Shadowing Practice: Transformers, the tech behind LLMs | Deep Learning Chapter 5 - Learn English Speaking with Video

The initials GPT stand for Generative Pre-trained Transformer.

So that first word is straightforward enough, these are bots that generate new text.

Pre-trained refers to how the model went through a process of learning from a massive amount of data,

and the prefix insinuates that there's more room to fine-tune it on specific tasks with additional training.

But the last word, that's the real key piece.

A transformer is a specific kind of neural network, a machine learning model, and it's That's the core invention underlying the current boom in AI.

What I want to do with this video

and the following chapters is go through a visually driven explanation for what actually happens inside a transformer.

We're going to follow the data that flows through it and go step by step.

There are many different kinds of models that you can build using transformers.

Some models take in audio and produce a transcript.

This sentence comes from a model going the other way around, producing synthetic speech just from text.

All those tools that took the world by storm in 2022, like Dolly and Midjourney that take in a text description and produce an image, are based on Transformers.

Even if I can't quite get it to understand what a pie creature is supposed to be, I'm still blown away that this kind of thing is even remotely possible.

And the original Transformer, introduced in 2017 by Google, was invented for the specific use case of translating text from one language into another.

But the variant that you and I will focus on, which is the type that underlies tools like ChatGPT, will be a model that's trained to take in a piece of text,

maybe even with some surrounding images or sound accompanying it, and produce a prediction for what comes next in the passage.

That prediction takes the form of a probability distribution over many different chunks of text that might follow.

At first glance, you might think that predicting the next word feels like a very different goal from generating new text.

But once you have a prediction model like this, a simple thing you could try to make it generate a

longer piece of text is to give it an initial snippet to work with, have it take a random sample from the distribution it just generated, append that sample to the text,

and then run the whole process again to make a new

prediction based on all the new text including what it just added.

I don't know about you, but it really doesn't feel like this should actually work.

In this animation, for example, I'm running GPT-2 on my laptop and having it repeatedly predict

and sample the next chunk of text to generate a story based on the seed text.

And the story just doesn't actually really make that much sense.

But if I swap it out for API calls to GPT-3 instead, which is the same basic model, just much bigger, suddenly, almost magically,

we do get a sensible story, one that even seems to infer that a pie creature would live in a land of math and computation.

process here of repeated prediction and sampling is essentially what's happening

when you interact with ChatGPT or any of these other large language models

and you see them producing one word at a time.

In fact, one feature

that I would very much enjoy is the ability to see the underlying distribution for each new word that it chooses.

Let's kick things off with a very high-level preview of how data flows through a transformer.

We will spend much more time motivating and interpreting and expanding on the details of each step, but in broad strokes.

When one of these chat bots generates a given word, here's what's going on under the hood.

First, the input is broken up into a bunch of little pieces.

These pieces are called tokens, and in the case of text, these tend to be words or little pieces of words or other common character combinations.

If images or sound are involved, then tokens could be little patches of that image or little chunks of that sound.

Each one of these tokens is then associated with a vector, meaning some list of numbers, which is meant to somehow encode the meaning of that piece.

If you think of these vectors as giving coordinates in some very high dimensional space, words with similar meanings tend to land on vectors that are close to each other in that space.

This sequence of vectors then passes through an operation that's known as an attention block,

and this allows the vectors to talk to each other and pass information back and forth to update their values. For example, the meaning of the word model in the phrase a machine

learning model is different from its meaning in the phrase a fashion model.

The attention block is what's responsible for figuring out

which words in the context are relevant to updating the meanings of which other words, and how exactly those meanings should be updated.

And again, whenever I use the word meaning, this is somehow entirely encoded in the entries of those vectors.

After that, these vectors pass through a different kind of operation, and depending on the source that you're reading, this will be referred to as a multi-layer perceptron, or maybe a feedforward layer.

And here, the vectors don't talk to each other, they all go through the same operation in parallel.

And while this block is a little bit harder to interpret, later on we'll talk about how this step is a little bit like asking a long list of questions about each vector,

and then updating them based on the answers to those questions.

All of the operations in both of these blocks look like a giant pile of matrix multiplications,

and our primary job is going to be to understand how to read the underlying matrices.

I'm glossing over some details about some normalization steps that happen in between, but this is after all a high-level preview.

After that, the process essentially repeats.

