t3toolbox.backend.probing.compute_tau_tildes

t3toolbox.backend.probing.compute_tau_tildes(deta_tildes: t3toolbox.backend.common.typ.Union[t3toolbox.backend.common.typ.Sequence[t3toolbox.backend.common.NDArray], t3toolbox.backend.common.NDArray], left_tt_cores: t3toolbox.backend.common.typ.Union[t3toolbox.backend.common.typ.Sequence[t3toolbox.backend.common.NDArray], t3toolbox.backend.common.NDArray], xis: t3toolbox.backend.common.typ.Union[t3toolbox.backend.common.typ.Sequence[t3toolbox.backend.common.NDArray], t3toolbox.backend.common.NDArray], mus: t3toolbox.backend.common.typ.Union[t3toolbox.backend.common.typ.Sequence[t3toolbox.backend.common.NDArray], t3toolbox.backend.common.NDArray], left_tt_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]

Adjoint-var-rightward edge variables tau_tilde. Used for computing transpose of mapping from a Tucker tensor train tangent vector to its actions.

See Section 5.2.4, particularly Formula (44), 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