Event-Driven Learning for Spiking Neural Networks

TL;DR

The demonstrated efficiency and efficacy of the proposed event-driven learning methods emphasize their potential to significantly advance the fields of neuromorphic computing and energy-efficiency applications, offering promising avenues for energy-efficiency applications.

Abstract

Brain-inspired spiking neural networks (SNNs) have gained prominence in the field of neuromorphic computing owing to their low energy consumption during feedforward inference on neuromorphic hardware. However, it remains an open challenge how to effectively benefit from the sparse event-driven property of SNNs to minimize backpropagation learning costs. In this paper, we conduct a comprehensive examination of the existing event-driven learning algorithms, reveal their limitations, and propose novel solutions to overcome them. Specifically, we introduce two novel event-driven learning methods: the spike-timing-dependent event-driven (STD-ED) and membrane-potential-dependent event-driven (MPD-ED) algorithms. These proposed algorithms leverage precise neuronal spike timing and membrane potential, respectively, for effective learning. The two methods are extensively evaluated on static and neuromorphic datasets to confirm their superior performance. They outperform existing event-driven counterparts by up to 2.51% for STD-ED and 6.79% for MPD-ED on the CIFAR-100 dataset. In addition, we theoretically and experimentally validate the energy efficiency of our methods on neuromorphic hardware. On-chip learning experiments achieved a remarkable 30-fold reduction in energy consumption over time-step-based surrogate gradient methods. The demonstrated efficiency and efficacy of the proposed event-driven learning methods emphasize their potential to significantly advance the fields of neuromorphic computing, offering promising avenues for energy-efficiency applications.

Figures (8)

• Figure 1: A case of the gradient reversal problem. (a) Neuron $i$ is connected to two afferent neurons $j_1$ and $j_2$ with positive synaptic weights. It generates a spike at time $t_{i,o}$, while we want it to fire earlier at $t_{i,o}^*$. (b) The spike $t_{i,o}$ is generated in the descending stage of PSP induced by $t_{j_1}$ and the rising stage of PSP induced by $t_{j_2}$. (c) To make neuron $i$ fire earlier towards $t_{i,o}^*$, the derivative of $\partial \mathcal{L}/\partial t_{i,o}$ should be positive according to the stochastic gradient descent rule, i.e., $t_{i,o}^*=t_{i,o}-\gamma \frac{\partial \mathcal{L}}{\partial t_{i,o}}$. In the backpropagation-based algorithm, the derivatives of $\partial \mathcal{L}/\partial t_{j_1}$ and $\partial \mathcal{L}/\partial t_{j_2}$ are expected to be positive due to the positive synaptic connections. However, due to the alpha-shaped kernel, the event-driven learning of SNNs is not well-suited for the backpropagation-based learning algorithm. In the event-driven learning process, achieving an early spike generation for neuron $i$ at $t_{i,o}^*$ requires an increase in the membrane potential $u(t_{i,o}^*)$, which involves enhancing the contributions of $t_{j_1}$ and $t_{j_2}$ to the membrane potential of neuron $i$. The event-driven learning of SNNs achieves this by guiding $t_{j_1}$ to occur later at $t_{j_1}^*$ and $t_{j_2}$ to occur earlier at $t_{j_2 }^*$, resulting in a positive derivative of $\partial \mathcal{L}/\partial t_{j_2}$ and a negative derivative of $\partial \mathcal{L}/\partial t_{j_1}$, where the derivative of $\partial \mathcal{L}/\partial t_{j_1}$ is not behave as expected.
• Figure 2: Adaptive firing threshold-based Integrate-and-Fire (AFT-IF) neuron.
• Figure 3: (a) Four typical surrogate gradient functions in SG algorithms. (b) Corresponding masked surrogate gradient functions in the MPD-ED.
• Figure 4: Ablation studies of the STD-ED on CIFAR datasets, where the IF kernel and the AFT mechanism are ablated. (a) Convergence curves of three comparative methods on CIFAR-10. (b) Accuracy of three comparative methods on CIFAR-10. (c) Convergence curves of three comparative methods on CIFAR-100. (d) Accuracy of three comparative methods on CIFAR-100.
• Figure 5: Ablation studies of the MPD-ED on CIFAR datasets, where only the AFT mechanism is ablated. (a) Convergence curves of two comparative methods on CIFAR-10. (b) Accuracy of two comparative methods on CIFAR-10. (c) Convergence curves of two comparative methods on CIFAR-100. (d) Accuracy of two comparative models on CIFAR-100.