1. Bibliographic Information

1.1. Title

The conceptual structure of human relationships across modern and historical cultures

1.2. Authors

Xi Cheng, Haroon Popal, Huanqing Wang, Renfen Hu, Yinyin Zang, Mingzhe Zhang, Mark A. Thornton, Yina Ma, Huajian Cai, Yanchao Bi, Jamie Reilly, Ingrid R. Olson & Yin Wang

1.3. Journal/Conference

Nature Human Behaviour. This is a highly reputable peer-reviewed scientific journal publishing research in psychology, economics, sociology, and neuroscience. Its high impact factor and selective publication process indicate the significant influence and quality of the research published within this venue, making it a leading platform for interdisciplinary studies on human behavior.

1.4. Publication Year

2025

1.5. Abstract

A defining characteristic of social complexity in Homo sapiens is the diversity of our relationships. We build connections of various types in our families, workplaces, neighbourhoods and online communities. How do we make sense of such complex systems of human relationships? The basic organization of relationships has long been studied in the social sciences, but no consensus has been reached. Here, by using online surveys, laboratory cognitive tasks and natural language processing in diverse modern cultures across the world (n = 20,427) and ancient cultures spanning 3,000 years of history, we examined universality and cultural variability in the ways that people conceptualize relationships. We discovered a universal representational space for relationship concepts, comprising five principal dimensions (formality, activeness, valence, exchange and equality) and three core categories (hostile, public and private relationships). Our work reveals the fundamental cognitive constructs and cultural principles of human relationship knowledge and advances our understanding of human sociality.

1.6. Original Source Link

/files/papers/68ffa09ebd968e29d463b620/paper.pdf (This appears to be a direct PDF link, indicating it's an officially published paper or at least the final accepted manuscript).

2. Executive Summary

2.1. Background & Motivation

The core problem the paper aims to solve is the lack of a comprehensive, unified understanding of how humans mentally conceptualize and organize their diverse relationships. Despite extensive study across various social science disciplines (sociology, anthropology, cognitive psychology, communication studies) over the past 50 years, no consensus has been reached on the fundamental structure and organization of human relationships.

This problem is critically important because relationships are a defining characteristic of social complexity in Homo sapiens. Humans form myriad connections in different contexts (family, work, online), and the quality and quantity of these relationships are integral to individual survival, thriving, cognition, behavior, development, and well-being. Understanding this conceptual structure—the common-sense way ordinary people make sense of their social worlds—is crucial for advancing human sociality.

The challenges or gaps in prior research include:

• Diversity and Complexity: Human relationships are incredibly diverse, context-dependent, and multifaceted, making it difficult to isolate and study individual components or establish objective measures. Non-human primate societies, for example, are largely defined by hierarchy and affiliation, whereas human societies involve far more complex types of relationships (e.g., frenemies, godparents).

• Subjectivity: Relationships are subjective beliefs, experiences, and practices shaped by individual perspectives and dynamic, unwritten rules, making objective comparison across individuals and cultures challenging. The degree of shared cognitive, behavioral, and cultural principles of relationships across time and cultures is underexplored.

• Disciplinary Silos: Different social science disciplines have explored relationships using their own theoretical perspectives and methodological approaches, leading to disparate findings and a lack of a unified understanding. For instance, sociologists found a three-factor model for role-based relationships, anthropologists proposed four elementary forms of social bonds, and cognitive psychologists suggested a four-dimensional framework. These approaches often tap into distinct feature spaces and relationship types.

  The paper's innovative idea or entry point is to focus on the common sense of human relationships—how ordinary people mentally conceptualize and understand relationship concepts. By leveraging diverse methodologies (online surveys, laboratory cognitive tasks, and advanced natural language processing) across a large global sample of modern cultures and historical texts spanning 3,000 years, the authors aim to build a unified framework that clarifies the underlying elements and organizational structures of the relationship concept system, while also revealing similarities and differences across cultures and time.

2.2. Main Contributions / Findings

The paper makes several primary contributions and key findings:

1. Discovery of a Universal Representational Space (FAVEE-HPP Framework):

   • The study identified a universal representational space for human relationship concepts, structured by five principal dimensions and three core categories.
   • The five principal dimensions, termed the FAVEE model, are: Formality, Activeness, Valence, Exchange, and Equality. These dimensions account for a significant portion of the variance in how relationships are conceptualized.
   • The three core categories, termed the HPP model, are: Hostile, Public, and Private relationships. The paper demonstrates that these categories emerge from the FAVEE dimensions.
   • This framework unifies existing theories from various disciplines and provides a parsimonious model for understanding relationship concepts.

2. Cross-Cultural Universality and Variability:

   • The FAVEE-HPP framework was found to be universally shared across diverse modern cultures (19 global regions, 10 languages, n = 17,686 participants), confirming its generalizability worldwide.
   • The FAVEE model outperformed 15 other existing theories in data fitting and explained variance across these global regions.
   • While the basic structure is universal, the study also revealed rich cultural variability in how specific relationship concepts are understood. This variability was quantitatively linked to religion and modernization levels. For instance, public relationships showed more cultural variability than familial or romantic relationships. Specific comparisons between the USA and China highlighted differences in conceptualizing closeness (physical vs. psychological distance), power within families, and social exchange in private relationships.
   • The model was further validated in a non-industrial society (the Chinese Mosuo tribe), demonstrating its robustness beyond industrialized contexts.

3. Historical Endurance:

   • By employing advanced Natural Language Processing (NLP) techniques and Pre-trained Language Models (PLMs) on large-scale historical text corpora (ancient China spanning 3,000 years), the paper demonstrated that the FAVEE-HPP structures are persistent through time.
   • The FAVEE-HPP model also outperformed other theoretical models in predicting relationship representations in both ancient and modern PLM embeddings.
   • Analysis of ancient vs. modern Chinese PLM embeddings revealed shifts in the relative importance of formality and equality dimensions over time, suggesting equality was more salient in ancient conceptualizations of relationships, and formality more so in modern times.

4. Generalizability to Non-Dyadic Relationships:

   • The FAVEE framework was extended and confirmed to be generalizable to non-dyadic relationships, including triadic relations (e.g., love triangle) and group relations (e.g., rich-poor, Democrats-Republicans).

     In essence, the paper provides a fundamental, robust, and empirically validated framework for understanding the cognitive and cultural principles underlying human relationship knowledge, thereby advancing the understanding of human sociality. It offers a computational framework for objective and quantitative measurement of human relationships, akin to the "Big Five" framework for personality.

3. Prerequisite Knowledge & Related Work

3.1. Foundational Concepts

To fully understand this paper, a beginner should be familiar with several key concepts from social science, cognitive science, and computational methods.

