Developer Guide for Intel® Data Analytics Acceleration Library 2019 Update 5

2D Convolution Backward Layer

The forward two-dimensional (2D) convolution layer applies a set of nKernels 2D kernels K of size m 3 x m 4 to the input tensor X. The library supports four-dimensional input tensors XR n 1 x n 2 x n 3 x n 4 . Therefore, the following formula applies:



where i + u < n 3, j + v < n 4, and r is the kernel index.

For more details, see Forward 2D Convolution Layer.

The backward 2D convolution layer computes the derivatives of the objective function E:

Problem Statement

Without loss of generality, let's assume that convolution kernels are applied to the last two dimensions.

Given:

For the above tensors:

The problem is to compute:

In the above formulas: