Spiking neural network models characterize the emergent collective dynamics of circuits of biological neurons and help engineer neuro-inspired solutions across fields. Most dynamical systems' models of spiking neural networks typically exhibit one of two major types of interactions: First, the response of a neuron's state variable to incoming pulse signals (spikes) may be additive and independent of its current state. Second, the response may depend on the current neuron's state and multiply a function of the state variable. Here we reveal that spiking neural network models with additive coupling are equivalent to models with multiplicative coupling for simultaneously modified intrinsic neuron time evolution. As a consequence, the same collective dynamics can be attained by state-dependent multiplicative and constant (state-independent) additive coupling. Such a mapping enables the transfer of theoretical insights between spiking neural network models with different types of interaction mechanisms as well as simpler and more effective engineering applications.

翻译：---- 脉冲神经网络模型表征生物神经元集合的集体动态，并帮助在各个领域中设计神经启发式解决方案。大多数脉冲神经网络的动力学模型通常表现出两种主要类型的相互作用。首先，神经元状态变量对传入脉冲信号（脉冲）的响应可能是加法的，与其当前状态无关。其次，响应可能取决于当前神经元状态，并乘以状态变量的函数。在这里，我们揭示了加性耦合的脉冲神经网络模型和乘性耦合模型在同时被修改的内在神经元时间演化方面是等效的。因此，通过状态相关的乘法耦合和常数（状态无关）的加法耦合可实现相同的集体动态。这种映射使得不同类型交互机制的脉冲神经网络模型之间的理论洞见可以互相传递，从而实现更简单、更有效的工程应用。