Spiking neural networks (SNNs) offer a promising energy-efficient alternative to artificial neural networks (ANNs), in virtue of their high biological plausibility, rich spatial-temporal dynamics, and event-driven computation. The direct training algorithms based on the surrogate gradient method provide sufficient flexibility to design novel SNN architectures and explore the spatial-temporal dynamics of SNNs. According to previous studies, the performance of models is highly dependent on their sizes. Recently, direct training deep SNNs have achieved great progress on both neuromorphic datasets and large-scale static datasets. Notably, transformer-based SNNs show comparable performance with their ANN counterparts. In this paper, we provide a new perspective to summarize the theories and methods for training deep SNNs with high performance in a systematic and comprehensive way, including theory fundamentals, spiking neuron models, advanced SNN models and residual architectures, software frameworks and neuromorphic hardware, applications, and future trends. The reviewed papers are collected at https://github.com/zhouchenlin2096/Awesome-Spiking-Neural-Networks
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