What the flock knows that the birds do not: exploring the emergence of joint agency in multi-agent active inference

TL;DR

Problem: how joint agency and implicit collective knowledge arise in systems of simple active inference agents. Approach: simulate 100 agents each minimizing local variational free energy, nest Markov blankets to form a flock as a higher-level autonomous agent, perturb the population with predators to probe sensing and response, and quantify information sharing with partial information decomposition (PID) to reveal synergy. Key contributions: formal demonstration that a flock can act as an emergent agent with its own state-boundaries, faster collective responses under perturbation, and explicit evidence of collective knowledge via significant synergistic information about predator location that exceeds individual capabilities. Significance: provides a principled framework linking dynamical self-organization and information-theoretic measures to understand and engineer collective cognition in biological and artificial multi-agent systems.

Abstract

Collective behavior pervades biological systems, from flocks of birds to neural assemblies and human societies. Yet, how such collectives acquire functional properties -- such as joint agency or knowledge -- that transcend those of their individual components remains an open question. Here, we combine active inference and information-theoretic analyses to explore how a minimal system of interacting agents can give rise to joint agency and collective knowledge. We model flocking dynamics using multiple active inference agents, each minimizing its own free energy while coupling reciprocally with its neighbors. We show that as agents self-organize, their interactions define higher-order statistical boundaries (Markov blankets) enclosing a ``flock'' that can be treated as an emergent agent with its own sensory, active, and internal states. When exposed to external perturbations (a ``predator''), the flock exhibits faster, coordinated responses than individual agents, reflecting collective sensitivity to environmental change. Crucially, analyses of synergistic information reveal that the flock encodes information about the predator's location that is not accessible to every individual bird, demonstrating implicit collective knowledge. Together, these results show how informational coupling among active inference agents can generate new levels of autonomy and inference, providing a framework for understanding the emergence of (implicit) collective knowledge and joint agency.

Figures (3)

• Figure 1: Formalizing individual and joint agency in flocking behavior through Markov blankets (a) Example simulation of flocking behavior among 100 birds over 8 time steps, showing the gradual alignment of headings. (b) Markov blankets, individual and joint agency. Schematic representation of an individual agent, whose internal states are separated from the external environment by a Markov blanket (dashed line). The blanket mediates the exchange of information through sensory $s$ and active $a$ states, defining the agent’s boundary for perception and action. (c) Illustration of a group of interacting agents whose collective dynamics are enclosed within a higher-level Markov blanket (dashed line). Through reciprocal coupling and shared information flow, the ensemble functions as a single, higher-order agent ('flock'), exemplifying the emergence of joint or shared agency from multiple interacting components. (d) The emergent Markov blanket around the flock during time steps 1--6 of the simulation in (a). Colors illustrate the statistical roles of individual birds relative to the flock Markov Blanket: internal (blue), active (red), and sensory (magenta). External states are depicted as cyan birds.
• Figure 2: Sensing and escaping predators in the flock. (a) Example of four configurations from a single simulation run. A predator (indicated by a white bird) arrives at time steps $t=5$ and $t=35$, at two distinct, random locations. Configurations are also shown 5 steps following each arrival ($t=10$ and $t=40$). White birds are shown in the plots for illustrative purposes only; they are not part of the simulation except at time steps $t=5$ and $t=35$. (b) System energy, representing the global degree of alignment among agents. The dashed lines show the arrival times of the first (red) and second (blue) predators. The gray band indicates the interquartile range across all simulations. (c) Agents' average stress state over time. The dashed lines show the arrival times of the first (red) and second (blue) predators. The gray band indicates the interquartile range across all simulations. See the main text for further explanation.
• Figure 3: Synergistic information about predator location in the flock. (a) Partial Information Decomposition (PID) of the mutual information between two source variables (agent states, $X_1$ and $X_2$, black birds) and a target variable (predator position, in one of four $5 \times 5$ quadrants, $Y$, white bird). The blue and red ellipses delineate the contribution of $X_1$ and $X_2$, respectively, while the green circle shows the combined contribution. The total information is partitioned into the four unique atoms: redundancy (the purple overlap) represents information available from both sources, synergy represents information available only when both sources are considered together (outside the ellipses), and unique information represents information available from only one source. (b) Temporal dynamics of the four PID atoms: unique information from the first (top left) and second (top right) agent in each pair, redundancy (bottom left), and synergy (bottom right). Each atom is averaged over 1000 simulations and all 4950 pairs of agents. The red curve shows the case where the target is the position of the first predator, and the blue curve shows the case where the target is the position of the second predator. Vertical dashed lines indicate the arrival times of the predators. The gray band represents the 5th to 95th percentile of the null distribution, obtained by 500 random permutations of the target variable. (c) Temporal dynamics of the synergy as a function of the spatial distance between agent pairs. Each panel shows the dynamics, mediated across the same 1000 simulations, calculated only for agent pairs separated by a specific Chebyshev distance $D = 1, 3, 5, 7$ (from left to right). The figure conventions (red/blue curves for predator targets, vertical dashed lines for arrival times, and gray band for the null distribution derived from target permutations) are identical to those in (b).