pysiglib.log_sig_combine_backprop

pysiglib.log_sig_combine_backprop#

Warning

Where possible, pysiglib.torch_api should be used rather than explicitly calling backpropagation functions. Explicit backpropagation can introduce subtle errors if called incorrectly. In addition, some pysiglib functions can only be backpropagated through using their pysiglib.torch_api variants and do not expose explicit backpropagation functions.

log_sig_combine_backprop(deriv, ls1, ls2, dimension, degree, *, time_aug=False, lead_lag=False, n_jobs=1)[source]#

Backpropagation through log_sig_combine(). Given derivatives of a scalar function \(F\) with respect to the output of log_sig_combine, computes the derivatives with respect to the two input log-signatures.

Parameters:

  • deriv (numpy.ndarray | torch.tensor) – Derivative with respect to the combined log-signature

  • ls1 (numpy.ndarray | torch.tensor) – The first truncated log-signature (Lyndon basis, method=2 or method=3)

  • ls2 (numpy.ndarray | torch.tensor) – The second truncated log-signature (Lyndon basis, method=2 or method=3)

  • dimension (int) – Dimension of the underlying space

  • degree (int) – Truncation level of the log-signatures

  • time_aug (bool) – Whether time augmentation was applied

  • lead_lag (bool) – Whether the lead-lag transformation was applied

  • n_jobs (int) – Number of threads (CPU only)

Returns:

Derivatives with respect to ls1 and ls2

Return type:

Tuple[numpy.ndarray | torch.tensor, numpy.ndarray | torch.tensor]


Citation#

If you found this library useful in your research, please consider citing the paper:

@article{shmelev2025pysiglib,
  title={pySigLib-Fast Signature-Based Computations on CPU and GPU},
  author={Shmelev, Daniil and Salvi, Cristopher},
  journal={arXiv preprint arXiv:2509.10613},
  year={2025}
}
Contents