Short Definition

Same padding preserves the spatial dimensions of an input after convolution, while valid padding applies no padding and reduces the output size.

Same = preserve size.
Valid = no padding, shrink size.

Definition

In convolutional neural networks (CNNs), padding determines how the convolutional kernel interacts with the borders of an input.

Two common padding strategies are:

1. Same Padding
2. Valid Padding

Padding influences:

• Output dimensions
• Edge behavior
• Receptive field coverage
• Information retention at boundaries

I. Valid Padding

Valid padding applies no padding to the input.

Convolution only occurs where the kernel fully overlaps the input.

Output size:

[
\text{Output} = \frac{N – K}{S} + 1
]

Where:

• N = input size
• K = kernel size
• S = stride

Result:

Output size is smaller than input.

Example:

Input: 5×5
Kernel: 3×3
Stride: 1

Output: 3×3

Valid padding reduces spatial resolution.

II. Same Padding

Same padding adds zeros around the input so that the output size equals the input size (for stride = 1).

Padding size is chosen so:

[
\text{Output} = N
]

For odd kernel size K:

[
\text{Padding} = \frac{K – 1}{2}
]

Example:

Input: 5×5
Kernel: 3×3
Stride: 1

Padding: 1 pixel on each side

Output: 5×5

Same padding preserves dimensions.

Minimal Conceptual Illustration

Valid:
[Input] → Convolution → Smaller output

Same:
[Input] → Zero padding → Convolution → Same size output

Padding determines border behavior.

Why Padding Matters

1. Feature Map Size Control

Same padding:

• Preserves resolution.
• Easier stacking of layers.
• Common in deep CNNs.

Valid padding:

• Shrinks feature maps.
• Useful for progressive spatial compression.

2. Edge Information

Valid padding:

• Ignores borders partially.
• Reduces boundary artifacts.

Same padding:

• Introduces artificial zero context.
• May distort edge activations.

Padding changes how edge features are treated.

Relationship to Receptive Fields

Valid padding:

• Shrinks spatial dimension.
• Receptive field grows relative to feature map size.

Same padding:

• Keeps spatial size constant.
• Receptive field grows more gradually.

Padding affects hierarchical representation scaling.

Interaction with Stride

If stride > 1:

Same padding no longer strictly preserves size.

General formula:$$\text{Output} = \left\lceil \frac{N}{S} \right\rceil$$Output=⌈SN​⌉

Same padding preserves relative scale but not exact size for S > 1.

Stride and padding interact jointly.

Relationship to Strided Convolution vs Pooling

Pooling often uses valid-style behavior (no padding).

Strided convolutions frequently use same padding.

Downsampling design combines stride and padding choices.

Practical Design Choices

Early CNNs:

• Often used valid padding.

Modern CNNs:

• Frequently use same padding for stability and simplicity.

Vision Transformers:

• Use patch embeddings instead of convolution padding.

Edge Effects & Bias

Zero padding (same):

• Assumes missing context equals zero.
• May introduce boundary bias.

Alternative padding strategies:

• Reflect padding
• Replicate padding
• Circular padding

These address edge artifacts differently.

Architectural Comparison

Aspect	Same Padding	Valid Padding
Padding added	Yes	No
Output size (S=1)	Same as input	Smaller
Edge influence	Zero-context assumption	Edge ignored partially
Common in deep nets	Yes	Less common
Spatial shrinkage	No	Yes

When to Use Each

Same Padding:

• Deep CNN stacks
• Feature alignment across layers
• Tasks needing spatial consistency

Valid Padding:

• When spatial shrinkage is desired
• When avoiding artificial edge assumptions
• Early feature compression stages

Long-Term Architectural Implications

Padding choices influence:

• Spatial bias
• Hierarchical feature formation
• Model inductive bias
• Boundary robustness

Small implementation choices accumulate across depth.

Related Concepts

• Convolution Operation
• Stride and Padding
• Receptive Fields
• Strided Convolution vs Pooling
• Dilated Convolutions
• Feature Maps