ut3_kronecker_weights#

t3toolbox.backend.ut3_operations.ut3_kronecker_weights(weights_A, weights_B)#
def ut3_kronecker_weights(
        weights_A: UT3WeightsData,  # (tucker_weight_supercore, tt_weight_supercore, masks)
        weights_B: UT3WeightsData,  # (tucker_weight_supercore, tt_weight_supercore, masks)
) -> UT3WeightsData:                # per-edge Kronecker: padded widths MULTIPLY, masks Kronecker

Per-edge Kronecker product of two uniform weights – the Hadamard (⊙) combine, where ranks multiply. Uniform twin of t3_kronecker_weights.

Kronecker the weights, Kronecker the masks – that is the whole operation. Treat the mask as just another weight that happens to hold 0s and 1s: what we need is weight_AB * mask_AB == kron(weight_A * mask_A, weight_B * mask_B), and it is satisfied by weight_AB = kron(weight_A, weight_B) and mask_AB = kron(mask_A, mask_B), because elementwise multiply commutes with the Kronecker product: kron(a∘p, b∘q) = kron(a,b) ∘ kron(p,q) (the mixed-product property, for any vectors – nothing here is special to booleans). So there is no mask cleverness: the same kron_last runs on both operands.

Each edge is a last-axis outer product, then reshape: (wA ⊗ wB)[..., a*nB + b] = wA[..., a] · wB[..., b] – A-major, over the PADDED widths, with the shared (d,)+stack prefix broadcast. This is the one real trap: not np.kron, which would Kronecker the mode/stack axes too (the ragged build hit exactly that). A-major must also agree with whatever core-combine pairs with it.

The resulting mask is not an interval – the real set is {a*nB + b : mask_A[a] and mask_B[b]}, strided over the padded width nB, so even two prefix inputs give holes ({0,1} of 3 times {0} of 2 gives {0, 2}; docs/uniform_masks_vs_ranks.md). That is a description of the output, not a difficulty: it costs nothing here, and only obliges consumers to read the mask rather than slice a prefix. It cannot be flattened to a prefix of rank rA*rB: slot a*nB + b with b >= rank_B holds wA[a] * <padding>, so a prefix mask would claim padding as real data (phantom rank).

Note there is currently no uniform Hadamard (ut3_add exists; ut3_mult does not), so this op ships verified against the ragged oracle but without a uniform core-combine partner – see docs/contributor/weighted_internals.md §3.

Parameters:

  • weights_A (UT3WeightsData)

  • weights_B (UT3WeightsData)

Return type:

UT3WeightsData