• Social Complexity: This refers to the intricate and diverse ways individuals interact and organize themselves within a society. In Homo sapiens, it's characterized by varied relationship types, social structures, and cultural norms, contrasting with simpler social hierarchies in many animal species.
• Conceptual Structure: This is how mental concepts are organized in the human mind. For relationships, it refers to the underlying cognitive map or framework people use to understand, categorize, and differentiate between various types of social connections. It represents the "common sense" or "lay theory" people hold about relationships.
• Universality vs. Cultural Variability: Universality implies that certain aspects of relationship conceptualization are common across all human cultures, suggesting a fundamental, shared cognitive basis. Cultural variability highlights how these conceptualizations can differ significantly due to specific cultural norms, beliefs, and societal structures.
• Natural Language Processing (NLP): This is a field of artificial intelligence that enables computers to understand, interpret, and generate human language. In this paper, NLP is used to:
  • Generate comprehensive lists of relationship terms from text.
  • Analyze large text corpora (collections of written texts) to infer how relationships are conceptualized in different cultures and historical periods.
• Pre-trained Language Models (PLMs): These are advanced NLP models (e.g., BERT, RoBERTa) that have been trained on vast amounts of text data (e.g., the entire internet or massive book collections) to learn general linguistic patterns, grammar, and semantic relationships between words. Pre-training involves tasks like Masked Language Modeling (MLM), where the model learns to predict missing words in a sentence. Once pre-trained, these models can generate word embeddings.
• Large Language Models (LLMs): A subset of PLMs, LLMs (e.g., GPT-4) are particularly large neural networks with billions of parameters, excelling at understanding and generating human-like text, performing tasks like summarization, translation, and answering complex questions. In this paper, LLMs like GPT-4 are used to generate descriptions ([DESC]) to provide context for PLMs when probing relationship understanding.
• Word Embeddings: These are numerical representations (vectors) of words or concepts in a multi-dimensional space. Words with similar meanings or contexts are mapped closer together in this space. PLMs generate embeddings that capture semantic and contextual information. By analyzing the embedding space of relationship terms, researchers can infer their conceptual similarities and differences.
• Principal Component Analysis (PCA): This is a statistical procedure that transforms a set of observations of possibly correlated variables into a set of values of linearly uncorrelated variables called principal components. It's a dimensionality reduction technique.
  • Goal: To reduce the number of dimensions (features) in a dataset while retaining as much variance (information) as possible.
  • How it works (simplified): PCA finds new axes (principal components) along which the data varies the most. The first principal component accounts for the largest possible variance, and each succeeding component accounts for the next highest variance possible and is orthogonal to the preceding components.
  • In this paper, PCA is used to reduce a large set of evaluative features (e.g., intimacy, formality) into a smaller, more manageable set of latent dimensions (e.g., formality, activeness, valence, exchange, equality).
• Clustering Algorithms (e.g., k-means, Hierarchical Clustering): These are unsupervised machine learning techniques used to group a set of objects in such a way that objects in the same group (called a cluster) are more similar to each other than to those in other groups.
  • k-means: A popular algorithm that aims to partition $n$ observations into $k$ clusters. It iteratively assigns data points to the nearest cluster centroid and then recomputes the centroids.
  • Hierarchical Clustering: Builds a hierarchy of clusters, either by merging smaller clusters into larger ones (agglomerative) or by splitting larger clusters into smaller ones (divisive).
  • In this paper, clustering is used to identify categories of relationships (e.g., hostile, public, private) based on their conceptual similarities in the representational space.
• Representational Dissimilarity Matrices (RDMs): An RDM is a square matrix where each entry (i, j) represents the dissimilarity (e.g., conceptual distance or difference) between two items (i) and (j). It's symmetric, with zeros on the diagonal (an item is perfectly similar to itself).
  • RDMs are a key tool in Representational Similarity Analysis (RSA) to compare different representations (e.g., human judgments, brain activity, computational models).
• Representational Similarity Analysis (RSA): A powerful framework for comparing the representational geometries (the patterns of similarities and dissimilarities among a set of items) between different sources of data.
  • Goal: To understand how closely different models or datasets reflect each other's underlying conceptual organization.
  • How it works (simplified): It involves computing RDMs for different data sources (e.g., human ratings, PLM embeddings, cultural variables) and then comparing these RDMs (typically using correlation coefficients like Spearman's $r$). A high correlation between two RDMs suggests that their underlying representational spaces are structurally similar.
  • In this paper, RSA is used to:
    • Assess cross-cultural concordance of relationship concepts.
    • Model cross-region variability using cultural/sociocultural variables.
    • Compare PLM embeddings with human ratings.
• Multi-arrangement Task: A cognitive task where participants arrange items (e.g., relationship terms) on a 2D screen such that the spatial distance between any two items reflects their conceptual dissimilarity. Closer items are more similar.
• Free Sorting Task: A cognitive task where participants categorize a set of items (e.g., relationship terms) into groups of their own choosing and provide labels for these categories.
• Uniform Manifold Approximation and Projection (UMAP): A non-linear dimensionality reduction technique often used for visualization and as a preprocessing step for clustering. It aims to preserve both local and global data structure, projecting high-dimensional data into a lower-dimensional space (e.g., 2D) while maintaining meaningful distances.

3.2. Previous Works

The paper highlights a historical lack of consensus in understanding the basic organization of relationships, despite efforts across various disciplines. It references several foundational works and theories, each contributing a piece to the puzzle but none offering a unified framework:

• Marwell & Hage (1970) - Sociological Perspective:
  • Focus: Formation and organization of social relationships.
  • Model: Discovered a three-factor model for role-based relationships: intimacy, visibility, and regulation.
  • Context: Sociologists were interested in how social roles shape interactions.
• Fiske (1992) - Anthropological Perspective (Relational Models Theory):
  • Focus: Foundations of social coordination across cultures.
  • Model: Proposed four elementary forms of social bonds: communal sharing, authority ranking, expected reciprocity, and market pricing.
  • Context: Anthropologists sought universal principles governing social interactions across diverse societies.
  • Explanation: Fiske's theory suggests that people organize their social lives using a limited number of fundamental relational models.
    • Communal Sharing: People feel that they are all the same, undifferentiated, and belong to a single group. Needs are met without regard for proportionality (e.g., family, close friends).
    • Authority Ranking: People are ordered hierarchically, with superiors having authority and protection, and subordinates having deference and loyalty (e.g., military, traditional family structures).
    • Equality Matching: People relate as peers who are distinct but equal, engaging in turn-taking, balanced reciprocity, and equal distributions (e.g., friends taking turns buying rounds, splitting chores).
    • Market Pricing: People relate in terms of proportional ratios or rates, often using a common metric like money, valuing efficiency and cost-benefit analysis (e.g., buying and selling, wages).
• Wish, Deutsch, & Kaplan (1976) - Cognitive Psychological Perspective:
  • Focus: Perception of interpersonal relations.
  • Model: Revealed a four-dimensional framework for describing relationships: valence (affective tone), equality (power balance), activeness (intensity/engagement), and formality (rules/structure).
  • Context: Cognitive psychologists investigated how individuals mentally represent and differentiate relationships.
• Montgomery (1988) - Communication Studies Perspective:

  • Focus: Communication quality in personal relationships.

  • Model: Proposed three factors for effective relational dialogues: positiveness, intimacy, and control.

  • Context: Communication scholars studied the dynamics of interaction within relationships.

    The paper notes that all these theories have been insightful and endured in their respective fields. However, a major limitation is that researchers "in different disciplines have approached the problem of human relationships using their unique features of interest and thus have tapped into distinct feature spaces and relationship types." This disciplinary fragmentation is precisely what the current paper aims to overcome by building a unified framework across these perspectives. The present work seeks to synthesize these diverse feature sets into a higher-order, more comprehensive model.

3.3. Technological Evolution

The study's ability to address the long-standing problem of relationship conceptualization is significantly enabled by recent technological advancements, particularly in Natural Language Processing (NLP) and computational modeling.

• From Manual Surveys to Large-Scale Online Data Collection: Traditionally, social science research relied on smaller, localized studies. The advent of online survey platforms (like MTurk, CloudResearch, Credamo, NaoDao) has revolutionized data collection, allowing for:
  • Massive Sample Sizes: Reaching thousands of participants (n = 20,427 in this study) across diverse geographical and cultural regions efficiently.
  • Cross-Cultural Reach: Accessing participants from 19 global regions, enabling robust cross-cultural comparisons.
  • Diverse Demographics: Capturing a broader range of human experiences and perspectives on relationships.
• Emergence of Advanced NLP and Language Models:
  • Early NLP: Focused on rule-based systems or simpler statistical models for text analysis.
  • Modern NLP with Deep Learning: The rise of deep learning, particularly transformer architectures, led to the development of powerful Pre-trained Language Models (PLMs) like BERT, RoBERTa, and Large Language Models (LLMs) like GPT-4. These models:
    • Capture Semantic Nuances: Can learn highly sophisticated representations of words (word embeddings) that capture subtle semantic and contextual relationships, far beyond what traditional methods could achieve.
    • Proxy for Human Cognition: The paper demonstrates that PLM embeddings can reflect human-like relationship understanding and even scholarly knowledge in historical contexts, serving as a proxy for the collective human mind at different periods.
    • Historical Access: Enabled the study of ancient cultures by analyzing historical text corpora, making populations otherwise inaccessible to modern researchers available for cognitive analysis.
• Sophisticated Computational Modeling Techniques:

  • Dimensionality Reduction: Techniques like Principal Component Analysis (PCA) and UMAP allow researchers to simplify complex datasets (e.g., 30 theoretical features) into interpretable lower-dimensional spaces (e.g., 5 dimensions), revealing underlying structures.

  • Clustering: Algorithms like k-means and hierarchical clustering enable the data-driven discovery of natural categories within relationship concepts.

