# Persistent Homology of Topic Networks for the Prediction of Reader Curiosity

Manuel D. S. Hopp, Vincent Labatut, Arthur Amalvy, Richard Dufour, Hannah Stone, Hayley Jach, Kou Murayama

► To cite this version:

Manuel D. S. Hopp, Vincent Labatut, Arthur Amalvy, Richard Dufour, Hannah Stone, et al. Per-sistent Homology of Topic Networks for the Prediction of Reader Curiosity. 63rd Annual Meeting of the Association for Computational Linguistics (ACL), Association for Computational Linguistics, Jul 2025, Vienna, France. hal-05098910v2

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<figure><img src="image_1.png" /></figure>
# Persistent Homology of Topic Networks for the Prediction of Reader Curiosity

Manuel D. S. Hopp<fnref n="1" />, Vincent Labatut<fnref n="2" />, Arthur Amalvy<fnref n="2" />, Richard Dufour<fnref n="3" />, Hannah Stone<fnref n="4" />, Hayley Jach<fnref n="5" />,<fnref n="1" />, Kou Murayama<fnref n="1" />

## Abstract

Reader curiosity, the drive to seek information, is crucial for textual engagement, yet remains relatively underexplored in NLP. Building on Loewenstein’s Information Gap Theory, we introduce a framework that models reader curiosity by quantifying semantic information gaps within a text’s semantic structure. Our approach leverages BERTopic-inspired topic modeling and persistent homology to analyze the evolving topology (connected components, cycles, voids) of a dynamic semantic network derived from text segments, treating these features as proxies for information gaps. To empirically evaluate this pipeline, we collect reader curiosity ratings from participants (n = 49) as they read S. Collins’s “The Hunger Games” novel. We then use the topological features from our pipeline as independent variables to predict these ratings, and experimentally show that they significantly improve curiosity prediction compared to a baseline model (73% vs. 30% explained deviance), validating our approach. This pipeline offers a new computational method for analyzing text structure and its relation to reader engagement.

*This version complements the ACL 2025 original article with significantly extended appendices.*

## 1 Introduction

Reader curiosity refers to the cognitive and affective drive that motivates individuals to seek additional information while reading. In the context of textual engagement, this can manifest as a reader’s urge to continue reading, explore related topics, or

seek clarifications (Schiefele, 1999). While curiosity is often studied in educational psychology, its computational modeling in natural language processing (NLP) remains relatively underexplored. Existing approaches to modeling reader engagement often rely on linguistic features, e.g., sentiment analysis, readability scores (Sotirakou et al., 2021), or word-level analyses (Berger et al., 2023; Maslej et al., 2021; Dvir et al., 2023). These methods, while valuable, primarily focus on surface-level characteristics and often fail to capture the broader semantic structure, narrative flow, and, crucially, the information gaps that stimulate curiosity. Related work leveraging knowledge graphs, while providing a richer semantic representation, does not explicitly model the reader’s evolving understanding and points of information need (Abu-Salih and Alotaibi, 2024).

Building on Loewenstein’s *Information Gap Theory* (Loewenstein, 1994)—where curiosity stems from recognizing a difference between known and desired information—we introduce a framework that models reader curiosity by quantifying semantic information gaps within a text’s semantic structure. Unlike prior work focused on micro-level textual features, our approach adopts a macro-level, cognitive perspective, operationalizing the concept of *plot holes*, or *information gaps*, to predict reader engagement. We hypothesize that these gaps, representing areas of missing connections or coherence in the textual flow, act as intrinsic motivators. Furthermore, we operationalize surprise, a key driver of curiosity, by measuring the dynamic shifts and transformations in these information gaps through-

<footnote n="1">¹Hector Research Institute of Education Sciences and Psychology, University of Tübingen, Germany
{firstname.lastname}@uni-tuebingen.de,</footnote>

<footnote n="2">²Laboratoire Informatique d'Avignon – LIA UPR 4128, Avignon Université, France
{firstname.lastname}@univ-avignon.fr,</footnote>

<footnote n="3">³Laboratoire des Sciences du Numérique de Nantes – LS2N UMR 6004, Nantes Université, France
richard.dufour@univ-nantes.fr,</footnote>

<footnote n="4">⁴Emerald Publishing, Reading, United Kingdom
hannah.j.stone@reading.ac.uk,</footnote>

<footnote n="5">⁵Melbourne School of Psychological Sciences, The University of Melbourne, Australia
hayley.jach@unimelb.edu.au</footnote>
out the text.

To realize this framework, we introduce a pipeline leveraging Topological Data Analysis (TDA). This pipeline integrates recent topic modeling (building upon BERTopic (Grootendorst, 2022)) to extract key topics, constructs a dynamic topic network representing the flow of these topics (Zhu, 2013), and applies TDA, specifically Persistent Homology (Munch, 2017), to identify and quantify topological cavities within this network (Patankar et al., 2023; Zhou et al., 2024). These cavities—disconnected components, cycles, and voids—represent information gaps. We further employ Wasserstein and Bottleneck distances to measure the evolution of these gaps, capturing the element of surprise. This study explores the potential of this novel approach of characterizing topological features of a text.

To demonstrate feasibility, we conducted a pilot study as a proof-of-concept using S. Collins's "The Hunger Games" (Collins, 2011) novel. Participants naïve to both the book and its movie adaptation provided chapter-wise curiosity ratings, enabling an initial analysis of curiosity dynamics in response to information gaps.

Our main contributions are threefold:

1. **Pipeline:** We designed a pipeline for the modeling of textual information gaps, integrating topic modeling and TDA.

2. **Engagement Data:** We conducted a survey in order to obtain reader engagement data for "The Hunger Game" novel.

3. **Experimental validation:** We leveraged the survey data to evaluate our approach empirically.

