Deep learning improved by biological activation functions
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`Biologically inspired' activation functions, such as the logistic sigmoid, have been instrumental in the historical development of machine learning techniques. However in the field of deep learning, they have been largely displaced by rectified (ReLU) or exponential (ELU) linear units to mitigate the effects of vanishing gradients associated with error back-propagation. The logistic sigmoid however does not represent the true input-output relation in real neurones under physiological conditions. Here, radical root unit (RRU) activation functions are introduced, exhibiting input-output non-linearities that are substantially more biologically plausible since their functional form is based on known current-frequency relationships. In order to evaluate whether RRU activations improve deep learning performance, networks are constructed with identical architectures except differing in their transfer functions (ReLU, ELU, and RRUs). Multilayer perceptrons, stacked auto-encoders, and convolutional networks are used to test supervised and unsupervised learning based on the MNIST dataset. Results of learning performance, quantified using loss and error measurements, demonstrate that the RRU networks not only train faster than their ReLU and ELU counterparts, but also lead to improved generalised models in the absence of formal regularisation. These results therefore confirm that revisiting the properties of biological neurones and their circuitry might prove invaluable in the field of deep learning.
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