  • Representational Similarity Analysis (RSA): Provides a robust framework for quantitatively comparing representational geometries from various sources (human judgments, computational models, cultural variables), allowing for precise measurement of agreement and disagreement across cultures and time.

    This paper's work fits within the technological timeline as a cutting-edge example of computational social science and digital humanities, leveraging big data and AI (specifically NLP) to tackle fundamental questions in psychology and anthropology that were previously limited by methodological constraints. It represents a shift from purely theoretical or small-scale empirical studies to large-scale, data-driven, and interdisciplinary investigations into human social cognition.

3.4. Differentiation Analysis

This paper's approach differentiates itself from previous works by addressing several limitations inherent in prior discipline-specific studies:

1. Unified, Interdisciplinary Framework vs. Fragmented Perspectives:

   • Previous Work: As noted, prior research typically focused within single disciplines (e.g., sociology, anthropology, cognitive psychology), each developing models based on their specific interests and methodological traditions. This led to different feature spaces (e.g., intimacy for sociologists, market pricing for anthropologists) and limited integration across fields. For instance, Wish et al. found a 4-dimensional framework for perception, while Fiske proposed 4 forms of social bonds.
   • This Paper's Innovation: The authors explicitly set out to "synthesize this cross-field literature and build a unified representational space across disciplines." They achieved this by:
     • Comprehensive Feature Collection: Systematically collecting and summarizing 30 conceptual features from 15 prominent existing theories. This ensures a broad, composite feature space.
     • Higher-Order Reduction: Instead of starting anew, they treated these existing theoretical features as inputs for further dimensionality reduction (PCA) to derive higher-order components (the FAVEE dimensions). This meta-analytic approach allows for the emergence of a more encompassing structure.

2. Broad Empirical Scope (Cross-Cultural and Historical) vs. Limited Contexts:

   • Previous Work: Many foundational studies were often conducted within specific cultural contexts (e e.g., Western, industrialized societies) or relied on smaller samples, limiting the generalizability of their findings. Studies on ancient cultures or non-industrial societies were rare or qualitative.
   • This Paper's Innovation: The study provides unprecedented breadth and depth in its empirical validation:
     • Global Modern Cultures: Tested the model across 19 diverse global regions and 10 languages (n = 17,686), far exceeding previous sample sizes and cultural diversity.
     • Non-Industrial Societies: Validated the model in the Chinese Mosuo tribe, a small-scale matrilineal society, demonstrating applicability beyond industrialized contexts.
     • Ancient Cultures: Pioneered the use of Pre-trained Language Models (PLMs) on historical text corpora (ancient China spanning 3,000 years) to infer relationship conceptualizations from the past, an otherwise inaccessible population for direct study. This provides a unique diachronic (across time) perspective.

3. Data-Driven and Computational Rigor vs. Predominantly Theoretical/Qualitative:

   • Previous Work: While some theories involved statistical methods (e.g., dimensionality reduction in Wish et al.), the overall landscape often involved theoretical models or qualitative anthropological observations.
   • This Paper's Innovation: Emphasizes a data-driven approach at every stage:
     • NLP to generate extensive relationship lists.
     • PCA for robust dimensionality reduction.
     • Clustering algorithms for category identification.
     • Representational Similarity Analysis (RSA) to quantitatively compare different representations and link cultural variables to conceptual variations.
     • Rigorous model comparison analysis (FAVEE vs. 15 other theories) demonstrating superior performance and consistency.
     • Quantification of universality and cultural variability through statistical modeling.

4. Integrated Dimensional and Categorical View vs. Separate Models:

   • Previous Work: Some theories focused on dimensions (e.g., Wish et al.), others on categories/forms (e.g., Fiske).

   • This Paper's Innovation: The FAVEE-HPP framework integrates both: dimensions (FAVEE) define a continuous representational space, and categories (HPP) emerge as clusters within this space. This provides a more complete picture of how people mentally organize relationships, moving from continuous features to discrete types.

     In essence, this paper moves beyond fragmented, context-limited, and often discipline-bound understandings to construct a truly universal, cross-cultural, and historically enduring framework for human relationship conceptualization, backed by massive empirical data and advanced computational methods.

4. Methodology

The paper outlines its methodology across three main studies, each building upon the previous one to establish the FAVEE-HPP framework and test its universality, cultural variability, and historical endurance.

4.1. Principles

The core idea behind the methodology is to identify the fundamental dimensions and categories that humans use to mentally organize their relationships. The theoretical basis or intuition is that despite the apparent diversity of relationships, there must be a limited set of underlying cognitive principles or constructs that allow humans to make sense of this complexity. The paper employs a multi-method approach, combining traditional social science surveys and cognitive tasks with cutting-edge Natural Language Processing (NLP) and Pre-trained Language Models (PLMs), to converge on these principles from various angles (self-report, behavioral, and linguistic data).

The methodology can be understood through three main phases, corresponding to the three studies:

1. Discovery (Study 1): Identify the latent dimensions and categories that structure human relationship concepts in a modern, Western culture (USA), by synthesizing existing theories and using empirical data.
2. Generalization and Variability (Study 2): Test the universality of the discovered structure across diverse modern global cultures and a non-industrial society, and quantify cultural variability by linking it to macro-level societal factors.
3. Historical Endurance (Study 3): Investigate the persistence of this structure over long historical periods using NLP tools to analyze ancient texts, thereby extending the framework's validity across time.

4.2. Core Methodology In-depth (Layer by Layer)

4.2.1. Participants

Across all studies, participants were native speakers who grew up or lived for the longest period of their life in the targeted regions. All studies were approved by the Institutional Review Board of Beijing Normal University (IRB_A_0024_2021002), and informed consent was obtained.

• Study 1:
  • 1,065 online US participants via MTurk for online surveys.
  • 60 offline US participants for laboratory cognitive tasks (within-subject design).
• Study 2:
  • 17,686 online participants from 19 global regions (e.g., USA, China, Israel, Portugal) via MTurk, CloudResearch, Credamo, and NaoDao platform.
  • 229 native Mosuo people (a non-industrial, matrilineal society in China) through face-to-face interviews and door-to-door paper surveys.
• Study 3:
  • 44 scholars specialized in ancient Chinese culture for expert evaluation of the NLP method.
• Generalizability Test (Non-dyadic relationships):
  • 380 online US participants (MTurk).
  • 242 online Chinese participants (NaoDao platform).

4.2.2. Sampling of Human Relationships

A data-driven Natural Language Processing (NLP) approach was used to generate comprehensive lists of human relationships to ensure ecological validity and cover a wide range of types.

1. Seed Words Generation: Brainstorming and social media searches by a set of participants (n=15 for USA, n=27 for China) were used to create initial seed words related to relationships.
2. Text Embedding & Co-occurrence: Text embedding (numerical representation of words) was used to find words that frequently co-occurred with these seed words. This was done by calculating the cosine distance between word vectors. Words with smaller cosine distance are more similar in meaning or context.
3. Filtering: The list was filtered to keep only nouns and then further filtered by frequency. Manual checks ensured only words related to human relationships were retained.
4. Pairing and Literature Integration: Words were paired based on their relationship meanings. Additionally, relationships pulled from existing literature were added.
   • Result: 159 typical relationships for English (USA) and 258 relationships for Chinese. These included common (e.g., siblings, friends) and uncommon (e.g., master-servant, friends with benefits) English terms, and Chinese-unique relationships (some untranslatable or culture-specific).

4.2.3. Evaluative Features

To capture a comprehensive understanding of relationship dimensions, the researchers synthesized features from prior work.

1. Literature Search: A comprehensive literature search was performed across 15 prominent theories in relationship science.
2. Feature Collection: 30 conceptual features were summarized and extracted (e.g., activeness, communality, concreteness, equality, endurance, formality, intensity, intimacy, reciprocity, valence). Redundant features were combined.
3. Cross-Cultural Additions: For Study 2, three additional theoretical features (morality, trust, generation gap) from cross-cultural literature were included.

4.2.4. Dimensional Survey

This was a primary data collection method across all studies.

