Stride, padding, and dilation

3.4.2 · AI-ML › Convolutional Neural Networks

Ye Kyun Matter Karte Hain

Standard convolution ek kernel ko pixel-by-pixel slide karta hai. Lekin:

1. Stride > 1: Pooling se bhi fast downsample karta hai, computation bachata hai
2. Padding: Spatial dimensions ko bahut tezi se shrink hone se rokta hai (border pixels fairly use hote hain)
3. Dilation: Long-range dependencies pakadta hai bina deep stacks ya bade kernels ke

Milke ye architectural flexibility dete hain: receptive field, output size, aur parameter count ko independently control karo.

1. Stride: The Step Size

Output Size Formula Derivation

Setup: Input size $W_{in}$, kernel size $k$, stride $s$, padding $p$.

YE FORMULA KYUN? Count karo ki kitni valid filter positions fit hoti hain:

• Padding ke baad, effective input size: $W_{in}+2p$
• Pehli filter position: pixel 0
• Har stride $s$ pixels move karta hai
• Last valid position: filter bilkul fit hona chahiye, isliye rightmost filter edge ≤ $W_{in}+2p-1$
• Rightmost filter shuru hota hai: $(W_{in}+2p)-k$ par

0 se $(W_{in}+2p-k)$ tak positions ki number, step $s$ ke saath:

$W_{out}=\lfloor \frac{W_{in}+2p-k}{s}\rfloor +1$

HAR TERM KA MATLAB:

• Numerator $(W_{in}+2p-k)$: pehla filter place karne ke baad "slack space"
• $s$ se divide karo: us slack mein kitne strides fit hote hain
• $+1$: starting position khud ko count karo
• Floor: sirf integer steps le sakte hain

2. Padding: Border Strategy

Types of Padding

Valid Padding ($p=0$): Koi padding nahi, output shrink hoti hai $W_{out}=W_{in}-k+1\text{(jab }s=1\text{)}$

Same Padding: $p$ choose karo taaki $W_{out}=W_{in}$ ho (jab $s=1$)

Derivation: Formula mein $W_{out}=W_{in}$ set karo: $W_{in}=\frac{W_{in}+2p-k}{1}+1$ $W_{in}-1=W_{in}+2p-k$ $2p=k-1$ $p=\frac{k-1}{2}$

Odd $k$ ke liye (jaise 3, 5, 7), ye integer $p$ deta hai. Even $k$ ke liye, asymmetrically pad karo.

Padding Kyun Matter Karta Hai

1. Information preservation: Edge pixels multiple convolutions mein participate karte hain
2. Depth control: Spatial collapse ke bina deep networks build kar sakte ho
3. Symmetry: Border pixels unfairly underrepresented nahi hote

3. Dilation: Receptive Field Expand Karna

Effective Kernel Size ki Derivation

DILATION KYA HAI? Adjacent kernel weights ke har pair ke beech $(d-1)$ zeros insert karo.

Original kernel: ek row mein $k$ elements
Gaps insert hue: $(k-1)$ gaps ($k$ elements ke beech)
Pixels per gap: $(d-1)$ pixels

Total span:

• Kernel elements: $k$ pixels
• Gap space: $(k-1)(d-1)$ pixels
• Total: $k+(k-1)(d-1)$

YE KAISE KAAM KARTA HAI: $3\times 3$ kernel ke saath $d=2$:

Original:        Dilated (d=2):
X X X            X . X . X
X X X    -->     . . . .
X X X            X . X . X
                . . . . .
                X . X . X

Effective size: $3+(3-1)(2-1)=3+2=5\times 5$ receptive field

Combined Formula

Design Patterns

Atrous Spatial Pyramid Pooling (ASPP): Multiple parallel dilations $(d=1,6,12,18)$ use karo $k=3$ ke saath multi-scale context efficiently capture karne ke liye.

Connections

• Convolutional Layer Basics - ye basic conv operation ke hyperparameters hain
• Receptive Field Analysis - stride aur dilation seedha receptive field expand karte hain
• Pooling Layers - stride downsampling ke liye pooling ka alternative provide karta hai
• Semantic Segmentation Architectures - dilated convolutions dense prediction ke liye critical hain
• Network Depth vs Width - dilation excessive parameters ke bina depth allow karta hai

#flashcards/ai-ml

Convolution mein stride kya hota hai? :: Vo number of pixels jitna filter applications ke beech move karta hai. Stride $s$ step size aur downsampling factor control karta hai.

Concept Map