Synchronizing Minds through Collective Predictive Coding: A Computational Model of Parent-Infant Homeostatic Co-Regulation

Technical Summary: Synchronizing Minds through Collective Predictive Coding

Problem Statement
Inter-brain synchrony (IBS) observed in real-time dyadic interactions, such as parent–infant exchanges, suggests that interacting agents develop aligned latent representations. However, computational accounts explaining how such alignment emerges between agents with only local sensory access and asymmetric internal knowledge remain underdeveloped. A central challenge is modeling how two agents, each possessing private internal states and limited sensory data, can coordinate to regulate bodily states while simultaneously aligning their latent representations without requiring direct access to each other's hidden states or maintaining deeply recursive models of the other.

Methodology
The authors propose a constructive computational model of parent–infant homeostatic co-regulation that integrates two primary frameworks:

1. Active Interoceptive Inference (POMDP): The interaction is modeled as a Partially Observable Markov Decision Process (POMDP). Two agents, a parent (Agent A) and an infant (Agent B), possess asymmetric generative-model knowledge:
   • The Parent possesses an accurate state-transition matrix ($B_A$) encoding how actions transform visceral states but must learn the sensory-generation matrix ($A_A$) linking its inference of the infant's state to observed exteroceptive cues (e.g., shivering).
   • The Infant possesses an accurate sensory-generation matrix ($A_B$) for direct interoceptive perception of its own state but must learn the state-transition matrix ($B_B$) capturing how actions affect its body.
   • Both agents process locally available sensory inputs and learn their respective unknown matrices online via Dirichlet distributions.
2. Collective Predictive Coding (CPC) via MHNG: To mediate agreement on regulatory actions, the agents utilize the Metropolis–Hastings Naming Game (MHNG). A shared communicative variable (symbol $w$) is sampled based on the agents' internal representations ($z$). The acceptance of a proposed symbol is determined by a locally computable Metropolis–Hastings probability, which depends only on the listener's internal generative model. This allows the agents to constrain each other's posterior beliefs without direct access to the partner's hidden states.

The simulation takes place in a $6 \times 6$ discrete grid world representing the infant's visceral state (energy and body temperature). The agents aim to maintain the state in a region of high prior preference ($C$) through cooperative actions (Cool, Warm, Eat, Play, Sleep).

Experimental Setup and Metrics
The study compares three conditions:

• MHNG: Symbols emerge through bidirectional parent–infant communication using the MHNG protocol.
• A-only: The infant always accepts the parent's proposal; the parent always rejects the infant's.
• B-only: The parent always accepts the infant's proposal; the infant always rejects the parent's.

Key metrics include:

• Adaptiveness ($C_{norm}$): The degree to which the infant's visceral state aligns with the high-prior preference region.
• Average Entropy ($\bar{H}$): The entropy of the learned generative matrices ($A$ for the parent, $B$ for the infant), indicating predictive accuracy.
• Mental Representation Similarity ($JSD_z$): The Jensen–Shannon distance between the posterior distributions of the parent's and infant's latent states ($q(z_A)$ and $q(z_B)$).

Key Results

1. Regulatory Performance: The MHNG-mediated interaction regulated the infant's visceral state more adaptively than the one-sided control conditions (A-only and B-only). The visceral state in the MHNG condition remained in the high prior preference region from the early phase of learning.
2. Rapid Latent-State Alignment: The Jensen–Shannon distance ($JSD_z$) between the agents' posteriors approached zero after approximately 20 iterations, indicating rapid synchronization of internal representations.
3. Decoupling of Alignment and Model Convergence: The convergence of the generative matrices (indicated by decreasing entropy $\bar{H}$) occurred much later, saturating around 500 iterations. Crucially, representational synchrony emerged far earlier than the convergence of the learned world models.
4. Mechanism of Asymmetry: The rapid alignment is attributed to the complementary nature of the agents' knowledge: the infant grasps its visceral state via accurate bottom-up sensory generation ($A_B$), while the parent grasps the state via accurate top-down state transitions ($B_A$).

Significance and Claims
The paper claims to offer a "minimal constructive account" of latent-state alignment that is compatible with IBS reported in hyperscanning studies. The primary contribution is demonstrating that representational synchrony does not presuppose fully shared world models. Instead, agents with asymmetric knowledge and local sensory access can achieve rapid alignment of their latent beliefs through a shared communicative variable governed by locally computable acceptance probabilities.

The authors position the Collective Predictive Coding (CPC) hypothesis, operationalized through MHNG, as a candidate computational basis for inter-brain alignment. They argue that this framework explains how social interaction can constrain posterior beliefs and facilitate co-regulation without requiring agents to directly access each other's observations or maintain complex recursive models of the other.

Limitations and Future Directions
The authors acknowledge that the current model uses a simplified, two-dimensional discrete grid world and assumes that prior preferences ($C$) and interpretation matrices ($E$) are shared and static. Consequently, the model does not address the dynamics of symbol emergence itself. Future work is proposed to align the model with real organisms or robots using continuous, multi-dimensional representations and to introduce learning rules for $C$ and $E$ matrices to model the emergence of social meaning.