1. Online Survey Design: Participants rated human relationships on bipolar Likert scales. Each page cued a specific evaluative feature (e.g., activeness) with two opposite phrases (e.g., passive vs. active) at the ends of a slider bar.
2. Detailed Definitions: Since some features were obscure (e.g., communality), each feature was presented with a detailed definition and an exemplary relationship.
3. Instructions: Participants were asked to consider all aspects of relationships (thinking, feeling, acting, talking, characteristics), focusing on general knowledge or stereotypical understanding rather than personal experiences.
4. Attention Checks: Questions were used to ensure active engagement and prevent random or patterned responses.
5. Efficiency:
   • Between-subject design (online): To avoid fatigue, each participant was randomly assigned a subset of relationships (5-8) and a subset of features (10-11).
   • Within-subject design (offline for Study 1): In contrast, offline participants rated all 159 relationships on all features (3 hours task).
6. Data Quality Control: Additional questions on common object knowledge (size/color of animals, fruits) were included to rule out cross-cultural variations in online data quality or general semantic knowledge. Low variation in object knowledge suggested cultural variability was unique to relationship concepts.

4.2.5. Cognitive Tasks (Study 1)

Two lab-based cognitive tasks were used to measure the categorization of relationship concepts.

1. Multi-arrangement Task:
   • Goal: Collect intuitive similarity judgments.
   • Procedure: Participants arranged the 159 relationships on a 2D computer screen by dragging and dropping. The rule was that conceptually similar relationships should be placed closer together, and dissimilar ones further apart.
   • Output: A dissimilarity matrix where values indicated distances in the 2D circle.
2. Free Sorting Task:
   • Goal: Understand how people deliberately classify relationships into categories.
   • Procedure: Participants classified the 159 relationships into labelled categories of their choosing, allowed up to eight groups.
3. Text Analysis on Categorical Labels (from Free Sorting Task):
   • 444 labels were initially obtained.
   • These were coded by assigning 159 relationships (e.g., family label assigned to wife-husband but not doctor-patient).
   • Hierarchical clustering (Ward method) was performed on the label $\times$ relationship matrix. This revealed three and six clusters after excluding noisy clusters.

4.2.6. Dimensionality Reduction and Clustering

These techniques were central to extracting the FAVEE dimensions and HPP categories.

1. Data Preprocessing:
   • Raw data was cleaned; participants failing attention checks were excluded (e.g., 2,441 out of 18,537 in Study 2).
   • A matrix of average ratings for each relationship on each evaluative feature across participants was created.
   • This matrix was normalized using scikit-learn.
2. Principal Component Analysis (PCA):
   • Purpose: The primary technique for dimensionality reduction to derive dimensional models.
   • Software: prcomp function from R (v.4.3.3).
   • Rotation: Varimax rotation was used to maximize loadings of individual evaluative features onto components, making them more interpretable.
   • Component Naming: Components were named by examining the top five highest absolute loadings and the distribution of relationship scores.
   • Optimal Component Number: Determined by checking four data-driven metrics (all explained below in Evaluation Metrics) and assessing the interpretability of each component. Solutions with cross-metrics agreement and high interpretability were chosen.
   • Robustness Check: Other dimensionality reduction techniques (Independent Component Analysis, Exploratory Factor Analysis, Multidimensional Scaling, Network Analysis) were also applied, consistently yielding the same five-factor solution (FAVEE).
3. Clustering Techniques:
   • Purpose: To derive categorical models (e.g., HPP).
   • Primary Technique: k-means clustering. Other techniques (e.g., hierarchical clustering, HDBSCAN) were used for validation.
   • Input: A dissimilarity matrix of 159 relationships.
     • For dimensional survey: Euclidean distance matrix calculated from relationships' ratings on all evaluative features.
     • For multi-arrangement task: Distance matrix directly from participant arrangements.
     • For free sorting task: Distance matrix based on the probability that two relationships were classified in the same category.
   • Preprocessing: Uniform Manifold Approximation and Projection (UMAP) was used as a preprocessing step for k-means to boost performance.
     • UMAP Parameters: nearest neighbour (15, for local vs. global structure) and minimum distance (0.01, for cluster tightness).
   • Optimal Cluster Number: Determined by the silhouette score (explained below in Evaluation Metrics), and the stability and interpretability of the output clusters.

4.2.7. Language Models and Embeddings (Study 3)

PLMs and LLMs were harnessed to infer relationship understanding in ancient contexts.

1. Modern Chinese PLM:
   • Model: word-based Chinese-RoBERTa-Base from UER-py Modelzoo.
   • Rationale: Chosen for its focus on the mask language modeling task during pre-training and its use of words (not characters) for Chinese. Trained on a large, public modern Chinese text corpus.
2. Ancient Chinese PLM:
   • Model: BERT-ancient-Chinese (Wang & Ren, 2023).
   • Rationale: Trained on a large-scale ancient Chinese corpus (historical texts from Zhou Dynasty (-1046 BCE) to Qing Dynasty (1912 CE)).
3. Generating Human-like PLM Embeddings:

   • Approach: Adapted from Cutler and Condon (2023), combining PLMs with LLMs.

   • Query Formulation: The following query (in Chinese) was used as input for the PLM: [DESC] The most salient feature of the relationship [TERM] is [MASK].

     • [TERM]: Substituted with one of the 258 Chinese relationship terms.
     • [MASK]: Represents the conceptualization of the target relationship, which the PLM predicts words for based on context.
     • [DESC]: Relationship-specific descriptions generated by GPT-4 (an LLM). This provided rich contextual information.
       • For ancient contexts, GPT-4 descriptions were generated for ancient China, then refined by human experts in ancient Chinese language/history to match linguistic features and relationship characteristics of the era.

   • Embedding Extraction: The last layer vector (768 dimensions) was extracted from the [MASK] token's position for each relationship, resulting in a 258 x 768 matrix.

   • Validation: Resemblance between human representations (similarity matrix from Chinese populations in Study 2) and PLM representations (pre-trained on modern Chinese corpus) was 0.553 ($P < 0.001$), confirming PLM embeddings could reflect human-like understanding.

   • PCA on PLM Embeddings: PCA was applied to PLM representations, and the resulting components corresponded well with FAVEE structures.

     The following figure (Figure 5a from the original paper) shows the pipeline for generating PLM embeddings:

     该图像是包含三部分的复合图表，展示了不同文化间人际关系的交叉区域可靠性。a部分为不同关系类型（依附、权力、交易、家庭、浪漫、敌对）的可靠性条形图；b部分展示敌对、公有和私人关系的可靠性小提琴图；c部分说明五个核心维度（正式性、活跃性、情感色彩、交换和平等）对应的可靠性分布。

4.2.8. Representational Similarity Analysis (RSA) and Model Comparison

These techniques were used for evaluating cross-cultural variability and model performance.

1. RSA Multiple Regression (Study 2):

   • Purpose: To identify which cultural variables account for cross-cultural variance in relationship representations.
   • Procedure:
     • Cultural Variables: Collected from multiple open databases (e.g., World Values Survey, Worldbank) for language, personality, socio-ecology (subsistence, disease, climate), modernization (composite of education, urbanization, wealth), genetics, religion, politics, and Hofstede 6D culture model.
     • Cultural Variable RDMs: For each cultural variable, an RDM was computed, where each cell represented the dissimilarity between two regions on that variable (e.g., dissimilarity in modernization level between China and Portugal).
     • Relationship Representational RDMs: For each representational geometry (full-feature, dimensional, categorical), an RDM was created to represent the dissimilarity of relationship representations across regions.
     • Linear Regression: A linear regression model was used, where cultural variable RDMs were predictors, and the relationship representational geometry RDM was the outcome variable.
   • Statistical Significance: Mantel test was used. This involves permuting the order of cultural variable RDMs (while holding relationship RDMs constant), recalculating regression, and repeating 10,000 times to compute a $P$-value for the $F$ statistic. A one-sided test was used as only positive similarities were expected.
   • Noise Ceiling: Estimated by using the mean relationship RDMs of n-1 regions to predict the remaining region's RDM, reflecting inherent heterogeneity.