4. **Interdisciplinary approach:** our method connects topic modeling and TDA with theories from motivational psychology, facilitating further interdisciplinary research.

We share our source code and data at https://github.com/mds-hopp/pers_homol_data.

The rest of this article is organized as follows. In Section 2, we review the literature directly related to our work. In Section 3, we present our narrative modeling pipeline. Section 4 describes our experimental setup, while our results are presented and discussed in Section 5. Finally, we review the salient points of our work and its perspectives in Section 6.

## 2 Related Work

This work builds upon and addresses limitations in computational reader engagement models, graph-based and topological methods in NLP, and network-based approaches to curiosity and exploration.

### Computational Models of Reader Engagement

Predicting user engagement is an important NLP task, often approached through text feature analysis. There are many features that are related to reader engagement. Early methods relied on surface characteristics like sentiment and readability (Sotirakou et al., 2021). Other approaches often relied on classical bag-of-words representations for word-level analysis (Maslej et al., 2021; Dvir et al., 2023). However, these methods, while useful, largely neglect semantic structure and cognitive processes. Other work incorporates cognitive aspects, highlighting uncertainty (Berger et al., 2023) and semantic cohesion (Ward and Litman, 2008). Yet, these typically operate at the word or sentence level, failing to model the reader's *evolving* information state —critical to theories like Loewenstein's Information Gap Theory (Loewenstein, 1994). Our pipeline directly addresses this, modeling the *dynamic* evolution of semantic information gaps. The use of text embeddings from multilingual large language models also opens the door to potential cross-cultural work on the topic, e.g. (Zhou et al., 2024).

### Graph & Topological Methods in NLP

The drive for higher-level text understanding has increased the use of graph representations in NLP. Knowledge graphs enhance tasks like question answering (Abu-Salih and Alotaibi, 2024), and graph-based retrieval augmented generation (RAG) methods, such as GraphRAG (Han et al., 2025) and LightRAG (Guo et al., 2024), leverage relational structure. Topic modeling also benefits from graph approaches. Traditional methods like Latent Dirichlet Allocation (LDA) are complemented by approaches using bipartite networks and community detection (Gerlach et al., 2018), and embedding-based methods like BERTopic (Grootendorst, 2022) or a combination of both embeddings and networks (Cao and Fairbanks, 2019), offering richer semantic representations. However, these generally do not analyze the *topological* structure of the resulting networks.

Topological Data Analysis (TDA), particularly
Persistent Homology, provides tools to analyze data shape, including networks. A recent review shows TDA's growing interest in NLP (Uchendu and Le, 2024). Christianson et al. (2020) used TDA to identify knowledge gaps in math textbooks, and Tymochko et al. (2021) to capture logical holes in abstracts. Critically, existing NLP applications of TDA primarily focus on *static* text representations. Our work significantly extends this, applying persistent homology to a *dynamic* topic network (inspired by the work of Zhu (2013)), tracking the evolution of topological features (specifically, cavities) over time. This dynamic aspect is crucial for modeling changing reader information gaps.

## Engagement and Graph & Topological Methods

Beyond NLP, network science has modeled text structure to understand its implications to learning and cognition, including curiosity-driven exploration (Zhou et al., 2024; Patankar et al., 2023). Patankar et al. (2023) tracked structural changes in time-varying graphs using persistent homology, conceptually related to our approach. However, their focus was on general graph dynamics, not reader engagement. We bridge this gap, connecting network models of exploration with cognitive theories of curiosity, specifically the Information Gap Theory, applying them to model reader engagement in NLP. Operationalizing information gaps as topological cavities in a dynamically evolving semantic network provides a novel, quantifiable measure of reader curiosity, directly linking computational methods and psychological theories. Moreover, our methodology targets continuous sequential texts (like narratives) to analyze intrinsic semantic evolution and its link to reader curiosity. To analyze how semantic evolution in continuous narratives relates to reader curiosity, we required paired text-curiosity annotations. As our literature review confirmed no dataset appropriate for tracking narrative semantic shifts exists, we collected our own for this study.

# 3 Methods for Narrative Modeling

We employ a combination of NLP, network analysis, and TDA to model narrative structure and its evolution, building on and extending previous work. Our analysis proceeds in three key stages:

1. **Preprocessing.** We obtain textual data and segment it using a sliding window approach.

2. **Dynamic Topic Modeling.** A dynamic topic

network is built to represent the evolving thematic structure of the text. Vertices represent topics, and edges connect topics appearing in consecutive text segments, with edge weights reflecting semantic similarity.

3. **Topological Feature Extraction via Persistent Homology.** Persistent homology quantifies the network's evolving topological features representing information gaps of the topic network.

An overview of our suggested pipeline (from text preprocessing to the topological feature extraction) is depicted in Figure 1. Details regarding the data and models we employed are located in Section 4.

## 3.1 Dataset and Preprocessing

Our approach works with either textual or multi-modal data (e.g., video), adaptable to the chosen embedding model. After data collection, the next step involves cleaning and segmenting the textual or multimodal data into smaller units. A key aspect is the collection of user engagement ratings periodically throughout content consumption. The human data allows us to validate the persistent homology measures as reader engagement.

## 3.2 Dynamic Topic Network

To capture the evolving thematic structure of the used texts, we construct a dynamic topic network. Each vertex in this network represents a topic and edges connect topics that occur across consecutive chunks, reflecting the narrative flow of the story. Each edge has a weight corresponding to the cosine similarity of the dyadic topics in the text embedding space.

### 3.2.1 Topic Modeling

We employ a pipeline inspired by the BERTopic approach for topic modeling (Grootendorst, 2022). It consists of the following three stages:

1. **Text Embedding:** Text segments are embedded into a high-dimensional vector space using the transformer-based embedding model voyage-3-large (Voyage AI, 2025). These embeddings capture the semantic meaning of the chunks, with similar chunks having closer embeddings.

