S2)reviews related work on topic models, temporal evolution, split/merge detection, and evaluation\. Section[3](https://arxiv.org/html/2608.18101#S3)presents BERTilda\. Section[4](https://arxiv.org/html/2608.18101#S4)describes datasets, baselines, and evaluation protocols\. Section[5](https://arxiv.org/html/2608.18101#S5)reports results, followed by discussion and limitations in Section[6](https://arxiv.org/html/2608.18101#S6)\.

## 2Related Work

### 2\.1Topic modeling for short and noisy texts

Early topic models represent documents as mixtures of latent components defined over vocabularies\. Classical examples include probabilistic latent semantic analysis\[[15](https://arxiv.org/html/2608.18101#bib.bib21)\]and LDA\[[6](https://arxiv.org/html/2608.18101#bib.bib2)\]\. Nonnegative matrix factorization \(NMF\) provides an alternative matrix\-decomposition perspective\[[20](https://arxiv.org/html/2608.18101#bib.bib22),[21](https://arxiv.org/html/2608.18101#bib.bib23)\], while Bayesian nonparametric approaches such as hierarchical Dirichlet processes address model selection\[[30](https://arxiv.org/html/2608.18101#bib.bib8)\]\.

Short texts such as tweets pose sparsity challenges for bag\-of\-words models, which motivates semantic representations based on contextual embeddings\. Embedding\-based topic models induce topics by clustering in embedding space, as in Top2Vec\[[3](https://arxiv.org/html/2608.18101#bib.bib17)\], or combine embeddings with sparse lexical representations to obtain interpretable descriptors, as in BERTopic\[[13](https://arxiv.org/html/2608.18101#bib.bib1)\], which has also been applied to the analysis of congressional Twitter discourse\[[22](https://arxiv.org/html/2608.18101#bib.bib41)\]\. A related line of work models topics directly in embedding spaces\[[12](https://arxiv.org/html/2608.18101#bib.bib27)\]or uses contextualized topic models\[[4](https://arxiv.org/html/2608.18101#bib.bib28)\]\.

### 2\.2Dynamic and online topic models

Dynamic topic models incorporate temporal dependencies, typically encouraging gradual evolution in topic representations\. DTM\[[5](https://arxiv.org/html/2608.18101#bib.bib6)\]uses state\-space dynamics over topic parameters; Topics over Time\[[33](https://arxiv.org/html/2608.18101#bib.bib7)\]models continuous timestamp distributions; and continuous\-time variants generalize to irregular time\[[32](https://arxiv.org/html/2608.18101#bib.bib13)\]\. Bayesian nonparametric models such as Timeline target birth and death processes\[[1](https://arxiv.org/html/2608.18101#bib.bib14)\]\.

For streaming scenarios, online variants update topics without reprocessing the full history\[[14](https://arxiv.org/html/2608.18101#bib.bib24),[2](https://arxiv.org/html/2608.18101#bib.bib25)\], and surveys summarize topic detection and tracking in social media streams\[[18](https://arxiv.org/html/2608.18101#bib.bib26)\]\. Recent neural dynamic models evolve latent representations \(e\.g\., DETM\[[11](https://arxiv.org/html/2608.18101#bib.bib18)\]\) and introduce structured dependencies that can support branching/merging behavior\[[23](https://arxiv.org/html/2608.18101#bib.bib15),[10](https://arxiv.org/html/2608.18101#bib.bib29)\]\. Contrastive and chain\-free evolution\-tracking formulations further relax one\-to\-one temporal identities\[[34](https://arxiv.org/html/2608.18101#bib.bib30)\]\. Although these approaches capture temporal regularities, discrete split/merge events often remain implicit or require post hoc interpretation\.

### 2\.3Cluster evolution, split/merge events, and explainability

Beyond probabilistic modeling, cluster evolution has been studied via similarity graphs and objectives that balance snapshot fit and temporal smoothness, such as evolutionary clustering\[[7](https://arxiv.org/html/2608.18101#bib.bib9)\]\. Visual analytics and alluvial\-style representations highlight branching and convergence patterns\[[28](https://arxiv.org/html/2608.18101#bib.bib4)\]\. In practice, split/merge detection is frequently performed by post\-processing snapshot clusters with graph\-based rules or matching procedures\.

BERTilda follows this alignment perspective but adds an explicit, interpretable*flow*constraint: similarity alone can produce ambiguous many\-to\-many matchings in dense semantic spaces, while document\-level coverage helps distinguish substantive transitions from weak topical proximity\.

### 2\.4Evaluation of topic quality and temporal behavior

Automated topic evaluation remains challenging\. Coherence measures correlate imperfectly with human judgments\[[8](https://arxiv.org/html/2608.18101#bib.bib31),[17](https://arxiv.org/html/2608.18101#bib.bib33)\], and different coherence formulations can behave inconsistently across models and domains\[[24](https://arxiv.org/html/2608.18101#bib.bib32),[25](https://arxiv.org/html/2608.18101#bib.bib34)\]\. Recent work proposes contextualized coherence using masked language models\[[27](https://arxiv.org/html/2608.18101#bib.bib35)\]and purpose\-oriented evaluation enabled by large language models\[[29](https://arxiv.org/html/2608.18101#bib.bib36)\]\.

