Fast path signatures, log signatures, and signature kernels on CPU and GPU

pySigLib is a Python library for fast computation of path signatures, log signatures, branched signatures, and signature kernels on CPU and GPU, with NumPy, PyTorch, and JAX support. Its PyTorch and JAX integrations keep these operations differentiable, jittable, and on the device your data already lives on.

Features

Signatures	Log‑signatures	Signature kernels
Branched signatures	Signature streams	Signature coefficients

Every operation is available from NumPy, PyTorch (with full autograd), and JAX (with jit, vmap, and grad), running on CPU via a multi-threaded C++ backend or on GPU via CUDA. Additional utilities cover path transforms (time augmentation, lead-lag) and words / Lyndon words.

Installation

pip install pysiglib              # CPU only
pip install pysiglib[cuda]        # with CUDA GPU support

The JAX integration is built into the wheel - install JAX separately (pip install jax) if you want to use it.

For detailed and up-to-date installation instructions, including how to build from source, see the installation guide.

Quick start

import numpy as np
import pysiglib

path = np.random.randn(32, 1000, 10)  # (batch, length, dimension)
sig  = pysiglib.sig(path, degree=5)

Documentation

Full documentation is available at https://pysiglib.readthedocs.io

Examples

Throughout the examples below, paths are arrays of shape (path length, dimension) or (batch size, path length, dimension). Inputs can be NumPy arrays, PyTorch tensors, or JAX arrays; the computation runs on whichever device the input lives on.

Signatures

import numpy as np
import pysiglib

X = np.random.uniform(size=(32, 1000, 10))
s = pysiglib.sig(X, degree=5)

Signature coefficients

path  = np.random.uniform(size=(32, 1000, 5))
words = [(0,), (1, 0), (1, 2, 4)]
coefs = pysiglib.sig_coef(path, words)

Log-signatures

pysiglib.prepare_log_sig(dimension=10, degree=5, method=1)

X  = np.random.uniform(size=(32, 1000, 10))
ls = pysiglib.log_sig(X, degree=5, method=1)

Branched signatures

pysiglib.prepare_branched_sig(dimension=5, degree=4)

X    = np.random.randn(32, 1000, 5)
bsig = pysiglib.branched_sig(X, degree=4)

Signature kernels

X = np.random.uniform(size=(32, 1000, 10))
Y = np.random.uniform(size=(32, 1000, 10))
k = pysiglib.sig_kernel(X, Y, dyadic_order=1)

# Different dyadic refinement per input when the paths have very different lengths:
X = np.random.uniform(size=(32,  100, 10))
Y = np.random.uniform(size=(32, 5000, 10))
k = pysiglib.sig_kernel(X, Y, dyadic_order=(3, 0))

PyTorch autograd

Every forward op has a backward implementation, so signatures compose cleanly with the rest of your PyTorch model.

import torch
from pysiglib.torch_api import sig

X = torch.randn(32, 1000, 10, requires_grad=True, device="cuda")
s = sig(X, degree=5)
loss = s.sum()
loss.backward()  # X.grad populated

JAX

The JAX API integrates via the XLA FFI, so every op works under jit, vmap, and grad.

import jax
import jax.numpy as jnp
from pysiglib.jax_api import sig

@jax.jit
def signature_norm(path):
    return jnp.sum(sig(path, degree=5) ** 2)

X    = jnp.array(np.random.randn(32, 1000, 10))
grad = jax.grad(signature_norm)(X)

Online signature streams

Incrementally update a signature as new points arrive, and query any interval in O(1) via Chen's identity - useful for real-time data or sliding-window features.

stream = pysiglib.SigStream(dimension=10, degree=5)
for point in incoming_points:
    stream.push(point)

full     = stream.sig_all()      # signature of the entire path so far
interval = stream.sig(100, 200)  # signature on [t=100, t=200]

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}
}

Contributing

Contributions are welcome! Please open an issue first to discuss what you'd like to change, then submit a pull request.

Sponsors

If you'd like to support development, please consider sponsoring the project.