Lecture on Building a Neural Network from Scratch

Overview

• Presenter: Samson
• Objective: Build a neural network from scratch using numpy and linear algebra, not utilizing TensorFlow or Keras.
• Application: Digit classification using the MNIST dataset.

Introduction to Neural Networks

• Neural networks consist of multiple layers and nodes.
• Often complex and used for predictions in AI/ML.
• Learning through implementation from scratch provides a deeper understanding.

Dataset: MNIST

• Consists of thousands of 28x28 grayscale images of handwritten digits.
• Each image has 784 pixels.

Neural Network Architecture

• Input Layer: 784 nodes corresponding to each pixel.
• Hidden Layer: 10 units.
• Output Layer: 10 units, each representing a digit from 0 to 9.
• Terminology: Input Layer, First Hidden Layer, Second Layer (Output Layer).

Steps in Building the Neural Network

1. Forward Propagation

• Input Layer (a0): Initial input, equal to X.
• First Layer (z1): Apply weights and biases using matrix operations.
• Activation Function: Uses ReLU (Rectified Linear Unit).
  • ReLU(x) = max(0, x).
• Second Layer (z2): Similar operations with different weights and biases.
• Softmax Activation: Applied to output layer for probabilities.

2. Backward Propagation

• Calculate prediction error.
• Adjust weights and biases based on contribution to error.
• Gradients: Compute derivatives to adjust parameters.

3. Updating Parameters

• Update weights and biases using gradient information and learning rate (alpha).
• Learning Rate (alpha) is a hyperparameter.

Implementation

• Code written in Python using numpy and pandas.
• Utilize functions for parameter initialization, forward and backward propagation, and parameter updates.
• Train using gradient descent; observe improvement through iterations.

Performance

• Initial accuracy reached around 84% on training data.
• Cross-validation (dev set) accuracy around 85.5%.
• Future improvements possible with more layers or units.

Conclusion

• Building a neural network from scratch enhances understanding.
• Emphasis on exploring variations like regularization and alternative optimization methods.
• Satisfaction in seeing accurate predictions from a self-built model.

Resources

• Follow-up materials and links to code and notes provided in the lecture.
• Encouragement to explore further into the mathematics and implementation of neural networks.

This lecture provides a comprehensive guide to understanding and implementing neural networks, emphasizing the value of hands-on learning.