Сверточная операция

The following two-step mathematical operation: 1. Element-wise multiplication of the convolutional filter and a slice of an input matrix. (The slice of the input matrix has the same rank and size as the convolutional filter.) 2. Summation of all the values in the resulting product matrix. For example, consider the following 5x5 input matrix: ![The 5x5 matrix: \\[\\[128,97,53,201,198\\], \\[35,22,25,200,195\\], \\[37,24,28,197,182\\], \\[33,28,92,195,179\\], \\[31,40,100,192,177\\]\\].](https://developers.google.com/static/machine-learning/glossary/images/ConvolutionalLayerInputMatrix.svg) Now imagine the following 2x2 convolutional filter: Each convolutional operation involves a single 2x2 slice of the input matrix. For example, suppose we use the 2x2 slice at the top-left of the input matrix. So, the convolution operation on this slice looks as follows: ![Applying the convolutional filter \\[\\[1, 0\\], \\[0, 1\\]\\] to the top-left 2x2 section of the input matrix, which is \\[\\[128,97\\], \\[35,22\\]\\]. The convolutional filter leaves the 128 and 22 intact, but zeroes out the 97 and 35. Consequently, the convolution operation yields the value 150 (128+22).](https://developers.google.com/static/machine-learning/glossary/images/ConvolutionalLayerOperation.svg) A convolutional layer consists of a series of convolutional operations, each acting on a different slice of the input matrix.