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1. Spike-train level backpropagation for training deep recurrent spiking neural networks

   Zhang, Wenrui ; Li, Peng ( December 2019 , Advances in neural information processing systems)

   Spiking neural networks (SNNs) well support spatio-temporal learning and energy-efficient event-driven hardware neuromorphic processors. As an important class of SNNs, recurrent spiking neural networks (RSNNs) possess great computational power. However, the practical application of RSNNs is severely limited by challenges in training. Biologically-inspired unsupervised learning has limited capability in boosting the performance of RSNNs. On the other hand, existing backpropagation (BP) methods suffer from high complexity of unfolding in time, vanishing and exploding gradients, and approximate differentiation of discontinuous spiking activities when applied to RSNNs. To enable supervised training of RSNNs under a well-defined loss function, we present a novel Spike-Train level RSNNs Backpropagation (ST-RSBP) algorithm for training deep RSNNs. The proposed ST-RSBP directly computes the gradient of a rate-coded loss function defined at the output layer of the network w.r.t tunable parameters. The scalability of ST-RSBP is achieved by the proposed spike-train level computation during which temporal effects of the SNN is captured in both the forward and backward pass of BP. Our ST-RSBP algorithm can be broadly applied to RSNNs with a single recurrent layer or deep RSNNs with multiple feedforward and recurrent layers. Based upon challenging speech and image datasets including TI46, N-TIDIGITS, Fashion-MNIST and MNIST, ST-RSBP is able to train SNNs with an accuracy surpassing that of the current state-of-the-art SNN BP algorithms and conventional non-spiking deep learning models. 

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2. Spiking Neural Networks with Laterally-Inhibited Self-Recurrent Units

   Zheng, Wenrui ; Li, Peng ( July 2021 , 2021 International Joint Conference on Neural Networks)

   null (Ed.)

   In biological brains, recurrent connections play a crucial role in cortical computation, modulation of network dynamics, and communication. However, in recurrent spiking neural networks (SNNs), recurrence is mostly constructed by random connections. How excitatory and inhibitory recurrent connections affect network responses and what kinds of connectivity benefit learning performance is still obscure. In this work, we propose a novel recurrent structure called the Laterally-Inhibited Self-Recurrent Unit (LISR), which consists of one excitatory neuron with a self-recurrent connection wired together with an inhibitory neuron through excitatory and inhibitory synapses. The self-recurrent connection of the excitatory neuron mitigates the information loss caused by the firing-and-resetting mechanism and maintains the long-term neuronal memory. The lateral inhibition from the inhibitory neuron to the corresponding excitatory neuron, on the one hand, adjusts the firing activity of the latter. On the other hand, it plays as a forget gate to clear the memory of the excitatory neuron. Based on speech and image datasets commonly used in neuromorphic computing, RSNNs based on the proposed LISR improve performance significantly by up to 9.26% over feedforward SNNs trained by a state-of-the-art backpropagation method with similar computational costs. 

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3. Hybrid macro/micro level backpropagation for training deep spiking neural networks

   Jin, Yingyezhe ; Zhang, Wenrui ; Li, Peng ( December 2018 , Advances in neural information processing systems)

   Spiking neural networks (SNNs) are positioned to enable spatio-temporal information processing and ultra-low power event-driven neuromorphic hardware. However, SNNs are yet to reach the same performances of conventional deep artificial neural networks (ANNs), a long-standing challenge due to complex dynamics and non-differentiable spike events encountered in training. The existing SNN error backpropagation (BP) methods are limited in terms of scalability, lack of proper handling of spiking discontinuities, and/or mismatch between the rate coded loss function and computed gradient. We present a hybrid macro/micro level backpropagation (HM2-BP) algorithm for training multi-layer SNNs. The temporal effects are precisely captured by the proposed spike-train level post-synaptic potential (S-PSP) at the microscopic level. The rate-coded errors are defined at the macroscopic level, computed and back-propagated across both macroscopic and microscopic levels. Different from existing BP methods, HM2-BP directly computes the gradient of the rate-coded loss function w.r.t tunable parameters. We evaluate the proposed HM2-BP algorithm by training deep fully connected and convolutional SNNs based on the static MNIST [14] and dynamic neuromorphic N-MNIST [26]. HM2-BP achieves an accuracy level of 99:49% and 98:88% for MNIST and N-MNIST, respectively, outperforming the best reported performances obtained from the existing SNN BP algorithms. Furthermore, the HM2-BP produces the highest accuracies based on SNNs for the EMNIST [3] dataset, and leads to high recognition accuracy for the 16-speaker spoken English letters of TI46 Corpus [16], a challenging spatio-temporal speech recognition benchmark for which no prior success based on SNNs was reported. It also achieves competitive performances surpassing those of conventional deep learning models when dealing with asynchronous spiking streams. 

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4. Temporal Spike Sequence Learning via Backpropagation for Deep Spiking Neural Networks

   Zhang, Wenrui ; Li, Peng ( December 2020 , Advances in neural information processing systems)

   Spiking neural networks (SNNs) are well suited for spatio-temporal learning and implementations on energy-efficient event-driven neuromorphic processors. However, existing SNN error backpropagation (BP) methods lack proper handling of spiking discontinuities and suffer from low performance compared with the BP methods for traditional artificial neural networks. In addition, a large number of time steps are typically required to achieve decent performance, leading to high latency and rendering spike based computation unscalable to deep architectures. We present a novel Temporal Spike Sequence Learning Backpropagation (TSSL-BP) method for training deep SNNs, which breaks down error backpropagation across two types of inter-neuron and intra-neuron dependencies and leads to improved temporal learning precision. It captures inter-neuron dependencies through presynaptic firing times by considering the all-or-none characteristics of firing activities, and captures intra-neuron dependencies by handling the internal evolution of each neuronal state in time. TSSL-BP efficiently trains deep SNNs within a much shortened temporal window of a few steps while improving the accuracy for various image classification datasets including CIFAR10. 

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5. Meta-learning spiking neural networks with surrogate gradient descent

   https://doi.org/10.1088/2634-4386/ac8828  

   Stewart, Kenneth M. ; Neftci, Emre O. ( September 2022 , Neuromorphic Computing and Engineering)

   Adaptive ‘life-long’ learning at the edge and during online task performance is an aspirational goal of artificial intelligence research. Neuromorphic hardware implementing spiking neural networks (SNNs) are particularly attractive in this regard, as their real-time, event-based, local computing paradigm makes them suitable for edge implementations and fast learning. However, the long and iterative learning that characterizes state-of-the-art SNN training is incompatible with the physical nature and real-time operation of neuromorphic hardware. Bi-level learning, such as meta-learning is increasingly used in deep learning to overcome these limitations. In this work, we demonstrate gradient-based meta-learning in SNNs using the surrogate gradient method that approximates the spiking threshold function for gradient estimations. Because surrogate gradients can be made twice differentiable, well-established, and effective second-order gradient meta-learning methods such as model agnostic meta learning (MAML) can be used. We show that SNNs meta-trained using MAML perform comparably to conventional artificial neural networks meta-trained with MAML on event-based meta-datasets. Furthermore, we demonstrate the specific advantages that accrue from meta-learning: fast learning without the requirement of high precision weights or gradients, training-to-learn with quantization and mitigating the effects of approximate synaptic plasticity rules. Our results emphasize how meta-learning techniques can become instrumental for deploying neuromorphic learning technologies on real-world problems.

    

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