2. RSA Correlations (Study 3):

   • Purpose: To compare PLM embeddings with human-rating FAVEE-HPP model in ancient and modern contexts.
   • Procedure:
     • PLM embeddings (e.g., $258 \times 768$ matrix for modern Chinese) were transformed into a cosine similarity matrix (e.g., $258 \times 258$).
     • This similarity matrix was then correlated (using Spearman correlation) with the lower triangle of RDMs derived from:
       • The FAVEE dimensions (distances between pairs of relationships in 5D FAVEE space).
       • The HPP categories.
   • Noise Ceiling: Estimated by correlating human-rating RDMs from FAVEE-HPP with human-rating RDMs from 33 dimensional features.

3. Model Comparison Analysis:

   • Purpose: To compare the performance of the FAVEE model against the 15 other existing theories.

   • Procedure: For each model, linear combinations of its features were used as regressors to predict each of the remaining theoretical features (not included in that model).

   • Metrics: $Adjusted R^2$ (explained variance) and BIC (Bayesian Information Criterion, for data fitting) were calculated for each region. FAVEE consistently outperformed others.

     The following figure (Figure 3b from the original paper) shows the computational modeling of representational geometries using RSA multiple regression:

     该图像是论文中的复合图，包括a部分的成分主成分分析碎石图，b部分的关系特征与五个主维度的相关性气泡图，以及c部分展示关系类别（私人、公有、敌意）网络结构的圆形聚类图，揭示了人类关系的概念结构。

4.2.9. Robustness Test

To ensure the reliability of the findings against data sparsity.

1. Procedure: Relationships were removed one by one, and all analyses (PCA, clustering, cross-cultural RSA) were re-performed.
2. Removal Sequence: Pairs of relationships were ranked from most to least similar (based on multi-arrangement task). The relationship with lower familiarity rating in each pair was removed first.
3. Metrics: Pearson correlations between metrics from the full set and from the subsets determined robustness. A subset of 40 relationships was found sufficient to replicate findings based on 159 relationships.

5. Experimental Setup

5.1. Datasets

The study utilized several datasets, primarily consisting of human judgments on relationships and linguistic data for Natural Language Processing.

• 159 English Relationships:
  • Source: Generated using a data-driven NLP approach based on seed words and text embeddings, supplemented by relationships from literature.
  • Characteristics: Included a mix of common (e.g., siblings, friends, enemies) and less common (e.g., master-servant, friends with benefits) dyadic relationships.
  • Domain: English-speaking cultures (primarily USA).
  • Purpose: Used in Study 1 for dimensional surveys and cognitive tasks, and in Study 2 for cross-cultural comparisons.
  • Example: A sample data point would be the relationship wife-husband being rated on features like formality or activeness.
• 258 Chinese Relationships:
  • Source: Generated using Chinese NLP algorithms, including Chinese-unique relationships (e.g., those related to Confucian ideals that are hard to translate directly).
  • Characteristics: Broader set of dyadic relationships specific to Chinese culture.
  • Domain: Chinese cultures (modern and ancient).
  • Purpose: Used for US-China comparisons in Study 2 and for PLM embeddings in Study 3.
  • Example: The relationship ancestor-descendant which holds different conceptual weight in Chinese culture due to ancestor veneration.
• 75 Mosuo Relationships:
  • Source: Identified through field work within the Mosuo culture.
  • Characteristics: Typical relationships specific to the Mosuo matrilineal society.
  • Domain: Mosuo (non-industrial) culture in China.
  • Purpose: Used for validation of the FAVEE-HPP model in a non-industrial society in Study 2.
• Group Relations (40) and Triadic Relations (34):
  • Source: Generated to test generalizability beyond dyadic relationships.
  • Domain: USA and China.
  • Purpose: Used to confirm the FAVEE model's applicability to more complex non-dyadic relationship structures.
  • Example: love triangle (triadic), rich-poor (group).
• Text Corpora for Pre-trained Language Models (PLMs):

  • Modern Chinese Corpus: A large-scale, publicly available corpus of modern Chinese text.

  • Ancient Chinese Corpus: A comprehensive compilation of historical Chinese texts ranging from the Zhou Dynasty (-1046 BCE) to the Qing Dynasty (1912 CE).

  • Domain: Linguistic data reflecting conceptualizations over time.

  • Purpose: To train and apply PLMs to infer relationship understanding in modern and ancient China, effectively serving as proxies for the collective human mind in those eras.

    These datasets were chosen for their effectiveness in validating the method's performance across diverse contexts:

• The large number of relationships and global participant pool ensured robust empirical validation of universality and cultural variability.
• The inclusion of unique Chinese relationships and the Mosuo culture allowed for the exploration of culturally specific nuances and generalizability beyond typical industrialized societies.
• The use of ancient text corpora enabled a novel historical validation, addressing the temporal endurance of the proposed framework.

5.2. Evaluation Metrics

The paper employs a variety of statistical and computational metrics to evaluate its models and findings.

• Pearson's Correlation Coefficient ($r$):

  1. Conceptual Definition: Measures the linear correlation between two sets of data. It indicates the strength and direction of a linear relationship.
  2. Mathematical Formula: $ r_{xy} = \frac{\sum_{i=1}^{n} (x_i - \bar{x})(y_i - \bar{y})}{\sqrt{\sum_{i=1}^{n} (x_i - \bar{x})^2 \sum_{i=1}^{n} (y_i - \bar{y})^2}} $
  3. Symbol Explanation:
     • $r_{xy}$: Pearson correlation coefficient between variables $x$ and $y$.
     • $n$: Number of data points.
     • $x_i, y_i$: Individual data points for variables $x$ and $y$.
     • $\bar{x}, \bar{y}$: Mean of variable $x$ and $y$, respectively.
  • Usage in Paper: Used to compare PCA loadings and relationship scores between subsamples and the full dataset in robustness tests, and generally for correlations between different measures.

• Spearman's Rank Correlation Coefficient ($\rho$):

  1. Conceptual Definition: A non-parametric measure of the strength and direction of monotonic association between two ranked variables. It assesses how well the relationship between two variables can be described using a monotonic function.
  2. Mathematical Formula: $ \rho = 1 - \frac{6 \sum d_i^2}{n(n^2 - 1)} $
  3. Symbol Explanation:
     • $\rho$: Spearman's rank correlation coefficient.
     • $d_i$: Difference between the ranks of corresponding items in the two variables.
     • $n$: Number of data points.
  • Usage in Paper: Used for Representational Similarity Analysis (RSA) correlations between language models and human ratings, and for cultural variable correlations (e.g., modernization level and formality score of neighbors).

• Explained Variance (e.g., in PCA, $R^2$, Adjusted $R^2$):

  1. Conceptual Definition: A measure of how much of the variability in a dataset is accounted for by a statistical model. In PCA, it indicates the proportion of total variance explained by each principal component. In regression, $R^2$ (coefficient of determination) measures the proportion of variance in the dependent variable that is predictable from the independent variable(s). $Adjusted R^2$ is a modified version that accounts for the number of predictors in the model, providing a more accurate measure for comparison between models with different numbers of predictors.
  2. Mathematical Formula (for $R^2$ in linear regression): $ R^2 = 1 - \frac{SS_{res}}{SS_{tot}} $ Mathematical Formula (for Adjusted $R^2$): $ \text{Adjusted } R^2 = 1 - (1 - R^2) \frac{n - 1}{n - k - 1} $
  3. Symbol Explanation:
     • $SS_{res}$: Sum of squares of residuals (the unexplained variance).
     • $SS_{tot}$: Total sum of squares (the total variance in the dependent variable).
     • $n$: Number of data points (observations).
     • $k$: Number of independent variables (predictors) in the model.
  • Usage in Paper:
    • PCA: Used to determine how much of the total variance in relationship features is captured by the five FAVEE dimensions (e.g., 82.14% in Study 1).
    • Model Comparison: $Adjusted R^2$ was used to assess how well a model (e.g., FAVEE) can predict remaining theoretical features across regions, providing a measure of explained variance.

• Bayesian Information Criterion (BIC):

  1. Conceptual Definition: A criterion for model selection among a finite set of models. It's a trade-off between model fit (likelihood) and model complexity (number of parameters). Lower BIC values generally indicate a better model.
  2. Mathematical Formula: $ \text{BIC} = k \ln(n) - 2 \ln(\hat{L}) $
  3. Symbol Explanation:
     • $k$: Number of parameters estimated by the model.
     • $n$: Number of observations (data points).
     • $\hat{L}$: The maximized value of the likelihood function for the model.
  • Usage in Paper: Used in model comparison analysis as a metric for data fitting, where a lower BIC indicates a better-fitting model, especially when comparing FAVEE against other theories.

