pathsig.LogSignature#

class pathsig.LogSignature(depth, projection=None, windows=None)#

Computes the log-signature of a path.

Parameters:

  • depth (int) – Truncation level.

  • projection (object | None) – (optional) Projection controlling which log-signature coordinates are computed and returned. See pathsig.projections for supported types.

  • windows (torch.Tensor | None) – (optional) Integer tensor of shape \((W,2)\) specifying windows \([start,end)\).

forward(x)#
Parameters:

x (torch.Tensor) – CUDA tensor of shape \((B,T,d)\) with dtype float32 or float64.

Returns:

Tensor of shape \((B,D)\) if windows is None, and \((B,W,D)\) otherwise.

Return type:

torch.Tensor

Here \(B\) is the batch size, \(T\) the sequence length, \(d\) the path dimension, \(W\) the number of windows, and \(D\) the output dimension. If no projection is provided then \(D=\sum_{k=1}^{\mathrm{depth}} d^k\). With a projection, \(D=\texttt{projection.sig\_size}\).

Notes

For a compact coordinate representation of the log-signature, a projection should be specified. A canonical choice is the Lyndon projection.

Autograd is supported for float32 and float64 in both windowed and non-windowed modes, with or without a projection.

Examples

import torch
import pathsig

x = torch.randn(32, 128, 8, device="cuda", dtype=torch.float32) # (B, T, d)

# Log-signature with a Lyndon projection
proj = pathsig.projections.lyndon(depth=4, path_dim=8)
logsig = pathsig.LogSignature(depth=4, projection=proj)
y = logsig(x)  # (B, proj.sig_size)

# Windowed log-signature with a Lyndon projection
windows = torch.tensor([[0, 32], [32, 64]], device="cuda") # (W, 2)
logsig = pathsig.LogSignature(depth=4, projection=proj, windows=windows)
y = logsig(x)  # (B, W, proj.sig_size)

# Full truncated log-signature
logsig = pathsig.LogSignature(depth=4)
y = logsig(x)  # (B, D)