Temporal coding in spiking neural networks with alpha synaptic function

Krzysztof Potempa
Luca Versari
Thomas Fischbacher
Jyrki Alakuijala


The timing of individual neuronal spikes is essential for biological brains to make fast responses to sensory stimuli. However, conventional artificial neural networks lack the intrinsic dimension of temporal coding present in biological networks. We propose a spiking neural network model that encodes information in the relative timing of individual neuron spikes. An image can be encoded in this manner by an input layer where each neuron spikes at a time proportional to the brightness of an individual pixel. In classification tasks, the output of the network is indicated by the first neuron to spike in the output layer. By encoding information in time in this manner, we are able to train the network to perform supervised learning with backpropagation, using exact derivatives of the postsynaptic spike times with respect to presynaptic spike times. The network operates using a biologically-plausible alpha synaptic transfer function. Additionally, we use trainable synchronisation pulses that provide bias, add more flexibility during the training process and allow the exploitation of the decay part of the alpha function. We show that such spiking networks can be trained successfully on noisy temporal Boolean logic problems. Moreover, they perform better than comparable spiking models on the MNIST benchmark when encoded in time. During training, we find that the network spontaneously discovers two operating regimes: a slow regime, where a decision is taken after all hidden neurons have spiked and the accuracy is very high, and a fast regime, where a decision is taken very fast but the accuracy is lower. These results demonstrate the computational power of spiking networks with biological characteristics that encode information in the timing of individual neurons. By studying temporal coding in spiking networks, we aim to create building blocks towards energy-efficient, state-based and more complex biologically-inspired neural architectures.

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