compute_manifold_dim#

t3toolbox.backend.ranks.compute_manifold_dim(shape, tucker_ranks, tt_ranks, sharing=None)#
def compute_manifold_dim(
        shape:          typ.Sequence[int],  # (N0, ..., N(d-1))
        tucker_ranks:   typ.Sequence[int],  # (n0, ..., n(d-1))
        tt_ranks:       typ.Sequence[int],  # (r0, ..., rd)

        sharing:        typ.Optional[typ.Sequence] = None,  # len=d, static; one hashable group label per mode (None = unshared)
) -> int:

Dimension of the fixed-rank Tucker tensor train manifold for the given structure.

Computed from the structurally-minimal ranks (gauge already quotiented). Because the reduction to minimal ranks happens here, this is the true tangent-space dimension for any structure of the given ranks, minimal or not: a rank the rest of the network cannot support adds no tangent directions, and passing the non-reduced ranks gives the same answer as passing the reduced ones.

With sharing, the dimension of the shared-factor manifold (Tucker factors tied within each group): the reduction to minimal ranks is the SHARED one (compute_minimal_ranks() with sharing – the unshared reduction can clip a group rank the group ceiling admits, and the formula applied to the clipped ranks miscounts), the TT-core term is unchanged (TT cores are never tied), and there is one Stiefel term n_g*(N_g - n_g) per GROUP instead of per mode. Cf. Molozhavenko & Rakhuba (2026), Thm. 5, which proves a single trailing block (and over-subtracts by one: the boundary bond r_d = 1 carries no gauge); arbitrary partitions are our extension, validated empirically against dense tied-tangent ranks.

Parameters:

  • shape (t3toolbox.backend.common.typ.Sequence[int])

  • tucker_ranks (t3toolbox.backend.common.typ.Sequence[int])

  • tt_ranks (t3toolbox.backend.common.typ.Sequence[int])

  • sharing (t3toolbox.backend.common.typ.Optional[t3toolbox.backend.common.typ.Sequence])

Return type:

int