Sig kernel functions

Sig kernel functions#

sig_kernel_cuda#

int sig_kernel_cuda_f(const float *gram, float *out, uint64_t batch_size, uint64_t dimension, uint64_t length1, uint64_t length2, uint64_t dyadic_order_1, uint64_t dyadic_order_2, bool return_grid = false) noexcept#

Computes signature kernels of a batch of paths from their gram matrices.

Parameters:

  • gram – Pointer to batch gram matrix data (row-major), size = batch_size * (length1 - 1) * (length2 - 1).

  • out – Pointer to output buffer (row-major, preallocated), size = batch_size * (return_grid ? (((length1 - 1) << dyadic_order_1) + 1) * (((length2 - 1) << dyadic_order_2) + 1) : 1).

  • batch_size – Batch size of the paths.

  • dimension – Dimension of the path.

  • length1 – Length of the first path.

  • length2 – Length of the second path.

  • dyadic_order_1 – Dyadic refinement for the first path.

  • dyadic_order_2 – Dyadic refinement for the second path.

  • return_grid – Whether to return the entire PDE grid (default = false).

Returns:

Status code (0 = success).

int sig_kernel_cuda_d(const double *gram, double *out, uint64_t batch_size, uint64_t dimension, uint64_t length1, uint64_t length2, uint64_t dyadic_order_1, uint64_t dyadic_order_2, bool return_grid = false) noexcept#

sig_kernel_backprop_cuda#

int sig_kernel_backprop_cuda_f(const float *gram, float *out, const float *derivs, const float *k_grid, uint64_t batch_size, uint64_t dimension, uint64_t length1, uint64_t length2, uint64_t dyadic_order_1, uint64_t dyadic_order_2, bool return_grid = false) noexcept#

Backpropagation through sig_kernel.

Parameters:

  • gram – Pointer to batch gram matrix data (row-major), size = batch_size * (length1 - 1) * (length2 - 1).

  • out – Pointer to output buffer (row-major, preallocated), size = batch_size * (length1 - 1) * (length2 - 1).

  • derivs – Pointer to input derivatives. If return_grid is false, size = batch_size. If return_grid is true, size = batch_size * (((length1 - 1) << dyadic_order_1) + 1) * (((length2 - 1) << dyadic_order_2) + 1).

  • k_grid – Pointer to batch of signature kernel PDE grids (row-major, precomputed), size = batch_size * (((length1 - 1) << dyadic_order_1) + 1) * (((length2 - 1) << dyadic_order_2) + 1).

  • batch_size – Batch size of the paths.

  • dimension – Dimension of the paths.

  • length1 – Length of the first paths.

  • length2 – Length of the second paths.

  • dyadic_order_1 – Dyadic refinement for the first paths.

  • dyadic_order_2 – Dyadic refinement for the second paths.

  • return_grid – If true, derivs is expected to be grid-sized per batch element; if false, derivs has one scalar per batch element.

Returns:

Status code (0 = success).

int sig_kernel_backprop_cuda_d(const double *gram, double *out, const double *derivs, const double *k_grid, uint64_t batch_size, uint64_t dimension, uint64_t length1, uint64_t length2, uint64_t dyadic_order_1, uint64_t dyadic_order_2, bool return_grid = false) noexcept#

branched_sig_kernel_cuda#

int branched_sig_kernel_cuda_f(const float *gram, float *out, uint64_t batch_size, uint64_t dimension, uint64_t length1, uint64_t length2, uint64_t depth, uint64_t dyadic_order_1, uint64_t dyadic_order_2, bool return_grid = false) noexcept#

Computes the depth-recursive branched signature kernel from batch gram matrices on the GPU.

Computes the non-planar BCK branched signature kernel using the Chevyrev-Oberhauser recursion. The core consumes precomputed static-kernel increments rather than path coordinates.

Parameters:

  • gram – Pointer to batch gram matrix data (row-major, on device), size = batch_size * (length1 - 1) * (length2 - 1).

  • out – Pointer to output buffer (row-major, preallocated, on device), size = batch_size * (return_grid ? (((length1 - 1) << dyadic_order_1) + 1) * (((length2 - 1) << dyadic_order_2) + 1) : 1).

  • batch_size – Batch size of the path pairs.

  • dimension – Dimension of the original paths. The kernel core uses gram, so this is retained for API parity.

  • length1 – Length of the first paths.

  • length2 – Length of the second paths.

  • depth – Truncation depth of the branched kernel recursion. If zero, the output is filled with ones.

  • dyadic_order_1 – Dyadic refinement for the first paths.

  • dyadic_order_2 – Dyadic refinement for the second paths.

  • return_grid – If true, returns the final-depth grid; otherwise returns the endpoint scalar per batch item.

Returns:

Status code (0 = success).

int branched_sig_kernel_cuda_d(const double *gram, double *out, uint64_t batch_size, uint64_t dimension, uint64_t length1, uint64_t length2, uint64_t depth, uint64_t dyadic_order_1, uint64_t dyadic_order_2, bool return_grid = false) noexcept#

Double-precision variant of branched_sig_kernel_cuda_f.

branched_sig_kernel_backprop_cuda#

int branched_sig_kernel_backprop_cuda_f(const float *gram, float *out, const float *derivs, const float *k_stack, uint64_t batch_size, uint64_t dimension, uint64_t length1, uint64_t length2, uint64_t depth, uint64_t dyadic_order_1, uint64_t dyadic_order_2, bool return_grid = false) noexcept#

Backpropagates through branched_sig_kernel_cuda_f with respect to the gram matrix on the GPU.

Computes derivatives with respect to the precomputed static-kernel increments used by the branched signature kernel. Path-coordinate derivatives are handled by the Python static-kernel wrappers.

Parameters:

  • gram – Pointer to batch gram matrix data (row-major, on device), size = batch_size * (length1 - 1) * (length2 - 1).

  • out – Pointer to output buffer for dF/d(gram) (row-major, preallocated, on device), size = batch_size * (length1 - 1) * (length2 - 1).

  • derivs – Pointer to input derivatives (on device). If return_grid is false, size = batch_size. If return_grid is true, size = batch_size * (((length1 - 1) << dyadic_order_1) + 1) * (((length2 - 1) << dyadic_order_2) + 1).

  • k_stack – Optional pointer to precomputed forward grids K_0, …, K_depth (row-major, on device). May be null. If supplied, size = batch_size * (depth + 1) * (((length1 - 1) << dyadic_order_1) + 1) * (((length2 - 1) << dyadic_order_2) + 1).

  • batch_size – Batch size of the path pairs.

  • dimension – Dimension of the original paths. The kernel core uses gram, so this is retained for API parity.

  • length1 – Length of the first paths.

  • length2 – Length of the second paths.

  • depth – Truncation depth of the branched kernel recursion. If zero, derivatives with respect to gram are zero.

  • dyadic_order_1 – Dyadic refinement for the first paths.

  • dyadic_order_2 – Dyadic refinement for the second paths.

  • return_grid – If true, derivs is expected to be grid-sized per batch item; otherwise it has one scalar per batch item.

Returns:

Status code (0 = success).

int branched_sig_kernel_backprop_cuda_d(const double *gram, double *out, const double *derivs, const double *k_stack, uint64_t batch_size, uint64_t dimension, uint64_t length1, uint64_t length2, uint64_t depth, uint64_t dyadic_order_1, uint64_t dyadic_order_2, bool return_grid = false) noexcept#

Double-precision variant of branched_sig_kernel_backprop_cuda_f.


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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