  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%.

Computer Vision and Pattern Recognition;Neural and Evolutionary Computing