• Optimal Number of PCA Components (Metrics):

  1. Conceptual Definition: Various statistical rules and visual tests are used to determine the ideal number of principal components to retain from a PCA analysis, balancing variance explained with interpretability and parsimony.
  2. Mathematical Formula / Explanation:
     • Parallel Analysis: Compares the eigenvalues from the actual data to eigenvalues from randomly generated data of the same size. Components are retained if their eigenvalue is larger than the corresponding random data eigenvalue.
     • Kaiser-Guttman Rule (Eigenvalue > 1 Rule): Retains principal components whose eigenvalues are greater than 1. An eigenvalue of 1 means the component explains as much variance as a single original variable.
     • Cattell's Scree Test: Involves plotting the eigenvalues in descending order and looking for the "elbow" or "scree" point, where the slope of the line changes dramatically, suggesting components after this point contribute little additional variance.
     • Optimal Coordinates: A more formal statistical approach to identify the elbow point in the scree plot.
  3. Usage in Paper: These metrics were used in Study 1 and Study 2 to determine that five principal components (the FAVEE dimensions) were optimal.

• Silhouette Score (for Clustering):

  1. Conceptual Definition: A measure of how similar an object is to its own cluster (cohesion) compared to other clusters (separation). It ranges from -1 to +1, where a high value indicates that the object is well matched to its own cluster and poorly matched to neighboring clusters. Scores near +1 indicate dense, well-separated clusters; scores near 0 indicate overlapping clusters; and negative scores suggest an object might be assigned to the wrong cluster.
  2. Mathematical Formula: $ s(i) = \frac{b(i) - a(i)}{\max(a(i), b(i))} $
  3. Symbol Explanation:
     • s(i): The silhouette score for data point $i$.
     • a(i): The average distance between data point $i$ and all other points in the same cluster.
     • b(i): The minimum average distance between data point $i$ and all points in a different cluster (i.e., the nearest cluster to $i$ that $i$ is not part of).
  • Usage in Paper: Used to determine the optimal number of clusters for the HPP categories and canonical relationship types, where the highest silhouette score indicates the best clustering solution.

• Mantel Test (for RSA):

  1. Conceptual Definition: A statistical test used to determine the correlation between two distance matrices (or dissimilarity matrices). It assesses whether the patterns of relationships among items in one matrix are significantly similar to the patterns in another matrix. Unlike standard correlation, it accounts for the non-independence of entries within a distance matrix.
  2. Mathematical Formula / Explanation: The Mantel test doesn't have a single simple formula like Pearson's $r$. Instead, it involves calculating a standard correlation coefficient (e.g., Pearson's $r$) between the vectorized lower triangles of the two RDMs. The significance ($P$-value) is then determined by permutation testing:
     • One of the RDMs is randomly permuted many times (e.g., 10,000 times).
     • The correlation is recalculated for each permutation.
     • The observed correlation is compared to the distribution of correlations from the permuted data to determine its statistical significance.
  3. Usage in Paper: Used to assess the statistical significance of RSA multiple regression coefficients (i.e., whether cultural variables significantly predict cross-regional variability in relationship representations).

• F-statistic (for ANOVA and Regression):

  1. Conceptual Definition: A value calculated in ANOVA (Analysis of Variance) or regression analysis to test the overall significance of the model or to compare means across multiple groups. A larger F-statistic generally indicates that the variation among group means (or explained by the model) is larger than the variation within groups (or unexplained by the model).
  2. Mathematical Formula (conceptual for ANOVA): $ F = \frac{\text{Variance between groups}}{\text{Variance within groups}} $
  3. Symbol Explanation:
     • Variance between groups: Measures how much the means of different groups vary from the overall mean.
     • Variance within groups: Measures the variability of observations within each group.
  • Usage in Paper: Used in ANOVA to compare cultural variability across HPP categories or FAVEE dimensions, and in RSA multiple regression to assess the overall significance of the model predicting RDMs.

5.3. Baselines

The paper primarily compared its proposed FAVEE model against 15 other existing theories from the social sciences that have attempted to describe the basic forms or underlying organization of human relationships. These theories served as the main baselines for evaluating the performance and consistency of the FAVEE model.

The specific theories are not explicitly named as a list in the main text, but they are implied by the comprehensive literature review that summarized 30 conceptual features from these 15 prominent existing theories (as mentioned in Study 1 and Extended Data Fig. 1). Each of these theories, with their own set of proposed dimensions or categories, implicitly served as a baseline model.

• Why these baselines are representative:

  • Disciplinary Coverage: They span different social science disciplines (e.g., sociology, anthropology, cognitive psychology, communication studies), reflecting the diverse historical approaches to understanding relationships.

  • Established Paradigms: These are "prominent existing theories" that have "proved insightful, as attested by their endurance in the field," indicating their foundational status and influence in relationship science.

  • Feature-Based Comparison: The paper's methodology allowed for a direct quantitative comparison by seeing how well the features (or dimensions) proposed by each of these 15 theories could explain the variance in the comprehensive set of relationship data, and how consistently they performed across different cultures.

    By demonstrating that the FAVEE model outperformed these 15 other theories in terms of data fitting and explained variance across global regions, the paper establishes the superior predictive power and parsimony of its proposed framework compared to the established, but often fragmented, understanding of relationships.

6. Results & Analysis

6.1. Core Results Analysis

The paper presents its findings across three studies, demonstrating the discovery, universality, cultural variability, and historical endurance of the FAVEE-HPP framework.

6.1.1. Study 1: A Unified Representational Space Across Disciplines

Discovery of FAVEE Dimensions:

• Through an extensive literature review, 30 conceptual features from 15 existing theories were identified.

• Principal Component Analysis (PCA) on ratings of 159 relationships across these 30 features from 1,065 US participants extracted five latent dimensions, accounting for 82.14% of the variance. These dimensions were named:

  1. Formality: Contrasting formal, occupational, rule-bound relationships (e.g., co-worker) with informal, socio-emotional, private ones (e.g., parent-infant).
  2. Activeness: Distinguishing close, engaged relationships (e.g., wife-husband) from distant ones (e.g., strangers).
  3. Valence: Differentiating friendly, harmonious relationships (e.g., church members) from conflictual, hostile ones (e.g., bully-victim).
  4. Exchange: Separating relationships involving concrete resource exchange (e.g., dealer-buyer) from those involving symbolic, intangible resources (e.g., brother-sister).
  5. Equality: Distinguishing relationships with equal power (e.g., sports rivals) from those with unequal power (e.g., man-god).

• This five-dimensional solution was robustly replicated using other dimensionality reduction techniques (e.g., ICA, EFA, MDS), leading to the FAVEE model.

  The following figure (Figure 1 from the original paper) shows the PCA loadings for the FAVEE model:

  

  Discovery of HPP Categories:

• Categorical representations were explored using multi-arrangement and free sorting tasks with 60 US participants.

• Clustering algorithms applied to the dimensional survey data revealed three core categories: Hostile, Private, and Public relationships (the HPP model).

  • Hostile: Antagonistic relationships (e.g., divorced spouses).
  • Private: Personal and family ties (e.g., siblings, close friends).
  • Public: Formal, occupational, impersonal ties (e.g., driver-passenger).

• Text analysis on free sorting labels further showed that these three HPP categories could be subdivided into six canonical relationship types: hostile, familial, romantic, affiliative, transactional, and power.

• A dimension-category hybrid model demonstrated that HPP categories emerge from the FAVEE dimensions (e.g., private and public clusters at poles of formality, hostile cluster low on valence).

  The following figure (Figure 2, now 6, from the original paper) illustrates the categorical and dimensional representations:

  该图像是图表，展示了图5中FAVEE-HPP模型在现代和古代中国中的验证过程，包括生成PLM嵌入的流程、主成分分析与人类评分的相关性及模型泛化性。图b和c中展示了PCA载荷分数及其与人类评分和嵌入的对应关系，图d-f呈现了模型泛化性和古今差异的比较。

6.1.2. Study 2: Universality and Variability Across Modern Cultures

Universality of FAVEE-HPP:

• The 5D FAVEE space and three HPP categories were consistently identified in globally aggregated data (n = 17,686) and regional data across 19 global regions.

