The synergy between spiking neural networks and neuromorphic hardware holds promise for the development of energy-efficient AI applications. Inspired by this potential, we revisit the foundational aspects to study the capabilities of spiking neural networks where information is encoded in the firing time of neurons. Under the Spike Response Model as a mathematical model of a spiking neuron with a linear response function, we compare the expressive power of artificial and spiking neural networks, where we initially show that they realize piecewise linear mappings. In contrast to ReLU networks, we prove that spiking neural networks can realize both continuous and discontinuous functions. Moreover, we provide complexity bounds on the size of spiking neural networks to emulate multi-layer (ReLU) neural networks. Restricting to the continuous setting, we also establish complexity bounds in the reverse direction for one-layer spiking neural networks.

翻译：脉冲神经网络与神经形态硬件之间的协同作用，为开发节能型人工智能应用带来了希望。受此潜力启发，我们重新审视基础层面，研究信息编码于神经元脉冲触发时间的脉冲神经网络的能力。基于作为具有线性响应函数的脉冲神经元数学模型的脉冲响应模型，我们比较了人工神经网络与脉冲神经网络的表达能力，初步表明它们均能实现分段线性映射。与ReLU网络不同，我们证明脉冲神经网络既能实现连续函数，也能实现不连续函数。此外，我们给出了脉冲神经网络模拟多层（ReLU）神经网络的复杂度上界。在连续函数设定下，我们还建立了单层脉冲神经网络反向模拟的复杂度上界。