论文标题
高斯混合卷积网络
Gaussian Mixture Convolution Networks
论文作者
论文摘要
本文提出了一种基于多维高斯混合物的分析卷积进行深度学习的新方法。与张量相反，这些不受维数的诅咒并允许紧凑的表示，因为数据仅在存在细节的情况下存储。卷积内核和数据是高斯混合物，具有不受限制的权重，位置和协方差矩阵。与离散的卷积网络类似，每个卷积步骤都会产生多个特征通道，以独立的高斯混合物表示。由于诸如Relus之类的传统转移功能不会产生高斯混合物，因此我们建议使用这些功能的拟合。如果适当减少高斯组件的数量，则此拟合步骤也充当汇总层。我们证明，基于此体系结构的网络对适合MNIST和ModelNet数据集的高斯混合物达到竞争精度。
This paper proposes a novel method for deep learning based on the analytical convolution of multidimensional Gaussian mixtures. In contrast to tensors, these do not suffer from the curse of dimensionality and allow for a compact representation, as data is only stored where details exist. Convolution kernels and data are Gaussian mixtures with unconstrained weights, positions, and covariance matrices. Similar to discrete convolutional networks, each convolution step produces several feature channels, represented by independent Gaussian mixtures. Since traditional transfer functions like ReLUs do not produce Gaussian mixtures, we propose using a fitting of these functions instead. This fitting step also acts as a pooling layer if the number of Gaussian components is reduced appropriately. We demonstrate that networks based on this architecture reach competitive accuracy on Gaussian mixtures fitted to the MNIST and ModelNet data sets.
