If the data dimension is 16 x 16, filter 5×5, and stride 1, then what is the amount of padding required so that convolution output has the same dimension as the input?
The correct answer and explanation is:
✅ Correct Answer:
Padding = 2
📘 Explanation:
To determine the amount of padding required so that the output size equals the input size after applying a convolutional filter, we use the convolution output size formula: Output size=(N+2P−F)S+1\text{Output size} = \frac{(N + 2P – F)}{S} + 1
Where:
- NN = Input size (16)
- FF = Filter size (5)
- SS = Stride (1)
- PP = Padding (what we’re solving for)
We want the output size = input size, so: 16=(16+2P−5)1+116 = \frac{(16 + 2P – 5)}{1} + 1
🔍 Step-by-step:
- Subtract 1 from both sides: 15=16+2P−515 = 16 + 2P – 5
- Simplify the right side: 15=11+2P15 = 11 + 2P
- Subtract 11 from both sides: 4=2P4 = 2P
- Divide both sides by 2: P=2P = 2
📌 Interpretation:
This means you must add a padding of 2 pixels on all sides (top, bottom, left, right) of the 16×16 input to ensure that, after applying a 5×5 filter with stride 1, the output remains 16×16.
🧠 Why Padding Matters:
Without padding, convolution reduces the dimensions of your feature map. In applications like image classification or deep learning, we often want to preserve spatial dimensions for consistency across layers—especially in same padding (also called “zero-padding”), which keeps the output size equal to the input size.
So, for “same” convolution:
- Filter size: 5×5
- Padding required: (Filter size – 1)/2 = (5 – 1)/2 = 2
✅ Hence, Padding = 2 is the correct and required value.