You go back and forth between attention blocks and multilayer perceptron blocks, until at At the very end, the hope is

that all of the essential meaning of the passage has somehow been baked into the very last vector in the sequence.

We then perform a certain operation on that last vector

that produces a probability distribution over all possible tokens that might come next.

And like I said, once you have a tool that predicts what comes next given a snippet of text,

you can feed it a little bit of seed text and have it repeatedly play this game predicting what comes next, sampling from the distribution, appending it, and then repeating over and over.

Some of you in the know may remember how long before chat GPT came into the scene.

This is what early demos of GPT-3 looked like.

You would have it autocomplete stories and essays based on an initial snippet.

To make a tool like this into a chatbot, the easiest starting point is to have a little bit of text

that establishes the setting of a user interacting with a helpful AI assistant, what you would call the system prompt,

and then you would use the user's initial question or prompt as the first bit of dialogue,

and then you have it start predicting what such a helpful AI assistant would say in response.

There is more to say about an added step of training that's required to make this work well, but at a high level this is the general idea. In this chapter you

and I are going to expand on the details of what

happens at the very beginning of the network at the very end of the network, and I also want to spend a lot of time reviewing some important bits of background knowledge,

things that would have been second nature to any machine learning engineer by the time Transformers came around.

If you're comfortable with that background knowledge and a little impatient, you could probably feel free to skip to the next chapter, which is going to focus on the attention blocks,

generally considered the heart of the Transformer.

After that, I want to talk more about these multi-layer perception blocks, how training works, and a number of other details that will have been skipped up to that point.

For broader context, these videos are additions to a mini-series about deep learning.

And it's okay if you haven't watched the previous ones, I think you can do it out of order.

But before diving into Transformers specifically, I do think it's worth making sure that we're on the same page about the basic premise and structure of deep learning.

At the risk of stating the obvious, this is one approach to machine learning, which describes any model where you're using data to somehow determine how a model behaves.

What I mean by that is, let's say you want a function that takes in an image, and it produces a label describing it, or our example of predicting the next word given a passage of text,

or any other task that seems to require some element of intuition and pattern recognition.

We almost take this for granted these days, but the idea with machine learning is

that rather than trying to explicitly define a procedure for how to do that task in code, which is what people would have done in the earliest days of AI.

Instead, you set up a very flexible structure with tunable parameters, like a bunch of knobs and dials,

and then, somehow, you use many examples of what the output should look like for a given input to tweak

and tune the values of those parameters to mimic this behavior.

For example, maybe the simplest form of machine learning is linear regression, where your inputs and your outputs are each single numbers,

something like the square footage of a house and its price.

And what you want is to find a line of best fit through this data, you know, to predict future house prices.

That line is described by two continuous parameters, say the slope and the y-intercept,

and the goal of linear regression is to determine those parameters to closely match the data.

Needless to say, deep learning models get much more complicated.

GPT-3, for example, has not two, but 175 billion parameters.

But here's the thing, it's not a given

that you can create some giant model with a huge number of parameters without it either grossly overfitting the training data, or being completely intractable to train.

Deep learning describes a class of models that in the last couple decades have proven to scale remarkably well.

What unifies them is that they all use the same training algorithm, It's called backpropagation, we talked about it in previous chapters.

And the context that I want you to have as we go in is

100

that in order for this training algorithm to work well at scale, these models have to follow a certain specific format.

101

And if you know this format going in, it helps to explain many of the choices for how a transformer processes language, which otherwise run the risk of feeling kind of arbitrary.

102

First, whatever kind of model you're making, the input has to be formatted as an array of real numbers.

103

This could simply mean a list of numbers, it could be a two-dimensional array, or very often you deal with higher dimensional arrays, where the general term used is tensor.

104

You often think of that input data as being progressively transformed into many distinct layers,

105

where again each layer is always structured as some kind of array of real numbers, until you get to a final layer which you consider the output.

106

For example, the final layer in our text processing model is a list of numbers representing the probability distribution

107

for all possible next tokens.

108

In deep learning, these model parameters are almost always referred to as weights, and this is because a key feature of these models is

109

that the only way these parameters interact with the data being processed is through weighted sums.

110

You also sprinkle some nonlinear functions throughout, but they won't depend on parameters.

111

Typically though, instead of seeing the weighted sums all naked and written out explicitly like this,

112

you'll instead find them packaged together as various components in a matrix vector product.