• Leave-one-region-out cross-validation showed high similarities in representational geometries across regions, suggesting FAVEE and HPP are universal structures.

• Model comparison analysis confirmed that the FAVEE model outperformed 15 other existing theories in data fitting (lower BIC) and explained variance (higher Adjusted $R^2$) across global regions, indicating its superior representation of relationship features.

  The following figure (Figure 3, now 7, from the original paper) shows the universality and cultural variability of relationship representational geometries:

  

  Cultural Variability:

• Despite universality, rich cultural variation was observed. Religion and modernization were the only two factors that significantly predicted cross-region variability in representational geometries (Extended Data Table 1). Regions with similar levels of religion and modernization had similar relationship conceptualizations.

• Public relationship concepts showed more cultural variability than hostile or private relationships. No single FAVEE dimension was selectively influenced by culture, but their relative importance could shift.

  The following figure (Extended Data Figure 4, now 12, from the original paper) shows cultural variability across relationships, dimensions, and categories:

  

  USA vs. China Comparisons:

• Closeness: Americans focused more on physical distance, while Chinese focused on psychological distance (e.g., ancestor-descendant was less distant for Chinese due to ancestor veneration).

• Power: Chinese held stronger stereotypes of inequality among family members (e.g., uncle-nephew), consistent with Confucian filial piety.

• Exchange: Americans experienced more concrete resource exchanges in private relationships than Chinese (e.g., gifts for long-distance lovers in USA vs. long phone calls in China), potentially linked to higher modernization/capitalism.

  The following figure (Figure 4, now 8, from the original paper) compares conceptualization between USA and China:

  

  Non-Industrial Society Validation:

• The FAVEE-HPP model was validated in the Mosuo tribe (a matrilineal, traditional agrarian society in China). Highly similar representational geometries were observed between Mosuo, Han Chinese, and other industrial societies, confirming its applicability beyond industrialized contexts.

6.1.3. Study 3: Relationship Representations in Ancient Cultures

PLMs as Proxies for Ancient Minds:

• The study demonstrated that PLMs can generate human-like relationship understanding by comparing PLM embeddings with human ratings ($r = 0.553, P < 0.001$).
• PCA on PLM embeddings revealed components corresponding well with FAVEE structures.

Historical Endurance of FAVEE-HPP:

• FAVEE structures were identified from an ancient Chinese PLM (trained on texts from -1046 BCE to 1912 CE).
• RSA correlations confirmed significant correlations between human ratings and ancient PLM embeddings for both FAVEE dimensions and HPP categories.
• The FAVEE model outperformed 15 other theoretical models in predicting ancient and modern PLM embeddings.

Ancient vs. Modern Differences:

• Formality explained more variance in modern Chinese PLMs (0.279) than ancient (0.178).

• Equality accounted for more variance in ancient Chinese PLMs (0.243) than modern (0.148). This suggests ancient Chinese weighted equality (e.g., social hierarchy) more and formality (e.g., occupations) less than modern Chinese.

• Expert validation showed ancient PLM embeddings agreed more with expert ratings on ancient Chinese culture, indicating it captured scholarly insights.

  The following figure (Figure 5, now 9, from the original paper) shows validation of the FAVEE-HPP model in modern and ancient China using language models:

  该图像是包含三部分的复合图表，展示了不同文化间人际关系的交叉区域可靠性。a部分为不同关系类型（依附、权力、交易、家庭、浪漫、敌对）的可靠性条形图；b部分展示敌对、公有和私人关系的可靠性小提琴图；c部分说明五个核心维度（正式性、活跃性、情感色彩、交换和平等）对应的可靠性分布。

6.1.4. Generalizability to Non-Dyadic Relationships

• The FAVEE framework successfully generalized to triadic relations (e.g., love triangle) and group relations (e.g., rich-poor, Democrats-Republicans) in both the US and China, with high correlations between dyadic and non-dyadic FAVEE structures.

6.2. Data Presentation (Tables)

The following are the results from [Extended Data Table 1] of the original paper:

This table shows the Representational Similarity Analysis (RSA) results in Study 2, detailing how various cultural variables (predictors) relate to representational geometries (outcome models) across different regions.

• Main Analysis: Considers broad cultural variables. Modernization and Religion are significant predictors for the Full-feature Model and Dimensional Model, while Modernization is significant for the Categorical Model. The beta ($\beta$) values indicate the standardized regression coefficients, and $p$ values indicate statistical significance.
• Follow-up Analysis: Breaks down Modernization into Education, Urbanization, and Wealth. Here, Urbanization consistently shows significance across all models, and Religion remains significant for the Dimensional Model.
• Adjusted R-squared values indicate the overall variance explained by the set of predictors for each representational geometry model. The Full-feature Model generally has the highest explained variance.
• Crucially, Object knowledge shows no significant predictive power, reinforcing that the observed cultural variability is specific to relationship concepts and not general semantic knowledge or data quality issues.

6.3. Ablation Studies / Parameter Analysis

The authors conducted several analyses to verify the robustness and generalizability of their findings, which can be seen as forms of ablation studies or parameter analysis.

6.3.1. Robustness of PCA Solution to Different Algorithms

• Purpose: To ensure that the identified five-dimensional FAVEE structure was not an artifact of the specific dimensionality reduction technique used.
• Procedure: In Study 1, after performing PCA, the authors also evaluated other dimensionality reduction techniques:
  • Independent Component Analysis (ICA)
  • Exploratory Factor Analysis (EFA)
  • Multidimensional Scaling (MDS)
• Results: All these techniques yielded the same five-factor solution (Supplementary Fig. 3), strongly confirming the robustness and inherent nature of the FAVEE dimensions. This indicates that the FAVEE model captures a fundamental structure independent of the specific mathematical method for its extraction.

6.3.2. Robustness of FAVEE-HPP to Different Numbers of Relationships

• Purpose: To determine if the findings were dependent on the full set of 159 relationships or if a smaller, more manageable subset could still capture the essential structure.
• Procedure: A robustness test was quantified by iteratively removing relationships one by one. The removal sequence prioritized less familiar relationships from pairs deemed most similar in the multi-arrangement task. All analyses (PCA, clustering, cross-cultural RSA) were re-performed on these reduced sets.
• Results: The study found that a subset of 40 relationships was good enough to replicate all findings based on 159 relationships (Supplementary Fig. 11). This is a crucial finding for future research, suggesting that simpler experimental designs with fewer relationships can still yield reliable results, making the FAVEE-HPP framework highly practical.

6.3.3. Determining Optimal Sample Size for Dimensional Survey (Monte Carlo Simulation)

• Purpose: To ensure adequate statistical power and stability of PCA results with minimal participant responses.
• Procedure: A Monte Carlo simulation test was conducted using pilot study data. PCA was performed on subsamples of varying sizes (from 2 to 40 participant responses per relationship-feature rating, with 1,000 iterations for each subsample). The loading scores and relationship scores from these subsamples were then compared to the overall dataset using Pearson's correlation.
• Results: Subsamples with ten responses per relationship-feature rating were almost identical to the entire dataset (rating correlation $r > 0.95$), and were adequate to ensure highly similar derived PCA components (loading score correlation $r > 0.90$, relationship score correlation $r > 0.95$). This informed the efficient design of the large-scale Study 2.

6.3.4. Model Comparison Performance and Consistency

• Purpose: To quantitatively demonstrate that the FAVEE model is superior to existing theories in representing relationship conceptualization.
• Procedure: Model comparison analysis was performed (Extended Data Fig. 3) where the FAVEE model was compared against 15 other existing theories. This involved using linear combinations of features from each model as regressors to predict remaining theoretical features and calculating $Adjusted R^2$ (explained variance) and BIC (data fitting).
• Results: Across global regions, the FAVEE model outperformed all 15 other theories in both explained variance (mean Adjusted $R^2 = 0.489$) and data fitting (mean BIC = 364.794), with 100,000 bootstrap resamples confirming significance. FAVEE was the best model in 17 out of 19 global regions. This directly validates the effectiveness of the proposed framework against established baselines, highlighting its advantages in comprehensiveness and parsimony.