2. **Dimensionality Reduction:** As a preprocessing step for clustering, we reduce the high-dimensional embedding vectors using
<figure><img src="image_2.png" /><figcaption>Figure 1: Pipeline from preprocessing (top) to persistent homology measures (bottom).</figcaption></figure>

UMAP (Uniform Manifold Approximation and Projection, (McInnes et al., 2020)) following the BERTopic approach (Grootendorst, 2022) for improving cluster quality with high-dimensional data (Asyaky and Mandala, 2021; Allaoui et al., 2020).

3. **Clustering:** We use HDBSCAN (Hierarchical Density-Based Spatial Clustering of Applications with Noise) (Campello et al., 2013), which identifies non-convex clusters of varying densities and handles noise explicitly. Furthermore, HDBSCAN automatically determines the cluster count, avoiding manual

parameter tuning and potential bias. Its strong empirical performance further justifies its use (scikit-learn developers, 2025; Asyaky and Mandala, 2021; McInnes et al., 2016). Each topic is represented by the weighted centroid of its constituent text chunk embeddings, using the cluster probability as the weight.

### 3.2.2 Dynamic Topic Network Construction

The dynamic topic network is built incrementally, based on the measurement points of the user engagement sampling.

* **Vertices:** Each vertex in the network represents one topic.

* **Edges:** Undirected edges are created between topic vertices appearing in consecutive text chunks. This captures the sequential flow of topics throughout the narrative, as suggested by Zhu (2013) and applied in studies such as (Patankar et al., 2023).

* **Edge Weights:** The weight of each edge is determined by the cosine similarity between the embedding vectors of the connected topics in the original embedding space. Higher cosine similarity results in a stronger connection.

* **Network Series:** We segment the narrative based on user engagement rating points. Each such segment is represented by a distinct static topic graph built upon the topics and relationships occurring in the narrative up to this point. This sequence of static graphs forms a cumulative dynamic network: The first graph represents only the topics and relationships up to the first user engagement rating point, the second graph contains these topics and relations plus those occurring in the second segment, and so on. The last graph in the sequence represents all topics and relationships.

## 3.3 Persistent Homology Measures

To evaluate the gaps in information flow within our dynamic topic networks, we employ persistent homology, a method derived from topological data analysis. In essence, persistent homology allows us to detect and monitor the evolution of specific topological features within a network (in our case, the topic network using cosine similarity-derived distances)—namely, connected components, cycles (loops), and voids (enclosed empty spaces) (Mironi and Pascali, 2021; Munch, 2017)—that we
compare in Figure 2. For a brief, non-technical
introduction to Topological Data Analysis and Per-
sistent Homology, please refer to Appendix B.

<figure><img src="image_3.png" /><figcaption>Figure 2: Identified topological features of the topic network: Components, cycles/ loops, and voids. Adapted from (Patankar et al., 2023).</figcaption></figure>

The core of persistent homology lies in exam-
ining how a network’s structure evolves as a func-
tion of a filtration parameter, denoted by ϵ. Intu-
itively, ϵ represents a proximity threshold. As ϵ
increases, connections (edges, and in more general
cases, higher-dimensional counterparts called sim-
plices) are progressively added between vertices
that are closer than the given ϵ. This process gen-
erates a nested sequence of simplicial complexes,
each representing the network’s structure at a spe-
cific proximity level. From this sequence, we can
count the number of topological features: β₀ rep-
resents the number of connected components, β₁
the number of cycles (or loops), and β₂ the number
of voids (enclosed empty spaces). Persistent ho-
mology tracks the “birth” (emergence) and “death”
(merging or disappearance) of these features as ϵ
increases. The results are summarized in a persis-
tence diagram, which plots each topological feature
as a point (b, d), where b signifies the ϵ value at
which the feature is born, and d represents the ϵ
value at which it dies. Figure 3 shows the persis-
tence diagram for the first chapter of our dataset,
revealing one highly persistent feature in dimen-
sion 1 (loop).

# 4 Experimental Setup

**4.1 Dataset and Preprocessing**

4.1.1 Dataset

The primary dataset for this pilot study consists
of the young adult novel “The Hunger Games”
by Collins (2011) and corresponding reader en-
gagement data (n = 76 participants; mean age =
41.4, 56% female, 100% UK residence) collected
through the online platform Prolific<fnref n="1" />. Participants

<figure><img src="image_4.png" /><figcaption>Figure 3: Persistence diagram of the first chapter of our dataset.</figcaption></figure>

were compensated in line with Prolific's recom-
mended minimum 7.50 British Pounds per hour.
Prior to reading, participants indicated their fami-
liarity with the book and its movie adaptation. Dur-
ing reading, participants provided continuous self-
reported ratings (0–100) on multiple engagement
dimensions after each chapter. For this analysis,
we focus specifically on curiosity ratings (“I was
curious about this chapter”) from readers unfamil-
iar with either the movie or book (n = 49). As
we wished to assess the general pattern of curiosity
responses (i.e., not individual reader differences,
which we could not examine in this work), we com-
puted the mean curiosity rating across participants
for each chapter. Inter-Rater Reliability for mean
chapter curiosity, calculated via mixed-effects mod-
els (Shrount and Fleiss, 1979) (cf. Appendix C),
is .71 (moderate), showing reasonable consistency
across chapters.

**4.1.2 Preprocessing**

We apply a two-step text preprocessing. First, we
remove part titles (e.g., “Part One”), chapter ti-
tles (e.g., “The Tributes”), chapter numbers (e.g.,
“Chapter 1”), and empty lines. Second, we employ
a sliding window approach to create text segments,
using windows of 5 sentences with a 2-sentence
overlap. This results in 2,656 text segments. The
median chunk length is 60 words (MAD = 20.76,
range = 13–155 words).