For dynamic topic models, evaluation must address temporal behavior\. Recent work proposes topic\-quality\-over\-time measures and temporal consistency diagnostics\[[19](https://arxiv.org/html/2608.18101#bib.bib12)\], and surveys discuss stability and robustness considerations\[[9](https://arxiv.org/html/2608.18101#bib.bib37),[16](https://arxiv.org/html/2608.18101#bib.bib38)\]\. In this work, we combine within\-window topic quality metrics with temporal diagnostics \(drift/volatility\) and human validation of discrete lifecycle labels\.

## 3Method

### 3\.1Overview

BERTilda has three stages\. First, it segments a timestamped corpus into \(possibly overlapping\) windows and fits a snapshot topic model per window\. Second, it aligns topics across adjacent windows by constructing a bipartite graph connecting topics that meet semantic similarity and bidirectional coverage thresholds\. Third, it applies transparent similarity and coverage\-based rules to classify lifecycle events \(continuation, split, merge, disappearance, or unclear\)\.

### 3\.2Windowing and snapshot topics

Let𝒟=\{d1,…,dN\}\\mathcal\{D\}=\\\{d\_\{1\},\\ldots,d\_\{N\}\\\}be timestamped documents\. We define a sequence of windowst=1,…,Tt=1,\\ldots,Twith startsts\_\{t\}and endete\_\{t\}:

st\+1\\displaystyle s\_\{t\+1\}=st\+Δstep,et=st\+Δwindow,\\displaystyle=s\_\{t\}\+\\Delta\_\{\\text\{step\}\},\\qquad e\_\{t\}=s\_\{t\}\+\\Delta\_\{\\text\{window\}\},𝒟t\\displaystyle\\mathcal\{D\}\_\{t\}=\{d∈𝒟:st≤time​\(d\)<et\}\.\\displaystyle=\\\{d\\in\\mathcal\{D\}:s\_\{t\}\\leq\\text\{time\}\(d\)<e\_\{t\}\\\}\.Within each window, a snapshot topic model yields a set of topics𝒦t=\{1,…,Kt\}\\mathcal\{K\}\_\{t\}=\\\{1,\\ldots,K\_\{t\}\\\}and an assignmentzt​\(d\)∈𝒦tz\_\{t\}\(d\)\\in\\mathcal\{K\}\_\{t\}for eachd∈𝒟td\\in\\mathcal\{D\}\_\{t\}\. Let𝒟t,k=\{d∈𝒟t:zt​\(d\)=k\}\\mathcal\{D\}\_\{t,k\}=\\\{d\\in\\mathcal\{D\}\_\{t\}:z\_\{t\}\(d\)=k\\\}andnt,k=\|𝒟t,k\|n\_\{t,k\}=\|\\mathcal\{D\}\_\{t,k\}\|\.

### 3\.3Topic representations and similarity

Each documentddis embedded asϕ​\(d\)∈ℝm\\phi\(d\)\\in\\mathbb\{R\}^\{m\}using a fixed encoder shared across windows\. Each topic is represented by an embeddingψ​\(t,k\)∈ℝm\\psi\(t,k\)\\in\\mathbb\{R\}^\{m\}, defined as the centroid of the document embeddings assigned to that topic within the corresponding window\. This centroid\-based representation ensures topic embeddings remain directly comparable across windows, as they are all derived from a shared document embedding space\.

We define topic similarity across adjacent windows via cosine similarity:

sim​\(\(t,k\),\(t\+1,j\)\)=cos⁡\(ψ​\(t,k\),ψ​\(t\+1,j\)\)\.\\mathrm\{sim\}\(\(t,k\),\(t\{\+\}1,j\)\)=\\cos\\big\(\\psi\(t,k\),\\psi\(t\{\+\}1,j\)\\big\)\.

### 3\.4Bidirectional coverage by cross\-window attribution

Similarity alone is insufficient to disambiguate many\-to\-many relations in dense semantic spaces\. BERTilda therefore estimates an interpretable*flow*signal by attributing documents across windows\.

##### Forward attribution \(outflow\)\.

For each documentd∈𝒟t,kd\\in\\mathcal\{D\}\_\{t,k\}we select the most similar topic in the next window,

j∗​\(d\)=arg⁡maxj∈𝒦t\+1⁡cos⁡\(ϕ​\(d\),ψ​\(t\+1,j\)\),j^\{\*\}\(d\)=\\arg\\max\_\{j\\in\\mathcal\{K\}\_\{t\+1\}\}\\cos\(\\phi\(d\),\\psi\(t\{\+\}1,j\)\),accepting the attribution only if the maximum similarity exceedsτdoc\\tau\_\{\\text\{doc\}\}\. We defineFtfwd​\(k→j\)F^\{\\text\{fwd\}\}\_\{t\}\(k\\to j\)as the number of documents in𝒟t,k\\mathcal\{D\}\_\{t,k\}attributed to topicjjin windowt\+1t\{\+\}1\. Outflow coverage is

covout​\(k→j\)=Ftfwd​\(k→j\)nt,k\.\\mathrm\{cov\}\_\{\\text\{out\}\}\(k\\to j\)=\\frac\{F^\{\\text\{fwd\}\}\_\{t\}\(k\\to j\)\}\{n\_\{t,k\}\}\.

