How a machine learns

Summary

This script delves into the workings of neural networks, the cornerstone of machine learning. It explains how ANNs learn through layers of neurons, utilizing weights and activation functions to process inputs and produce outputs. The importance of non-linearity introduced by activation functions like ReLU, sigmoid, and softmax is highlighted. The script also covers the backpropagation process using gradient descent to minimize loss functions like MSE and cross-entropy, adjusting weights for improved predictions. Hyperparameters' role in guiding the learning process is also underscored.

Takeaways

• 🧠 **Neural Networks Fundamentals**: Neural networks like DNN, CNN, RNN, and LLMs are based on the basic structure of ANN.
• 🌐 **Structure of ANN**: ANNs consist of an input layer, hidden layers, and an output layer, with neurons connected by synapses.
• 🔢 **Learning Process**: ANNs learn by adjusting weights through the training process to make accurate predictions.
• 📈 **Weighted Sum Calculation**: The first step in learning is calculating the weighted sum of inputs multiplied by their weights.
• 📉 **Activation Functions**: These are crucial for introducing non-linearity into the network, allowing complex problem-solving.
• 🔄 **Output Layer Calculation**: The weighted sum is calculated for the output layer, potentially using different activation functions.
• 🎯 **Prediction Representation**: The predicted result is denoted as \( \hat{y} \), while the actual result is \( y \).
• 📊 **Activation Functions Explained**: ReLU, sigmoid, and Tanh are common functions, with softmax used for multi-class classification.
• 📉 **Loss and Cost Functions**: These measure the difference between predicted and actual values, guiding the learning process.
• 🔍 **Backpropagation**: A method for adjusting weights and biases based on the significant difference between predictions and actual results.
• 🔄 **Gradient Descent**: An optimization algorithm used to minimize the cost function by iteratively adjusting weights.
• 🔁 **Iteration and Epochs**: The training process is repeated through epochs until the cost function reaches an optimum value.
• 🛠️ **Hyperparameters**: Parameters like learning rate and number of epochs that determine the learning process, set before training begins.

Q & A

What is the fundamental structure of an artificial neural network (ANN)?

An ANN has three layers: an input layer, a hidden layer, and an output layer. Each node in these layers represents a neuron.

How do neural networks learn from examples?

Neural networks learn from examples by adjusting the weights through a training process, aiming to minimize the difference between predicted and actual results.

What is the purpose of the weights in a neural network?

The weights in a neural network retain the information learned through the training process and are used to calculate the weighted sum of inputs.

Why are activation functions necessary in neural networks?

Activation functions are necessary to introduce non-linearity into the network, allowing it to learn complex patterns that linear models cannot capture.

What is the difference between a cost function and a loss function?

A loss function measures the error for a single training instance, while a cost function measures the average error across the entire training set.

How does gradient descent help in training a neural network?

Gradient descent is an optimization algorithm that adjusts the weights and biases to minimize the cost function by iteratively moving in the direction of the steepest descent.

What is the role of the learning rate in gradient descent?

The learning rate determines the step size during the gradient descent process, influencing how quickly the neural network converges to the optimal solution.

Why might a neural network with only linear activation functions not be effective?

A neural network with only linear activation functions would essentially be a linear model, which cannot capture complex, non-linear relationships in the data.

What is the significance of the number of epochs in training a neural network?

The number of epochs determines how many times the entire training dataset is passed through the network. It affects the thoroughness of the training process.

How does backpropagation contribute to the learning process of a neural network?

Backpropagation is the process of adjusting the weights and biases in the opposite direction of the gradient to minimize the cost function when there is a significant difference between predicted and actual results.

What is the softmax activation function used for, and how does it differ from the sigmoid function?

The softmax activation function is used for multi-class classification problems, outputting a probability distribution across multiple classes. The sigmoid function, on the other hand, is used for binary classification, outputting a probability between 0 and 1 for a single class.

Outlines

00:00

🧠 Neural Networks Learning Process

This paragraph introduces the fundamental concepts of machine learning, particularly focusing on how neural networks learn. It explains the structure of an artificial neural network (ANN), which consists of an input, hidden, and output layer. Each neuron in these layers is connected by synapses, analogous to the human brain. The learning process is described through the calculation of weighted sums, application of activation functions to introduce non-linearity, and the prediction of outcomes. Activation functions such as ReLU, sigmoid, and softmax are mentioned, each serving different purposes in the learning process. The paragraph also touches on the importance of activation functions in preventing linearity and enabling the network to handle complex problems.

