Signax: Computing signatures in JAX

Goal

To have a library that supports signature computation in JAX. See this paper to see how to adopt signatures in machine learning.

This implementation is inspired by patrick-kidger/signatory.

Examples

Basic usage

import jax
import jax.random as jrandom
import signax


key = jrandom.PRNGKey(0)
depth = 3

# compute signature for a single path
length = 100
dim = 20
path = jrandom.normal(shape=(length, dim), key=key)
output = signax.signature(path, depth)
# output is a list of array representing tensor algebra

# compute signature for batches (multiple) of paths
path = jrandom.normal(shape=(batch_size, length, dim), key=key)
# new signax API can handle this case two
output = signax.signature(path, depth)

Integrate with the equinox library

import equinox as eqx
import jax.random as jrandom

from signax.module import SignatureTransform

# random generator key
key = jrandom.PRNGKey(0)
mlp_key, data_key = jrandom.split(key)

depth = 3
length, dim = 100, 3

# create a signature transform at the specified depth
signature_layer = SignatureTransform(depth=depth)

# stack a MLP layer after that
last_layer = eqx.nn.MLP(
    depth=1, in_size=3 + 3**2 + 3**3, width_size=4, out_size=1, key=mlp_key
)

model = eqx.nn.Sequential(layers=[signature_layer, last_layer])
x = jrandom.normal(shape=(length, dim), key=data_key)
output = model(x)

Also, check the notebooks in examples folder for some experiments that reproduce the results of the deep signature transforms paper.

Installation

Via pip

python3 -m pip install signax

Via source

git clone https://github.com/anh-tong/signax.git
cd signax
python3 -m pip install -v -e .

Parallelism

This implementation makes use of jax.vmap to perform the parallelism over batch dimension.

Paralelism over chunks of paths is done using jax.vmap as well.

A quick comparison can be found at in the notebook examples/compare.ipynb. Below plots are comparison of forward and backward pass in both GPU and CPU for path size=(32, 128, 8) and signature depth=5

Forward	Backward

Why is using pure JAX good enough?

Because JAX make use of just-in-time (JIT) compilations with XLA, Signax can be reasonably fast.

We observe that the performance of this implementation is similar to Signatory in CPU and slightly better in GPU. It could be because of the optimized operators of XLA in JAX. Note that Signatory contains highly optimized C++ source code (PyTorch with Pybind11).

Acknowledgement

This repo is based on

• Signatory
• Deep-Signature-Transforms
• Equinox