Spiking neural networks (SNNs) have garnered a great amount of interest for supervised and unsupervised learning applications. This paper deals with the problem of training multilayer feedforward SNNs. The non-linear integrate-and-fire dynamics employed by spiking neurons make it difficult to train SNNs to output desired spike train in response to a given input. To tackle this, first the problem of training a multilayer SNN is formulated as an optimization problem such that its objective function is based on the deviation in membrane potential rather than the spike arrival instants. Then, an optimization method named Normalized Approximate Descent (NormAD), hand-crafted for such non-convex optimization problems, is employed to derive the iterative synaptic weight update rule. Next it is reformulated for a more efficient implementation, which can also be interpreted to be spatio-temporal error backpropagation. The learning rule is validated by employing it to solve generic spike based training problem as well as a spike based formulation of the XOR problem. Thus, the new algorithm is a key step towards building deep spiking neural networks capable of event-triggered learning.
Another notable spike-domain learning rule is PBSNLR @cite_28 , which is an offline learning rule for the spiking perceptron neuron (SPN) model using the perceptron learning rule. The PSD algorithm @cite_17 uses Widrow-Hoff rule to empirically determine an equivalent learning rule for spiking neurons. The SPAN rule @cite_25 converts input and output spike signals into analog signals and then applies the Widrow-Hoff rule to derive a learning algorithm . black Further, it is applicable to the training of SNNs with only one layer. The SWAT algorithm @cite_13 uses STDP and BCM rule to derive a weight adaptation strategy for SNNs. The Normalized Spiking Error Back-Propagation (NSEBP) method proposed in @cite_11 is based on approximations of the simplified Spike Response Model for the neuron. The multi-STIP algorithm proposed in @cite_36 defines an inner product for spike trains to approximate a learning cost function. black As opposed to the above approaches which attempt to develop weight update rules for fixed network topologies, there are also some efforts in developing feed-forward networks based on evolutionary algorithms where new neuronal connections are progressively added and their weights and firing thresholds updated for every class label in the database @cite_4 @cite_32 . black
@cite_4 @cite_28 @cite_36 @cite_17 @cite_32 @cite_13 @cite_25 @cite_11
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Spiking Neural Networks (SNN) were shown to be suitable tools for the processing of spatio-temporal information. However, due to their inherent complexity, the formulation of efficient supervised learning algorithms for SNN is difficult and remains an important problem in the research area. This article presents SPAN — a spiking neuron that is able to learn associations of arbitrary spike trains in a supervised fashion allowing the processing of spatio-temporal information encoded in the precise timing of spikes. The idea of the proposed algorithm is to transform spike trains during the learning phase into analog signals so that common mathematical operations can be performed on them. Using this conversion, it is possible to apply the well-known Widrow–Hoff rule directly to the transformed spike trains in order to adjust the synaptic weights and to achieve a desired input output spike behavior of the neuron. In the presented experimental analysis, the proposed learning algorithm is evaluated regarding its learning capabilities, its memory capacity, its robustness to noisy stimuli and its classification performance. Differences and similarities of SPAN regarding two related algorithms, ReSuMe and Chronotron, are discussed. The spiking neural networks (SNNs) are the third generation of neural networks and perform remarkably well in cognitive tasks such as pattern recognition. The spike emitting and information processing mechanisms found in biological cognitive systems motivate the application of the hierarchical structure and temporal encoding mechanism in spiking neural networks, which have exhibited strong computational capability. However, the hierarchical structure and temporal encoding approach require neurons to process information serially in space and time respectively, which reduce the training efficiency significantly. For training the hierarchical SNNs, most existing methods are based on the traditional back-propagation algorithm, inheriting its drawbacks of the gradient diffusion and the sensitivity on parameters. To keep the powerful computation capability of the hierarchical structure and temporal encoding mechanism, but to overcome the low efficiency of the existing algorithms, a new training algorithm, the Normalized Spiking Error Back Propagation (NSEBP) is proposed in this paper. In the feedforward calculation, the output spike times are calculated by solving the quadratic function in the spike response model instead of detecting postsynaptic voltage states at all time points in traditional algorithms. Besides, in the feedback weight modification, the computational error is propagated to previous layers by the presynaptic spike jitter instead of the gradient decent rule, which realizes the layer-wised training. Furthermore, our algorithm investigates the mathematical relation between the weight variation and voltage error change, which makes the normalization in the weight modification applicable. Adopting these strategies, our algorithm outperforms the traditional SNN multi-layer algorithms in terms of learning efficiency and parameter sensitivity, that are also demonstrated by the comprehensive experimental results in this paper. A supervised learning rule for Spiking Neural Networks (SNNs) is presented that can cope with neurons that spike multiple times. The rule is developed by extending the existing SpikeProp algorithm which could only be used for one spike per neuron. The problem caused by the discontinuity in the spike process is counteracted with a simple but effective rule, which makes the learning process more efficient. Our learning rule is successfully tested on a classification task of Poisson spike trains. We also applied the algorithm on a temporal version of the XOR problem and show that it is possible to learn this classical problem using only one spiking neuron making use of a hair-trigger situation. This paper presents a synaptic weight association training (SWAT) algorithm for spiking neural networks (SNNs). SWAT merges the Bienenstock-Cooper-Munro (BCM) learning rule with spike timing dependent plasticity (STDP). The STDP BCM rule yields a unimodal weight distribution where the height of the plasticity window associated with STDP is modulated causing stability after a period of training. The SNN uses a single training neuron in the training phase where data associated with all classes is passed to this neuron. The rule then maps weights to the classifying output neurons to reflect similarities in the data across the classes. The SNN also includes both excitatory and inhibitory facilitating synapses which create a frequency routing capability allowing the information presented to the network to be routed to different hidden layer neurons. A variable neuron threshold level simulates the refractory period. SWAT is initially benchmarked against the nonlinearly separable Iris and Wisconsin Breast Cancer datasets. Results presented show that the proposed training algorithm exhibits a convergence accuracy of 95.5 and 96.2 for the Iris and Wisconsin training sets, respectively, and 95.3 and 96.7 for the testing sets, noise experiments show that SWAT has a good generalization capability. SWAT is also benchmarked using an isolated digit automatic speech recognition (ASR) system where a subset of the TI46 speech corpus is used. Results show that with SWAT as the classifier, the ASR system provides an accuracy of 98.875 for training and 95.25 for testing.