t3toolbox.backend.probing.compute_dxis

t3toolbox.backend.probing.compute_dxis(var_tucker_cores: t3toolbox.backend.common.typ.Union[t3toolbox.backend.common.typ.Sequence[t3toolbox.backend.common.NDArray], t3toolbox.backend.common.NDArray], ww: t3toolbox.backend.common.typ.Union[t3toolbox.backend.common.typ.Sequence[t3toolbox.backend.common.NDArray], t3toolbox.backend.common.NDArray], outer_tucker_weights: t3toolbox.backend.common.typ.Union[t3toolbox.backend.common.typ.Sequence[t3toolbox.backend.common.NDArray], t3toolbox.backend.common.NDArray] = None, use_jax: bool = False) → t3toolbox.backend.common.typ.Union[t3toolbox.backend.common.typ.Sequence[t3toolbox.backend.common.NDArray], t3toolbox.backend.common.NDArray]

Compute var-upward edge variables dxi. Used for probing a tangent vector.

Same as t3_compute_dxis(), except with var_tucker_cores in place of tucker_cores.

See Section 5.2.3, particularly Formula (34), in:

Alger, N., Christierson, B., Chen, P., & Ghattas, O. (2026). “Tucker Tensor Train Taylor Series.” arXiv preprint arXiv:2603.21141. https://arxiv.org/abs/2603.21141

See also

compute_xis, compute_sigmas, compute_taus, compute_detas, assemble_tangent_probes, probe_tangent