  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.
