08. Convolutional Operations: Kernels, Filters, Strides, Padding & Feature Map Dilation • Deep Learning & PyTorch Neural Networks Architecture • Rishabh Ki Kaksha

Deep Learning & PyTorch Neural Networks Architecture › 08. Convolutional Operations: Kernels, Filters, Strides, Padding & Feature Map Dilation

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Course Syllabus

Module 1: PyTorch Tensors, Autograd & Computational Graphs

01. PyTorch Tensor Architecture: Strides, Storage Buffers, Memory Layout (Contiguous vs Non-Contiguous) 02. Dynamic Computational Graphs & The PyTorch Autograd Engine (grad_fn, requires_grad, backward) 03. GPU Acceleration with CUDA: Tensor Device Placement (to("cuda")), CUDA Streams & Pinned Memory

Module 2: Multi-Layer Perceptrons (MLPs) & Custom Training Loops

04. Building Custom nn.Module Classes, Custom Parameters & Activation Functions (ReLU, GELU, Swish) 05. Custom Datasets & High-Performance DataLoaders (num_workers, collate_fn, pin_memory) 06. The Enterprise Training Loop: Forward Pass, Loss Computation, Zero Grad, Backward Pass & Optimizer Step 07. Neural Regularization Techniques: Dropout, Batch Normalization (BatchNorm1d) & Layer Normalization (LayerNorm)

Module 3: Convolutional Neural Networks (CNNs) & Computer Vision Architecture

08. Convolutional Operations: Kernels, Filters, Strides, Padding & Feature Map Dilation 09. Modern CNN Architectures: Residual Connections (ResNet), Squeeze-and-Excitation & ConvNeXt 10. Transfer Learning & Vision Fine-Tuning with Torchvision Pretrained Models

Module 4: Recurrent Architectures: RNNs, LSTMs & GRUs for Sequential Data

11. Sequential Modeling: Vanilla RNNs & The Vanishing / Exploding Gradient Problem 12. Long Short-Term Memory (LSTM) Networks: Forget Gate, Input Gate, Candidate State & Output Gate Math 13. Gated Recurrent Units (GRUs) & Bidirectional Sequence Processing in PyTorch

Module 5: Modern Transformer Architecture from Scratch in PyTorch

14. Scaled Dot-Product Attention: Query, Key, Value Matrices & Attention Softmax Calculation 15. Multi-Head Attention (MHA) & Causal Masking Implementation from Scratch in Pure PyTorch 16. Building a Complete GPT-Style Decoder-Only Transformer Language Model from Scratch

Module 6: PyTorch Distributed (DDP), Mixed Precision (AMP) & Model Checkpointing

17. Automatic Mixed Precision (torch.cuda.amp.autocast & GradScaler) for 2x Faster GPU Training 18. Distributed Data Parallel (DDP) Architecture: Multi-GPU Synchronization with torch.distributed 19. Robust Checkpointing: Saving State Dicts, Resuming Training & Early Stopping Callbacks 20. Model Export & Production Serialization: TorchScript (JIT Tracing), ONNX & TensorRT Compilation

Interactive Lesson Studio

# 08. Convolutional Operations: Kernels, Filters, Strides, Padding & Feature Map Dilation

> Deep Learning & PyTorch Notes by Rishabh - Topic 08

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### 1. The Output Dimension Formula 📐

Given Input size $W$, Kernel size $K$, Padding $P$, Stride $S$, and Dilation $D$:
$$W_{\text{out}} = \left\lfloor \frac{W - (D(K - 1) + 1) + 2P}{S} \right\rfloor + 1$$

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### 2. PyTorch Conv2d Layer Implementation

```python
import torch
import torch.nn as nn

# Input: [Batch=16, Channels=3, Height=224, Width=224]
x = torch.randn(16, 3, 224, 224)

# 64 filters of 3x3 kernel, padding=1 (Preserves spatial resolution):
conv = nn.Conv2d(in_channels=3, out_channels=64, kernel_size=3, stride=1, padding=1)
out = conv(x)
print(out.shape) # torch.Size([16, 64, 224, 224])
```

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### 3. Master Comparison Matrix

| Property | Standard Convolution | Dilated / Atrous Conv | Depthwise Separable Conv |
| :--- | :--- | :--- | :--- |
| **Receptive Field** | Standard ($K \times K$) | ⚡ **Exponentially Large** | Standard |
| **Parameter Count** | $C_{\text{in}} \times C_{\text{out}} \times K^2$ | $C_{\text{in}} \times C_{\text{out}} \times K^2$ | ⚡ **~9x Fewer Parameters (MobileNet)** |

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### 4. Interview Ke 3 Sawal Is Topic Se

1. **Translation Equivariance kya hoti hai?** -> Agar input image me object shift hota hai ($f(g(x))$), toh output feature map bhi exactly utna hi shift hota hai ($g(f(x))$).
2. **$1 \times 1$ Convolution (Network-in-Network) kya karta hai?** -> Spatial dimensions ko bina chhede channel dimensions ko expand ya compress (dimensionality reduction) karta hai.
3. **Transposed Convolution (`nn.ConvTranspose2d`) GANs me kyu use hoti hai?** -> Learnable upsampling karke feature map spatial dimensions ko expand karna.

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**Next Topic:** 09. Modern CNN Architectures: Residual Connections (ResNet), Squeeze-and-Excitation & ConvNeXt

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