# Learning with Signatures

arXiv: https://arxiv.org/abs/2204.07953 · HTML: https://mlsanity.com/paper/2204.07953/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 26 of its 45 references that are in the map.
- First posted on arXiv 17 Apr 2022.

## Builds on (most cited first, 26 of 26)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Mask R-CNN](https://mlsanity.com/paper/1703.06870/) (2017)
- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [Fully Convolutional Networks for Semantic Segmentation](https://mlsanity.com/paper/1411.4038/) (2014)
- [You Only Look Once: Unified, Real-Time Object Detection](https://mlsanity.com/paper/1506.02640/) (2015)
- [Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification](https://mlsanity.com/paper/1502.01852/) (2015)
- [DeepLab: Semantic Image Segmentation with Deep Convolutional Nets, Atrous Convolution, and Fully Connected CRFs](https://mlsanity.com/paper/1606.00915/) (2016)
- [Progressive Growing of GANs for Improved Quality, Stability, and Variation](https://mlsanity.com/paper/1710.10196/) (2017)
- [Sequence to Sequence Learning with Neural Networks](https://mlsanity.com/paper/1409.3215/) (2014)
- [Fast R-CNN](https://mlsanity.com/paper/1504.08083/) (2015)
- [Large Scale GAN Training for High Fidelity Natural Image Synthesis](https://mlsanity.com/paper/1809.11096/) (2018)
- [Rich feature hierarchies for accurate object detection and semantic segmentation](https://mlsanity.com/paper/1311.2524/) (2013)
- [StarGAN v2: Diverse Image Synthesis for Multiple Domains](https://mlsanity.com/paper/1912.01865/) (2019)
- [Show and Tell: A Neural Image Caption Generator](https://mlsanity.com/paper/1411.4555/) (2014)
- [Image Transformer](https://mlsanity.com/paper/1802.05751/) (2018)
- [Contrastive Learning for Unpaired Image-to-Image Translation](https://mlsanity.com/paper/2007.15651/) (2020)
- [Video-to-Video Synthesis](https://mlsanity.com/paper/1808.06601/) (2018)
- [PIXOR: Real-time 3D Object Detection from Point Clouds](https://mlsanity.com/paper/1902.06326/) (2019)
- [Photographic Image Synthesis with Cascaded Refinement Networks](https://mlsanity.com/paper/1707.09405/) (2017)
- [A Primer on the Signature Method in Machine Learning](https://mlsanity.com/paper/1603.03788/) (2016)
- [Kernels for sequentially ordered data](https://mlsanity.com/paper/1601.08169/) (2016)
- [Deep Signature Transforms](https://mlsanity.com/paper/1905.08494/) (2019)
- [The iisignature library: efficient calculation of iterated-integral signatures and log signatures](https://mlsanity.com/paper/1802.08252/) (2018)
- [Preserving Color in Neural Artistic Style Transfer](https://mlsanity.com/paper/1606.05897/) (2016)
- [Sparse arrays of signatures for online character recognition](https://mlsanity.com/paper/1308.0371/) (2013)
- [On the Convergence of Alternating Direction Lagrangian Methods for Nonconvex Structured Optimization Problems](https://mlsanity.com/paper/1409.8033/) (2014)

## Abstract (arXiv)

In this work we investigate the use of the Signature Transform in the context of Learning. Under this assumption, we advance a supervised framework that potentially provides state-of-the-art classification accuracy with the use of few labels without the need of credit assignment and with minimal or no overfitting. We leverage tools from harmonic analysis by the use of the signature and log-signature, and use as a score function RMSE and MAE Signature and log-signature. We develop a closed-form equation to compute probably good optimal scale factors, as well as the formulation to obtain them by optimization. Techniques of Signal Processing are addressed to further characterize the problem. Classification is performed at the CPU level orders of magnitude faster than other methods. We report results on AFHQ, MNIST and CIFAR10, achieving 100% accuracy on all tasks assuming we can determine at test time which probably good optimal scale factor to use for each category.