论文标题
神经网络与高斯混合物分布的收敛
Convergence of neural networks to Gaussian mixture distribution
论文作者
论文摘要
我们提供了一个证明，在相对温和的条件下，完全连接的馈送深层随机神经网络会收敛到高斯混合物分布，因为最后一个隐藏层的宽度仅为无穷大。我们进行了一个简单模型的实验，以支持我们的结果。此外，它详细描述了收敛性，即最后一个隐藏层的生长使分布更接近高斯混合物，而另一层依次使高斯混合物更接近正态分布。
We give a proof that, under relatively mild conditions, fully-connected feed-forward deep random neural networks converge to a Gaussian mixture distribution as only the width of the last hidden layer goes to infinity. We conducted experiments for a simple model which supports our result. Moreover, it gives a detailed description of the convergence, namely, the growth of the last hidden layer gets the distribution closer to the Gaussian mixture, and the other layer successively get the Gaussian mixture closer to the normal distribution.
