Developer Guide for Intel® Data Analytics Acceleration Library 2017 Update 3

# 2D Convolution Forward Layer

The forward two-dimensional (2D) convolution layer computes the tensor Y of values by applying 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.

## Problem Statement

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

Given:

• Four-dimensional tensor X R n 1 x n 2 x n 3 x n 4 with input data

• Four-dimensional tensor K R nKernels x m 2 x m 3 x m 4 with kernel parameters/weights of kernels (convolutions)

• One-dimensional tensor B R nKernels with the bias of each kernel.

For the above tensors:

• and p i is the respective padding.

• nGroups is defined as follows: let's assume that n 2 is the group dimension. The input tensor is split along this dimension into nGroups groups, the tensors of values and weights are split into nGroups groups along the nKernels dimension. nKernels and n 2 must be multiples of nGroups. Each group of values is computed using the respective group in tensors of input data, weights, and biases.

The problem is to compute the four-dimensional tensor of values Y R n 1 x nKernels x l 3 x l 4 such that:

where:

• s 3 and s 4 are strides