Structure of Convolutions

Introduction

Convolutions are the core building blocks of Convolutional Neural Networks (CNNs), enabling efficient learning from image and signal data by capturing spatial hierarchies.

1️⃣ What is a Convolution?

A convolution is a mathematical operation that slides a filter (kernel) across the input data, computing dot products at each position to extract features like edges, textures, and patterns.

2️⃣ Key Concepts

Filters (Kernels)

Small matrices (e.g., 3x3, 5x5) with learnable weights that scan over the input.

Stride

Determines how many pixels the filter moves at each step.

✅ A stride of 1 scans pixel by pixel. ✅ A stride of 2 skips every other pixel, reducing output size.

Padding

Adds borders of zeros around the input to:

✅ Preserve input size (“same” padding). ✅ Allow filters to fully scan border areas.

3️⃣ Why Convolutions?

✅ Reduce the number of parameters compared to fully connected layers.
✅ Preserve spatial relationships in data.
✅ Capture local patterns and build hierarchical representations in deeper layers.

4️⃣ Convolution Operation Intuition

For a 3x3 filter sliding over a 5x5 input:

• Multiply overlapping elements.
• Sum them up.
• Output a single value per position.

This process is repeated across the entire input to produce a feature map.

5️⃣ Example in TensorFlow

import tensorflow as tf

# Example input: grayscale image of size 28x28
model = tf.keras.Sequential([
    tf.keras.layers.Conv2D(filters=32, kernel_size=(3, 3), strides=(1, 1), padding='same', activation='relu', input_shape=(28, 28, 1)),
    tf.keras.layers.MaxPooling2D(pool_size=(2, 2)),
    tf.keras.layers.Flatten(),
    tf.keras.layers.Dense(10, activation='softmax')
])

6️⃣ Pooling Layers

Pooling layers often follow convolutional layers to:

✅ Reduce spatial dimensions (downsampling).
✅ Retain important features while reducing computation.
✅ Common: Max Pooling (takes the max value in each region).

7️⃣ Stacking Convolutions

By stacking multiple convolutional layers:

✅ Lower layers learn edges and textures.
✅ Higher layers learn shapes and complex patterns.
✅ CNNs build hierarchical feature representations essential for image tasks.

Conclusion

✅ Convolutions allow CNNs to efficiently process and learn from spatial data.
✅ Understanding filters, strides, padding, and pooling will help you design effective CNNs for image classification, object detection, and beyond.

What’s Next?

✅ Experiment with different filter sizes, strides, and padding.
✅ Visualize feature maps to see what your CNN is learning.
✅ Continue your deep learning journey on superml.org to explore advanced CNN architectures.

Join the SuperML Community to share your CNN experiments and get feedback.

Happy Learning! 📷