  Inspired by chaotic firing of neurons in the brain, we propose ChaosNet -- a
novel chaos based artificial neural network architecture for classification
tasks. ChaosNet is built using layers of neurons, each of which is a 1D chaotic
map known as the Generalized Luroth Series (GLS) which has been shown in
earlier works to possess very useful properties for compression, cryptography
and for computing XOR and other logical operations. In this work, we design a
novel learning algorithm on ChaosNet that exploits the topological transitivity
property of the chaotic GLS neurons. The proposed learning algorithm gives
consistently good performance accuracy in a number of classification tasks on
well known publicly available datasets with very limited training samples. Even
with as low as 7 (or fewer) training samples/class (which accounts for less
than 0.05% of the total available data), ChaosNet yields performance accuracies
in the range 73.89 % - 98.33 %. We demonstrate the robustness of ChaosNet to
additive parameter noise and also provide an example implementation of a
2-layer ChaosNet for enhancing classification accuracy. We envisage the
development of several other novel learning algorithms on ChaosNet in the near
future.