113

It amounts to saying the same thing.

114

If you think back to how matrix vector multiplication works, each component in the output looks like a weighted sum.

115

It's just often conceptually cleaner for you and me to think about matrices

116

that are filled with tunable parameters that transform vectors that are drawn from the data being processed.

117

For example, those 175 billion weights in GPT-3 are organized into just under 28,000 distinct matrices.

118

Those matrices in turn fall into eight different categories, and what you

119

and I are going to do is step through each one of those categories to understand what that type does.

120

As we go through, I think it's kind of fun to reference the specific numbers

121

from GPT-3 to count up exactly where those 175 billion come from.

122

Even if nowadays there are bigger and better models, this one has a certain charm as the first large language model to really capture the world's attention outside of ML communities.

123

Also, practically speaking, companies tend to keep much tighter lips around the specific numbers for more modern networks.

124

I just want to set the scene going in

125

that as you peek under the hood to see what happens inside a tool like ChatGPT, almost all of the actual computation looks like matrix vector multiplication.

126

There's a little bit of a risk getting lost in the sea of billions of numbers, but you should draw a very sharp distinction in your mind between the weights of the model

127

which I'll always color in blue or red, and the data being processed, which I'll always color in gray.

128

The weights are the actual brains.

129

They are the things learned during training, and they determine how it behaves.

130

The data being processed simply encodes whatever specific input is fed into the model for a given run, like an example snippet of text.

131

With all of that as foundation, let's dig into the first step of this text processing example, which is to break up the input into little chunks and turn those chunks into vectors.

132

I mentioned how those chunks are called tokens, which might be pieces of words or punctuation, but every now and then in this chapter, and especially in the next one,

133

I'd like to just pretend that it's broken more cleanly into words.

134

Because we humans think in words, this'll just make it much easier to reference little examples and clarify each step.

135

The model has a predefined vocabulary, some list of all possible words, say 50,000 of them, and the first matrix that we'll encounter, known as the embedding matrix,

136

has a single column for each one of these words.

137

These columns are what determines what vector each word turns into in that first step.

138

We label it we, and like all the matrices we see, its values begin random, but they're going to be learned based on data.

139

Turning words into vectors was common practice in machine learning long before transformers, But it's a little weird if you've never seen it before,

140

and it sets the foundation for everything that follows, so let's take a moment to get familiar with it.

141

We often call this embedding a word, which invites you to think of these vectors very geometrically, as points in some high-dimensional space.

142

Visualizing a list of three numbers as coordinates for points in 3D space would be no problem, but word embeddings tend to be much, much higher dimensional.

143

In GPT-3, they have 12,288 dimensions, and as you'll see, it matters to work in a space that has a lot of distinct directions.

144

In the same way that you could take a two-dimensional slice through a 3D space

145

and project all the points onto that slice, for the sake of animating word embeddings that a simple model is giving me,

146

I'm going to do an analogous thing by choosing a three-dimensional slice through this very high-dimensional space

147

and projecting the word vectors down onto that and displaying the results.

148

The big idea here is that as a model tweaks and tunes its weights

149

to determine how exactly words get embedded as vectors during training, it tends to settle on a set of embeddings where directions in the space have a kind of semantic meaning.

150

For the simple word-to-vector model I'm running here, if I run a search for all the words whose embeddings are closest to that of tower,

151

you'll notice how they all seem to give very similar tower-ish vibes.

152

And if you want to pull up some Python and play along at home, this is the specific model that I'm using to make the animations.

153

It's not a transformer, but it's enough to illustrate the idea that directions in the space can carry semantic meaning.

154

A very classic example of this is how if you take the difference between the vectors for woman and man,

155

something you would visualize as a little vector in the space connecting the tip of one to the tip of the other,

156

it's very similar to the difference between king and queen.

157

So let's say you didn't know the word for a female monarch.

158

You could find it by taking King,

159

adding this woman-man direction, and searching for the embeddings closest to that point. At least, kind of.

160

Despite this being a classic example, for the model I'm playing with, the true embedding of Queen is actually a little farther off than this would suggest,

161

presumably because the way Queen is used in training data is not merely a feminine version of King.

162

When I played around, family relations seemed to illustrate the idea much better.

163

The point is, it looks like during training the model found it advantageous to choose embeddings such

164

that one direction in this space encodes gender information.

