We derive the backpropagation algorithm for spiking neural networks composed of leaky integrate-and-fire neurons operating in continuous time. This algorithm, EventProp, computes the exact gradient of an arbitrary loss function of spike times and membrane potentials by backpropagating errors in time . For the first time, by leveraging methods from optimal control theory, we are able to backpropagate errors through spike discontinuities without approximationsor smoothing operations. As errors are backpropagated in an event-based manner ( at spike times ), EventProp requires storing state variables only at these times, providing favorable memory requirements. EventProp can be applied to spiking networks with arbitrary connectivity, including recurrent, convolutional and deep feed-forward architectures. While we consider the leaky integrate-and-fire neuron model in this work, our methodology to derive the gradient can be applied to other spiking neuron models. We demonstrate learning using gradients computed via EventProp in a deep spiking network using an event-based simulator and a non-linearly separable dataset encoded using spike time latencies . Our work supports the rigorous study of gradient-based methods to train spiking neural networks while providing insights toward the development of learning algorithms in neuromorphic hardware.
Spiking neural networks combine analog computation with event-based communication using discrete spikes. While the impressive advances of deep learning are enabled by training non-spiking artificial neural networks using the backpropagation algorithm, applying this algorithm to spiking networks was previously hindered by the existence of discrete spike events and discontinuities . For the first time, this work derives the backpropagation algorithm for a continuous-time spiking neural network and a general loss function by applying the adjoint method together with the proper partial derivative jumps, allowing for backpropagation through discrete spike events without approximations. This algorithm, EventProp, backpropagates errors at spike times in order to compute the exact gradient in an event-based, temporally and spatially sparse fashion. We use gradients computed via EventProp to train networks on the Yin-Yang and MNIST datasets using either a spike time or voltage based loss function and report competitive performance . Our work supports the rigorous study of gradient-based learning algorithms in spiking neural networks and provides insights toward their implementation in novel brain-inspired hardware.
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We derive the backpropagation algorithm for spiking neural networks composed of leaky integrate-and-fire neurons operating in continuous time. This algorithm, EventProp, computes the exact gradient of an arbitrary loss function of spike times and membrane potentials by backpropagating errors in time
Spiking neural networks combine analog computation with event-based communication using discrete spikes. While the impressive advances of deep learning are enabled by training non-spiking artificial neural networks using the backpropagation algorithm, applying this algorithm to spiking networks was previously hindered by the existence of discrete spike events and discontinuities
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by leveraging methods from optimal control theory, we are able to backpropagate errors through spike discontinuities without approximationsor smoothing operations. As errors are backpropagated in an event-based manner (
this work derives the backpropagation algorithm for a continuous-time spiking neural network and a general loss function by applying the adjoint method together with the proper partial derivative jumps, allowing for backpropagation through discrete spike events without approximations. This algorithm, EventProp, backpropagates errors
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), EventProp requires storing state variables only at these times, providing favorable memory requirements. EventProp can be applied to spiking networks with arbitrary connectivity, including recurrent, convolutional and deep feed-forward architectures. While we consider the leaky integrate-and-fire neuron model in this work, our methodology to derive the gradient can be applied to other spiking neuron models. We demonstrate learning using
in order to compute the exact gradient in an event-based, temporally and spatially sparse fashion. We use
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in a deep spiking network using an event-based simulator and a non-linearly separable dataset encoded using spike time latencies
to train networks on the Yin-Yang and MNIST datasets using either a spike time or voltage based loss function and report competitive performance
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methods to train
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while providing insights toward the development of learning algorithms in neuromorphic
and provides insights toward their implementation in novel brain-inspired