Belief sharing: a blessing or a curse

TL;DR

The paper analyzes belief-sharing in multi-agent active inference and shows that naive sharing of posterior beliefs can induce echo chambers and self-doubt, degrading collaborative performance. It formalizes the belief-sharing mechanism, identifies double-counting of priors when communicating posteriors, and proposes likelihood-sharing where others' observations contribute as independent evidence via $\mu^2_{\uparrow A_3} = \mu^{2,other}_{\uparrow A_2}$. Through graph-based object-finding simulations, the authors demonstrate that likelihood-sharing mitigates the pathologies while maintaining competitive task success. These findings offer a practical design principle for robust, cooperative communication in multi-agent systems operating under active inference, with future work exploring adversarial settings and broader environments.

Abstract

When collaborating with multiple parties, communicating relevant information is of utmost importance to efficiently completing the tasks at hand. Under active inference, communication can be cast as sharing beliefs between free-energy minimizing agents, where one agent's beliefs get transformed into an observation modality for the other. However, the best approach for transforming beliefs into observations remains an open question. In this paper, we demonstrate that naively sharing posterior beliefs can give rise to the negative social dynamics of echo chambers and self-doubt. We propose an alternate belief sharing strategy which mitigates these issues.

Figures (7)

• Figure 1: Two active inference agents sharing beliefs. The generative model of each agent is a POMDP, where observations are generated from a hidden state $s_t$. Actions $a_t$, generated from a policy $\pi$, transition this state. In addition to the typical observation $o_t$ at each timestep $t$, each agent also receives a shared observation $o^{s}_t$ that is generated from the other agent's internal beliefs $s'_t$. Blue variables are observed from the perspective of the focal agent, i.e. they observe their own actions, observations and the observations shared with the other agent.
• Figure 2: Illustration of the graph environment and the agent's factor graph. (a) agents are located on a connected graph of locations and need to find a rewarding object that might be present at one of the locations. (b) a factor graph representation of the agent's generative model. Two latent state factors that model the agent's location and the object's location respectively, give rise to two sensory modalities through a likelihood factor: the agent's location ($A_1$) and whether the object is visible ($A_2$). In addition, agents can share beliefs about the object location through belief sharing ($A_3$). The agent's location can change conditioned on move actions ($B_1$), whereas the object is kept static in our experiments ($B_2 = I$).
• Figure 3: Simulation of an echo-chamber. We initialize both agents with a small prior belief that the object will be present at location 11 or 13. Then, we let the agents share their beliefs. Note that this reinforces the belief that the object will be at either one of the locations. The next columns show the evolution of both agents where they keep observing the environment. We see that in the transition from time 1 to time 2 the agents increase the belief that the object is at the a priori believed location even though there is no new evidence to support this belief. Agent location is depicted using the blue dots in both panels.
• Figure 4: Simulation of self-doubt for 4 agents. Again, each panel displays the evolution of the posterior belief as a function of time, where darker colors indicates a higher degree of belief. Blue dots indicate the agent location. All agents are initialized with a strong prior belief that the object will be at location 1, as indicated by the dark shaded area. This reflects a potential situation where all agents have been acting in the environment for a long time, accruing faulty evidence. In this case the communication mechanism prohibits the agents from discovering that the object is not there, even after observing its absence multiple times.
• Figure 5: Illustration of the lack of echo-chamber like behaviour when sharing likelihoods. In this figure, the situation leading to an echo chamber is recreated. Both agents are initialized with the same prior belief that the object is most likely at locations 11 and 13; however, because of the sharing of likelihoods, they do not get stuck in an echo chamber and do not increase the beliefs when there is no new evidence.