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  and dynamic neuromorphic N-MNIST . 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 producesmore »
Spike-train level backpropagation for training deep recurrent spiking neural networks
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 more »
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- NSF-PAR ID:
- Journal Name:
- Advances in neural information processing systems
- Sponsoring Org:
- National Science Foundation
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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.
Algorithm and Hardware Design of Discrete-Time Spiking Neural Networks Based on Back Propagation with Binary ActivationsWe present a new back propagation based training algorithm for discrete-time spiking neural networks (SNN). Inspired by recent deep learning algorithms on binarized neural networks, binary activation with a straight-through gradient estimator is used to model the leaky integrate-fire spiking neuron, overcoming the difficulty in training SNNs using back propagation. Two SNN training algorithms are proposed: (1) SNN with discontinuous integration, which is suitable for rate-coded input spikes, and (2) SNN with continuous integration, which is more general and can handle input spikes with temporal information. Neuromorphic hardware designed in 28nm CMOS exploits the spike sparsity and demonstrates high classification accuracy (>98% on MNIST) and low energy (51.4–773 nJ/image).
Approximating Back-propagation for a Biologically Plausible Local Learning Rule in Spiking Neural NetworksAsynchronous event-driven computation and communication using spikes facilitate the realization of spiking neural networks (SNN) to be massively parallel, extremely energy efficient and highly robust on specialized neuromorphic hardware. However, the lack of a unified robust learning algorithm limits the SNN to shallow networks with low accuracies. Artificial neural networks (ANN), however, have the backpropagation algorithm which can utilize gradient descent to train networks which are locally robust universal function approximators. But backpropagation algorithm is neither biologically plausible nor neuromorphic implementation friendly because it requires: 1) separate backward and forward passes, 2) differentiable neurons, 3) high-precision propagated errors, 4) coherent copy of weight matrices at feedforward weights and the backward pass, and 5) non-local weight update. Thus, we propose an approximation of the backpropagation algorithm completely with spiking neurons and extend it to a local weight update rule which resembles a biologically plausible learning rule spike-timing-dependent plasticity (STDP). This will enable error propagation through spiking neurons for a more biologically plausible and neuromorphic implementation friendly backpropagation algorithm for SNNs. We test the proposed algorithm on various traditional and non-traditional benchmarks with competitive results.
Skip-Connected Self-Recurrent Spiking Neural Networks With Joint Intrinsic Parameter and Synaptic Weight TrainingAbstract As an important class of spiking neural networks (SNNs), recurrent spiking neural networks (RSNNs) possess great computational power and have been widely used for processing sequential data like audio and text. However, most RSNNs suffer from two problems. First, due to the lack of architectural guidance, random recurrent connectivity is often adopted, which does not guarantee good performance. Second, training of RSNNs is in general challenging, bottlenecking achievable model accuracy. To address these problems, we propose a new type of RSNN, skip-connected self-recurrent SNNs (ScSr-SNNs). Recurrence in ScSr-SNNs is introduced by adding self-recurrent connections to spiking neurons. The SNNs with self-recurrent connections can realize recurrent behaviors similar to those of more complex RSNNs, while the error gradients can be more straightforwardly calculated due to the mostly feedforward nature of the network. The network dynamics is enriched by skip connections between nonadjacent layers. Moreover, we propose a new backpropagation (BP) method, backpropagated intrinsic plasticity (BIP), to boost the performance of ScSr-SNNs further by training intrinsic model parameters. Unlike standard intrinsic plasticity rules that adjust the neuron's intrinsic parameters according to neuronal activity, the proposed BIP method optimizes intrinsic parameters based on the backpropagated error gradient of a well-defined global lossmore »