# \[ANN\] ChenSignatures.jl — Path signatures in Julia

**URL:** https://discourse.julialang.org/t/ann-chensignatures-jl-path-signatures-in-julia/134361
**Category:** Package Announcements
**Tags:** package, announcement, machine-learning, math
**Created:** [December 4, 2025, 5:44pm UTC](https://discourse.julialang.org/t/ann-chensignatures-jl-path-signatures-in-julia/134361 "2025-12-04T17:44:22Z")
**Posts on this page:** 1
**Page:** 1

<div class="post-metadata">

### Author: ![aleCombi](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/alecombi/32/212382_2.png) [@aleCombi](https://discourse.julialang.org/u/aleCombi)
#### Post date: [December 4, 2025, 5:44pm UTC](https://discourse.julialang.org/t/ann-chensignatures-jl-path-signatures-in-julia/134361/1 "2025-12-04T17:44:22Z")

</div>

## Path signatures in Julia

I am excited to share [ChenSignatures.jl](https://github.com/aleCombi/ChenSignatures.jl), a Julia package for computing path signatures and log-signatures.

**What are signatures?** The signature of a path X : [0,T] \to \mathbb{R}^d is the sequence of iterated integrals:

S(X)\_m = \left(1, \int\_0^T dX\_{t\_1}, \int\_0^T \int\_0^{t\_2} dX\_{t\_1} \otimes dX\_{t\_2}, \ldots, \int\_0^T \int\_0^{t\_m} \cdots \int\_0^{t\_2} dX\_{t\_1} \otimes \cdots \otimes dX\_{t\_m}\right)

The k-th level is a tensor S^k(X) \in (\mathbb{R}^d)^{\otimes k} with components:

S^k(X)^{i\_1 \ldots i\_k} = \int\_{0 \< t\_1 \< \cdots \< t\_k \< T} dX^{i\_1}\_{t\_1} \cdots dX^{i\_k}\_{t\_k}

This object uniquely characterizes the path up to tree-like equivalence and has applications in machine learning (time series classification, generative models) and mathematical finance (rough path pricing, expected signatures).

I got interested in signatures while working on derivatives pricing, where they provide a natural way to encode path-dependent payoffs. When I looked for Julia implementations, I found the ecosystem lacking — so I decided to build one.

### Why another implementation?

Julia’s ecosystem lacked an actively maintained option — [PathSignatures.jl](https://github.com/jameslao/PathSignatures.jl) has been dormant for 5 years. ChenSignatures.jl aims to fill this gap with:

- Native Julia implementation with attention to performance (SIMD, StaticArrays)
- AD support via Enzyme and ForwardDiff
- Python interop through the [chen-signatures](https://pypi.org/project/chen-signatures/) wrapper

### Benchmarks

Comparison against [iisignature](https://github.com/bottler/iisignature) and [pysiglib](https://github.com/daniil-shmelev/pySigLib) on signature computation:

| Config (N, d, m) | iisignature | pysiglib | ChenSignatures.jl | chen-signatures (Python wrapper) |
| --- | --- | --- | --- | --- |
| (200, 2, 4) | 0.04 ms | 0.12 ms | 0.013 ms | 0.07 ms |
| (1000, 2, 6) | 0.62 ms | 0.26 ms | 0.19 ms | 0.31 ms |
| (200, 10, 4) | 6.2 ms | 0.93 ms | 0.57 ms | 0.73 ms |
| (1000, 10, 4) | 32 ms | 3.2 ms | 2.1 ms | 3.1 ms |
| (1000, 10, 6) | 8.1 s | 1.0 s | 0.83 s | 0.94 s |

_N = path length, d = dimension, m = truncation depth._

**Methodology** : Each configuration was run twice with 5 repeats per measurement on the same machine. Times shown are conservative (slower of the two runs). Full results and scripts available at [github.com/aleCombi/sig-benchmarks](https://github.com/aleCombi/sig-benchmarks).

### Quick start

```julia
using ChenSignatures, StaticArrays

# Path as vector of SVectors (recommended for performance)
path = [SVector(sin(t), cos(t)) for t in 0:0.01:1]

sig = signature(path, 4) # Truncation depth 4
logsig = logsignature(path, 4)

```

### Current status

- Dense signatures and log-signatures (flattened vector representation): optimized and tested
- Cross-validated against iisignature
- AD support via Enzyme and ForwardDiff: tested on Julia 1.10 LTS
- AD on Julia 1.12: experimental (Enzyme ecosystem still stabilizing)
- Sparse tensors: experimental
- Known issue: [log-signature memory blowup at high depths in Python wrapper](https://github.com/aleCombi/ChenSignatures.jl/issues/XXX) — investigating

### Contributions

I am not accepting PRs at the moment (I have too many new features and ideas to test), but issues and discussions are welcome!

**Links** : [Documentation](https://aleCombi.github.io/ChenSignatures.jl) · [GitHub](https://github.com/aleCombi/ChenSignatures.jl) · [Benchmarks](https://github.com/aleCombi/sig-benchmarks)