论文标题
用广义置换的枚举最大响应的枚举
Enumeration of max-pooling responses with generalized permutohedra
论文作者
论文摘要
我们研究了最大层层的组合，这些层是通过将输入坐标的最大移动窗口放置在输入阵列的函数，并且通常在卷积神经网络中使用。我们通过等效地计算某些Minkowski简单总和的顶点数量来获得这些函数线性区域数量的结果。我们表征了此类多型的面部，并根据合并窗口和大步的大小以及在2D Max-Max-Pooling的特殊情况下，在1D最大式层中获得了最大最大层的顶点和刻面数量的封闭公式。
We investigate the combinatorics of max-pooling layers, which are functions that downsample input arrays by taking the maximum over shifted windows of input coordinates, and which are commonly used in convolutional neural networks. We obtain results on the number of linearity regions of these functions by equivalently counting the number of vertices of certain Minkowski sums of simplices. We characterize the faces of such polytopes and obtain generating functions and closed formulas for the number of vertices and facets in a 1D max-pooling layer depending on the size of the pooling windows and stride, and for the number of vertices in a special case of 2D max-pooling.
