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摘要: 生成式对抗网络（Generative adversarial network，GAN）是目前人工智能领域的一个研究热点，引起了众多学者的关注.针对现有GAN生成模型效率低下和判别模型的梯度消失问题，本文提出一种基于重构误差的能量函数意义下的生成式对抗网络模型（Energy reconstruction error GAN，E-REGAN）.首先，将自适应深度信念网络（Adaptive deep belief network，ADBN）作为生成模型，来快速学习给定样本数据的概率分布并进一步生成相似的样本数据.其次，将自适应深度自编码器（Adaptive deep autoencoder，ADAE）的重构误差（Reconstruction error，RE）作为一个表征判别模型性能的能量函数，能量越小表示GAN学习优化过程越趋近纳什均衡的平衡点，否则反之.同时，通过反推法给出了E-REGAN的稳定性分析.最后在MNIST和CIFAR-10标准数据集上的实验结果表明，相较于现有的类似模型，E-REGAN在学习速度和数据生成能力两方面均有较大提高.Abstract: Generative adversarial network (GAN) has become a hot research in artificial intelligence, and has received much attention from scholars. In view of low efficiency of generative model and gradient disappearance of discriminative model, a GAN based on energy function (E-REGAN) is proposed in this paper, in which reconstruction error (RE) acts as the energy function. Firstly, an adaptive deep belief network (ADBN) is presented as the generative model, which is used to fast learn the probability distribution of given sample data and further generate new data with similar probability distribution. Secondly, the RE in adaptive deep auto-encoder (ADAE) acts as an energy function evaluating the performance of discriminative model; the smaller energy function, the closer to Nash equilibrium the learning optimization process of GAN will be, and vice versa. Meanwhile, the stability analysis of the proposed E-REGAN is given using the inverse inference method. Finally, the simulation results from MNIST and CIFAR-10 benchmark dataset experiments show that, compared with the existing similar models, the proposed E-REGAN achieves significant improvement in learning rate and data generation capability.1) 本文责任编委 王坤峰
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表 1 MNIST数据集测试中ADBN的固有参数
Table 1 Fixed parameters of ADBN on MNIST dataset
$\eta_0$ $\tau$ $t$ $u$ $v$ $\lambda$ $\gamma $ 0.1 200 2 1.5 0.7 0.02 0.01 $ \eta _0 $表示学习率的初始值 
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表 3 CIFAR-10数据集测试中ADBN的固有参数
Table 3 Fixed parameters of ADBN on CIFAR-10 dataset
$\eta_0$ $\tau$ $t$ $u$ $v$ $\lambda$ $\gamma $ 0.1 300 2 1.7 0.5 0.05 0.02 $ \eta _0 $表示学习率的初始值.
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表 4 CIFAR-10数据集实验结果对比
Table 4 Result comparison on CIFAR-10 dataset
方法 能量函数 测试误差 平均运行时间(s) 均值 方差 均值 方差 E-REGAN 0.0048 0.0831 0.0160 0.0831 65.38 SS-E-REGAN 0.0473 2.2406 0.0431 2.2406 65.75 SN-E-REGAN 0.2097 2.8119 0.0633 2.8119 67.92 标准GAN – – 0.0802 1.9227 90.68 LS-GAN[27] – – 0.0358 0.1076 78.24 LR-GAN[28] – – 0.0263 0.1547 84.36 Bayesian GAN[29] – – 0.0386 0.2037 86.19 粗体表示最优值.
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