The result of the dimension after applying a convolutional operation depends on several factors, including the input size, filter size, stride, and padding. The formula to calculate the output size of a convolutional layer can be expressed as follows:

Here's a breakdown of the terms in the formula:

**Input Size**: The size of the input feature map or image.

**Filter Size**: The size of the convolutional filter (kernel).

**Padding**: The number of pixels added around the input to avoid **border effects**. It can be zero (valid/no padding), or the filter size minus one divided by 2 (same/symmetric padding).

Stride: The step size at which the filter moves across the input.

Let's go through an example to illustrate how the output size is calculated:

These examples demonstrate how changes in the filter size, padding, and stride affect the size of the output feature map after a convolutional operation. The specific values for these parameters depend on the design choices made for the convolutional layer in a neural network.

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