manifold#

The tangent bundle and geometries: T3Tangent, MANIFOLD (Hilbert-Schmidt), COREWISE.

T3Tangent bundles (T3Frame, T3Variations). The metric lives on the geometry, not the tangent: MANIFOLD.inner/norm is the Hilbert-Schmidt metric (safe mode checks same-frame + orthogonal + gauged); COREWISE.inner/norm is the Euclidean coordinate metric (same-frame only). The frame flows as a jax pytree leaf – the same-frame guard is numerical (safety.frames_equal), so jit does not recompile per frame.

Attributes#

MANIFOLD

COREWISE

Classes#

T3Tangent

Tangent vector to the manifold of fixed-rank Tucker tensor trains.

ManifoldGeometry

The Riemannian geometry of the fixed-rank Tucker tensor train manifold M.

CorewiseGeometry

The Euclidean geometry of the core parameter space P (the over-parametrized cover of M).

Functions#

manifold_dim(s)

Get the dimension of the fixed rank T3 manifold with a given structure.

Module Contents#

MANIFOLD#
COREWISE#