pysiglib.sig_backprop

Added in version v0.2.

sig_backprop(path, sig, sig_derivs, degree, time_aug=False, lead_lag=False, end_time=1.0, n_jobs=1)

This function is required to backpropagate through the signature computation. Given the derivatives of a scalar function \(F\) with respect to the signature, \(\partial F / \partial S(x)\), returns the derivatives of \(F\) with respect to the underlying path, \(\partial F / \partial x\).

Parameters:

• path (numpy.ndarray | torch.tensor) – The underlying path or batch of paths, given as a numpy.ndarray or torch.tensor. For a single path, this must be of shape (length, dimension). For a batch of paths, this must be of shape (batch_size, length, dimension).

• sig (numpy.ndarray | torch.tensor) – Signature(s) of the path or batch of paths.

• sig_derivs (numpy.ndarray | torch.tensor) – Derivatives of the scalar function \(F\) with respect to the signature(s), \(\partial F / \partial S(x)\). This must be an array of the same shape as the provided signature(s).

• degree (int) – The truncation level of the signature, \(N\).

• time_aug (bool) – If set to True, will compute the signature of the time-augmented path, \(\hat{x}_t := (t, x_t)\), defined as the original path with an extra channel set to time, \(t\). This channel spans \([0, t_L]\), where \(t_L\) is given by the parameter end_time.

• lead_lag (bool) – If set to True, will compute the signature of the path after applying the lead-lag transformation.

• end_time (float) – End time for time-augmentation, \(t_L\).

Returns:

Derivatives of the scalar function \(F\) with respect to the path(s), \(\partial F / \partial x\). This is an array of the same shape as the provided path(s).

Return type:

numpy.ndarray | torch.tensor

Note

Ideally, any array passed to pysiglib.sig_backprop should be both contiguous and own its data. If this is not the case, pysiglib.sig_backprop will internally create a contiguous copy, which may be inefficient.

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}
}