Hierarchical Gaussian Filter

The HGF is a Bayesian model in which agents invert a generative model whose hidden states evolve as coupled random walks. Approximate HGF inversion yields closed-form one-step updates for posterior means and precisions. The HGF formulation reaches an analytic stationary point in one forward-backward sweep without iterating to equilibrium. The paper expresses deep predictive coding networks as generalised HGFs to restore precision-weighted message passing and replace iterative inference.