pysiglib.branched_sig_to_log_sig_backprop

pysiglib.branched_sig_to_log_sig_backprop#

branched_sig_to_log_sig_backprop(bsig, blogsig_derivs, dimension, degree, *, time_aug=False, lead_lag=False, planar=False, n_jobs=1)[source]#

Backpropagates through the pysiglib.branched_sig_to_log_sig function. Given the derivatives of a scalar function \(F\) with respect to the branched log signature, returns the derivatives of \(F\) with respect to the branched signature.

Parameters:

  • bsig (numpy.ndarray | torch.tensor) – The branched signature or batch of branched signatures used in the forward pass, given as a numpy.ndarray or torch.tensor. For a single branched signature, this must be of shape branched_sig_length. For a batch of paths, this must be of shape (batch_size, branched_sig_length). The leading scalar term may be present or omitted.

  • blogsig_derivs (numpy.ndarray | torch.tensor) – Derivatives of the scalar function \(F\) with respect to the branched log signature(s). This must be an array of the same shape as the branched log signature(s).

  • dimension (int) – Dimension of the underlying path(s).

  • degree (int) – Truncation degree of the branched signature(s).

  • time_aug (bool) – Whether the branched signature(s) were computed with time_aug=True.

  • lead_lag (bool) – Whether the branched signature(s) were computed with lead_lag=True.

  • planar (bool) – If True, use planar branched signatures.

  • n_jobs (int) – Number of threads to run in parallel. If n_jobs = 1, the computation is run serially. If set to -1, all available threads are used. For n_jobs below -1, (max_threads + 1 + n_jobs) threads are used. For example if n_jobs = -2, all threads but one are used.

Returns:

Derivatives of the scalar function \(F\) with respect to the branched signature(s). This is an array of the same shape as bsig.

Return type:

numpy.ndarray | torch.tensor

Example:#

import torch
import pysiglib

path = torch.rand((10, 100, 5))
bsig = pysiglib.branched_sig(path, 3)
blogsig = pysiglib.branched_sig_to_log_sig(bsig, 5, 3)
blogsig_derivs = torch.ones_like(blogsig)
bsig_derivs = pysiglib.branched_sig_to_log_sig_backprop(
    bsig, blogsig_derivs, 5, 3,
)
print(bsig_derivs)

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}
}
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