05:03

📊 Evaluating Neural Network Performance

This section delves into how neural networks assess their learning effectiveness. It introduces the concepts of loss and cost functions, which are used to measure the discrepancy between predicted and actual results. The paragraph explains that these functions are crucial for guiding the learning process by identifying areas where the model's predictions are inaccurate. The use of mean squared error (MSE) for regression and cross-entropy for classification problems is highlighted. The paragraph also discusses the backpropagation algorithm, which is used to adjust the weights and biases of the network to minimize the cost function. Gradient descent is introduced as the method for finding the optimal direction and step size for these adjustments, with the learning rate being a key hyperparameter influencing the training speed and convergence. The iterative nature of learning is emphasized, where multiple epochs of training are performed until the cost function reaches an optimum.

10:07

🔧 Hyperparameters and Automated Machine Learning

The final paragraph discusses the role of hyperparameters in determining the learning process of a neural network. It mentions that data scientists typically select these parameters through experimentation to find the best combination for model performance. However, tools like AutoML can automate this process, saving time and resources. The paragraph also reviews the key terms introduced in the script, such as weights, biases, activation functions, learning rate, and epochs. It emphasizes that understanding these components is essential for building effective machine learning models. The script concludes by encouraging learners to revisit these concepts in upcoming lessons and labs.

Keywords

💡Neural Networks

Neural networks are a set of algorithms modeled loosely after the human brain. They are designed to recognize patterns. In the context of the video, neural networks are the primary subject, with a focus on how they learn and the various types such as DNN, CNN, RNN, and LLMs. The script explains that all these models stem from the basic artificial neural network (ANN), which is used to solve different problems by learning from data.

💡Artificial Neural Network (ANN)

ANN, also known as a neural network or shallow neural network, is a simple model that consists of an input layer, a hidden layer, and an output layer. Each node in these layers represents a neuron. ANNs are fundamental to understanding how neural networks learn, as they process information through a series of weighted connections, which are adjusted during training to improve performance.

💡Weights

Weights in a neural network are the numeric values that represent the strength of the connection between neurons. They are adjusted during the training process to help the network make accurate predictions. The script mentions that weights retain information that a neural network learns and are crucial for the network to discover patterns in the data.

💡Activation Functions

Activation functions introduce non-linearity into the neural network, allowing it to learn complex patterns. The video script explains that without activation functions, the network would only be able to model linear relationships, which is insufficient for most real-world problems. Examples given include ReLU, sigmoid, and Tanh functions, each serving different purposes in the network.

💡Backpropagation

Backpropagation is the process by which a neural network learns from its mistakes. It involves the calculation of the gradient of the loss function with respect to each weight by the chain rule, propagating these gradients back through the network from the output layer to the input layer. The script describes backpropagation as a way to adjust weights and biases to minimize the cost function.

💡Gradient Descent

Gradient descent is an optimization algorithm used to minimize the cost function by iteratively moving in the direction of steepest descent as defined by the negative of the gradient. The script likens it to walking down the surface of a cost function to find its minimum, adjusting the weights accordingly to improve the network's predictions.

💡Learning Rate

The learning rate is a hyperparameter that defines how big of a step to take when updating the weights during gradient descent. It determines the speed at which the neural network learns. If the learning rate is too high, the network may overshoot the minimum; if it's too low, learning may be very slow. The script emphasizes the importance of finding the right learning rate.

💡Epochs

An epoch refers to one complete pass through the entire training dataset. The script explains that epochs are a hyperparameter that defines how many times the learning process iterates. More epochs can lead to better learning, but also increase the risk of overfitting.

💡Cost Function

A cost function, also known as a loss function, measures the difference between the predicted output and the actual output. It is used to evaluate the performance of the neural network and to guide the training process by indicating how well the network is doing. The script mentions MSE for regression and cross-entropy for classification.

💡Hyperparameters

Hyperparameters are parameters set before the training process begins, such as the number of layers and neurons, the learning rate, and the number of epochs. The script explains that hyperparameters determine how a machine learns and are typically chosen by data scientists through experimentation.

💡AutoML

AutoML refers to automated machine learning, a tool that selects the best hyperparameters for a model, saving time that would otherwise be spent on manual experimentation. The script briefly mentions AutoML as a way to automate the process of choosing hyperparameters for optimal machine learning performance.

