Understanding convolutions

1. How do you explain convolution?
2. How are convolutions calculated?
3. How do convolutions work in CNN?
4. Why does a 1X1 convolution do?

How do you explain convolution?

The term convolution refers to both the result function and to the process of computing it. It is defined as the integral of the product of the two functions after one is reflected about the y-axis and shifted.

How are convolutions calculated?

The height of the function at a time t=i·ΔT is f(i·ΔT). The area of the impulse at t=i·ΔT is f(i·ΔT)·ΔT. The delayed and shifted impulse response is given by f(i·ΔT)·ΔT·h(t-i·ΔT). This is the Convolution Theorem.

How do convolutions work in CNN?

Convolution is a mathematical operation that allows the merging of two sets of information. In the case of CNN, convolution is applied to the input data to filter the information and produce a feature map. This filter is also called a kernel, or feature detector, and its dimensions can be, for example, 3x3.

Why does a 1X1 convolution do?

1x1 convolutions are used to compute reductions before the expensive 3x3 and 5x5 convolutions. Besides being used as reductions, they also include the use of rectified linear activation which makes them dual-purpose.