##### Backward attribution \(inflow\)\.

Symmetrically, for eachd∈𝒟t\+1,jd\\in\\mathcal\{D\}\_\{t\+1,j\}we select the most similar topic in the previous window,

k∗​\(d\)=arg⁡maxk∈𝒦t⁡cos⁡\(ϕ​\(d\),ψ​\(t,k\)\),k^\{\*\}\(d\)=\\arg\\max\_\{k\\in\\mathcal\{K\}\_\{t\}\}\\cos\(\\phi\(d\),\\psi\(t,k\)\),again requiring the maximum similarity to exceedτdoc\\tau\_\{\\text\{doc\}\}\. LetFtbwd​\(k→j\)F^\{\\text\{bwd\}\}\_\{t\}\(k\\to j\)be the number of documents in𝒟t\+1,j\\mathcal\{D\}\_\{t\+1,j\}attributed back to topickk\. Inflow coverage is

covin​\(k→j\)=Ftbwd​\(k→j\)nt\+1,j\.\\mathrm\{cov\}\_\{\\text\{in\}\}\(k\\to j\)=\\frac\{F^\{\\text\{bwd\}\}\_\{t\}\(k\\to j\)\}\{n\_\{t\+1,j\}\}\.
Intuitively, outflow answers “where did topic\(t,k\)\(t,k\)go?”, while inflow answers “where did topic\(t\+1,j\)\(t\{\+\}1,j\)come from?”\. This bidirectionality is particularly important for merges: outflow alone can be dominated by large source topics, whereas inflow normalizes by the target topic mass\.

### 3\.5Event rules and temporal topic graph

For each adjacent pair of windows\(t,t\+1\)\(t,t\{\+\}1\), we compute cosine similarities between topic centroids and bidirectional coverage by cross\-window attribution\. We then build a bipartite directed graph from topics in windowttto topics int\+1t\{\+\}1\. A candidate relation\(k→j\)\(k\\to j\)is retained as an edge if it satisfies three minimum requirements,

sim​\(\(t,k\),\(t\+1,j\)\)≥τtopic,covout​\(k→j\)≥τcovout,covin​\(k→j\)≥τcovin\.\\mathrm\{sim\}\(\(t,k\),\(t\{\+\}1,j\)\)\\geq\\tau\_\{\\text\{topic\}\},\\qquad\\mathrm\{cov\}\_\{\\text\{out\}\}\(k\\to j\)\\geq\\tau\_\{\\text\{cov\}\}^\{\\text\{out\}\},\\qquad\\mathrm\{cov\}\_\{\\text\{in\}\}\(k\\to j\)\\geq\\tau\_\{\\text\{cov\}\}^\{\\text\{in\}\}\.\(1\)LetEtE\_\{t\}be the set of retained edges for the pair\(t,t\+1\)\(t,t\{\+\}1\), and define the successor and predecessor sets

St​\(k\)=\{j:\(k→j\)∈Et\},Pt\+1​\(j\)=\{k:\(k→j\)∈Et\}\.S\_\{t\}\(k\)=\\\{j:\(k\\to j\)\\in E\_\{t\}\\\},\\qquad P\_\{t\+1\}\(j\)=\\\{k:\(k\\to j\)\\in E\_\{t\}\\\}\.\(2\)
We label lifecycle events using simple, auditable rules\. Topic\(t,k\)\(t,k\)is labeled as*continued*ifSt​\(k\)=\{j\}S\_\{t\}\(k\)=\\\{j\\\}and the unique successor satisfies a stricter similarity\-and\-coverage condition,

sim​\(k,j\)≥αcont,covout​\(k→j\)≥αcontout,covin​\(k→j\)≥αcontin\.\\mathrm\{sim\}\(k,j\)\\geq\\alpha\_\{\\text\{cont\}\},\\qquad\\mathrm\{cov\}\_\{\\text\{out\}\}\(k\\to j\)\\geq\\alpha\_\{\\text\{cont\}\}^\{\\text\{out\}\},\\qquad\\mathrm\{cov\}\_\{\\text\{in\}\}\(k\\to j\)\\geq\\alpha\_\{\\text\{cont\}\}^\{\\text\{in\}\}\.\(3\)
It is labeled as a*split*if it has at least two validated successors and a substantial fraction of its mass flows to them,