6.3.5. Validation of Clustering Results

• Purpose: To confirm the stability and interpretability of the HPP categories and six canonical types.

• Procedure: While k-means clustering was the primary method, other clustering techniques (e.g., hierarchical clustering, HDBSCAN) were also employed. UMAP was used as a preprocessing step to improve clustering performance. The silhouette score was used to identify the optimal number of clusters, and the stability and interpretability of the output clusters were examined.

• Results: Solutions were chosen that were insensitive to algorithm/parameter choice, consistent across different clustering algorithms, and had high interpretability and high silhouette scores. This confirms the robustness of the identified categorical structures.

  These ablation studies and parameter analyses collectively underscore the rigor of the methodology, ensuring that the FAVEE-HPP framework is not only empirically derived but also statistically robust, generalizable, and superior to existing alternatives.

7. Conclusion & Reflections

7.1. Conclusion Summary

This paper makes a groundbreaking contribution to the understanding of human relationships by identifying a universal conceptual structure that transcends diverse cultures and historical periods. The core finding is the FAVEE-HPP framework, comprising five principal dimensions (Formality, Activeness, Valence, Exchange, Equality) and three core categories (Hostile, Public, Private relationships).

The study rigorously established this framework through:

1. Discovery (Study 1): Synthesizing 15 existing theories and using extensive human ratings from US participants to derive the FAVEE dimensions and HPP categories, demonstrating how categories emerge from the continuous dimensional space.

2. Universality and Cultural Variability (Study 2): Validating the FAVEE-HPP framework across 19 global regions and a non-industrial society (Mosuo tribe), showing its global generalizability. Crucially, it outperformed 15 other theories. It also quantified cultural variability, linking it to religion and modernization, and highlighting nuanced differences (e.g., US vs. China).

3. Historical Endurance (Study 3): Employing advanced NLP and PLMs on ancient Chinese texts, demonstrating that the FAVEE-HPP structures are detectable and persistent over 3,000 years. This study also revealed shifts in the relative importance of formality and equality over time.

4. Generalizability Beyond Dyads: The framework's applicability was extended to triadic and group relations.

   The significance of this work lies in providing a unified, parsimonious, and empirically robust model for human relationship knowledge, offering a computational framework for objective measurement and advancing our understanding of human sociality. It serves as a foundational "Big Five" for relationship science, much like its counterpart in personality research.

7.2. Limitations & Future Work

The authors candidly acknowledge several limitations and propose future research directions:

• Focus on Lay Theory: The current work primarily taps into lay theory (vernacular beliefs/common sense) about relationships. It may differ from the actual, dynamic organization of relationships observed through social acts and interactions.
  • Future Work: Examine social acts and interactions across relationships to complement lay theory.
• Universality of FAVEE-HPP Not Conclusive: While extensively validated, the FAVEE-HPP framework's universality is "far from conclusive." The reliance on online populations and data-driven approaches (while powerful) necessitates further investigation into boundary conditions that might influence its stability, validity, and generalizability.
  • Future Work: Explore factors that could influence the FAVEE-HPP model's stability, validity, representativeness, and generalizability. Investigate the different ordering of dimensions in different regions, as it could reveal further cultural insights.
• Need for Scientifically Rigorous Taxonomy: The FAVEE-HPP model was derived from theoretical features originating from layperson languages.
  • Future Work: A more scientifically rigorous approach is needed to create a valid and reliable taxonomy of human relationships.
• Limited Historical Contexts: Due to resource limitations and the availability of high-quality PLMs, Study 3 focused only on ancient China.
  • Future Work: Validate the FAVEE-HPP model in other historical contexts (e.g., Hebrew, Greek, Tamil, Old English) to further confirm its historical endurance across diverse civilizations.
• Individual-Level Variation: The current work focuses on cultural and population levels. However, relationship cognition is subjective, varied, and dynamic at the individual level.
  • Future Work: Investigate how relationship representations are constructed during human development (e.g., from infancy to adulthood) and how individuals form idiosyncratic impressions.
  • Future Work: Develop psychometric tests based on the FAVEE-HPP framework to measure individual differences across the five dimensions (analogous to the Big Five personality test).
  • Future Work: Examine how individual differences in relationship representations link to interpersonal difficulties or abnormalities in clinical populations (e.g., autism, sociopathy).

7.3. Personal Insights & Critique

This paper represents a monumental achievement in social science, offering an unprecedentedly comprehensive and empirically validated framework for understanding human relationships.

Innovations and Strengths:

• Interdisciplinary Synthesis: The approach of synthesizing 15 existing theories into a higher-order model is highly innovative. It moves beyond disciplinary silos to identify genuinely fundamental dimensions.
• Methodological Rigor and Scope: The sheer scale of data collection across diverse modern cultures (n = 20,427), the validation in a non-industrial society, and the pioneering use of PLMs for historical analysis are truly impressive. This multi-method, multi-context approach lends exceptional credibility to the FAVEE-HPP framework.
• Computational Social Science at its Best: The seamless integration of online surveys, cognitive tasks, and advanced NLP techniques showcases the power of computational social science for tackling complex, abstract psychological constructs. The use of PLMs as "proxies" for the ancient mind is particularly compelling and opens new avenues for historical psychology.
• Practical Implications: The analogy to the "Big Five" for personality is apt. A standardized, quantifiable framework for relationships has immense practical value for designing interventions, informing cross-cultural communication, diplomacy, and even developing more socially intelligent AI.
• Clarifying Universality and Cultural Nuance: The paper skillfully balances the demonstration of universal structures with the identification of crucial cultural specificities. This nuanced approach is essential for a true understanding of human behavior globally.

Potential Issues and Areas for Improvement:

• "Lay Theory" Limitation: While acknowledged, the reliance on "lay theory" is a significant point for continued research. How do these conceptual structures actually manifest in real-time social interactions, behavioral choices, and emotional responses? Future work integrating observational or behavioral data with the FAVEE-HPP framework would be critical.
• Causality of Cultural Variables: While religion and modernization were identified as predictors of cultural variability, the correlational nature of RSA means causality cannot be definitively established. Deeper dives into how these factors shape relationship conceptualization (e.g., through specific religious doctrines or aspects of urban life) would be valuable.
• Interpretation of PLM Embeddings: While the paper validates PLM embeddings against human ratings and expert knowledge, the exact mechanism by which a PLM "understands" relationships and how that correlates with human cognition remains a complex area of research. Further theoretical work on the cognitive interpretability of PLMs would strengthen this aspect.
• The "Why" Behind FAVEE-HPP: The paper beautifully describes what the FAVEE-HPP structure is and where/when it applies. Further theoretical exploration of why these particular five dimensions and three categories might be evolutionarily or cognitively fundamental would add depth. Extended Data Fig. 8 offers some initial ideas linking to Maslow's hierarchy and Baumeister's theory of cultural animals, which is a promising start.
• Generalizability of "Formality" and "Equality" Shifts: The finding that formality and equality differed in importance between ancient and modern China is fascinating. Repeating this analysis for other cultures and historical periods would confirm if this is a universal pattern of conceptual evolution or culture-specific.

Transferability and Application:

• AI and Social Robotics: The FAVEE-HPP framework offers a structured way to imbue AI systems and social robots with a more human-like understanding of social interactions, leading to more context-aware and appropriate responses.

• Cross-Cultural Communication and Diplomacy: The insights into cultural variability (e.g., physical vs. psychological distance, concrete vs. symbolic exchange) can directly inform cross-cultural training, diplomacy, marketing, and international relations, fostering better understanding and reducing miscommunication.

• Mental Health and Interpersonal Therapy: Developing psychometric tools based on FAVEE-HPP could help diagnose interpersonal difficulties and tailor therapeutic interventions for individuals or couples by identifying specific dimensions where their relationship conceptualization might be atypical or problematic.

• Content Creation and Storytelling: Writers, filmmakers, and game designers could use this framework to create more realistic, relatable, and culturally resonant characters and storylines by consciously mapping their relationships onto the FAVEE-HPP space.

  In conclusion, this paper provides a robust and deeply insightful map of the conceptual structure of human relationships, establishing a new benchmark for interdisciplinary research in social cognition. Its impact will likely resonate across psychology, anthropology, and even the burgeoning field of artificial social intelligence.