3,243 research outputs found

    Supervised Learning in Multilayer Spiking Neural Networks

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    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

    SuperSpike: Supervised learning in multi-layer spiking neural networks

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    A vast majority of computation in the brain is performed by spiking neural networks. Despite the ubiquity of such spiking, we currently lack an understanding of how biological spiking neural circuits learn and compute in-vivo, as well as how we can instantiate such capabilities in artificial spiking circuits in-silico. Here we revisit the problem of supervised learning in temporally coding multi-layer spiking neural networks. First, by using a surrogate gradient approach, we derive SuperSpike, a nonlinear voltage-based three factor learning rule capable of training multi-layer networks of deterministic integrate-and-fire neurons to perform nonlinear computations on spatiotemporal spike patterns. Second, inspired by recent results on feedback alignment, we compare the performance of our learning rule under different credit assignment strategies for propagating output errors to hidden units. Specifically, we test uniform, symmetric and random feedback, finding that simpler tasks can be solved with any type of feedback, while more complex tasks require symmetric feedback. In summary, our results open the door to obtaining a better scientific understanding of learning and computation in spiking neural networks by advancing our ability to train them to solve nonlinear problems involving transformations between different spatiotemporal spike-time patterns

    Storage of phase-coded patterns via STDP in fully-connected and sparse network: a study of the network capacity

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    We study the storage and retrieval of phase-coded patterns as stable dynamical attractors in recurrent neural networks, for both an analog and a integrate-and-fire spiking model. The synaptic strength is determined by a learning rule based on spike-time-dependent plasticity, with an asymmetric time window depending on the relative timing between pre- and post-synaptic activity. We store multiple patterns and study the network capacity. For the analog model, we find that the network capacity scales linearly with the network size, and that both capacity and the oscillation frequency of the retrieval state depend on the asymmetry of the learning time window. In addition to fully-connected networks, we study sparse networks, where each neuron is connected only to a small number z << N of other neurons. Connections can be short range, between neighboring neurons placed on a regular lattice, or long range, between randomly chosen pairs of neurons. We find that a small fraction of long range connections is able to amplify the capacity of the network. This imply that a small-world-network topology is optimal, as a compromise between the cost of long range connections and the capacity increase. Also in the spiking integrate and fire model the crucial result of storing and retrieval of multiple phase-coded patterns is observed. The capacity of the fully-connected spiking network is investigated, together with the relation between oscillation frequency of retrieval state and window asymmetry

    The chronotron: a neuron that learns to fire temporally-precise spike patterns

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    In many cases, neurons process information carried by the precise timing of spikes. Here we show how neurons can learn to generate specific temporally-precise output spikes in response to input spike patterns, thus processing and memorizing information that is fully temporally coded, both as input and as output. We introduce two new supervised learning rules for spiking neurons with temporal coding of information (chronotrons), one that is analytically-derived and highly efficient, and one that has a high degree of biological plausibility. We show how chronotrons can learn to classify their inputs and we study their memory capacity

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

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    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 22-layer SNNs to solve a spike based formulation of the XOR problem as well as training 33-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

    Synthesis of neural networks for spatio-temporal spike pattern recognition and processing

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    The advent of large scale neural computational platforms has highlighted the lack of algorithms for synthesis of neural structures to perform predefined cognitive tasks. The Neural Engineering Framework offers one such synthesis, but it is most effective for a spike rate representation of neural information, and it requires a large number of neurons to implement simple functions. We describe a neural network synthesis method that generates synaptic connectivity for neurons which process time-encoded neural signals, and which makes very sparse use of neurons. The method allows the user to specify, arbitrarily, neuronal characteristics such as axonal and dendritic delays, and synaptic transfer functions, and then solves for the optimal input-output relationship using computed dendritic weights. The method may be used for batch or online learning and has an extremely fast optimization process. We demonstrate its use in generating a network to recognize speech which is sparsely encoded as spike times.Comment: In submission to Frontiers in Neuromorphic Engineerin
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