  Gradients play a pivotal role in neural networks explanation. The inherent
high dimensionality and structural complexity of neural networks result in the
original gradients containing a significant amount of noise. While several
approaches were proposed to reduce noise with smoothing, there is little
discussion of the rationale behind smoothing gradients in neural networks. In
this work, we proposed a gradient smooth theoretical framework for neural
networks based on the function mollification and Monte Carlo integration. The
framework intrinsically axiomatized gradient smoothing and reveals the
rationale of existing methods. Furthermore, we provided an approach to design
new smooth methods derived from the framework. By experimental measurement of
several newly designed smooth methods, we demonstrated the research potential
of our framework.
