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特性，并有助于跨领域工程化神经启发式解决方案。大多数脉冲神经网络的动力学系统模型通常呈现两种主要相互作用类型：其一，神经元状态变量对传入脉冲信号的响应可能是加性的，且独立于其当前状态；其二，该响应可能依赖于神经元当前状态，并与状态变量的函数相乘。本文揭示，对于同时修正的固有神经元时间演化，具有加性耦合的脉冲神经网络模型与具有乘性耦合的模型等价。因此，通过依赖于状态的乘性耦合与恒定（状态无关）的加性耦合，能够实现相同的集体动力学特性。这一映射关系使得理论洞见可在具有不同类型相互作用机制的脉冲神经网络模型之间迁移，并促进更简单高效的工程应用。