Spiking Neural Networks: Learning as Point Processes

During task learning, neurons adjust their synaptic connections through local mechanisms, enabling them to fire together in response to specific concepts, forming what are known as neuronal assemblies and driving global behaviors. These processes have inspired early machine learning algorithms and continue to yield increasing empirical results in biologically inspired neural networks. However, a gap remains between the empirical findings and the underlying theory, and the transition from neuronal mechanisms to cognitive behavior remains poorly understood.
To address this issue, we designed a simple biologically inspired neural network and mathematically proved that it can achieve global learning by automatically producing neuronal assemblies while relying solely on learning rules local to the synapse. Then, we established strong approximation results between cognitive models renowned for accurately modeling behavior, and spiking neural models including our own, providing evidence on how neural dynamics lead to specific behaviors.