Chapter 2: The Low Road to Active Inference

authors: year: 2022 See in Zotero

Literature Notes

The brain is constantly using statistical inference to understand the world/ environment. It creates a probabilistic model of the world based on the data that it can perceive.

The world is too complex to understand in its entirety. So the brain simplifies with a probabilistic model. This model (the perceptions the brain receives/ uses for inference) depends both on the environment and parameters set inside the brain. The brain then can use actions which affect the environment.

The brain’s goal is to minimize the surprise (both surprise (statistical) and Bayesian surprise). This can be done mathematically by minimizing variational free energy. In cases where survival depends on staying in certain states (like temperature) then there is a lot of certainty (a high probability in the prior) for these states. Thus, to change out of the state would represent a lot of variational free energy.

There are two different ways the brain can try to minimize variational free energy ($F[Q(x),y]$). It can change the mental model $Q(x)$ (through Bayesian updating) to be better at predicting the world - perception. Or it can change its choice of data sampled - action.

The brain must also plan for future action. This is done using the current mental model $Q(x)$. Using this mental model about how the world (and how your actions can affect the world), the brain can calculate probabilities of how sequences of actions $\pi$ will change the (hidden) states of the world $P(\underline{\tilde{x}}|\pi )$.

Then the brain can use the model for how outcomes or perceptions are generated by the hidden states $P(\tilde{y}|\tilde{x})$ to decide how likely the desired outcome is. This can be done mathematically by minimizing expected free energy.

Note on existence of $P(x,y)$

The generative model $P(x,y)$ is given though the states are those used by the organism. There might be another ‘objective/ real’ generative function for the entire environment with states the organism isn’t incorporating, but in some sense it doesn’t matter since the organism isn’t using them in its inference. No inference or action comes from states outside the organism’s state space. You can think of an organism as coming with the model (though parameters can be learned). In active inference, the posterior $P(x|y)$ is approximated and replaced by $Q(x)$, and the variational free energy $F[Q,y]$ stands in for $-\log P(y)$.

@parr2022 - entire book