But what is a neural network? | Chapter 1, Deep learning

Introduction

This tutorial will guide you through the foundational concepts of neural networks as introduced in the video "But what is a neural network?" by 3Blue1Brown. Understanding these concepts is essential for anyone interested in deep learning and artificial intelligence. We will explore the structure of neural networks, including neurons, layers, and the mathematics involved.

Step 1: Understand What Neurons Are

• Neurons are the basic building blocks of neural networks.
• Each neuron receives inputs, processes them, and produces output.
• The output is typically transformed using an activation function to introduce non-linearity.
• Common activation functions include ReLU (Rectified Linear Unit) and Sigmoid.

Step 2: Learn About Layers

• Neural networks consist of multiple layers:
  • Input Layer: Receives the initial data.
  • Hidden Layers: Process the inputs through weighted connections.
  • Output Layer: Produces the final result.
• Each layer consists of neurons that transform the data passed from the previous layer.
• Layers enable the network to learn hierarchical representations of data.

Step 3: Why Are Layers Important?

• Layers allow the network to capture complex patterns in data.
• Each additional layer increases the network's capacity to learn and model intricate relationships.
• More layers can help in tasks such as image recognition, where different features are identified at different levels.

Step 4: Explore Edge Detection Example

• Neural networks can be used for edge detection in images.
• The first layer might detect simple edges, while deeper layers can recognize more complex shapes or objects.
• This illustrates how layers work together to build understanding from raw data.

Step 5: Count Weights and Biases

• Each connection between neurons has an associated weight, which adjusts during training.
• Biases are additional parameters that allow the model to fit the data better.
• The total number of weights and biases can be calculated based on the number of neurons in each layer.

Step 6: Understand Learning in Neural Networks

• Learning involves adjusting weights and biases through a process called backpropagation.
• The network minimizes the difference between predicted outputs and actual outcomes (loss).
• Gradient descent is commonly used to optimize the weights.

Step 7: Familiarize with Notation and Linear Algebra

• Neural networks use linear algebra for operations between layers.
• Key concepts include vectors and matrices, which represent inputs, outputs, weights, and biases.
• Understanding matrix multiplication is crucial for grasping how data flows through the network.

Step 8: Review Activation Functions

• Two common activation functions are:
  • ReLU: Outputs the input directly if positive; otherwise, it outputs zero.
  • Sigmoid: Outputs values between 0 and 1, useful for binary classification.
• Each function has its advantages and is chosen based on the specific problem being solved.

Conclusion

Neural networks are powerful tools for learning from data. By understanding the structure of neurons and layers, the importance of weights and biases, and the underlying mathematics, you lay a solid foundation for delving deeper into deep learning. Consider exploring additional resources such as Michael Nielsen's book on neural networks or Chris Olah's blog for a more in-depth understanding.