Supervised Learning in Multilayer Spiking Neural Networks

The current article introduces a supervised learning algorithm for multilayer spiking neural networks. The algorithm presented here overcomes some limitations of existing learning algorithms as it can be applied to neurons firing multiple spikes and it can in principle be applied to any linearisable neuron model. The algorithm is applied successfully to various benchmarks, such as the XOR problem and the Iris data set, as well as complex classifications problems. The simulations also show the flexibility of this supervised learning algorithm which permits different encodings of the spike timing patterns, including precise spike trains encoding.Comment: 38 pages, 4 figure

Training Multi-layer Spiking Neural Networks using NormAD based Spatio-Temporal Error Backpropagation

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 multi-layer feedforward SNNs. The non-linear integrate-and-fire dynamics employed by spiking neurons make it difficult to train SNNs to generate desired spike trains in response to a given input. To tackle this, first the problem of training a multi-layer 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 to efficiently train multi-layer SNNs, and is shown to be effectively performing spatio-temporal error backpropagation. The learning rule is validated by training $2$-layer SNNs to solve a spike based formulation of the XOR problem as well as training $3$-layer SNNs for generic spike based training problems. Thus, the new algorithm is a key step towards building deep spiking neural networks capable of efficient event-triggered learning.Comment: 19 pages, 10 figure

Spiking neural networks trained with backpropagation for low power neuromorphic implementation of voice activity detection

Recent advances in Voice Activity Detection (VAD) are driven by artificial and Recurrent Neural Networks (RNNs), however, using a VAD system in battery-operated devices requires further power efficiency. This can be achieved by neuromorphic hardware, which enables Spiking Neural Networks (SNNs) to perform inference at very low energy consumption. Spiking networks are characterized by their ability to process information efficiently, in a sparse cascade of binary events in time called spikes. However, a big performance gap separates artificial from spiking networks, mostly due to a lack of powerful SNN training algorithms. To overcome this problem we exploit an SNN model that can be recast into an RNN-like model and trained with known deep learning techniques. We describe an SNN training procedure that achieves low spiking activity and pruning algorithms to remove 85% of the network connections with no performance loss. The model achieves state-of-the-art performance with a fraction of power consumption comparing to other methods.Comment: 5 pages, 2 figures, 2 table

An Efficient Threshold-Driven Aggregate-Label Learning Algorithm for Multimodal Information Processing

The aggregate-label learning paradigm tackles the long-standing temporary credit assignment (TCA) problem in neuroscience and machine learning, enabling spiking neural networks to learn multimodal sensory clues with delayed feedback signals. However, the existing aggregate-label learning algorithms only work for single spiking neurons, and with low learning efficiency, which limit their real-world applicability. To address these limitations, we first propose an efficient threshold-driven plasticity algorithm for spiking neurons, namely ETDP. It enables spiking neurons to generate the desired number of spikes that match the magnitude of delayed feedback signals and to learn useful multimodal sensory clues embedded within spontaneous spiking activities. Furthermore, we extend the ETDP algorithm to support multi-layer spiking neural networks (SNNs), which significantly improves the applicability of aggregate-label learning algorithms. We also validate the multi-layer ETDP learning algorithm in a multimodal computation framework for audio-visual pattern recognition. Experimental results on both synthetic and realistic datasets show significant improvements in the learning efficiency and model capacity over the existing aggregate-label learning algorithms. It, therefore, provides many opportunities for solving real-world multimodal pattern recognition tasks with spiking neural networks

Supervised Learning in Spiking Neural Networks for Precise Temporal Encoding

Precise spike timing as a means to encode information in neural networks is biologically supported, and is advantageous over frequency-based codes by processing input features on a much shorter time-scale. For these reasons, much recent attention has been focused on the development of supervised learning rules for spiking neural networks that utilise a temporal coding scheme. However, despite significant progress in this area, there still lack rules that have a theoretical basis, and yet can be considered biologically relevant. Here we examine the general conditions under which synaptic plasticity most effectively takes place to support the supervised learning of a precise temporal code. As part of our analysis we examine two spike-based learning methods: one of which relies on an instantaneous error signal to modify synaptic weights in a network (INST rule), and the other one on a filtered error signal for smoother synaptic weight modifications (FILT rule). We test the accuracy of the solutions provided by each rule with respect to their temporal encoding precision, and then measure the maximum number of input patterns they can learn to memorise using the precise timings of individual spikes as an indication of their storage capacity. Our results demonstrate the high performance of FILT in most cases, underpinned by the rule's error-filtering mechanism, which is predicted to provide smooth convergence towards a desired solution during learning. We also find FILT to be most efficient at performing input pattern memorisations, and most noticeably when patterns are identified using spikes with sub-millisecond temporal precision. In comparison with existing work, we determine the performance of FILT to be consistent with that of the highly efficient E-learning Chronotron, but with the distinct advantage that FILT is also implementable as an online method for increased biological realism.Comment: 26 pages, 10 figures, this version is published in PLoS ONE and incorporates reviewer comment