\|St​\(k\)\|≥2,∑j∈St​\(k\)covout​\(k→j\)≥αsplitout,covin​\(k→j\)≥αsplitin​∀j∈St​\(k\)\.\|S\_\{t\}\(k\)\|\\geq 2,\\quad\\sum\_\{j\\in S\_\{t\}\(k\)\}\\mathrm\{cov\}\_\{\\text\{out\}\}\(k\\to j\)\\geq\\alpha\_\{\\text\{split\}\}^\{\\text\{out\}\},\\quad\\mathrm\{cov\}\_\{\\text\{in\}\}\(k\\to j\)\\geq\\alpha\_\{\\text\{split\}\}^\{\\text\{in\}\}\\;\\;\\forall j\\in S\_\{t\}\(k\)\.\(4\)
It*disappears*if it has no validated successor, or if the total outflow to all validated successors is negligible,

St​\(k\)=∅or∑j∈St​\(k\)covout​\(k→j\)<αdispoutor∑j∈St​\(k\)covin​\(k→j\)<αdispin\.S\_\{t\}\(k\)=\\emptyset\\quad\\text\{or\}\\quad\\sum\_\{j\\in S\_\{t\}\(k\)\}\\mathrm\{cov\}\_\{\\text\{out\}\}\(k\\to j\)<\\alpha\_\{\\text\{disp\}\}^\{\\text\{out\}\}\\quad\\text\{or\}\\quad\\sum\_\{j\\in S\_\{t\}\(k\)\}\\mathrm\{cov\}\_\{\\text\{in\}\}\(k\\to j\)<\\alpha\_\{\\text\{disp\}\}^\{\\text\{in\}\}\.\(5\)
Separately, topic\(t\+1,j\)\(t\{\+\}1,j\)is labeled as a*merge target*if it has at least two validated predecessors and receives substantial inflow from them,

\|Pt\+1​\(j\)\|\\displaystyle\|P\_\{t\+1\}\(j\)\|≥2,∑k∈Pt\+1​\(j\)covin\(k→j\)≥αmergein,and\\displaystyle\\geq 2\\quad,\\quad\\sum\_\{k\\in P\_\{t\+1\}\(j\)\}\\mathrm\{cov\}\_\{\\text\{in\}\}\(k\\to j\)\\geq\\alpha\_\{\\text\{merge\}\}^\{\\text\{in\}\},\\quad\\text\{and\}\(6\)covout​\(k→j\)≥αmergeout∀k∈Pt\+1​\(j\)\.\\displaystyle\\mathrm\{cov\}\_\{\\text\{out\}\}\(k\\to j\)\\geq\\alpha\_\{\\text\{merge\}\}^\{\\text\{out\}\}\\quad\\forall k\\in P\_\{t\+1\}\(j\)\.
Remaining cases are labeled*unclear*\. After relations are established and labeled, we construct a directed temporal topic graph whose nodes are time\-indexed topics and whose edges correspond to validated cross\-window relations\.

### 3\.6Implementation and complexity notes

BERTilda is implemented as a modular pipeline in which the snapshot topic model can be replaced, provided it returns per\-window topic assignments and interpretable topic descriptors\. For short texts, we compute document embeddings with a fixed sentence\-transformer encoder \(all\-MiniLM\-L6\-v2\) shared across windows and precompute them once to ensure a common semantic space\. Topic discovery uses BERTopic \(transformer embeddings \+ HDBSCAN clustering \+ c\-TF\-IDF descriptors\), with a minimum topic size to filter noisy micro\-clusters\.

For each adjacent window pair, the dominant cost is cross\-window attribution, which naively requires comparing each document embedding to all topic embeddings in the neighboring window\. In practice,KtK\_\{t\}is typically far smaller than\|𝒟t\|\|\\mathcal\{D\}\_\{t\}\|, and efficient matrix multiplication makes attribution practical\. Candidate edges are additionally pruned byτtopic\\tau\_\{\\text\{topic\}\},τcovout\\tau\_\{\\text\{cov\}\}^\{\\text\{out\}\}, andτcovin\\tau\_\{\\text\{cov\}\}^\{\\text\{in\}\}\.

### 3\.7Algorithm

Algorithm 1BERTilda: temporal topic graph and lifecycle labeling0:Timestamped corpus

𝒟\\mathcal\{D\}; window scheme

\(Δwindow,Δstep\)\(\\Delta\_\{\\text\{window\}\},\\Delta\_\{\\text\{step\}\}\); thresholds

τdoc,τtopic,τcovout,τcovin\\tau\_\{\\text\{doc\}\},\\tau\_\{\\text\{topic\}\},\\tau\_\{\\text\{cov\}\}^\{\\text\{out\}\},\\tau\_\{\\text\{cov\}\}^\{\\text\{in\}\}\.

1:for

t=1t=1to

TTdo

2:Fit a snapshot topic model on

𝒟t\\mathcal\{D\}\_\{t\}; obtain topics

𝒦t\\mathcal\{K\}\_\{t\}and representations

ψ​\(t,⋅\)\\psi\(t,\\cdot\)\.

