Generative model approaches to deep learning are of interest in the quest for both better understanding as well as training methods requiring fewer labeled samples. Recent works use generative model approaches to produce the deep net's input given the value of a hidden layer several levels above. However, there is no accompanying "proof of correctness," for the generative model, showing that the feedforward deep net is the correct inference method for recovering the hidden layer given the input. Furthermore, these models are complicated. The current paper takes a more {\em theoretical} tack. It presents a very simple generative model for RELU deep nets, with the following characteristics: (a) The generative model is just the {\em reverse} of the feedforward net: if the forward transformation at a layer is $A$ then the reverse transformation is $A^T$. (This can be seen as an explanation of the old {\em weight tying} method for denoising autoencoders.) (b) Its correctness can be {\em proven} under a clean theoretical assumption: the edge weights in real-life deep nets behave like random numbers. Under this assumption ---which is experimentally tested on real-life nets like AlexNet--- it is formally proved that feed forward net is a correct inference method for recovering the hidden layer. (c) The generative model suggests a simple modification for training---use an input to produce several synthetic inputs with the same label, and include them in the backprop training. This appears to yield benefits similar to dropout, and can also be seen as a generative explanation for the efficacy of dropout.

本文简单证明根据生成模型产生的反向网络是正确的推理方法。在一个简单的生成模型中，证明前向神经网络是正确的推理方法，它通过实验证明了像AlexNet这样的现实的深度神经网络的边缘权重的行为类似于随机数。它利用生成模型来产生带有标签的合成数据，并将其包含在训练集中，为深度学习提供改进和标准训练方法。

深度神经网络为什么是可逆的：一个简单的理论，以及对训练的影响