## 4.2 Topic Modeling

**Text Embedding:** We embed text segments into a 1,024-dimensional vector space using the Voyage-AI voyage-3-large transformer-based embedding model (Voyage AI, 2025) via the VoyageAI API,

<footnote n="1">¹https://www.prolific.com</footnote>
accessed through Python. We select transformer-
based models, and especially this one, due to its
state-of-the-art performance on the Massive Text
Embedding Benchmark (MTEB) (Muennighoff
et al., 2022), indicating its ability to capture nu-
anced semantic relationships (Morris et al., 2023;
Yu, 2024).

**Dimensionality Reduction:** As a preprocess-
ing step for clustering, we reduce the 1,024-
dimensional embedding vectors to 32 dimensions
using UMAP (McInnes et al., 2020). The UMAP
parameters are set to the cosine similarity metric
and 15 nearest neighbors to ensure the preservation
of both global and local structures in the lower-
dimensional representation.

**Clustering:** Clustering is performed using HDBSCAN (Campello et al., 2013)) with a minimum cluster size of 3 data points, for fine-grained results. This results in the identification of 302 topics. Embeddings identified as noise (n = 717, 27%) are excluded from further analysis.

These steps were implemented in R (R Core
Team, 2024) using the uwot package (Melville,
2024) for the UMAP implementation, and
dbscan (Campello et al., 2013) for hierarchical
density-based clustering.

**4.3 Persistent Homology Measures**

We first create a series of 27 static topic graphs (as
outlined in section 3.2.2) and then use a Vietoris-
Rips filtration to construct a simplicial complex
from each graph (Sheehy, 2012). The filtration
is based on the edge weights (cosine similarity),
with simplices (edges, triangles, etc.) added as
the distance threshold increases. From the result-
ing persistence diagrams, we extract the following
topological features:

* **Betti Numbers:** $\beta_0, \beta_1, \beta_2$ represent the numbers of connected components, one-dimensional cycles (loops), and two-dimensional voids, respectively. They indicate information gaps in the graph.

* **Bottleneck Distance:** $dist_B$ measures the maximum difference between the persistence diagrams of consecutive graphs (i.e., between graphs representing chapters *n* and *n* + 1). A large bottleneck distance indicates a significant singular structural change, such as the creation or filling of a large void.

* **Wasserstein Distance:** $dist_W$ measures the average difference between the persistence diagrams of consecutive graphs. A large Wasserstein distance indicates a significant average structural change, such as a shift in the average void size.

We detrend the data using residuals from a linear
model fitted to the chapter index and winsorized
due to the presence of outliers. Specifically, for
each feature, values below the 2.5th percentile are
capped at the 2.5th percentile, and values above the
97.5th percentile are capped at the 97.5th percentile.

Network analysis is handled by the igraph package (Csardi and Nepusz, 2006) with qgraph (Epskamp et al., 2012), in R. Persistent homology and related distance measures are computed using the R packages TDA (Fasy et al., 2024) and TDAstats (Wadhwa et al., 2018). Single-threaded persistent homology calculations take approximately 100 seconds on an AMD Ryzen 7 7840U (64 GB RAM).

**4.4 Generalized Additive Model**

To investigate the relationship between the topo-
logical features extracted from the text and the
readers’ reported curiosity, we employ a Gener-
alized Additive Model (GAM) using the R package
mgcv (Wood, 2011). We choose GAMs for two
key reasons: their ability to capture non-linear re-
lationships and their robust options for addressing
overfitting, which is crucial given our limited sam-
ple size.

We assess topological features’ unique contribu-
tion to explaining variance in reader curiosity by
comparing a *Null Model* (control variables: novel
topics per chapter, chapter index) and a *Full Model*
(control variables + topological features: Betti num-
bers, Wasserstein distances, Bottleneck distances).

Due to the limited number of observations (n =
27 chapters), our primary goal is to explore the
explained deviance of the model using topological
features, rather than making definitive claims about
the precise functional form of the relationships.
The dependent variable (DV) is the mean curiosity
reported per chapter (based on n = 49 observations
per chapter). Predictor variables (IVs) include de-
trended Betti numbers, Wasserstein and Bottleneck
distances between chapters, and, as control vari-
ables, the number of novel topics per chapter and
the chapter index number itself.

We use cubic regression splines for all smooth
functions, setting the basis dimension *k* to 4 for all smooth terms based on GAM diagnostics, as recommended by Wood (2017, Section 5.9). To avoid overfitting, we use Restricted Maximum Likelihood (REML) for parameter estimation with an additional penalty term ($\gamma = 1$) during model fitting. To assess the significance of the explained deviance and $R^2$, we employ a permutation test with 1,000 iterations, where we permute the values of the mean curiosity across chapters and refit the model.

# 5 Results

## 5.1 Distribution of the Detected Topics

HDBSCAN identifies 302 distinct clusters, i.e., topics, over the entire text. A comprehensive summary of these topics, generated using DeepSeek V3 (DeepSeek-AI et al., 2024), is provided on the online repository hosting our source code. Figure 4 shows the distribution of topics across chapters and the number of new topics by chapter, respectively. On average, each chapter contains 25 topics (SD = 5, range: 15–35). Chapter 9 exhibits the highest number of topics, while Chapter 11 contains the largest number of newly introduced topics ($n = 28$). In contrast, Chapter 14 has the fewest total topics, and Chapter 25 introduces the fewest new topics ($n = 1$).

