Human-AI Coevolution Dynamics: A Formal Theory of Social Intelligence Emergence Through Long-Term Interaction

Abstract: Current conversational AI systems have made significant progress in language generation, personalization, and long-context interaction. However, most existing methods model social behavior through isolated components such as emotion modeling, memory retrieval, or persona conditioning, lacking a unified framework to explain the emergence of stable social relationships and social intelligence in long-term human-AI interaction.To address this, we propose the Human-AI Coevolution Dynamics Framework (HACD-H), a formal model of human-AI interaction as a self-organizing social cognitive system. HACD-H integrates emotional adaptation, relational organization, social memory, and personality consistency into a unified dynamical framework and introduces principles including multi-timescale social cognition, relational attractors, trust basins, developmental phase transitions, and social cognitive energy dynamics.We construct a conversational dataset with approximately 14,700 interaction turns and develop a theory-driven empirical evaluation framework. Results reveal a hierarchy of temporal persistence in social cognition, stable relational attractors, phase-transition-like developmental patterns, and a structured social cognitive energy landscape. Social intelligence shows a significant negative correlation with social cognitive energy (r = -0.391, p < 0.001), and interaction trajectories exhibit progressive energy reduction over time.These findings suggest that social intelligence emerges from long-term social cognitive coevolution rather than isolated conversational capabilities. HACD-H provides a unified theoretical foundation for modeling adaptive human-AI social interaction and developing socially intelligent AI systems.

• The paper introduces HACD-H, a formal computational framework for emergent social intelligence in persistent human-AI interactions.
• It employs a multi-timescale analysis integrating emotional, relational, memory, and personality dynamics with rigorous statistical validation.
• Empirical results reveal a negative energy–intelligence correlation and stable trust attractor formation, suggesting new directions for adaptive AI design.

Formal Theory and Empirical Analysis of Social Intelligence Emergence in Human-AI Interaction

Introduction

"Human-AI Coevolution Dynamics: A Formal Theory of Social Intelligence Emergence Through Long-Term Interaction" (2606.19144) presents a comprehensive computational framework—the HACD-H (Human-AI Coevolution Dynamics for Human)—for modeling and empirically analyzing the emergence of social intelligence in persistent human-AI interaction. The paper addresses a fundamental gap in conversational AI: existing systems largely optimize local conversational modules (emotion, memory, persona) independently, lacking a unified dynamical perspective for the emergence and development of stable social relationships and social intelligence. HACD-H leverages concepts from machine learning, cognitive science, and nonlinear dynamical systems to propose and validate a formal theory governing long-term social adaptation, attractor formation, trust dynamics, and organizational energy in the human-AI coevolutionary process.

The HACD-H Framework

HACD-H models human-AI interaction as a multi-timescale social cognitive dynamical system, comprising four principal processes:

• Emotional adaptation ($E$): Rapid affective responses.
• Relational organization ($R$): Intermediate-timescale adaptation for relationship stability.
• Social memory accumulation ($M$): Longer-timescale persistence of interaction histories.
• Personality consistency ($P$): Longest timescale, supporting trait-based behavioral stability.

Interaction state at time $t$ is encoded as $X_t = (E_t, R_t, M_t, P_t)$, with the evolution dictated by $X_{t+1} = F(X_t, U_t)$, where $U_t$ represents current input and $F(\cdot)$ encapsulates coupled dynamics. HACD-H introduces theoretical constructs including multi-timescale social cognition, relational attractors, trust basins, developmental phase transitions, social cognitive energy landscapes, and emergent social intelligence as macroscopic system properties. Notably, social intelligence $SI$ is defined as a function of the coordinated interaction of $R$0, $R$1, $R$2, $R$3 rather than as a static capability.

Theoretical and Empirical Validation

The framework is validated using a socially enriched, multi-turn Chinese conversational dataset (DuLeMon-derived), annotated with high fidelity emotional, personality, relational, behavioral, and memory variables (totaling ~14,700 turns). The empirical analysis reconstructs latent social cognitive trajectories and operationalizes theoretical constructs for robust statistical evaluation.

