Title: Adaptive Smoothing Gradient Learning for Spiking Neural Networks. Abstract: Spiking neural networks (SNNs) with biologically inspired spatio-temporal dynamics show higher energy efficiency on neuromorphic architectures. Error backpropagation in SNNs is prohibited by the all-or-none nature of spikes. The existing solution circumvents this problem by a relaxation on the gradient calculation using a continuous function with a constant relaxation degree, so-called surrogate gradient learning. Nevertheless, such solution introduces additional smoothness error on spiking firing which leads to the gradients being estimated inaccurately. Thus, how to adjust the relaxation degree adaptively and eliminate smoothness error progressively is crucial. Here, we propose a methodology such that training a prototype neural network will evolve into training an SNN gradually by fusing the learnable relaxation degree into the network with random spike noise. In this way, the network learns adaptively the accurate gradients of loss landscape in SNNs. The theoretical analysis further shows optimization on such a noisy network could be evolved into optimization on the embedded SNN with shared weights progressively. Moreover, we conduct extensive experiments on static images, dynamic event streams, speech, and instrumental sounds. The results show the proposed method achieves state-of-the-art performance across all the datasets with remarkable robustness on different relaxation degrees.