3:endfor

4:for

t=1t=1to

T−1T\-1do

5:Compute topic similarities

sim​\(\(t,k\),\(t\+1,j\)\)\\mathrm\{sim\}\(\(t,k\),\(t\{\+\}1,j\)\)\.

6:Compute bidirectional coverage

covout​\(k→j\)\\mathrm\{cov\}\_\{\\text\{out\}\}\(k\\to j\)and

covin​\(k→j\)\\mathrm\{cov\}\_\{\\text\{in\}\}\(k\\to j\)by cross\-window attribution\.

7:Retain edges by Eq\.[1](https://arxiv.org/html/2608.18101#S3.E1); define

St​\(k\)S\_\{t\}\(k\)and

Pt\+1​\(j\)P\_\{t\+1\}\(j\)by Eq\.[2](https://arxiv.org/html/2608.18101#S3.E2)\.

8:Label continuation/split/disappearance/merge/unclear\.

9:endfor

## 4Experiments

### 4\.1Experimental design

Our experiments are structured around four questions\. First, does the snapshot topic discovery component yield coherent and diverse topics on short political texts, relative to common baselines? Second, does bidirectional coverage improve the interpretability of split/merge labels relative to minimal alternatives that rely only on topic\-to\-topic similarity or only on forward flow? Third, how stable are topic\-quality diagnostics over time compared to dynamic topic models with explicit temporal priors? Fourth, do qualitative case studies illustrate that detected events correspond to meaningful narrative reorganizations?

### 4\.2Datasets

We evaluate on three political corpora\.*Congress tweets*: 357,896 tweets from 544 official accounts of the 119th U\.S\. Congress \(September 26, 2024–September 22, 2025\)\.*UN General Debates*: annual speeches indexed by year\[[31](https://arxiv.org/html/2608.18101#bib.bib19)\]\.*State of the Union*: presidential addresses indexed by year\[[26](https://arxiv.org/html/2608.18101#bib.bib20)\]\.

Table[1](https://arxiv.org/html/2608.18101#S4.T1)summarizes dataset characteristics and the temporal segmentation used for evaluation\.

Table 1:Datasets and temporal segmentation used in experiments\.
### 4\.3Preprocessing and topic discovery

We apply standard text normalization \(entity decoding, URL/mention cleanup, lemmatization\) and retain English\-language content\. For tweets, we optionally perform named\-entity canonicalization for political actors and organizations\.

For snapshot topic discovery, we use BERTopic\[[13](https://arxiv.org/html/2608.18101#bib.bib1)\]with a transformer encoder \(MiniLM\) and HDBSCAN clustering\. Topics with fewer than 50 documents are discarded \(20 for the UN Debates and 1 for the State of the Union\)\. Topic descriptors are defined using the top\-NNc\-TF\-IDF words per topic\.

### 4\.4Baselines and ablations

##### Topic discovery baselines\.

We benchmark within\-window topic quality against Top2Vec\[[3](https://arxiv.org/html/2608.18101#bib.bib17)\]and include bag\-of\-words baselines \(LDA\[[6](https://arxiv.org/html/2608.18101#bib.bib2)\]and NMF\[[21](https://arxiv.org/html/2608.18101#bib.bib23)\]\) in supplementary material\.

##### Temporal\-context baselines\.

To contextualize stability diagnostics, we compare with DTM\[[5](https://arxiv.org/html/2608.18101#bib.bib6)\]\(Tomotopy implementation\) and DETM\[[11](https://arxiv.org/html/2608.18101#bib.bib18)\]\. Because topic identity differs across modeling families, we interpret drift/volatility as behavioral diagnostics rather than tracking accuracy\.

##### Event\-detection baselines \(minimal\)\.

To isolate the contribution of bidirectional coverage and document\-level flow, we implement three minimal baselines that operate on the*same*snapshot topics and windows as BERTilda\. \(i\)*Similarity\-only*: build the temporal graph using onlysim\\mathrm\{sim\}and derive pseudo\-flow by normalizing similarities per source/target\. \(ii\)*Lexical\-only*: replace embedding similarity by c\-TF\-IDF cosine \(or top\-word overlap\) and normalize analogously\. \(iii\)*Forward\-only*: compute outflow by forward attribution only, using forward counts to approximate inflow\. Section[4\.5](https://arxiv.org/html/2608.18101#S4.SS5)details the protocol and how we ensure comparability\.

### 4\.5Baseline protocol and comparability safeguards

All event\-detection baselines reuse the same preprocessing, windowing, snapshot topics, and \(where applicable\) topic representationsψ​\(t,k\)\\psi\(t,k\)\. This avoids conflating event detection quality with differences in topic discovery\. For each adjacent window pair, we compute the topic sets𝒦t,𝒦t\+1\\mathcal\{K\}\_\{t\},\\mathcal\{K\}\_\{t\+1\}once and storent,kn\_\{t,k\}, c\-TF\-IDF descriptors, andψ​\(t,k\)\\psi\(t,k\)\.

