Equivalence of Additive and Multiplicative Coupling in Spiking Neural Networks

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 deterministic 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 results between spiking neural network models with different types of interaction mechanisms and at the same time extends the option space for hardware implementation or modeling. By allowing to choose the coupling type or neuron type that is the simplest one to implement in a given practical situation where a specific dynamic or functionality is required, it potentially allows simpler or more effective engineering applications.