<figure><img src="image_5.png" /><figcaption>Figure 4: Total number of topics by chapter (top) and number of new topics by chapter (bottom). The x-axis represents chapter numbers, and the y-axis shows the number of topics and new topics identified within that chapter, respectively.</figcaption></figure>

Visual inspection of the topic clusters across chapters reveals notable shifts in thematic content, particularly around Chapters 11 and 26, as

displayed in Figure 5. These shifts correspond to key narrative transitions within the book: Chapter 11 marks the beginning of the Hunger Games, the deadly battle to be the last person standing, and Chapter 26 signifies their conclusion.

<figure><img src="image_6.png" /><figcaption>Figure 5: Distribution of topics across chapters. The chapter number is on the x-axis, and the topics are listed on the y-axis. Color indicates the frequency of each topic within a chapter, calculated as the base-2 logarithm of the number of text chunks assigned to that topic.</figcaption></figure>

## 5.2 Description of the Extracted Topic Network

Figure 6 shows the last graph constituting our dynamic network, which contains all topics and relationships for the whole novel. It consists of 302 vertices, representing the 302 identified topics, and 778 weighted undirected edges. It exhibits an average degree of 5.15 (SD = 3.13, median = 4, MAD = 3.00, range = 1–31), a weighted diameter of 1.49 (8 when considering unweighted edges), and its degree distribution follows a log-normal law (mean-log = 1.48, SDlog = 0.56).

The small-worldness index, as defined by Humphries and Gurney (2008), is 3.40, indicating a small-world network structure. The average shortest path length (unweighted) is 3.80. A significant hierarchical tendency is observed (hierarchical clustering coefficient = 0.16, *p* < .001, (Mones et al., 2012)).

Community detection, using the Walktrap algorithm (Pons and Latapy, 2006), which showed
<figure><img src="image_7.png" /><figcaption>Figure 6: Topic network. The radius and the color of the vertices are proportional to their degree. The thickness of the edges is proportional to the cosine distance between the topic embeddings.</figcaption></figure>

<table><caption>Table 1: Descriptive statistics. The Bottleneck and Wasserstein distances are denoted by $dist_B$ and $dist_W$.</caption><thead><tr><th>Variable</th><th>Mean</th><th>SD</th><th>Min</th><th>Max</th></tr></thead><tbody><tr><td>Curiosity</td><td>69.5</td><td>3.9</td><td>60.3</td><td>77.0</td></tr><tr><td>Novel topics</td><td>11.2</td><td>6.3</td><td>1.0</td><td>28.0</td></tr><tr><td>β<sub>0</sub></td><td>187.0</td><td>88.9</td><td>24.0</td><td>301.0</td></tr><tr><td>β<sub>1</sub></td><td>165.7</td><td>112.3</td><td>4.0</td><td>368.0</td></tr><tr><td>β<sub>2</sub></td><td>202.6</td><td>176.0</td><td>3.0</td><td>555.0</td></tr><tr><td>dist<sub>B</sub>(β<sub>0</sub>)</td><td>0.4</td><td>0.0</td><td>0.3</td><td>0.5</td></tr><tr><td>dist<sub>B</sub>(β<sub>1</sub>)</td><td>0.5</td><td>0.2</td><td>0.3</td><td>1.0</td></tr><tr><td>dist<sub>B</sub>(β<sub>2</sub>)</td><td>0.3</td><td>0.1</td><td>0.2</td><td>1.0</td></tr><tr><td>dist<sub>W</sub>(β<sub>0</sub>)</td><td>4.5</td><td>2.5</td><td>0.5</td><td>11.6</td></tr><tr><td>dist<sub>W</sub>(β<sub>1</sub>)</td><td>6.2</td><td>2.1</td><td>2.4</td><td>9.8</td></tr><tr><td>dist<sub>W</sub>(β<sub>2</sub>)</td><td>3.2</td><td>1.9</td><td>0.5</td><td>6.4</td></tr></tbody></table>

good performance in previous work (Yang et al., 2016), reveals a minimum of two distinct communities within the network. A qualitative analysis of these communities reveals a strong correspondence with the narrative structure: one community primarily encompasses topics from Chapters 11–25 (the Hunger Games phase), while the other represents topics from the remaining chapters.

## 5.3 Persistent Homology

All derived topological features are detrended, and are shown in Figure 7. The trends observed in the three plots exhibit a resemblance to the overarching narrative structure of “The Hunger Games”, where the Games themselves commence in Chapter 11 and conclude in Chapter 25. Additional descriptive statistics are shown in Table 1.

<figure><img src="image_8.png" /><figcaption>Figure 7: Betti numbers per chapter (top), Bottleneck distances between chapters (middle), and Wasserstein distances between chapters (bottom). All measures are detrended.</figcaption></figure>

## 5.4 Generalized Additive Model

The dependent variable in the generalized additive model (GAM) is the average curiosity score per chapter (M = 69.5, SD = 3.8, range: 60.3–77.0), as shown in Figure 8. Figure 9 presents the bivariate Spearman's rank correlation matrix for all variables (Spearman, 1904).

<figure><img src="image_9.png" /><figcaption>Figure 8: Average curiosity per chapter.</figcaption></figure>

We compare two GAMs to assess the unique contribution of topological features towards modeling the readers' curiosity:

**Null Model (Control Variables only)**: It explains 23.8% of the variance and 29.7% of the variance (permutation tests, both *p* < .001).

**Full Model (Topological Features + Control Variables)**: It explains 65.7% of the variance (permutation test, *p* < .05) and 72.9% of the variance (permutation test, *p* < .06).