*Similarity\-only*computes a similarity matrixSk,j=sim​\(\(t,k\),\(t\+1,j\)\)S\_\{k,j\}=\\mathrm\{sim\}\(\(t,k\),\(t\{\+\}1,j\)\)and retains entries aboveτtopic\\tau\_\{\\text\{topic\}\}\. To make rules comparable to coverage\-based thresholds, we derive normalized weights

cov~out​\(k→j\)=Sk,j∑j′Sk,j′,cov~in​\(k→j\)=Sk,j∑k′Sk′,j,\\widetilde\{\\mathrm\{cov\}\}\_\{\\text\{out\}\}\(k\\to j\)=\\frac\{S\_\{k,j\}\}\{\\sum\_\{j^\{\\prime\}\}S\_\{k,j^\{\\prime\}\}\},\\qquad\\widetilde\{\\mathrm\{cov\}\}\_\{\\text\{in\}\}\(k\\to j\)=\\frac\{S\_\{k,j\}\}\{\\sum\_\{k^\{\\prime\}\}S\_\{k^\{\\prime\},j\}\},and apply the same event rules using\(cov~out,cov~in\)\(\\widetilde\{\\mathrm\{cov\}\}\_\{\\text\{out\}\},\\widetilde\{\\mathrm\{cov\}\}\_\{\\text\{in\}\}\)\. Only the entries ofSk,jS\_\{k,j\}above the thresholdτtopic\\tau\_\{\\text\{topic\}\}are considered when computing the normalized weights\.

*Lexical\-only*repeats the procedure using a lexical similarity matrix \(c\-TF\-IDF cosine, or Jaccard overlap of top\-NNwords\)\.

*Forward\-only*runs only the forward attribution step, computesFtfwd​\(k→j\)F^\{\\text\{fwd\}\}\_\{t\}\(k\\to j\), and sets

covoutfwd​\(k→j\)=Ftfwd​\(k→j\)nt,k,covinfwd​\(k→j\)=Ftfwd​\(k→j\)nt\+1,j,\\mathrm\{cov\}\_\{\\text\{out\}\}^\{\\text\{fwd\}\}\(k\\to j\)=\\frac\{F^\{\\text\{fwd\}\}\_\{t\}\(k\\to j\)\}\{n\_\{t,k\}\},\\qquad\\mathrm\{cov\}\_\{\\text\{in\}\}^\{\\text\{fwd\}\}\(k\\to j\)=\\frac\{F^\{\\text\{fwd\}\}\_\{t\}\(k\\to j\)\}\{n\_\{t\+1,j\}\},thereby approximating inflow without backward attribution\.

Finally, all methods share the same default decision thresholds for alignment and event labeling \(Table[2](https://arxiv.org/html/2608.18101#S4.T2)\) and apply the same post\-processing \(minimum topic size and candidate\-edge pruning\)\.

### 4\.6Evaluation metrics

We report within\-window topic quality using coherence \(CV, NPMI, UMass\) and diversity; we combine coherence and diversity into an overall topic\-quality score following common practice,

TQ=CV×Diversity\.\\mathrm\{TQ\}=\\mathrm\{CV\}\\times\\mathrm\{Diversity\}\.\(7\)Because automated coherence has known failure modes\[[17](https://arxiv.org/html/2608.18101#bib.bib33)\], we treat these metrics as comparative diagnostics rather than definitive quality measures\.

To summarize temporal behavior, we compute drift and short\-term volatility of topic\-quality metrics over time\. Drift is estimated by linear regression,

yt=β0\+β1​t\+εt,y\_\{t\}=\\beta\_\{0\}\+\\beta\_\{1\}t\+\\varepsilon\_\{t\},\(8\)whereβ1\\beta\_\{1\}measures drift and significance is tested with a two\-sidedtt\-test\. Volatility is computed as a rolling standard deviation over a window of sizeww\.

### 4\.7Gold\-standard event validation

Three independent annotators evaluated a curated subset of detected events from the congressional corpus, balanced across event types\. Rather than asking annotators to label events directly \(split/merge/continue\), we present them with candidate topic correspondences across adjacent windows\. For continuation, split, and disappearance items, the focal topic is in windowttand annotators see its keywords and representative tweets, together with the three most similar candidate successors int\+1t\{\+\}1\. For merge items, the focal topic is int\+1t\{\+\}1and annotators see the three most similar candidate predecessors intt\. Annotators select which candidates are genuinely related, from which we infer event validity\. Thirty events per type \(excluding unclear\) were randomly sampled from BERTilda’s output\. Validation rates are computed using majority agreement\.

