Transitioning to Computer Vision: Why CNNs?

Transitioning to Computer Vision

We transition today from handling simple, structured data using basic linear layers to tackling high-dimensional image data. A single color image introduces significant complexity that standard architectures cannot handle efficiently. Deep Learning for vision requires a specialized approach: the Convolutional Neural Network (CNN).

1. Why Fully Connected Networks (FCNs) Fail

In an FCN, every input pixel must be connected to every neuron in the subsequent layer. For high-resolution images, this results in a computational explosion, making training infeasible and generalization poor due to extreme overfitting.

Input Dimension: A standard $224 \times 224$ RGB image results in $150,528$ input features ($224 \times 224 \times 3$).
Hidden Layer Size: If the first hidden layer uses 1,024 neurons.
Total Parameters (Layer 1): $\approx 154$ million weights ($150,528 \times 1024$) just for the first connection block, requiring massive memory and compute time.

The CNN Solution

CNNs solve the FCN scaling problem by exploiting the spatial structure of images. They identify patterns (like edges or curves) using small filters, reducing the parameter count by orders of magnitude and promoting robustness.

TERMINAL bash — model-env

> Ready. Click "Run" to execute.

PARAMETER EFFICIENCY INSPECTOR Live

Run comparison to visualize parameter counts.

Question 1

What is the primary benefit of using Local Receptive Fields in CNNs?

Filters only focus on a small, localized region of the input image.

It allows the network to process the entire image globally at once.

It ensures all parameters are initialized to zero.

It removes the need for activation functions.

Question 2

If a $3 \times 3$ filter is applied across an entire image, what core CNN concept is being utilized?

Kernel Normalization

Shared Weights

Full Connectivity

Feature Transposition

Question 3

Which CNN component is responsible for progressively reducing the spatial dimensions (width and height) of the feature maps?

ReLU Activation

Pooling Layers (Subsampling)

Batch Normalization

Challenge: Identifying Key CNN Components

Relate CNN mechanisms to their functional benefits.

We need to build a vision model that is highly parameter efficient and can recognize an object even if it slightly shifts its position in the image.

Step 1

Which mechanism ensures the network can identify a feature (like a diagonal line) regardless of where it is in the frame?

Solution:
Shared Weights. By using the same filter across all locations, the network learns translation invariance.

Step 2

What architectural choice allows a CNN to detect features with fewer parameters than an FCN?

Solution:
Local Receptive Fields (or Sparse Connectivity). Instead of connecting to every pixel, each neuron only connects to a small, localized region of the input.

Step 3

How does the CNN structure lead to hierarchical feature learning (e.g., edges $\to$ corners $\to$ objects)?

Solution:
Stacked Layers. Early layers learn simple features (edges) using convolution. Deeper layers combine the outputs of earlier layers to form complex, abstract features (objects).