# Sparse arrays of signatures for online character recognition

arXiv: https://arxiv.org/abs/1308.0371 · HTML: https://mlsanity.com/paper/1308.0371/

## Key facts

- Cited by 18 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Aug 2013.

## Built on by (most cited first, 18 of 18)

- [Structured Linear CDEs: Maximally Expressive and Parallel-in-Time Sequence Models](https://mlsanity.com/paper/2505.17761/) (2025)
- [Recognition of Handwritten Chinese Text by Segmentation: A Segment-annotation-free Approach](https://mlsanity.com/paper/2207.14801/) (2022)
- [Lecture notes on rough paths and applications to machine learning](https://mlsanity.com/paper/2404.06583/) (2024)
- [Logsig-RNN: a novel network for robust and efficient skeleton-based action recognition](https://mlsanity.com/paper/2110.13008/) (2021)
- [Feature Engineering with Regularity Structures](https://mlsanity.com/paper/2108.05879/) (2021)
- [2-d signature of images and texture classification](https://mlsanity.com/paper/2205.11236/) (2022)
- [Global universal approximation with Brownian signatures](https://mlsanity.com/paper/2512.16396/) (2025)
- [Path classification by stochastic linear recurrent neural networks](https://mlsanity.com/paper/2108.03090/) (2021)
- [Recognition of Handwritten Japanese Characters Using Ensemble of Convolutional Neural Networks](https://mlsanity.com/paper/2306.03954/) (2023)
- [Path Signatures for Feature Extraction. An Introduction to the Mathematics Underpinning an Efficient Machine Learning Technique](https://mlsanity.com/paper/2506.01815/) (2025)
- [Signature and Log-signature for the Study of Empirical Distributions Generated with GANs](https://mlsanity.com/paper/2203.03226/) (2022)
- [Learning with Signatures](https://mlsanity.com/paper/2204.07953/) (2022)
- [Rotation-free Online Handwritten Character Recognition Using Linear Recurrent Units](https://mlsanity.com/paper/2602.01533/) (2026)
- [From Path Signatures to Sequential Modeling: Incremental Signature Contributions for Offline RL](https://mlsanity.com/paper/2602.11805/) (2026)
- [Global universality via discrete-time signatures](https://mlsanity.com/paper/2603.09773/) (2026)
- [Extending SSMs with the Exponentially Weighted Signature](https://mlsanity.com/paper/2603.19198/) (2026)
- [Advances in Neural Controlled Differential Equations](https://mlsanity.com/paper/2607.05280/) (2026)
- [Online Signature Verification Using Augmented Path Signature and T-Mamba](https://mlsanity.com/paper/2609.08276/) (2026)

## Abstract (arXiv)

In mathematics the signature of a path is a collection of iterated integrals, commonly used for solving differential equations. We show that the path signature, used as a set of features for consumption by a convolutional neural network (CNN), improves the accuracy of online character recognition---that is the task of reading characters represented as a collection of paths. Using datasets of letters, numbers, Assamese and Chinese characters, we show that the first, second, and even the third iterated integrals contain useful information for consumption by a CNN. On the CASIA-OLHWDB1.1 3755 Chinese character dataset, our approach gave a test error of 3.58%, compared with 5.61% for a traditional CNN [Ciresan et al.]. A CNN trained on the CASIA-OLHWDB1.0-1.2 datasets won the ICDAR2013 Online Isolated Chinese Character recognition competition. Computationally, we have developed a sparse CNN implementation that make it practical to train CNNs with many layers of max-pooling. Extending the MNIST dataset by translations, our sparse CNN gets a test error of 0.31%.