Table 2:Default decision thresholds used in the alignment and event\-labeling stages\. Dataset\-specific window size and step are described in the experimental setup\.SymbolMeaningValueSimilarity and edge validationτdoc\\tau\_\{\\text\{doc\}\}min doc\-to\-topic similarity for attribution0\.40τtopic\\tau\_\{\\text\{topic\}\}min topic\-to\-topic similarity for candidate edge0\.70τcovout=τcovin\\tau\_\{\\text\{cov\}\}^\{\\text\{out\}\}=\\tau\_\{\\text\{cov\}\}^\{\\text\{in\}\}min coverage for a validated edge0\.30Event\-labeling thresholdsαcont\\alpha\_\{\\text\{cont\}\}continuation similarity threshold0\.90αcontout=αcontin\\alpha\_\{\\text\{cont\}\}^\{\\text\{out\}\}=\\alpha\_\{\\text\{cont\}\}^\{\\text\{in\}\}min inflow/outflow coverage for continuation0\.50αsplitout\\alpha\_\{\\text\{split\}\}^\{\\text\{out\}\}min total outflow coverage for split0\.70αsplitin\\alpha\_\{\\text\{split\}\}^\{\\text\{in\}\}min inflow coverage per successor0\.50αdispout=αdispin\\alpha\_\{\\text\{disp\}\}^\{\\text\{out\}\}=\\alpha\_\{\\text\{disp\}\}^\{\\text\{in\}\}min inflow/outflow coverage for disappearance0\.40αmergeout\\alpha\_\{\\text\{merge\}\}^\{\\text\{out\}\}min outflow coverage per predecessor0\.50αmergein\\alpha\_\{\\text\{merge\}\}^\{\\text\{in\}\}min total inflow coverage for merge target0\.70

## 5Results

We first report within\-window topic quality and fragmentation on the congressional tweets corpus, then validate event labels on a human\-annotated gold set and compare to minimal baselines\. Finally, we provide temporal stability diagnostics on historical corpora and illustrate the resulting event narratives via a qualitative case study\.

### 5\.1Static topic quality and fragmentation \(Congress\)

For fair comparison, Top2Vec was configured with the same embedding model \(MiniLM\), 10 top words per topic, and a minimum of 50 documents per topic\. Across all temporal windows, BERTilda produced 2,569 topics, while Top2Vec produced 5,717 topics, often exceeding 70 topics per week, which is consistent with greater fragmentation\. Table[3](https://arxiv.org/html/2608.18101#S5.T3)summarizes topic quality metrics\.

Table 3:Static topic quality metrics on the congressional tweets dataset\.
### 5\.2Gold\-standard event validation \(Congress\)

Annotators evaluated a curated subset of 120 detected events from the congressional dataset \(30 per event type, sampled from BERTilda outputs\)\. We report annotator\-confirmed validation rate, interpreted as precision on detected events, using majority agreement across three annotators\. Table[4](https://arxiv.org/html/2608.18101#S5.T4)reports the distribution of event labels predicted by each method on the same 120 annotated items\. Table[5](https://arxiv.org/html/2608.18101#S5.T5)reports precision per predicted event type; entries are marked as*n/a*when a method predicts zero events of that type on the annotated set\.

### 5\.3Baselines and ablations on event detection

Table[5](https://arxiv.org/html/2608.18101#S5.T5)compares BERTilda with minimal baselines/ablations designed to isolate key design choices\. Because all variations operate on the same snapshot topics and windows, performance differences can be attributed to the alignment and labeling mechanism rather than topic discovery\.

Table 4:Distribution of predicted event labels on the 120 annotated gold\-set items\.Table 5:Annotator\-confirmed validation rate \(precision\) on predicted events, using majority vote across three annotators\.Across all four event types, BERTilda yields the highest macro\-average validation rate among the compared methods \(0\.775\), ahead of similarity\-only \(0\.571\) and forward\-only \(0\.725\)\. Forward\-only remains competitive on split and merge precision, and is slightly higher on those two event types in this subset, but it drops on disappearance, which is consistent with backward attribution helping to normalize inflow and reduce spurious continuations\.

### 5\.4Robustness to threshold perturbations

To test whether event validation depends on a narrow hyperparameter choice, we performed a local one\-at\-a\-time sensitivity analysis around the default configuration on the congressional gold set\. Preprocessing, windowing, snapshot topics, topic representations, the 120 annotated items, and the majority\-vote evaluation protocol were kept fixed, and we varied only one threshold at a time\. We focused on the thresholds most directly tied to alignment and labeling, namelyτtopic\\tau\_\{\\text\{topic\}\},τdoc\\tau\_\{\\text\{doc\}\},αsplitout\\alpha\_\{\\text\{split\}\}^\{\\text\{out\}\},αmergein\\alpha\_\{\\text\{merge\}\}^\{\\text\{in\}\}, andαdispout\\alpha\_\{\\text\{disp\}\}^\{\\text\{out\}\}, and compared BERTilda against forward\-only, the strongest ablation\.

![Refer to caption](https://arxiv.org/html/2608.18101v1/images/tau_doc.png)

![Refer to caption](https://arxiv.org/html/2608.18101v1/images/alpha_out_disp.png)

Figure 1:Representative local threshold\-sensitivity analyses on the congressional gold set\. Left: varyingτdoc\\tau\_\{\\text\{doc\}\}\. Right: varyingαdispout\\alpha\_\{\\text\{disp\}\}^\{\\text\{out\}\}\. Full curves for all five thresholds are reported in the supplementary material\.Across the five perturbation analyses, BERTilda’s macro\-average validated precision remained between 0\.663 and 0\.718, whereas forward\-only ranged from 0\.623 to 0\.669\. The advantage was most stable for disappearance detection; split and merge were more sensitive, but the method did not collapse into degenerate label distributions under small threshold changes\. This supports the claim that BERTilda’s gains are not confined to one hand\-tuned threshold configuration\.

