Means no padding.
$$n \times n * f \times f = (n - f + 1) \times (n - f + 1)$$

Valid Convolution in DNN

Means padding so that output size is the same as the input size.
$$(n + 2p) \times (n + 2p) * f \times f = (n + 2p - f + 1) \times (n + 2p - f + 1)$$
In order to make the output size the same as the input size:
$$n + 2p - f + 1 = n \Rightarrow p = \frac{f - 1}{2}$$

Same Convolution in DNN

There are generally two types of padding configurations used in convolutional neural networks: 'valid' convolution, which means no padding is applied, and 'same' convolution, which applies padding such that the output size matches the input size.

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