Crate infogeom 

infogeom: information geometry on the probability simplex.

Provides geodesic interpolation, natural gradient, and Fisher information for categorical distributions. Builds on logp for divergence primitives.

Geodesics

Three geodesic families on the simplex, corresponding to the alpha-connection framework of Amari & Nagaoka (2000, Ch. 3):

• fisher_rao_geodesic: the unique Riemannian (alpha=0) geodesic via the sphere embedding
• m_geodesic: the mixture (alpha=-1) geodesic – linear interpolation in probability space
• e_geodesic: the exponential (alpha=+1) geodesic – linear interpolation in log space

Distances

• rao_distance_categorical: Fisher-Rao distance (radians) via the Bhattacharyya coefficient
• Hellinger distance: re-exported from logp as hellinger

Fisher information

• fisher_information_diagonal: diagonal of the Fisher information matrix for categoricals
• natural_gradient: multiply Euclidean gradient by the inverse Fisher metric

Fisher-orthogonal projection

• fisher_orthogonal_project: project gradient onto Fisher-orthogonal complement of past task gradients (diagonal Fisher approximation)
• fisher_orthogonal_project_full: same, with full Fisher matrix

Quick example

use infogeom::{fisher_rao_geodesic, rao_distance_categorical};

let p = [0.7, 0.2, 0.1];
let q = [0.1, 0.2, 0.7];

let mid = fisher_rao_geodesic(&p, &q, 0.5, 1e-12).unwrap();
let d_full = rao_distance_categorical(&p, &q, 1e-12).unwrap();
let d_half = rao_distance_categorical(&p, &mid, 1e-12).unwrap();

// Midpoint is equidistant from both endpoints.
assert!((d_half - d_full / 2.0).abs() < 1e-10);

Built on

• logp: provides the underlying divergences (KL, Hellinger) that infogeom’s geodesics are built from.

Enums

Error

Errors produced by infogeom operations.

Functions

alpha_geodesic

Alpha-geodesic on the simplex (Amari alpha-connection), unifying the mixture, exponential, and Fisher-Rao families in one parametric surface.

e_geodesic

Exponential geodesic (alpha = +1): linear interpolation in log space.

fisher_information_diagonal

Fisher information matrix diagonal for a categorical distribution.

fisher_orthogonal_project

Project a gradient onto the Fisher-orthogonal complement of past gradients, using a diagonal Fisher approximation.

fisher_orthogonal_project_full

Project a gradient onto the Fisher-orthogonal complement of past gradients, using a full Fisher information matrix.

fisher_rao_geodesic

Fisher-Rao geodesic (slerp on the simplex via the sphere embedding).

hellinger

Re-export Hellinger distance from logp. Hellinger distance: the square root of the squared Hellinger distance.

m_geodesic

Mixture geodesic (alpha = -1): linear interpolation in probability space.

natural_gradient

Natural gradient on the categorical manifold.

rao_distance_categorical

Fisher-Rao (Rao) distance between categorical distributions p and q (in radians).

Type Aliases

Result

Crate-level result type.