### 5\.5Temporal stability diagnostics \(historical corpora\)

To contextualize the temporal behavior of within\-window topic quality metrics, we report results on the UN General Debates dataset below\. Additional State of the Union results are deferred to the supplementary material\. Because topic identity differs across model families, these metrics should be read as qualitative points of reference rather than tracking accuracy\.

#### 5\.5\.1UN General Debates \(1970–2015\)

All texts were preprocessed using a unified pipeline \(lowercasing, punctuation/digit removal, lemmatization, stopword removal\)\. Paragraphs were temporally indexed by year\. For BERTilda we use 3\-year windows with a 2\-year step\.

Table 6:Overall topic quality metrics on UN General Debates \(mean±\\pmstd across windows\)\.Table 7:Temporal drift on UN General Debates \(drift =β1\\beta\_\{1\}\)\.

### 5\.6Qualitative case study \(Congress\)

*Holocaust/Israel–Antisemitism\.*From mid\-April to mid\-May, BERTilda tracks a topic that shifts from Holocaust remembrance to contemporary Israel/Hamas and antisemitism discourse\. The system marks this transition as an unclear continuation, followed by a split that separates geopolitical conflict from campus\-focused antisemitism debates\. The resulting branches then continue independently until disappearance, as illustrated in Figure[2](https://arxiv.org/html/2608.18101#S5.F2)\.

![Refer to caption](https://arxiv.org/html/2608.18101v1/images/HolocaustGraph.png)Figure 2:Example temporal evolution of a topic \(Holocaust/Israel–Antisemitism\), illustrating split, continuations, and disappearance across consecutive windows\.

## 6Discussion and Limitations

BERTilda provides an explicit representation of topic lifecycles through a temporal topic graph and yields lifecycle labels that are often interpretable under human validation\. In our annotated subset, continuation and disappearance receive the strongest validation rates, while split and merge remain more ambiguous\. This is particularly visible for merges, which can reflect partial thematic overlap rather than a single unambiguous fusion\.

Several limitations remain\. First, although the local sensitivity analysis suggests that the main conclusions are not tied to a single threshold setting, threshold calibration remains an important open issue, especially for the more ambiguous split and merge cases\. Second, overlapping windows may inflate continuity by construction; ablations with non\-overlapping windows or computing flow on window deltas are needed to quantify this effect\. Third, comparisons with DTM/DETM require caution because topic identity is defined differently across modeling families; we treat drift/volatility as behavioral diagnostics rather than tracking correctness\. Finally, our event evaluation focuses on annotator\-confirmed precision on detected events; estimating recall would require additional negative sampling beyond the current gold set\.

## 7Conclusion

We presented BERTilda, a graph\-based framework for topic lifecycle tracking designed to make split and merge events explicit when topics are discovered independently in each time window\. Our core contribution is an explainable alignment mechanism that combines semantic similarity with bidirectional document flow, supporting explicit successor/predecessor linking and rule\-based labeling of continuation, split, merge, disappearance, and unclear transitions\.

Empirically, BERTilda achieves competitive topic\-quality diagnostics across corpora and yields lifecycle outputs that are often interpretable under human validation\. The ablation\-style baselines suggest that document flow, particularly bidirectional coverage, is most helpful for disappearance detection in our setting, while split and merge remain harder and forward\-only remains competitive\. Beyond quantitative results, the framework provides an analyst\-facing representation \(temporal topic graphs\) that exposes why an event was labeled as a split or merge, supporting inspection and error analysis\.

Future work will focus on three directions\. First, we will conduct systematic robustness analyses over windowing choices and threshold configurations, including calibration against annotated subsets\. Second, we will extend document\-to\-topic attribution to better handle multi\-membership and ambiguity, reducing brittle assignments near cluster boundaries\. Finally, we will broaden the evaluation to additional domains and event types, and explore alternative transport\-based or distributional alignment criteria to further improve structural event detection\.

## Use of Generative AI

Generative AI tools were used to support manuscript preparation in three ways: \(i\) proofreading and language polishing to improve readability \(e\.g\., grammar correction\), \(ii\) bibliography analysis \(e\.g\., helping identify and organize relevant references\), and \(iii\) formatting and layout assistance \(e\.g\., LaTeX structuring\)\. All content produced with AI assistance was reviewed and edited by the authors\. The authors remain fully responsible for the originality of the manuscript and for the correctness of all technical content, claims, and conclusions\.

## Acknowledgments

This work is funded by national funds through FCT – Fundação para a Ciência e a Tecnologia, I\.P\., under the support UID/50014/2025 \(https://doi\.org/10\.54499/UID/50014/2025\)\.

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