コンピュータビジョンへの移行
今日、私たちは単純な構造化データを基本的な線形層で扱う方法から、高次元の画像データに挑戦する段階へと移行します。1枚のカラー画像は、従来のアーキテクチャでは効率的に処理できないほど大きな複雑さをもたらします。ビジョン向けの深層学習には、専門的なアプローチが必要です： 畳み込みニューラルネットワーク（CNN）。
1. 全結合ネットワーク（FCN）が失敗する理由
FCNでは、入力のすべてのピクセルが次の層のすべてのニューロンに接続される必要があります。高解像度の画像では、これにより計算量が爆発的に増加し、トレーニングが不可能になり、過剰適合によって汎化性能が著しく低下します。
- 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.
CNNによる解決策
CNNは、画像の空間的構造を活用することで、FCNのスケーラビリティ問題を解決します。小さなフィルタを使ってパターン（エッジやカーブなど）を検出することで、パラメータ数を桁違いに削減し、堅牢性を高めます。
TERMINALbash — 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?
Question 2
If a $3 \times 3$ filter is applied across an entire image, what core CNN concept is being utilized?
Question 3
Which CNN component is responsible for progressively reducing the spatial dimensions (width and height) of the feature maps?
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.
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.
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).
Stacked Layers. Early layers learn simple features (edges) using convolution. Deeper layers combine the outputs of earlier layers to form complex, abstract features (objects).