A likelihood ratio test comparing the full model to the null model reveals a significant improvement in model fit ($\chi^2 = 11.25$, *df* = 4.7, *p* < .001). This indicates that the inclusion of topological features
<figure><img src="image_10.png" /><figcaption>Figure 9: Spearman's bivariate rank correlations. Circle size and color are proportional to the correlation coefficient magnitude.</figcaption></figure>

tures significantly improves the model’s ability to
explain variation in chapter-level curiosity, even
after accounting for the number of novel topics
and chapter index. These results show that our
proposed pipeline, based on topological analysis
of a dynamic topic network, can effectively model
readers’ curiosity ratings.

6 Conclusion

In this study, we combined existing methods into a
pipeline for modeling semantic information gaps
and explored their connection to reader curiosity,
grounded in motivational psychology theories link-
ing information gaps to curiosity. By construct-
ing dynamic topic networks and using Topological
Data Analysis to identify topological cavities as
proxies for information gaps, we explored a dis-
tinct method from text structure analysis. Our pre-
liminary findings demonstrate the feasibility of this
approach, with statistical modeling indicating that
topological features significantly enhance the pre-
diction of reader curiosity beyond basic content
and chapter progression. This proof-of-concept
study provides a first step towards a quantifiable
understanding of textual features associated with
curiosity, potentially informing future research in
computational text analysis and narrative under-
standing. Further research is needed to refine this
pipeline, evaluate its generalizability across differ-
ent text and media types, and investigate the spe-
cific contributions of various topological features
to reader curiosity and engagement.

Limitations

First, our study includes a small sample size with
limited measurement points focusing solely on the
young adult novel “The Hunger Games”. Because
of this, and to avoid overfitting, we intentionally re-
stricted our topological data analysis to simple mea-
sures like Betti numbers and distances. This may
affect the robustness of our conclusions. Follow-
ing this interdisciplinary proof-of-concept on one
text, future work is essential to test the pipeline’s
robustness and applicability across diverse texts,
genres (e.g., expository texts, news articles), and
languages.

Second, based on our relatively homogeneous
UK-based sample, results may not directly gen-
eralize to different cultural contexts, where there
can be significant cultural variations in reader re-
sponse (Chesnokova et al., 2017). The observed cu-
riosity patterns are, thus, primarily reflective of this
specific demographic group. Moderate reliability
for mean curiosity ratings suggests that modeling
individual reader differences is a key area for future
work.

Third, we model texts as topic networks rather
than knowledge graphs, which could limit granu-
larity. A possibility would be to explore semantic
representation with LightRAG or GraphRAG (Han
et al., 2025; Guo et al., 2024).

Fourth, our network is undirected, which may
overlook important learning dependencies, particu-
larly in educational texts (Liu et al., 2012). Future
work could explore directed networks to better cap-
ture the sequential progression of knowledge.

Fifth, we rely on shortest-path distances, but
diffusion-based measures might better reflect how
information evolves and interacts. Additionally,
our focus on narrative structure constrains the appli-
cability of our approach to raw embedding spaces.
Investigating how to integrate narrative progres-
sion directly into embeddings, potentially through
learning-theoretic models, should be explored. A
sensitivity analysis exploring the impact of dif-
ferent embedding models and chunking parame-
ters is provided in Appendix A. Though focusing
on semantic/topological features was a purposeful
choice for this study, the integration of linguistic
features would be a valuable direction for future
research. Finally, since our analysis is based on
a narrative text, further research is needed to as-
sess its effectiveness across different genres and
domains.
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## A Sensitivity Analysis

To assess the robustness of our findings, we conducted a sensitivity analysis examining the influence of two key methodological choices: 1) the text embedding model and 2) the text segmentation parameters (window and overlap size). This analysis ensures that our primary conclusion—that topological features of a dynamic topic network significantly predict reader curiosity—is not an artifact of a specific parameterization but holds across different analytical conditions.

For this analysis, we re-ran our entire pipeline using two alternative state-of-the-art embedding models: Multilingual E5 Text Embeddings Large Instruct (Wang et al., 2024) and Qwen3 Embedding 0.6B (Zhang et al., 2025), both 1024 using embedding dimensions. We compared their performance against our primary model, Voyage 3 Large (Voyage AI, 2025), across several segmentation configurations: a larger window ($w = 10, o = 3$), medium windows ($w = 7, o = 2$, and $w = 5, o = 2$), and a smaller window ($w = 3, o = 1$). The rest of the analytical pipeline, including UMAP dimensionality reduction, HDBSCAN clustering, and GAM modeling, remained consistent with the main analysis. It is important to note that for the $w = 3, o = 1$ configuration, which produces very short text segments, the minimum cluster size for HDBSCAN was increased from 3 to 4 to ensure the formation of meaningful topics.

The comprehensive results, including network metrics and model fit statistics, are presented in Table 2. A focused summary comparing the deviance

explained by the full and null models across all conditions is provided in Table 3.

<table><caption>Table 2: Network Metrics across Embedding Models. Abbreviations: W/O = Window/Overlap, Wtd. Diam. = Weighted Diameter, Unwtd. Diam. = Unweighted Diameter.</caption><thead><tr><th>W/O</th><th>Topics</th><th>Wtd. Diam.</th><th>Unwtd. Diam.</th></tr></thead><tbody><tr><td colspan="4"><em>Voyage 3 Large</em></td></tr><tr><td>5/2 (Paper)</td><td>302</td><td>1.49</td><td>8</td></tr><tr><td>10/3</td><td>121</td><td>1.20</td><td>7</td></tr><tr><td>7/2</td><td>179</td><td>1.60</td><td>8</td></tr><tr><td>3/1</td><td>280</td><td>1.07</td><td>5</td></tr><tr><td colspan="4"><em>E5 Large Instruct</em></td></tr><tr><td>10/3</td><td>131</td><td>0.64</td><td>7</td></tr><tr><td>7/2</td><td>165</td><td>0.58</td><td>6</td></tr><tr><td>5/2</td><td>271</td><td>0.66</td><td>7</td></tr><tr><td>3/1</td><td>200</td><td>0.37</td><td>4</td></tr><tr><td colspan="4"><em>Qwen3 0.6B</em></td></tr><tr><td>10/3</td><td>125</td><td>2.33</td><td>5</td></tr><tr><td>7/2</td><td>183</td><td>2.29</td><td>6</td></tr><tr><td>5/2</td><td>284</td><td>3.21</td><td>6</td></tr><tr><td>3/1</td><td>181</td><td>1.94</td><td>4</td></tr></tbody></table>

