1x1 convolution for inception module

Question

When understanding the inception module, I once saw the following statement from an online post. What's the calculation underline the "192 28×28 sized feature maps can be reduced to 64 28×28 feature maps through 64 1×1 convolutions"

Inception modules in convolutional networks were designed to allow for deeper and larger convolutional layers while at the same time allowing for more efficient computation. This is done by using 1×1 convolutions with small feature map size, for example, 192 28×28 sized feature maps can be reduced to 64 28×28 feature maps through 64 1×1 convolutions.

Answer 1

My two cents on understanding the 1x1 convolution:

It is a two dimension version of dense layer

From 192x28x28 to 64x28x28, it is like a dense layer with 192 inputs and 64 outputs, and this layer is applied to 28x28 image. So the calculation is performing feature maps combination and dimension reduction on the axis of 192.

Answer 2

Here is an illustration of a similar conversion.

There are 32 filters(in your case 64) converting the channel dimension from 192 to 32.

Answer 3

For every convolution, you can freely choose the number of filters (= depth) . In you example, this choice was 64. So there is no calculation behind the number 64 at all.

The feature map size remains 28 because there are no strides > 1 and no boundary effects.