论文标题
通过与重新归一化组建立严格的相应关系来解释深度学习
Interpreting Deep Learning by Establishing a Rigorous Corresponding Relationship with Renormalization Group
论文作者
论文摘要
在本文中，我们关注深神经网络的可解释性。我们的工作是由统计力学重新归一化组（RG）激励的。 RG扮演着连接微观特性和宏观特性的桥梁的作用，其粗晶状程序与神经网络算法的正向传播中层之间的计算非常相似。从这个角度来看，我们建立了深层神经网络（DNN）和RG之间的严格相应关系。具体而言，我们考虑了一维iSing模型的最通用的完全连接的网络结构和真实空间RG。我们证明，当神经网络的参数达到其最佳值时，神经网络输出的耦合常数的极限等于耦合常数的固定点，以一个维度ISING模型的RG中的RG。该结论表明，神经网络的训练过程相当于RG，因此从输入数据中的RG等网络提取宏观特征。
In this paper, we focus on the interpretability of deep neural network. Our work is motivated by the renormalization group (RG) in statistical mechanics. RG plays the role of a bridge connecting microscopical properties and macroscopic properties, the coarse graining procedure of it is quite similar with the calculation between layers in the forward propagation of the neural network algorithm. From this point of view we establish a rigorous corresponding relationship between the deep neural network (DNN) and RG. Concretely, we consider the most general fully connected network structure and real space RG of one dimensional Ising model. We prove that when the parameters of neural network achieve their optimal value, the limit of coupling constant of the output of neural network equals to the fixed point of the coupling constant in RG of one dimensional Ising model. This conclusion shows that the training process of neural network is equivalent to RG and therefore the network extract macroscopic feature from the input data just like RG.
