# Deep Signature Transforms

arXiv: https://arxiv.org/abs/1905.08494 · HTML: https://mlsanity.com/paper/1905.08494/

## Key facts

- Cited by 75 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 May 2019.

## Built on by (most cited first, 30 of 75)

- [Theoretical Foundations of Deep Selective State-Space Models](https://mlsanity.com/paper/2402.19047/) (2024)
- [Efficient and Accurate Gradients for Neural SDEs](https://mlsanity.com/paper/2105.13493/) (2021)
- [ContiFormer: Continuous-Time Transformer for Irregular Time Series Modeling](https://mlsanity.com/paper/2402.10635/) (2024)
- [Vector Quantized Time Series Generation with a Bidirectional Prior Model](https://mlsanity.com/paper/2303.04743/) (2023)
- [Neural Controlled Differential Equations for Online Prediction Tasks](https://mlsanity.com/paper/2106.11028/) (2021)
- [GT-GAN: General Purpose Time Series Synthesis with Generative Adversarial Networks](https://mlsanity.com/paper/2210.02040/) (2022)
- [Non-adversarial training of Neural SDEs with signature kernel scores](https://mlsanity.com/paper/2305.16274/) (2023)
- [Higher Order Kernel Mean Embeddings to Capture Filtrations of Stochastic Processes](https://mlsanity.com/paper/2109.03582/) (2021)
- [Neural signature kernels as infinite-width-depth-limits of controlled ResNets](https://mlsanity.com/paper/2303.17671/) (2023)
- [Recent Developments in Machine Learning Methods for Stochastic Control and Games](https://mlsanity.com/paper/2303.10257/) (2023)
- [Framing RNN as a kernel method: A neural ODE approach](https://mlsanity.com/paper/2106.01202/) (2021)
- [Structured Linear CDEs: Maximally Expressive and Parallel-in-Time Sequence Models](https://mlsanity.com/paper/2505.17761/) (2025)
- [Rough Transformers: Lightweight and Continuous Time Series Modelling through Signature Patching](https://mlsanity.com/paper/2405.20799/) (2024)
- [PCF-GAN: generating sequential data via the characteristic function of measures on the path space](https://mlsanity.com/paper/2305.12511/) (2023)
- [Signatured Deep Fictitious Play for Mean Field Games with Common Noise](https://mlsanity.com/paper/2106.03272/) (2021)
- [Approximate Bayesian Computation with Path Signatures](https://mlsanity.com/paper/2106.12555/) (2021)
- [New directions in the applications of rough path theory](https://mlsanity.com/paper/2302.04586/) (2023)
- [Logsig-RNN: a novel network for robust and efficient skeleton-based action recognition](https://mlsanity.com/paper/2110.13008/) (2021)
- [Path Development Network with Finite-dimensional Lie Group Representation](https://mlsanity.com/paper/2204.00740/) (2022)
- [Feature Engineering with Regularity Structures](https://mlsanity.com/paper/2108.05879/) (2021)
- [Optimal Estimation of Generic Dynamics by Path-Dependent Neural Jump ODEs](https://mlsanity.com/paper/2206.14284/) (2022)
- [SigFormer: Signature Transformers for Deep Hedging](https://mlsanity.com/paper/2310.13369/) (2023)
- [Dynamical Survival Analysis with Controlled Latent States](https://mlsanity.com/paper/2401.17077/) (2024)
- [Deep Signature Algorithm for Multi-dimensional Path-Dependent Options](https://mlsanity.com/paper/2211.11691/) (2022)
- [Sparse Signature Coefficient Recovery via Kernels](https://mlsanity.com/paper/2412.08579/) (2024)
- [pySigLib -- Fast Signature-Based Computations on CPU and GPU](https://mlsanity.com/paper/2509.10613/) (2025)
- [Risk of Transfer Learning and its Applications in Finance](https://mlsanity.com/paper/2311.03283/) (2023)
- [Deep Signature FBSDE Algorithm](https://mlsanity.com/paper/2108.10504/) (2021)
- [G-Signatures: Global Graph Propagation With Randomized Signatures](https://mlsanity.com/paper/2302.08811/) (2023)
- [Novelty Detection on Radio Astronomy Data using Signatures](https://mlsanity.com/paper/2402.14892/) (2024)

## Abstract (arXiv)

The signature is an infinite graded sequence of statistics known to characterise a stream of data up to a negligible equivalence class. It is a transform which has previously been treated as a fixed feature transformation, on top of which a model may be built. We propose a novel approach which combines the advantages of the signature transform with modern deep learning frameworks. By learning an augmentation of the stream prior to the signature transform, the terms of the signature may be selected in a data-dependent way. More generally, we describe how the signature transform may be used as a layer anywhere within a neural network. In this context it may be interpreted as a pooling operation. We present the results of empirical experiments to back up the theoretical justification. Code available at https://github.com/patrick-kidger/Deep-Signature-Transforms.