Title: Accelerating spiking neural network training using the $d$-block model. Abstract: There is a growing interest in using spiking neural networks (SNNs) to study the brain \textit{in silico} and in emulating them on neuromorphic computers due to their lower energy consumption compared to artificial neural networks (ANNs). Significant progress has been made in directly training SNNs to perform on a par with ANNs in terms of accuracy. However, these methods are slow due to their sequential nature and require careful network regularisation to avoid overfitting. We propose a new SNN model, the $d$-block model, with stochastic absolute refractory periods and recurrent conductance latencies, which reduces the number of sequential computations using fast vectorised operations. Our model obtains accelerated training speeds and state-of-the-art performance across various neuromorphic datasets without the need for any regularisation and using fewer spikes compared to standard SNNs.