跟讀練習: The Essential Main Ideas of Neural Networks - 通過影片學習英語口語
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Neural networks seem so complicated, but they're not.
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StatQuest!
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Hello, I'm Josh Starmer and welcome to StatQuest.
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Today we're going to talk about Neural Networks Part 1, Inside the Black Box.
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Neural networks, one of the most popular algorithms in machine learning, learning, cover a broad range of concepts and techniques.
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However, people call them a black box because it can be hard to understand what they're doing.
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The goal of this series is to take a peek into the black box by breaking down each concept
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and technique into its components and walking through how they fit together, step by step.
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In this first part, we will learn about what neural networks do and how they do it.
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In part two, we'll talk about how neural networks are fit to data with backpropagation.
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Then, we will talk about variations on the simple neural network presented in this part, including deep learning.
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Crazy awesome news!
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I have a new way to think about neural networks
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that will help beginners and seasoned experts alike gain a deep insight into what neural networks do.
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For example, most tutorials use cool-looking but hard-to-understand graphs and fancy mathematical notation to represent neural networks. In contrast,
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I'm going to label every little thing on the neural network to make it easy to keep track of the details.
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And the math will be as simple as possible while still being true to the algorithm.
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These differences will help you develop a deep understanding of what neural networks actually do.
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So, with that said, let's imagine we tested a drug that was designed to treat an illness,
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and we gave the drug to three different groups of people with three different dosages.
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Low, Medium, and High.
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The low dosages were not effective, so we set them to zero on this graph.
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In contrast, the medium dosages were effective, so we set them to 1.
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And the high dosages were not effective, so those are set to 0.
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Now that we have this data, we would like to use it to predict whether or not a future dosage will be effective.
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However, we can't just fit a straight line to the data to make predictions, because no matter how we rotate the straight line,
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it can only accurately predict two of the three dosages.
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The good news is that a neural network can fit a squiggle to the data.
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The green squiggle is close to zero for low dosages, close to one for medium dosages,
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and close to zero for high dosages.
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And even if we have a really complicated data set like this, a neural network can fit a squiggle to it.
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In this StatQuest, we're going to use this super simple data set and show how this neural network creates this green squiggle.
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But first, let's just talk about what a neural network is.
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A neural network consists of nodes and connections between the nodes.
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Note, the numbers along each connection represent parameter values that were estimated when this neural network was fit to the data.
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For now, just know that these parameter estimates are analogous to the slope
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and intercept values that we solve for when we fit a straight line to data.
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Likewise, a neural network starts out with unknown parameter values
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that are estimated when we fit the neural network to a dataset using a method called backpropagation.
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And we will talk about how backpropagation estimates these parameters in part 2 in this series.
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But for now, just assume that we've already fit this neural network to this specific dataset.
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And that means we have already estimated these parameters.
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Also, you may have noticed that some of the nodes have curved lines inside of them.
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These bent or curved lines are the building blocks for fitting a squiggle to data.
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The goal of this StatQuest is to show you how these identical curves can be reshaped by the parameter values
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and then added together to get a green squiggle that fits the data.
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Note, there are many common bent or curved lines that we can choose for a neural network.
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This specific curved line is called Soft Plus, which sounds like a brand of toilet paper.
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Alternatively, we could use this bent line called RelU, which is short for Rectified Linear Unit and sounds like a robot.
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Or we could use a sigmoid shape or any other bent or curved line.
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Oh no, it's the dreaded terminology alert!
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The curved or bent lines are called activation functions.
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When you build a neural network, you have to decide which activation function or functions you want to use.
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When most people teach neural networks, they use the sigmoid activation function.
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However, in practice, it is much more common to use the ReLU activation function, or the soft plus activation function.
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So we'll use the soft plus activation function in this stat quest.
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Anyway, we'll talk more about how you choose activation functions later in this series.
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Note, this specific neural network is about as simple as they get.
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It only has one input node where we plug in the dosage, only one output node to tell us the predicted effectiveness,
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and only two nodes between the input and output nodes.
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However, in practice, neural networks are usually much fancier and have more than one input node,
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more than one output node, different layers of nodes between the input and output nodes,
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and a spider web of connections between each layer of nodes.
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Oh no!
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It's another terminology alert!
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These layers of nodes between the input and output nodes are called hidden layers.
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When you build a neural network, one of the first things you do is decide how many hidden layers you want
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and how many nodes go into each hidden layer.
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Although there are rules of thumb for making decisions about the hidden layers, you essentially make a guess and see how well the neural network performs,
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adding more layers and nodes if needed.
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Now, even though this neural network looks fancy, it is still made from the same parts used in this simple neural network,
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which has only one hidden layer with two nodes.