165

Another example is that if you take the embedding of Italy, and you subtract the embedding of Germany, and then you add that to the embedding of Hitler,

166

you get something very close to the embedding of Mussolini.

167

It's as if the model learned to associate some directions with Italian-ness, and others with World War II Axis leaders.

168

Maybe my favorite example in this vein is how in some models, if you take the difference between Germany and Japan and you add it to sushi,

169

you end up very close to Broadwurst.

170

Also in playing this game of finding nearest neighbors, I was very pleased to see how close Cat was to both Beast and Monster.

171

One bit of mathematical intuition that's helpful to have in mind, especially for the next chapter,

172

is how the dot product of two vectors can be thought of as a way to measure how well they align.

173

Computationally, dot products involve multiplying all the corresponding components and then adding the results,

174

which is good since so much of our computation has to look like weighted sums.

175

Geometrically, the dot product is positive when vectors point in similar directions, it's zero if they're perpendicular,

176

and it's negative whenever they point in opposite directions.

177

For example, let's say you were playing with this model

178

and you hypothesize that the embedding of cats minus cat might represent a sort of plurality direction in this space.

179

To test this, I'm going to take this vector

180

and compute its dot product against the embeddings of certain singular nouns

181

and compare it to the dot products with the corresponding plural nouns.

182

If you play around with this, you'll notice that the plural ones do indeed seem to consistently give higher values than the singular ones, indicating that they align more with this direction.

183

It's also fun how if you take this dot product with the embeddings of the words 1, 2, 3, and so on,

184

they give increasing values, so it's as if we can quantitatively measure how plural the model finds a given word.

185

Again, the specifics for how words get embedded is learned using data.

186

This embedding matrix, whose columns tell us what happens to each word, is the first pile of weights in our model.

187

And using the GPT-3 numbers, the vocabulary size specifically is 50,257, and again, technically this consists not of words per se, but of tokens.

188

And the embedding dimension is 12,288.

189

Multiplying those tells us this consists of about 617 million weights.

190

Let's go ahead and add this to a running tally, remembering that by the end we should count up to 175 billion.

191

In the case of transformers, you really want to think of the vectors in this embedding space as not merely representing individual words.

192

For one thing, they also encode information about the position of that word, which we'll talk about later,

193

but more importantly, you should think of them as having the capacity to soak in context.

194

A vector that started its life as the embedding of the word king, for example, might progressively get tugged and pulled by various blocks in this network,

195

so that by the end it points in a much more specific and nuanced direction

196

that somehow encodes that it was a king who lived in Scotland, and who had achieved his post after murdering the previous king, and who's being described in Shakespearean language.

197

Think about your own understanding of a given word.

198

The meaning of that word is clearly informed by the surroundings, and sometimes this includes context from a long distance away.

199

So in putting together a model that has the ability to predict what word comes next, the goal is to somehow empower it to incorporate context efficiently.

200

To be clear, in that very first step, when you create the array of vectors based on the input text, each one of those is simply plucked out of the embedding matrix,

201

so initially each one can only encode the meaning of a single word without any input from its surroundings.

202

But you should think of the primary goal of this network that it flows through, as being to enable each one of those vectors to soak up a meaning that's much more rich

203

and specific than what mere individual words could represent.

204

The network can only process a fixed number of vectors at a time, known as its context size.

205

For GPT-3, it was trained with a context size of 2048, so the data flowing through the network always looks like this array of 2048 columns,

206

each of which has 12,000 dimensions.

207

This context size limits how much text the transformer can incorporate when it's making a prediction of the next word.

208

This is why long conversations with certain chatbots, like the early versions of ChatGPT, often gave the feeling of the bot kind of losing the thread of conversation as you continued too long.

209

We'll go into the details of attention in due time, but skipping ahead, I want to talk for a minute about what happens at the very end.

210

Remember, the desired output is a probability distribution over all tokens that might come next.

211

For example, if the very last word is professor, and the context includes words like Harry Potter, and immediately preceding we see least favorite teacher,

212

and also if you give me some leeway by letting me pretend that tokens simply look like full words,

213

then a well-trained network that had built up knowledge of Harry Potter would presumably assign a high number to the word Snape.

214

This involves two different steps.

215

The first one is to use another matrix

216

that maps the very last vector in that context to a list of 50,000 values, one for each token in the vocabulary.

217

Then there's a function that normalizes this into a probability distribution.

