# Copyright 2026 Daniil Shmelev
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
# http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
# =========================================================================
from typing import Union
import numpy as np
import torch
from .param_checks import check_type, check_non_neg, check_n_jobs
from .error_codes import err_msg
from .dtypes import CPSIG_SIG_JOIN_BACKPROP, CUSIG_SIG_JOIN_BACKPROP_CUDA
from .sig_length import sig_length, _infer_scalar_term
from .data_handlers import SigInputHandler, SigOutputHandler
[docs]
def sig_join_backprop(
d_out : Union[np.ndarray, torch.tensor],
sig : Union[np.ndarray, torch.tensor],
displacement : Union[np.ndarray, torch.tensor],
dimension : int,
degree : int,
*,
prepend : bool = False,
n_jobs : int = 1
):
"""
This function is required to backpropagate through ``pysiglib.sig_join``.
Given the derivatives of a scalar function :math:`F` with respect to the
result of ``pysiglib.sig_join``, :math:`\\partial F / \\partial S(x * v)`,
returns the derivatives of :math:`F` with respect to the original signature
and the displacement vector,
:math:`\\partial F / \\partial S(x)` and :math:`\\partial F / \\partial v`.
:param d_out: Derivative with respect to the output of sig_join,
:math:`\\partial F / \\partial S(x * v)`
:type d_out: numpy.ndarray | torch.tensor
:param sig: The original truncated signature, :math:`S(x)`
:type sig: numpy.ndarray | torch.tensor
:param displacement: The displacement vector, :math:`v`
:type displacement: numpy.ndarray | torch.tensor
:param dimension: Dimension of the underlying space, :math:`d`.
:type dimension: int
:param degree: Truncation level of the signatures, :math:`N`
:type degree: int
:param prepend: Must match the value used in the forward ``sig_join`` call. If True, the linear
segment was prepended to the front of the path rather than appended. Default is False.
:type prepend: bool
:param n_jobs: 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.
:type n_jobs: int
:return: Derivatives with respect to ``sig`` and ``displacement``
:rtype: Tuple[numpy.ndarray | torch.tensor, numpy.ndarray | torch.tensor]
Example:
---------
.. code-block:: python
import numpy as np
import pysiglib
dimension, degree = 5, 3
path = np.random.uniform(size=(100, dimension))
sig = pysiglib.sig(path, degree)
displacement = np.random.uniform(size=(dimension,))
extended = pysiglib.sig_join(sig, displacement, dimension, degree)
d_out = np.ones_like(extended)
d_sig, d_displacement = pysiglib.sig_join_backprop(
d_out, sig, displacement, dimension, degree
)
print(d_sig.shape, d_displacement.shape)
"""
check_type(dimension, "dimension", int)
check_non_neg(dimension, "dimension")
check_type(degree, "degree", int)
check_non_neg(degree, "degree")
check_n_jobs(n_jobs)
scalar_term = _infer_scalar_term(sig, dimension, degree)
sig_len = sig_length(dimension, degree, scalar_term=scalar_term)
d_out_data = SigInputHandler(d_out, sig_len, "d_out")
sig_data = SigInputHandler(sig, sig_len, "sig")
disp_data = SigInputHandler(displacement, dimension, "displacement")
if d_out_data.type_ != sig_data.type_ or sig_data.type_ != disp_data.type_:
raise ValueError("d_out, sig and displacement must all be numpy arrays or all torch tensors")
if d_out_data.dtype != sig_data.dtype or sig_data.dtype != disp_data.dtype:
raise ValueError("d_out, sig and displacement must have the same dtype")
if not (d_out_data.batch_shape == sig_data.batch_shape == disp_data.batch_shape):
raise ValueError("d_out, sig and displacement must have the same batch shape")
if d_out_data.device != sig_data.device or sig_data.device != disp_data.device:
raise ValueError("d_out, sig and displacement must be on the same device")
d_sig = SigOutputHandler(d_out_data, sig_len)
d_disp = SigOutputHandler(d_out_data, dimension)
if d_out_data.batch_size == 0:
return d_sig.data, d_disp.data
if d_out_data.device == "cpu":
err_code = CPSIG_SIG_JOIN_BACKPROP[d_out_data.dtype](
d_out_data.data_ptr, d_sig.data_ptr, d_disp.data_ptr,
sig_data.data_ptr, disp_data.data_ptr,
d_out_data.batch_size, dimension, degree, prepend, scalar_term, n_jobs)
else:
err_code = CUSIG_SIG_JOIN_BACKPROP_CUDA[d_out_data.dtype](
d_out_data.data_ptr, d_sig.data_ptr, d_disp.data_ptr,
sig_data.data_ptr, disp_data.data_ptr,
d_out_data.batch_size, dimension, degree, prepend, scalar_term)
if err_code:
raise Exception("Error in pysiglib.sig_join_backprop: " + err_msg(err_code))
return d_sig.data, d_disp.data