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So let's learn how this neural network creates new shapes from the curved or bent lines in the hidden layer,
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and then adds them together to get a green squiggle that fits the data.
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To keep the math simple, let's assume dosages go from 0, for low, to 1, for high.
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The first thing we are going to do is plug the lowest dosage, 0, into the neural network.
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Now, to get from the input node to the top node in the hidden layer,
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this connection multiplies the dosage by negative 34.4 and then adds 2.14.
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And the result is an X-axis coordinate for the activation function.
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For example, the lowest dosage, 0, is multiplied by negative 34.4,
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and then we add 2.14 to get 2.14 as the x-axis coordinate for the activation function.
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To get the corresponding y-axis value, we plug 2.14 into the activation function,
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which, in this case, is the soft plus function.
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Note, if we had chosen the sigmoid curve for the activation function, then we would plug 2.14 into the equation for the sigmoid curve.
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And if we had chosen the relu bent line for the activation function, then we would plug 2.14 into the relu equation.
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But since we are using soft plus for the activation function, we plug 2.14 into the soft plus equation.
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And the log of 1 plus e raised to the 2.14 power is 2.25.
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Note, in statistics, machine learning, and most programming languages, the log function implies the natural log, or the log base e.
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Anyway, the y-axis coordinate for the activation function is 2.25.
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So let's extend this y-axis up a little bit, and put a blue dot at 2.25 for when dosage equals 0.
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Now, if we increase the dosage a little bit and plug 0.1 into the input,
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the x-axis coordinate for the activation function is negative 1.3,
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and the corresponding y-axis value is 0.24.
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So let's put a blue dot at 0.24 for when dosage equals 0.1.
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And if we continue to increase the dosage values all the way to 1, the maximum dosage, we get this blue curve.
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Note, before we move on, I want to point out
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that the full range of dosage values from 0 to 1
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corresponds to this relatively narrow range of values from the activation function function.
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In other words, when we plug dosage values from 0 to 1 into the neural network,
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and then multiply them by negative 34.4 and add 2.14,
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we only get x-axis coordinates that are within the red box.
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And thus, only the corresponding y-axis values in the red box are used to make this new blue curve.
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Bam!
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Now we scale the y-axis values for the blue curve by negative 1.3.
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For example, when dosage equals zero, the current y-axis coordinate for the blue curve is 2.25.
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So we multiply 2.25 by negative 1.3 and get negative 2.93.
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and negative 2.93 corresponds to this position on the y-axis.
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Likewise, we multiply all of the other y-axis coordinates on the blue curve by negative 1.3,
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and we end up with a new blue curve.
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BAM!
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Now let's focus on the connection from the input node to the bottom node in the hidden layer.
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However, this time we multiply the dosage by negative 2.52 instead of negative 34.4,
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and we add 1.29 instead of 2.14 to get the x-axis coordinate for the activation function.
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Remember, these values come from fitting the neural network to the data with backpropagation, and we'll talk about that in Part 2 in this series.
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Now, if we plug the lowest dosage, 0, into the neural network,
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then the x-axis coordinate for the activation function is 1.29.
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Now we plug 1.29 into the activation function to get the corresponding y-axis value, and get 1.53.
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And that corresponds to this yellow dot.
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Now we just plug in dosage values from 0 to 1 to get the corresponding y-axis values.
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And we get this orange curve.
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Note, just like before, I want to point out that the full range of dosage values from 0 to 1
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corresponds to this narrow range of values from the activation function.
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In other words, when we plug dosage values from 0 to 1 into the neural network,
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we only get X-axis coordinates that are within the red box.
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And thus, only the corresponding y-axis values in the red box are used to make this new orange curve.
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So we see that fitting a neural network to data gives us different parameter estimates on the connections,
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And that results in each node in the hidden layer using different portions of the activation functions
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to create these new and exciting shapes.
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Now, just like before, we scale the Y-axis coordinates on the orange curve.
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Only this time, we scale by a positive number, 2.28.
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Boop, boop, boop, boop, boop, boop.
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And that gives us this new orange curve.
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Now the neural network tells us to add the y-axis coordinates from the blue curve to the orange curve.
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And that gives us this green squiggle.
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Then, finally, we subtract 0.58 from the y-axis values on the green squiggle.
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And we have a green squiggle that fits the data.
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Bam!
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Now, if someone comes along and says that they are using dosage equal to 0.5,
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we can look at the corresponding y-axis coordinate on the green squiggle and see that the dosage will be effective.
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Or, we can solve for the y-axis coordinate by plugging dosage equals 0.5 into the neural network, and do the math.
