We also provide some examples for the kinds of models you can now build within the HGF framework – from global volatility beliefs, multimodal inference, multisensory cue combination over time, etc etc – check it out! arxiv.org/abs/2305.10937

There’s plenty more in the preprint. For example, we find that the message passing implied by value hierarchies in the HGF is mostly equivalent to what has been proposed for PC, with small, but interesting differences.

Here, we generalise the HGF to encompass *both* value and volatility belief hierarchies, all under the same framework, with one-step belief updates driven by precision-weighted prediction errors, and a modular belief network architecture.