t3_probe_corewise_derivatives_transpose#

t3toolbox.backend.sampling_derivatives.t3_probe_corewise_derivatives_transpose(ztildes, ww, pp, core_pair, order, sum_over_probes=False, chunk_size=100)#
def t3_probe_corewise_derivatives_transpose(
        ztildes:    typ.Sequence[NDArray],  # residual jets, len=d, elm_shape=(order+1)+W+C+(Ni,)
        ww:         typ.Sequence[NDArray],  # probe vectors X,        len=d, elm_shape=W+(Ni,)
        pp:         typ.Sequence[NDArray],  # perturbation vectors P, len=d, elm_shape=W+(Ni,)
        core_pair:  typ.Tuple[
            typ.Sequence[NDArray],          # tucker_cores, len=d, elm_shape=C+(ni,Ni)
            typ.Sequence[NDArray],          # tt_cores,     len=d, elm_shape=C+(ri,ni,r(i+1))
        ],                                  # = TuckerTensorTrain.data
        order:      int,                    # highest derivative order
        sum_over_probes: bool = False,      # True: sum the sample stack W (the gradient J^T r)
        chunk_size: typ.Optional[int] = 100,   # W-chunk size for the gradient assembly; None -> dense. docs/chunking.md
) -> typ.Tuple[
    typ.Tuple[NDArray, ...],  # tucker-core gradients, same shapes as tucker_cores
    typ.Tuple[NDArray, ...],  # tt-core gradients,     same shapes as tt_cores
]:

Corewise (non-manifold) transpose of t3_probe_derivatives(): gradient of the probe-derivative jets w.r.t. the frame core_pair’s cores, as independent variables (for core-wise optimizers). The Section 6.3 substitution P,Q,O -> G into tv_probe_derivatives_transpose() (frame (U, G, G, G); orthogonality not required). Returns gradients shaped like (tucker_cores, tt_cores). Verified vs jax.grad.

Parameters:

  • ztildes (t3toolbox.backend.common.typ.Sequence[NDArray])

  • ww (t3toolbox.backend.common.typ.Sequence[NDArray])

  • pp (t3toolbox.backend.common.typ.Sequence[NDArray])

  • core_pair (t3toolbox.backend.common.typ.Tuple[t3toolbox.backend.common.typ.Sequence[NDArray], t3toolbox.backend.common.typ.Sequence[NDArray]])

  • order (int)

  • sum_over_probes (bool)

  • chunk_size (t3toolbox.backend.common.typ.Optional[int])

Return type:

t3toolbox.backend.common.typ.Tuple[t3toolbox.backend.common.typ.Tuple[NDArray, Ellipsis], t3toolbox.backend.common.typ.Tuple[NDArray, Ellipsis]]