Highlights

Neural networks are fundamental to machine learning.

Different types of neural networks solve various problems.

Artificial Neural Networks (ANN) are the basis for all neural network models.

ANNs consist of an input, hidden, and output layer.

Neurons and synapses are the building blocks of ANNs.

Neural networks learn through examples and make predictions.

The learning process involves calculating the weighted sum.

Activation functions introduce non-linearity to neural networks.

Activation functions like ReLU, sigmoid, and Tanh are widely used.

Softmax is used for multi-class classification.

Loss functions measure the difference between predicted and actual results.

Backpropagation is used to adjust weights and biases.

Gradient descent is a method to minimize the cost function.

The learning rate determines the step size in gradient descent.

An epoch represents one complete pass of the training process.

Weights are adjusted iteratively until the cost function is optimized.

Hyperparameters are set by humans and determine how a machine learns.

AutoML can automatically select hyperparameters.

The learning process of neural networks is iterative and continuous.

Transcripts

To understand machine learning, you must first understand how neural networks learn.

This includes exploring this learning process and the terms associated with it.

If you are already familiar with the ML theories and terminologies, feel free to skip this

lesson.

How do machines learn?

And how do they assess their learning?

Before you dive into building an ML model, let's take a look at how a neural network

learns.

You may already know about various neural networks, such as deep neural networks (or

DNN), convolutional neural networks (or CNN), recurrent neural networks (or RNN), and more

recently large language models (LLMs).

These networks are used to solve different problems.

All of these models stem from the most basic: artificial neural network (or ANN).

ANNs are also referred to as neural networks or shallow neural networks.

Let’s focus on ANN to see how a neural network learns.

An ANN has three layers: an input layer, a hidden layer, and an output layer.

Each node represents a neuron.

The lines between neurons stimulate synopses, which is how information is transmitted in

a human brain.

For instance, if you input article titles from multiple resources, the neural network

can tell you which media outlet or platform the article belongs to, such as GitHub, New

York Times, and TechCrunch.

How does an ANN learn from examples and then make predictions?

Let’s examine how it works in depth.

[Animation: Zoom/fade into the center of the “Hidden Layer” above, transitioning to

next slide] Let’s assume you have two input neurons or nodes, one hidden neuron, and one

output neuron.

Above the link between neurons are weights.

The weights retain information that a neural network learned through the training process

and are the mysteries that a neural network aims to discover.

The first step is to calculate the weighted sum.

This is done by multiplying each input value by its corresponding weight, and then summing

the products.

It normally includes a bias component bi . However, to focus on the core idea, ignore it for now.

The second step is to apply an activation function to the weighted sum.

What is an activation function, and why do you need it?

Let’s pause your curiosity for just a moment and get back to that soon.

In the third step, the weighted sum is calculated for the output layer, assuming multiple neurons

in the hidden layers.

The fourth step is to apply an activation function to the weighted sum.

This activation function can be different from the one applied to the hidden layers.

The result is the predicted y, which consists of the output layer.

You use y hat to represent the predicted result and y as the actual result.

Now let’s get back to activation functions.

What does an activation function do?

Well, an activation function is used to prevent linearity or add non-linearity.

What does that mean?

Think about a neural network.

Without activation functions, the predicted result y hat will always be a linear function

of the input x, regardless of the number of layers between input and output.

Let’s walk through this for clarity.

Without the activation function, the value of the hidden layer h equals a total of w1

times x1 and w2 times x2.

Please note that to make this illustration easy, we ignored the bias component b, which

you often see in other ML materials.

The output y hat therefore equals to w3 times h, and eventually equals to a total of constant

number a times x1 and a constant number b times x2 In other words, the output Y is a

linear combination of the input X.

If y is a linear function of x, you don’t need all the hidden layers, but only one input

and one output.

You might already know that linear models do not perform well when handling comprehensive

problems.

That’s why you must use activation functions to convert a linear network to a non-linear

one.

What are the widely used activation functions?

You can use the rectified linear unit (or ReLU) function, which turns an input value

to zero if it’s negative, or keeps the original value if it’s positive.

You can use the sigmoid function, which turns the input to a value between 0 and 1.

And hyperbolic tangent (Tanh) function, which shifts the sigmoid curve and generates a value

between -1 and +1.

Another interesting and important activation function is called softmax.

Think about sigmoid: it generates a value from zero to one and is used for binary classification

in logistic regression models.

