In the theory of active inference, Bayesian belief updates refer to the process by which an agent updates its beliefs about the world based on new sensory information. These updates involve probabilistic computations that allow the agent to infer the most likely state of the world given the available evidence.
Phase transitions in active inference refer to sudden changes in the agent's belief updating strategy that occur when the agent transitions from a regime of low uncertainty to high uncertainty. In this context, uncertainty refers to the agent's uncertainty about the world, which is represented by the agent's beliefs or probability distributions. When the agent is in a regime of low uncertainty, it updates its beliefs in a linear and predictable manner, similar to a first-order phase transition. However, as the agent's uncertainty increases, its belief updating strategy may change abruptly, resulting in a second-order phase transition. At this point, the agent may switch to a different belief updating strategy that is more adaptive to the new level of uncertainty. Phase transitions in active inference are important because they enable the agent to adapt to changing levels of uncertainty in the environment. By adjusting its belief updating strategy, the agent can maintain accurate beliefs about the world even in the face of highly uncertain or rapidly changing information. This allows the agent to make more informed decisions and take more effective actions, improving its overall performance.
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