Spiking neural networks are being investigated both as biologically plausible models of neural computation and also as a potentially more efficient type of neural network. While convolutional spiking neural networks have been demonstrated to achieve near state-of-the-art performance, only one solution has been proposed to convert gated recurrent neural networks, so far.
 Recurrent neural networks in the form of networks of gating memory cells have been central in state-of-the-art solutions in problem domains that involve sequence recognition or generation. Here, we design an analog gated LSTM cell where its neurons can be substituted for efficient stochastic spiking neurons. These adaptive spiking neurons implement an adaptive form of sigma-delta coding to convert internally computed analog activation values to spike-trains. For such neurons, we approximate the effective activation function, which resembles a sigmoid. We show how analog neurons with such activation functions can be used to create an analog LSTM cell; networks of these cells can then be trained with standard backpropagation. We train these LSTM networks on a noisy and noiseless version of the original sequence prediction task from Hochreiter & Schmidhuber (1997), and also on a noisy and noiseless version of a classical working memory reinforcement learning task, the T-Maze. Substituting the analog neurons for corresponding adaptive spiking neurons, we then show that almost all resulting spiking neural network equivalents correctly compute the original tasks. With the manifold success of biologically inspired deep neural networks, networks of spiking neurons are being investigated as potential models for computational and energy efficiency. Spiking neural networks mimic the pulse-based communication in biological neurons, where in brains, neurons spike only sparingly -on average 1-5 spikes per second BID0 . A number of successful convolutional neural networks based on spiking neurons have been reported BID7 BID13 BID6 BID15 BID12 , with varying degrees of biological plausibility and efficiency. Still, while spiking neural networks have thus been applied successfully to solve image-recognition tasks, many deep learning algorithms use recurrent neural networks (RNNs), in particular using Long Short-Term Memory (LSTM) layers BID11 . Compared to convolutional neural networks, LSTMs use memory cells to store selected information and various gates to direct the flow of information in and out of the memory cells. To date, the only spike-based version of LSTM has been realized for the IBM TrueNorth platform Shrestha et al.: this work proposes a method to approximate LSTM specifically for the constrains of this neurosynaptic platform by means of a store-and-release mechanism that synchronizes the modules. This translates to a frame-based rate coding computation, which is less biological plausible and energy efficient than an asynchronous approach, as the one proposed here.Here, we demonstrate a gated recurrent spiking neural network that corresponds to an LSTM unit with a memory cell and an input gate. Analogous to recent work on spiking neural networks (O 'Connor et al., 2013; BID6 BID19 BID20 , we first train a network with modified LSTM units that computes with analog values, and show how this LSTMnetwork can be converted to a spiking neural network using adaptive stochastic spiking neurons that encode and decode information in spikes using a form of sigma-delta coding BID18 BID19 BID14 . In particular, we develop a binary version of the adaptive sigma-delta coding proposed in BID19 : we approximate the shape of the transfer function that this model of fast-adapting spiking neurons exhibits, and we assemble the analog LSTM units using just this transfer function. Since input-gating is essential for maintaining memorized information without interference from unrelated sensory inputs BID11 , and to reduce complexity, we model a limited LSTM neuron consisting of an input cell, input gating cell, a Constant Error Carousel (CEC) and output cell. The resultant analog LSTM network is then trained on a number of classical sequential tasks, such as the noise-free and noisy Sequence Prediction and the T-Maze task BID11 BID1 . We demonstrate how nearly all the corresponding spiking LSTM neural networks correctly compute the same function as the analog version.Note that the conversion of gated RNNs to spike-based computation implies a conversion of the neural network from a time step based behavior to the continuous-time domain: for RNNs, this means having to consider the continuous signal integration in the memory cell. We solve the time conversion problem by approximating analytically the spiking memory cell behavior through time.Together, this work is a first step towards using spiking neural networks in such diverse and challenging tasks like speech recognition and working memory cognitive tasks. Gating is a crucial ingredient in recurrent neural networks that are able to learn long-range dependencies BID11 . Input gates in particular allow memory cells to maintain information over long stretches of time regardless of the presented -irrelevant -sensory input BID11 . The ability to recognize and maintain information for later use is also that which makes gated RNNs like LSTM so successful in the great many sequence related problems, ranging from natural language processing to learning cognitive tasks BID1 .To transfer deep neural networks to networks of spiking neurons, a highly effective method has been to map the transfer function of spiking neurons to analog counterparts and then, once the network has been trained, substitute the analog neurons with spiking neurons O' Connor et al. (2013); BID6 ; BID19 . Here , we showed how this approach can be extended to gated memory units, and we demonstrated this for an LSTM network comprised of an input gate and a CEC. Hence , we effectively obtained a low-firing rate asynchronous LSTM network.The most complex aspect of a gating mechanism turned out to be the requirement of a differentiable gating function, for which analog networks use sigmoidal units. We approximated the activation function for a stochastic Adaptive Spiking Neurons, which, as many real neurons, approximates a half-sigmoid (Fig. 1) . We showed how the stochastic spiking neuron has an effective activation even below the resting threshold ϑ 0 . This provides a gradient for training even in that area. The resultant LSTM network was then shown to be suitable for learning sequence prediction tasks, both in a noise-free and noisy setting, and a standard working memory reinforcement learning task. The learned network could then successfully be mapped to its spiking neural network equivalent for at least 90% of the trained analog networks. Figure 6 : The values of the analog CECs and spiking CECs for the noise-free Sequence Prediction (left, only one CEC cell was used) and noise-free T-maze (right, three CEC cells were used) tasks. The spiking CEC is the internal stateŜ of the output cell of the Adaptive Spiking LSTM.We also showed that some difficulties arise in the conversion of analog to spiking LSTM. Principally, the ASN activation function is derived for steady-state adapted spiking neurons, and this difference causes an error that may be large for fast changing signals. Analog-valued spikes as explored in BID19 could likely resolve this issue, at the expense of some loss of representational efficiency.Although the adaptive spiking LSTM implemented in this paper does not have output gates BID11 , they can be included by following the same approach used for the input gates: a modulation of the synaptic strength. The reasons for our approach are multiple: first of all, most of the tasks do not really require output gates; moreover, modulating each output synapse independently is less intuitive and biologically plausible than for the input gates. A similar argument can be made for the forget gates, which were not included in the original LSTM formulation: here, the solution consists in modulating the decaying factor of the CEC.Finally, which gates are really needed in an LSTM network is still an open question, with answers depending on the kind of task to be solved BID9 BID21 . For example, the AuGMEnT framework does not use gates to solve many working memory RL tasks BID16 . In addition, it has been shown by BID4 ; BID9 that a combination of input and forget gates can outperform LSTM on a variety of tasks while reducing the LSTM complexity.
 We demonstrate a gated recurrent asynchronous spiking neural network that corresponds to an LSTM unit.
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