An example for this would be deciding whether an email is spam.

What if you have multiple categories, such as GitHub, NYTimes, and TechCrunch?

Here you must use softmax, which is the activation function for multi-class classification.

It maps each output to a [0,1] range in a way that the total adds up to 1.

Therefore, the output of softmax is a probability distribution.

Skipping the math, you can conclude that softmax is used for multi-class classification, whereas

sigmoid is used for binary-class classification in logistic regression models.

Also note that you don’t need to have the same activation function across different

layers.

For instance, you can have ReLU for hidden layers and softmax for the output layer.

Now that you understand the activation function and get a predicted y, how do you know if

the result is correct?

You use an assessment called loss function or cost function to measure the difference

between the predicted y and the actual y.

Loss function is used to calculate errors for a single training instance, whereas cost

function is used to calculate errors from the entire training set.

Therefore, in step five, you calculate the cost function to minimize the difference.

If the difference is significant, the neural network knows that it did a bad job in predicting

and must go back to learn more and adjust parameters.

Many different cost functions are used in practice.

For regression problems, mean squared error, or MSE, is a common one used in linear regression

models.

MSE equals the average of the sum of squared differences between y hat and y.

For classification problems, cross-entropy is typically used to measure the difference

between the predicted and actual probability distributions in logistic regression models.

If the difference between the predicted and actual results is significant, you must go

back to adjust weights and biases to minimize the cost function.

This potential sixth step is called backpropagation.

The challenge now is how to adjust the weights.

The solution is slightly complex, but indeed the most interesting part of a neural network.

The idea is to take cost functions and turn them into a search strategy.

That’s where gradient descent comes in.

Gradient descent refers to the process of walking down the surface formed by the cost

function and finding the bottom.

It turns out that the problem of finding the bottom can be divided into two different and

important questions: The first is: which direction should you take?

The answer involves the derivative.

Let’s say you start from the top left.

You calculate the derivative of the cost function and find it’s negative.

This means the angle of the slope is negative and you are at the left side of the curve.

To get to the bottom, you must go down and right.

Then, at one point, you are on the right side of the curve, and you calculate the derivative

again.

This time the value is positive, and you must slide again to the left.

You calculate the derivative of the cost function every time to decide which direction to take.

Repeat this process, according to gradient descent, and you will eventually reach the

regional bottom.

The second question in finding the bottom is what size should the steps be?

The step size depends on the learning rate, which determines the learning speed of how

fast you bounce around to reach the bottom.

Step size or “learning rate” is a hyperparameter that is set before training.

If the step size is too small, your training might take too long.

If the step size is too large, you might bounce from wall to wall or even bounce out of the

curve entirely, without converging.

When step size is just right, you’re set.

The seventh, and last step, is iteration.

One complete pass of the training process from step 1 to step 6 is called an epoch.

You can set the number of epochs as a hyperparameter in training.

Weights or parameters are adjusted until the cost function reaches its optimum.

You can tell that the cost function has reached its optimum when the value stops decreasing,

even after many iterations.

This is how a neural network learns.

It iterates the learning by continuously adjusting weights to improve behavior until it reaches

the best result.

This is similar to a human learning lessons from the past.

We have illustrated a simple example with two input neurons (nodes), one hidden neuron,

and one output neuron.

In practice, you might have many neurons in each layer.

Regardless of the number of neurons in the input, hidden, and output layer, the fundamental

process of how a neural network learns remains the same.

Learning about neural networks can be exciting, but also overwhelming with the large number

of new terms.

Let’s take a moment to review them.

In a neural network, weights and biases are parameters learned by the machine during training.

You have no control of the parameters except to set the initial values.

The number of layers and neurons, activation functions, learning rate, and epochs are hyperparameters,

which are decided by a human before training.

The hyperparameters determine how a machine learns.

For example, the learning rate decides how fast a machine learns and the number of epochs

defines how many times the learning interates.

Normally, data scientists choose the hyperparameters and experiment with them to find the optimum

combination.

However, if you use a tool like AutoML, it automatically selects the hyperparameters

for you and saves you plenty of experiment time.

You also learned about cost or loss functions, which are used to measure the difference between

the predicted and actual value.

They are used to minimize error and improve performance.

You use backpropagation to modify the weights and bias if the difference is significant,

and gradient descent to decide how to tune the weights and bias and when to stop.

These terms are your best friends when building an ML model.

You’ll revisit them in upcoming lessons and labs.