Pooling

Reducing a matrix (or matrixes) created by an earlier convolutional layer to a smaller matrix. Pooling usually involves taking either the maximum or average value across the pooled area. For example, suppose we have the following 3x3 matrix: A pooling operation, just like a convolutional operation, divides that matrix into slices and then slides that convolutional operation by strides. For example, suppose the pooling operation divides the convolutional matrix into 2x2 slices with a 1x1 stride. As the following diagram illustrates, four pooling operations take place. Imagine that each pooling operation picks the maximum value of the four in that slice: ![The input matrix is 3x3 with the values: \\[\\[5,3,1\\], \\[8,2,5\\], \\[9,4,3\\]\\]. The top-left 2x2 submatrix of the input matrix is \\[\\[5,3\\], \\[8,2\\]\\], so the top-left pooling operation yields the value 8 (which is the maximum of 5, 3, 8, and 2). The top-right 2x2 submatrix of the input matrix is \\[\\[3,1\\], \\[2,5\\]\\], so the top-right pooling operation yields the value 5. The bottom-left 2x2 submatrix of the input matrix is \\[\\[8,2\\], \\[9,4\\]\\], so the bottom-left pooling operation yields the value 9. The bottom-right 2x2 submatrix of the input matrix is \\[\\[2,5\\], \\[4,3\\]\\], so the bottom-right pooling operation yields the value 5. In summary, the pooling operation yields the 2x2 matrix \\[\\[8,5\\], \\[9,5\\]\\].](https://developers.google.com/static/machine-learning/glossary/images/PoolingConvolution.svg) Pooling helps enforce translational invariance in the input matrix. Pooling for vision applications is known more formally as spatial pooling . Time-series applications usually refer to pooling as temporal pooling . Less formally, pooling is often called subsampling or downsampling.