218

It's called Softmax, and we'll talk more about it in just a second.

219

But before that, it might seem a little bit weird to only use this last embedding to make a prediction, when after all, in that last step,

220

there are thousands of other vectors in the layer just sitting there with their own context-rich meanings.

221

This has to do with the fact that in the training process, it turns out to be much more efficient

222

if you use each one of those vectors in the final

223

layer to simultaneously make a prediction for what would come immediately after it.

224

There's a lot more to be said about training later on, but I just want to call that out right now.

225

This matrix is called the unembedding matrix, and we give it the label W U.

226

Again, like all the weight matrices we see, its entries begin at random, but they are learned during the training process.

227

Keeping score on our total parameter count, this unembedding matrix has one row for each word in the vocabulary, and each row has the same number of elements as the embedding dimension.

228

It's very similar to the embedding matrix, just with the order swapped, so it adds another 617 million parameters to the network,

229

meaning our count so far is a little over a billion.

230

A small, but not wholly insignificant fraction of the 175 billion that we'll end up with in total.

231

As the very last mini-lesson for this chapter, I want to talk more about the softmax function, since it makes another appearance for us once we dive into the attention blocks.

232

The idea is that if you want a sequence of numbers to act as a probability distribution, say, a distribution over all possible next words, then each value has to be between 0 and 1,

233

and you also need all of them to add up to 1.

234

However, if you're playing the deep learning game, where everything you do looks like matrix vector multiplication,

235

the outputs that you get by default don't abide by this at all.

236

The values are often negative, or much bigger than 1, and they almost certainly don't add up to 1.

237

Softmax is the standard way to turn an arbitrary list of numbers into a valid distribution in such a way

238

that the largest values end up closest to 1, and the smaller values end up very close to 0.

239

That's all you really need to know.

240

But if you're curious, the way that it works is to first raise e to the power of each of the numbers, which means you now have a list of positive values,

241

and then you can take the sum of all those positive values and divide each term by that sum, which normalizes it into a list that adds up to 1.

242

You'll notice that if one of the numbers in the input is meaningfully bigger than the rest, then in the output the corresponding term dominates the distribution,

243

so if you were sampling from it you'd almost certainly just be picking the maximizing input.

244

But it's softer than just picking the max in the sense that when other values are similarly large, they also get meaningful weight in the distribution,

245

and everything changes continuously as you continuously vary the inputs.

246

In some situations, like when ChatGPT is using this distribution to create a next word,

247

There's room for a little bit of extra fun by adding a little extra spice into this function, with a constant t thrown into the denominator of those exponents.

248

We call it the temperature, since it vaguely resembles the role of temperature in certain thermodynamics equations, and the effect is that when t is larger,

249

you give more weight to the lower values, meaning the distribution is a little bit more uniform, and if t is smaller, then the bigger values will dominate more aggressively.

250

Where in the extreme, setting t equal to zero means all of the weight goes to that maximum value.

251

For example, I'll have GPT-3 generate a story with the seed text, once upon a time there was A, but I'm going to use different temperatures in each case.

252

Temperature zero means that it always goes with the most predictable word, and what you get ends up being kind of a trite derivative of Goldilocks.

253

A higher temperature gives it a chance to choose less likely words, but it comes with a risk.

254

In this case, the story starts out a bit more originally, about a young web artist from South Korea, but it quickly degenerates into nonsense.

255

Technically speaking, the API doesn't actually let you pick a temperature bigger than two.

256

There is no mathematical reason for this, it's just an arbitrary constraint imposed, I suppose, to keep their tool from being seen generating things that are too nonsensical.

257

So if you're curious the way this animation is actually working, is I'm taking the 20 most probable NEXT tokens that GPT-3 generates, which seems to be the maximum they'll give me,

258

and then I tweak the probabilities based on an exponent of 1 fifth.

259

As another bit of jargon, in the same way that you might call the components of the output of this function probabilities, people often refer to the inputs as logits.

260

Or some people say logits, some people say logits, I'm going to say logits.

261

So for instance, when you feed in some text, you have all these word embeddings flow through the network, and you do this final multiplication with the unembedding matrix,

262

machine learning people would refer to the components in that raw unnormalized output as the logits for the next word prediction.

263

A lot of the goal with this chapter was to lay the foundations for understanding the attention mechanism, Karate Kid wax on wax off style.

