论文标题
随机矩阵理论证明，Gan-Data的深度学习表示形式是高斯混合物
Random Matrix Theory Proves that Deep Learning Representations of GAN-data Behave as Gaussian Mixtures
论文作者
论文摘要
本文表明，生成对抗网（gans）产生的数据的深度学习（DL）表示是随机向量，它们属于所谓的\ textit {浓缩}随机向量的类别。进一步利用以下事实：gram矩阵，$ g = x^t x $，$ x = [x_1，\ ldots，x_n] \ in \ mathbb {r}^{r}^{p \ times n} $和$ x_i $ $ x_i $ $ $ $ $ $ $ $ $从高斯混合物中得出的，这表明GAN-DATA的DL表示可以通过其前两个统计矩对广泛的标准分类器进行充分描述。我们的理论发现是通过使用BigGan模型以及通过不同流行的深层表示网络生成图像来验证的。
This paper shows that deep learning (DL) representations of data produced by generative adversarial nets (GANs) are random vectors which fall within the class of so-called \textit{concentrated} random vectors. Further exploiting the fact that Gram matrices, of the type $G = X^T X$ with $X=[x_1,\ldots,x_n]\in \mathbb{R}^{p\times n}$ and $x_i$ independent concentrated random vectors from a mixture model, behave asymptotically (as $n,p\to \infty$) as if the $x_i$ were drawn from a Gaussian mixture, suggests that DL representations of GAN-data can be fully described by their first two statistical moments for a wide range of standard classifiers. Our theoretical findings are validated by generating images with the BigGAN model and across different popular deep representation networks.
