机器学习（39）

摘要

本文主要讨论了生成式对抗神经网络。首先，本文介绍了生成式对抗网络的设计思路。在此基础下，本文阐述了GAN的网络结构以及训练过程。生成器与解释器相互迭代，随着更新，生成器的效果趋近于真实图片。其次，本文展示了题为Generative Adversarial Networks论文的主要内容。这篇论文提出了生成式对抗网络的网络结构以及训练过程，该模型填补了生成任务方面神经网络的空白。此外，这篇论文还从理论角度证明了生成器的数据分布能够达到全局最优以及训练算法的可收敛性。最后，本文基于pytorch以及MNIST数据集实现了GAN绘制手写数字。

Abstract

This article mainly discusses Generative Adversarial Networks (GANs). Firstly, this article introduces design philosophy of Generative Adversarial Networks is d. Building upon this foundation, the article elucidates the network structure and training process of GANs. The generator and discriminator iteratively improve, and with updates, the generator’s output approaches that of real images. Next, the article presents the key contents of the paper titled “Generative Adversarial Networks”. This paper proposes the network structure and training process of Generative Adversarial Networks, filling a gap in neural networks for generative tasks. Furthermore, the paper theoretically proves that the generator’s data distribution can reach global optimality and demonstrates the convergence of the training algorithm. Finally, based on PyTorch and the MNIST dataset, this article implements GANs to generate hand-written digits.

一、文献阅读

1. 题目

标题：Generative Adversarial Networks

作者：Ian J. Goodfellow, Jean Pouget-Abadie, Mehdi Mirza, Bing Xu, David Warde-Farley, Sherjil Ozair, Aaron Courville, Yoshua Bengio

期刊名：Communications of the ACM

链接：arXiv:1406.2661

2. abstract

该文提出了名为对抗性生成模型的新框架。该框架同时训练两个模型：生成模型G提取数据分布特征，判别模型D分辨输入数据来自训练数据还是由G生成。G的训练过程时最大限度的提高D出错的概率。在文中实验通过对生成样本进行定性和定量评估，展示了该框架的潜力。

This article proposes a new framework for estimating generative models via an adversarial process. This framework includes two model: a generative model G that captures the data distribution, and a discriminative model D that estimates the probability that a sample came from the training data rather than G. Experiments demonstrate the potential of the framework through qualitative and quantitative evaluation of the generated samples in this article.

3. 网络架构

为了学习生成器在数据x上的分布$p_g$，定义输入噪声变量$p_{\mathbf{z}}(\mathbf{z})$的先验概率，然后将到数据空间的映射表示为$G(\mathbf{z};{\theta }_g)$，其中G是由多层感知器表示的可微函数，该函数的参数为${\theta }_g$。此外，定义了输出单个标量的第二个多层感知器$D(\mathbf{x};{\theta }_d)$。 D(x)表示x来自数据而不是$p_g$的概率。以最大化训练数据和G生成样本分配正确标签的概率为目标训练D。同时训练G以最小化$\text{log}(1-D(G(\mathbf{z})))$。从而有如下损失函数：
$${\text{min}}_G{\text{max}}_{D}V(D,G)={\mathbb{E}}_{x\sim p_{data}(\mathbf{x})}[\text{log}D(\mathbf{x})]+{\mathbb{E}}_{x\sim z_z(z)}[\text{log}(1-D(G(\mathbf{z})))]\text{\hspace{1em}(1)}$$

GAN训练时同步更新判别分布（D，蓝色虚线），从而区分数据分布$p_x$（黑色虚线）和生成数据分布$p_g(G)$的样本（绿色实线）。下面水平线是在本例中均匀分布的从z采样的域。上面水平线是x域的一部分。箭头表示$x=G(z)$在变换后样本上施加非均匀分布 p g p_g p