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Biddup boop boop boop boop boop boop
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And we see that the y-axis coordinate on the green squiggle is 1.03.
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And since 1.03 is closer to 1 than 0, we will conclude that a dosage equal to 0.5 is effective.
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Double bam!
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Now, if you've made it this far, you may be wondering why this is called a neural network, instead of a big fancy squiggle-fitting machine.
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The reason is that way back in the 1940s and 50s, when neural networks were invented, they thought the nodes were vaguely like neurons,
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and the connections between the nodes were sort of like synapses.
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However, I think they should be called big, fancy squiggle-fitting machines, because that's what they do.
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Whether or not you call it a squiggle-fitting machine, the parameters that we multiply are called weights.
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and the parameters that we add are called biases.
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Note, this neural network starts with two identical activation functions, but the weights and biases on the connections slice them,
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flip them, and stretch them into new shapes, which are then added together to get a squiggle that is entirely new,
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and then the squiggle is shifted to fit the data.
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Now, if we can create this green squiggle with just two nodes in a single hidden layer,
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just imagine what types of green squiggles we could fit with more hidden layers and more nodes in each hidden layer.
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In theory, neural networks can fit a green squiggle to just about any data set, no matter how complicated.
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And I think that's pretty cool.
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Triple bam!
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Now it's time for some shameless self-promotion.
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If you want to review statistics and machine learning offline, check out the StatQuest study guides at StatQuest.org.
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There's something for everyone.
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Hooray!
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We've made it to the end of another exciting StatQuest.
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If you like this StatQuest and want to see more, please subscribe.
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And if you want to support StatQuest, consider contributing to my Patreon campaign,
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becoming a channel member, buying one or two of my original songs or a t-shirt or a hoodie, or just donate.
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The links are in the description below.
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Alright, until next time, quest on!
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為何用這個影片練習英語口語？
這個影片以通俗易懂的方式講解神經網路，語速適中、邏輯清晰，非常適合作為英語口語練習的素材。講解中大量使用日常表達和專業術語的結合，既能鍛鍊基礎口語能力，又能積累科技領域詞彙。通過英語影子跟讀（shadowspeaks）模仿 speaker 的語調與節奏，不僅能提升發音準確性，還能培養自然的語言流暢度，對雅思口語練習也有很大幫助——畢竟雅思口語考試中清晰表達複雜概念的能力至關重要。
語境中的語法與表達
- “...seem so complicated, but they're not!” 這一轉折句結構簡單卻有力，適合練習口語中的情感起伏。模仿時注意“but”後的重讀，增強表達的說服力。
- “the goal of this series is to take a peek into the black box by breaking down each concept...” 其中“by + 動名詞”結構用於說明方式，是口語中解釋做法的常用句式。練習時需流暢讀出“breaking down”的連讀。
- “however, in practice, it is much more common to use...” 這裡“however”和“in practice”的插入使表達更自然，體現口語的靈活性。模仿時注意停頓位置，避免生硬。
常見發音陷阱
影片中部分詞彙的發音容易出錯，需特別注意：
- “neural networks” 中“neural”的發音為/ˈnʊərəl/，而非/ˈnjʊərəl/，避免將“neu-”發成“牛”的音；
- “activation” 的重音在第⼆個音節/ˌæktɪˈveɪʃn/，不要誤讀為/ækˈtɪveɪʃn/；
- “sigmoid” 的正確發音是/ˈsɪɡmɔɪd/，注意“g”發濁子音，避免發成清子音。
通過影子跟讀反覆練習這些詞彙，可有效提高英語發音的準確性。
影片中的語法
說話人最常用的結構，並附上影片中的原話：
| 結構 | 影片中的用法 |
|---|---|
| 被動語態 be + 過去分詞 — 強調發生了什麼，而不是誰做的 | was designed · are set · were estimated |
| 現在完成時 have/has + 過去分詞 — 過去發生但與現在仍有關聯的事 | have already estimated · have curved · you've made |
| 定語從句 who / which + 從句 — 補充說明人或事物 | RelU, which is · shapes, which are |
什麼是跟讀法？
跟讀法 (Shadowing) 是一種有科學依據的語言學習技巧，最初開發用於專業口譯員的培訓，並由多語言者Alexander Arguelles博士普及。這個方法簡單而強大：您在聽英語母語原聲的同時立即大聲重複——就像是一個延遲1-2秒緊跟說話者的影子。與被動聽力或語法練習不同，跟讀法強迫您的大腦和口腔肌肉同時處理並模模擬實的講話模式。研究表明它能顯著提高發音準確性，語調，節奏，連讀，聽力理解和口語流利度——使其成為雅思口語備考和真實英語交流最有效的方法之一。