264

You see, if you have a strong intuition for word embeddings, for softmax, for how dot products measure similarity,

265

and also the underlying premise that most of the calculations have to look like matrix multiplication with matrices full of tunable parameters.

266

Then, understanding the attention mechanism, this cornerstone piece and the whole modern boom in AI, should be relatively smooth.

267

For that, come join me in the next chapter.

268

As I'm publishing this, a draft of that next chapter is available for review by Patreon supporters.

269

A final version should be up in public in a week or two, it usually depends on how much I end up changing based on that review.

270

In the meantime, if you want to dive into attention and if you want to help the channel out a little bit, it's there waiting.

📺 Same Channel

Essence of linear algebra preview

Business EnglishUniversity StudentsWorking Adults

Linear combinations, span, and basis vectors | Chapter 2, Essence of linear algebra

Cambridge Exam PrepUniversity StudentsWorking Adults

✨ Recommend Video

66 sentences

The one OpenAI announcement that can actually make you money...

Business EnglishUniversity StudentsWorking Adults

33 sentences

PyTorch in 100 Seconds

Business EnglishUniversity StudentsWorking Adults

73 sentences

ChatGPT Tutorial | Chat GPT Explained | What is Chat GPT ? | Edureka

Business EnglishUniversity StudentsWorking Adults

108 sentences

How I Learned Procedural Generation

Business EnglishUniversity StudentsWorking Adults

175 sentences

What is a PLC and how does it work?

Business EnglishUniversity StudentsWorking Adults

105 sentences

Google’s AI Course for Beginners (in 10 minutes)!

Business EnglishUniversity StudentsWorking Adults

17 sentences

Did someone say... SecondBrain?

Business EnglishUniversity StudentsWorking Adults

173 sentences

You’ll stop using ChatGPT after listening to this | Jonathan Pageau [ARC 2026]

Business EnglishUniversity StudentsWorking Adults

32 sentences

Gemini Robotics 2 brings whole body intelligence to robots

Business EnglishUniversity StudentsWorking Adults

26 sentences

How does AI actually work?

Business EnglishUniversity StudentsWorking Adults

58 sentences

Natural Language Processing - Tokenization (NLP Zero to Hero - Part 1)

Business EnglishUniversity StudentsWorking Adults

Vocabulary and speaking notes for this lesson

This video has 270 sentences and 5151 words to shadow. The speech runs for 26:53. The speaker talks fast, about 192 words per minute, so expect linked and reduced sounds. Only 81% of the words are among the 3,000 most common in English, so the vocabulary is demanding.

Key vocabulary in this video

15 less common words from the video, with pronunciation and meaning:

matrix /ˈmeɪ.tɹɪks/ (noun) — The cavity or mold in which anything is formed.
vector /ˈvɛktɚ/ (noun) — A directed quantity, one with both magnitude and direction; the signed difference between two points.
input /ˈɪnpʊt/ (noun) — The act or process of putting in; infusion.
parameter /pəˈɹæm.ə.tɚ/ (noun) — A value kept constant during an experiment, equation, calculation, or similar, but varied over other versions of the experiment, equation, calculation, etc.
token /ˈtoʊkən/ (noun) — Something serving as an expression of something else.
layer /ˈleɪ̯ɚ/ (noun) — A single thickness of some material covering a surface.
generate /ˈd͡ʒɛn.ə.ɹeɪt/ (verb) — To bring into being; give rise to.
prediction /pɹɪˈdɪkʃən/ (noun) — A statement of what will happen in the future.
dimensional /daɪˈmɛn.ʃə.nəl/ (adjective) — Of or pertaining to dimensions.
output /ˈaʊtpʊt/ (noun) — Production; quantity produced, created, or completed.
predict /pɹɪˈdɪkt/ (verb) — To make a prediction: to forecast, foretell, or estimate a future event on the basis of knowledge and reasoning; to prophesy a future event on the basis of…
probability /ˌpɹɑ.bəˈbɪl.ə.ti/ (noun) — The state of being probable.
component /kəmˈpoʊ.nənt/ (noun) — A smaller, self-contained part of a larger entity. Often refers to a manufactured object that is part of a larger device.
array /əˈɹeɪ/ (noun) — Clothing and ornamentation; raiment.
underlying (adjective) — Lying underneath.