<table><caption>Table 3: Model Performance across Embedding Models. Abbreviations: W/O = Window/Overlap, Dev. = Deviance, p-val = Permutation Test p-value.</caption><thead><tr><th>W/O</th><th>Full Dev. (%)</th><th>Null Dev. (%)</th><th>Full Dev. p-val</th></tr></thead><tbody><tr><td colspan="4"><em>Voyage 3 Large</em></td></tr><tr><td>5/2 (Paper)</td><td>72.9</td><td>29.7</td><td>&lt;0.06</td></tr><tr><td>10/3</td><td>45.2</td><td>27.6</td><td>0.288</td></tr><tr><td>7/2</td><td>74.4</td><td>19.0</td><td>0.036</td></tr><tr><td>3/1</td><td>67.3</td><td>7.49</td><td>0.075</td></tr><tr><td colspan="4"><em>E5 Large Instruct</em></td></tr><tr><td>10/3</td><td>64.6</td><td>7.49</td><td>0.069</td></tr><tr><td>7/2</td><td>28.6</td><td>7.49</td><td>0.418</td></tr><tr><td>5/2</td><td>84.3</td><td>7.49</td><td>0.017</td></tr><tr><td>3/1</td><td>75.8</td><td>7.49</td><td>0.022</td></tr><tr><td colspan="4"><em>Qwen3 0.6B</em></td></tr><tr><td>10/3</td><td>78.8</td><td>22.7</td><td>0.032</td></tr><tr><td>7/2</td><td>68.5</td><td>7.49</td><td>0.073</td></tr><tr><td>5/2</td><td>88.1</td><td>7.49</td><td>0.016</td></tr><tr><td>3/1</td><td>74.6</td><td>7.49</td><td>0.039</td></tr></tbody></table>

### A.1 Results

The sensitivity analysis confirms that the central finding of our study demonstrates considerable robustness. As shown in Table 3, the inclusion of
topological features led to a statistically significant improvement in model fit ($p < 0.05$) compared to the null model across nearly all tested embedding models and segmentation parameters. This indicates that the relationship between the topological structure of the text and reader curiosity is a stable phenomenon.

Both the E5 and Qwen3 models proved to be viable alternatives, often producing models with high explanatory power. In particular, the Qwen3 model with a window of 5 and an overlap of 2 ($w = 5, o = 2$) achieved the highest explained deviance (88.1%) of all tested configurations, closely followed by the E5 model with the same parameters (84.3%). This suggests that the approach is effective with different modern embedding architectures.

The choice of window and overlap size influences the results, though no single configuration was universally optimal across all embeddings. Larger windows (e.g., $w = 10$) tend to identify fewer, broader topics, while smaller windows (e.g., $w = 3$) produce a more granular topic structure. The configurations using a window size of 5 or 7 sentences appear to strike an effective balance, frequently resulting in models with high predictive power. Although some alternative configurations resulted in slightly higher explanation of deviation, the performance of our primary model (Voyage 3 Large, $w = 5, o = 2, 72.9\%$ explained deviation) is comparable to the best performing alternatives and is strongly supported by this analysis.

In summary, the sensitivity analysis confirms that our pipeline is not narrowly tuned to a single set of parameters. The ability of topological features to predict reader curiosity is a robust phenomenon, observable across different state-of-the-art embedding models and reasonable variations in text segmentation. This strengthens our confidence in the primary conclusions of the article and suggests the generalizability of the proposed method.

# B A Short Introduction to Topological Data Analysis and Persistent Homology

This section provides a brief, non-technical introduction to the concepts from Topological Data Analysis (TDA) used in our study, based on (Munch, 2017) and (Chazal and Michel, 2021). Our aim is to equip unfamiliar readers with the foundational understanding necessary to interpret how our topological measures of “information gaps” were derived from the textual data.

## B.1 Understanding Data Shape with Topology

Topological Data Analysis (TDA) is a modern field that leverages principles from algebraic topology to discern the intrinsic “shape” or “structure” of data. Unlike traditional methods that might focus on local metrics or individual data points, TDA aims to identify robust global features, such as clusters, loops, and voids (see Figure 2). The central tool within TDA for this purpose is *persistent homology*.

To apply topological methods, data must first be represented in a suitable geometric form, typically as a *simplicial complex*. A simplicial complex is a collection of fundamental building blocks called *simplices*, which are analogous to points, line segments, filled triangles, and filled tetrahedra, and their higher-dimensional equivalents. Specifically, a *0-simplex* is a single point (a vertex), a *1-simplex* is an edge connecting two vertices, a *2-simplex* is a filled triangle defined by three mutually connected vertices, and so on. In our work, the topics identified in the text serve as the fundamental points, or 0-simplices, of our topological analysis.

## B.2 Constructing Topological Spaces: The Vietoris–Rips Filtration

Persistent homology does not analyze a static, singular complex; instead, it examines how the topological features of a complex evolve across a filtration. A filtration is a nested sequence of simplicial complexes, where simplices are progressively added based on an increasing distance threshold, denoted by $\epsilon$. This process allows us to observe the data's structure at multiple scales, from fine-grained local connections to broader, global architectures.

