Information encoding in the nervous system is supported through the precise spike timings of neurons; however, an understanding of the underlying processes by which such representations are formed in the first place remains an open question. Here we examine how multilayered networks of spiking neurons can learn to encode for input patterns using a fully temporal coding scheme. To this end, we introduce a new supervised learning rule, MultilayerSpiker, that can train spiking networks containing hidden layer neurons to perform transformations between spatiotemporal input and output spike patterns. The performance of the proposed learning rule is demonstrated in terms of the number of pattern mappings it can learn, the complexity of network structures it can be used on, and its classification accuracy when using multispike-based encodings. In particular, the learning rule displays robustness against input noise and can generalize well on an example data set. Our approach contributes to both a systematic understanding of how computations might take place in the nervous system and a learning rule that displays strong technical capability.

We introduce a supervised learning algorithm for multilayer spiking neural networks. The algorithm overcomes a limitation of existing learning algorithms: it can be applied to neurons firing multiple spikes in artificial neural networks with hidden layers. It can also, in principle, be used with any linearizable neuron model and allows different coding schemes of spike train patterns. The algorithm is applied successfully to classic linearly nonseparable benchmarks such as the XOR problem and the Iris data set, as well as to more complex classification and mapping problems. The algorithm has been successfully tested in the presence of noise, requires smaller networks than reservoir computing, and results in faster convergence than existing algorithms for similar tasks such as SpikeProp.

Simple recurrent networks (SRNs) in symbolic time-series prediction (e.g., language processing models) are frequently trained with gradient descent--based learning algorithms, notably with variants of backpropagation (BP). A major drawback for the cognitive plausibility of BP is that it is a supervised scheme in which a teacher has to provide a fully specified target answer. Yet agents in natural environments often receive summary feedback about the degree of success or failure only, a view adopted in reinforcement learning schemes. In this work, we show that for SRNs in prediction tasks for which there is a probability interpretation of the network's output vector, Elman BP can be reimplemented as a reinforcement learning scheme for which the expected weight updates agree with the ones from traditional Elman BP. Network simulations on formal languages corroborate this result and show that the learning behaviors of Elman backpropagation and its reinforcement variant are very similar also in online learning tasks.