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：脉冲神经网络模型刻画了生物神经元回路中涌现的集体动力学，并有助于跨领域设计神经启发式工程方案。多数脉冲神经网络的动力学模型通常呈现两类主要相互作用：其一，神经元状态变量对传入脉冲信号的响应是加性的，且不依赖于其当前状态；其二，响应可能依赖于当前神经元状态，并与状态变量的函数相乘。本文揭示，在同时调整内在神经元时间演化规律的情况下，具有加性耦合的脉冲神经网络模型等价于具有乘性耦合的模型。因此，相同的集体动力学可通过状态依赖的乘性耦合与恒定（状态无关的）加性耦合实现。这种映射机制使得不同相互作用类型的脉冲神经网络模型之间能够迁移理论洞见，同时简化并提升工程应用的有效性。