For our dynamic topic networks, we use a specific type of filtration known as the *Vietoris–Rips (VR) filtration*. This filtration is constructed upon a metric space where the points are the vertices of our topic network. The distance between any two vertices in this metric space is defined as the *shortest path distance* between them within the graph. As the distance threshold $\epsilon$ increases, the VR filtration builds its complex: a $k$-simplex (a group of $k + 1$ vertices) is added to the complex if the shortest path distance between every pair of its constituent vertices is less than or equal to $\epsilon$. This means that if three topics are all mutually reachable within $\epsilon$ steps in the network, they will form a 2-simplex (a triangle), effectively “filling in” the space between
<figure><img src="image_11.png" /><figcaption>Figure 10: An illustration of a filtration and its corresponding persistence diagram. A point cloud (top left) is analyzed by progressively adding connections as a distance parameter *r* (radius) increases. This reveals a prominent circular feature (a loop) that persists across multiple scales. The persistence diagram (bottom right) summarizes this process, with the point far from the diagonal representing the robust, significant loop, and points close to the diagonal representing topological noise. Figure from Munch (2017).</figcaption></figure>

them.

**Figure 10** illustrates a filtration on a point cloud sampled from a circle. As the proximity parameter increases (shown as an expanding radius *r*, where the distance threshold $\epsilon = 2r$), more edges and triangles are added to the complex. Initially, only disconnected points exist. As the radius grows, local connections form, creating many small, transient loops. Crucially, a large, central loop emerges that reflects the circular shape of the data. This feature persists for a significant range of the filtration before the complex becomes dense enough to “fill it in.”

## B.3 Quantifying Gaps: Betti Numbers and Persistence

As filtration progresses and simplices are added, we use *homology* to count the topological characteristics present in each value $\epsilon$. These counts are formalized by *Betti numbers* ($\beta_k$), which quantify the number of $k$-dimensional “holes” or “gaps” within the complex (see Figure 2). In the context of our topic networks, these topological gaps offer interpretations regarding the information flow and thematic coherence:

* $\beta_0$ (Betti-0): Measures the number of connected components. A high $\beta_0$ corresponds to many distinct topics. This can be interpreted as a thematic “gap” or disjunction in the narrative.

* $\beta_1$ (Betti-1): Counts the number of one-dimensional *loops or cycles*. These represent sequences of topics that form a closed cycle

of relationships without being “filled in” by a higher-dimensional simplex. Such loops can indicate recurring themes, conceptual circularity in the narrative or “plot holes” that might provoke curiosity.

* $\beta_2$ (Betti-2): Quantifies the number of two-dimensional *voids or cavities*. These are hollow, sphere-like structures formed by collections of triangles that enclose an empty space. In our context, $\beta_2$ features could represent complex thematic “plot holes” where topics form a shell around an absent or implicit concept, potentially indicating a significant information gap.

The core idea of *persistent homology* is to track the “birth” (emergence) and “death” (disappearance or filling) of these topological features across the entire filtration. For instance, a loop ($\beta_1$ feature) is born when its final edge completes the cycle and dies when a triangle is added that fills the loop. The *persistence* of a feature is defined as the difference between its death and birth $\epsilon$ values ($\epsilon_{death} - \epsilon_{birth}$). While features with long persistence are typically considered robust and indicative of significant structure, for this initial proof-of-concept study, we primarily focused on the presence and count of these features (Betti numbers) at various $\epsilon$ values, rather than explicitly filtering for noise based on persistence. This decision was also influenced by the fact that the preceding HDBSCAN clustering step already addresses some noise within the embedding data, consequently leading to improved quality in the unfiltered Betti numbers. The results of persistent homology are typically visualized in a *persistence diagram* (Figure 3 and 10), which plots each feature as a point indicating its birth and death times. By measuring distances between these persistence diagrams (e.g., using Wasserstein or Bottleneck distances), we can quantify the degree of structural change in the topic network between consecutive text segments, thereby providing a computational proxy for the evolving information gaps that drive reader curiosity.

For a more detailed introduction to TDA, we recommend the work by Munch (2017), Carlsson (2020), and Chazal and Michel (2021).

## C Inter-Rater Reliability

In order to assess Inter-Rater Reliability for mean chapter curiosity (cf. Section 4.1), we used the
following formula by Shrount and Fleiss (1979):

$$ICC = \frac{\sigma_c^2}{\sigma_c^2 + \sigma_{r,e}^2/k}, \quad (1)$$

where $\sigma_c^2$ is the variance between chapters, $\sigma_{r,e}^2$ residual variance (which includes the rater-by-chapter interaction and measurement error), and $k$ is the number of raters.

A linear mixed-effects model was fitted to predict curiosity scores, including random intercepts for both chapter and subject. This model served to estimate the necessary variance components for the reliability assessment. The analysis, based on 1323 observations collected from 27 distinct chapters and 49 subjects, resulted in an estimated overall mean curiosity score (Intercept) of 69.54 (SE = 2.29, 95% CI [65.05, 74.03]), which was statistically significant ($p < .001$). The estimated variance components were: variance between chapters ($\sigma_{chapter}^2$) = 10.48, variance between subjects ($\sigma_{subject}^2$) = 229.95, and residual variance ($\sigma_{residual}^2$) = 214.36.

Specifically, to assess the reliability of the aggregated curiosity scores for distinguishing between chapters, with $k = 49$ participants serving as raters, an ICC of 0.71 was calculated using the estimated chapter variance component ($\sigma_c^2 = 10.48$) and the residual variance ($\sigma_{r,e}^2 = 214.36$). The calculated reliability of 0.71 for aggregated curiosity scores across 49 participants, while acceptable, indicates a moderate to limited ability to robustly distinguish between chapters. Achieving higher precision in differentiating chapters might benefit from a larger sample of participants.