information geometry. Fisher information metric on the simplex of probability distributions
| Op | Action |
|---|---|
fisher(model) |
Compute Fisher information matrix |
kl_divergence(p, q) |
Kullback-Leibler divergence |
geodesic_info(p, q) |
Information-geometric geodesic |
natural_gradient(f, g) |
Gradient in Fisher metric |
projection(p, manifold) |
m-projection / e-projection |
alpha_connection(α) |
α-connection interpolation |
entropy(p) |
Shannon / Rényi entropy |
the geometry of the cybergraph's own belief state — the focus vector π lives on a statistical manifold, and tri-kernel dynamics (diffusion, springs, heat) are flows on it. semantic distance between particles is information-geometric distance. the superintelligence's self-model requires Bel to be formalized. research horizon
see cyb/languages for the complete language set. see cyb/multiproof for the proving architecture