Multi-Timescale Social Cognition

Empirical temporal persistence hierarchy reveals:

• Emotional dynamics exhibit lowest stability (0.866), indicating rapid, context-sensitive fluctuations.
• Relationship variables demonstrate highest persistence (1.000), reflecting gradual adaptation.
• Memory (0.946) and personality (0.983) exhibit intermediate and high stability respectively.

This supports the hierarchical timescale theory ($R$4), foundational for modeling adaptive behavior across short-to-long temporal horizons.

Relational Attractors and Trust Basins

State-space analysis identifies high-density attractor basins in relational properties (trust, intimacy), confirming non-uniform distribution and self-organizing macrostructure. Kernel density estimation reveals two dominant relational attractors, consistent with theoretical predictions. Trust trajectories display convergence toward stable basins over interaction progression, substantiating a self-reinforcing feedback loop for trust accumulation and basin formation.

Developmental Phase Transitions

Trajectories of a composite social intelligence index detect critical regions of rapid organizational change, indicative of phase-transition-like behavior in social development. Growth rates increase sharply in these regions, revealing non-linear developmental dynamics. This illustrates that social intelligence emergence is not linear but governed by cumulative, synergistic adaptations.

Emergent Social Intelligence

Social intelligence exhibits progressive increase across interaction progress, with emergent properties arising from coordinated emotional, relational, mnemonic, and personality dynamics. The results empirically validate that social intelligence is a system-level phenomenon generated through persistent coevolution rather than fixed module programming.

Social Cognitive Energy Landscape and Optimization

Social cognitive energy is formalized as $R$5, quantifying organizational instability, uncertainty, and adaptation cost. Reconstructed energy landscapes show non-uniform distributions, with identifiable low-energy regions corresponding to attractors and trust basins.

Critically, energy-intelligence analysis yields a significant negative correlation (r = -0.391, p < 0.001): higher social intelligence states occupy lower-energy regions. Longitudinal trend analysis reports a negative mean energy slope (-0.0684), evidencing persistent energy minimization across interaction trajectories—contradicting conventional notions equating intelligence with increasing energy expenditure. This mechanism underpins attractor-driven self-organization and system efficiency.

Implications and Future Directions

The HACD-H framework offers several implications:

• AI system design: Suggests a paradigm shift from sequence prediction and local optimization to dynamical modeling of emotional adaptation, memory integration, trust formation, and personality consistency for sustained, energy-efficient social interactions.
• Optimization objectives: Proposes social cognitive energy minimization as a candidate loss/objective for next-generation socially adaptive AI, promoting long-term coherence and trust.
• Emergence paradigms: Positions social intelligence as an emergent property, arguing for multi-component adaptive architectures rather than monolithic capability enhancement.
• Intervention and manipulation: Opens avenues for active guidance of attractor and trust basin structures via targeted interventions (e.g., affective prompts, relationship modulation).

Limitations include reliance on a single corpus and computational annotation models, suggesting further multimodal, cross-domain, and community-level analyses. Extension to multi-agent systems and empirical testing of basin interventions remain critical directions.

Conclusion

This paper establishes HACD-H as a formal, empirically grounded theory for modeling and understanding the emergence of social intelligence in human-AI relationships. It provides a principled, unified dynamical perspective integrating emotional adaptation, relational organization, memory accumulation, and personality stability. The empirical results support strong numerical claims—particularly the negative energy-intelligence correlation and progressive trajectory optimization—contradicting traditional modular approaches. HACD-H advances both the theoretical and practical state of knowledge in social AI, offering a blueprint for designing adaptive, persistent agents capable of sustaining coherent and meaningful long-term relationships.

The theoretical framework and dataset are made openly available, facilitating further research and reproducibility in the broader AI and cognitive science communities.