Leveraging chaotic transients in the training of artificial neural networks

Abstract

Traditional algorithms to optimize artificial neural networks when confronted with a supervised learning task are usually exploitation-type relaxational dynamics such as gradient descent (GD). Here, we explore the dynamics of the neural network trajectory along training for unconventionally large learning rates. We show that for a region of values of the learning rate, the GD optimization shifts away from purely exploitation-like algorithm into a regime of exploration-exploitation balance, as the neural network is still capable of learning but the trajectory shows sensitive dependence on initial conditions --as characterized by positive network maximum Lyapunov exponent--. Interestingly, the characteristic training time required to reach an acceptable accuracy in the test set reaches a minimum precisely in such learning rate region, further suggesting that one can accelerate the training of artificial neural networks by locating at the onset of chaos. Our results --initially illustrated for the MNIST classification task-- qualitatively hold for a range of supervised learning tasks, {learning architectures (including both shallow and deep multilayer perceptrons and convolutional neural networks) and other hyperparameters (different activation functions and weight regularisation),} and showcase the emergent, constructive role of transient chaotic dynamics in the training of artificial neural networks.