Phrasal verbs you will hear

end up (verb) — To bring to a conclusion.
add up to (verb) — To have a particular effect in combination.
go through (verb) — To travel from one end of something to the other.
take in /teɪk‿ˈɪn/ (verb) — To receive.
come from (verb) — To have as one's origin, birthplace or nationality.
do with (verb) — Only used in to do with
go in (verb) — To become obscured by clouds.
play with (verb) — To fiddle with; make small adjustments to, for example to something mechanical in order to improve its performance.

Pronunciation to watch

The speaker uses 53 contractions and reduced forms, such as I'm, you're, we'll. Say them the short way, as you hear them.

The “th” sounds: mathematical /ˌmæθ(.ə)ˈmæt.ɪ.kəl/, algorithm /ˈælɡəɹɪðm̩/, thread /ˈθɹɛd/, smooth /smuːð/, mathematics /mæθ(.ə)ˈmæt.ɪks/
The “sh” and “zh” sounds: prediction /pɹɪˈdɪkʃən/, dimensional /daɪˈmɛn.ʃə.nəl/, dimension /daɪˈmɛn.ʃən/, intuition /ˌɪn.tjuːˈɪʃ.ən/, essentially /ɪˈsɛnʃəli/
Long words — get the stress right: parameter /pəˈɹæm.ə.tɚ/, dimensional /daɪˈmɛn.ʃə.nəl/, probability /ˌpɹɑ.bəˈbɪl.ə.ti/, vocabulary /vəˈkæb.jə.lə.ɹi/, arbitrary /ˈɑː.bɪ.tɹə.ɹi/

How to practise with this video

Listen to the whole video once without speaking and note the words you do not know.
Start at 0.75× speed, shadow it sentence by sentence, then go back to normal speed once it feels easy.
Record yourself and compare with the original, paying attention to words like matrix, vector, input.

Grammar in this video

The structures the speaker uses most, with the exact words from the video:

Structure	In the video
Conditional sentences if + clause, will/would + verb — a condition and its result	If you play around with this, you'll notice · if you were sampling from it you'd almost
Passive voice be + past participle — the focus is on what happens, not who does it	are based · was invented · is broken
Relative clauses who / which + clause — extra information about a person or thing	instead, which is · numbers, which is · chapter, which is
Present perfect have/has + past participle — a past action that still matters now	have been skipped · haven't watched · have proven

What is the Shadowing Technique?

Shadowing is a science-backed language learning technique originally developed for professional interpreter training and popularized by polyglot Dr. Alexander Arguelles. The method is simple but powerful: you listen to native English audio and immediately repeat it out loud — like a shadow following the speaker with just a 1–2 second delay. Unlike passive listening or grammar drills, shadowing forces your brain and mouth muscles to simultaneously process and reproduce real speech patterns. Research shows it significantly improves pronunciation accuracy, intonation, rhythm, connected speech, listening comprehension, and speaking fluency — making it one of the most effective methods for IELTS Speaking preparation and real-world English communication.

Shadowing technique: read the full step-by-step guide →

Shadowing Practice: Transformers, the tech behind LLMs | Deep Learning Chapter 5 - Learn English Speaking with Video

Essence of linear algebra preview

Linear combinations, span, and basis vectors | Chapter 2, Essence of linear algebra

Euler's Formula Poem

The inscribed square problem

The Newton art puzzle

How might LLMs store facts | Deep Learning Chapter 7

Fourier series

Hilbert's Curve: Is infinite math useful?

Large Language Models explained briefly

Vectors | Chapter 1, Essence of linear algebra

But what is a neural network? | Deep learning chapter 1

Oh, wait, actually the best Wordle opener is not “crane”…

Divergence and curl: The language of Maxwell's equations, fluid flow, and more

But what is quantum computing? (Grover's Algorithm)

Tie random ends: How many loops?

The one OpenAI announcement that can actually make you money...

PyTorch in 100 Seconds

ChatGPT Tutorial | Chat GPT Explained | What is Chat GPT ? | Edureka

How I Learned Procedural Generation

What is a PLC and how does it work?

Google’s AI Course for Beginners (in 10 minutes)!

Did someone say... SecondBrain?

You’ll stop using ChatGPT after listening to this | Jonathan Pageau [ARC 2026]

Gemini Robotics 2 brings whole body intelligence to robots

How does AI actually work?

Natural Language Processing - Tokenization (NLP Zero to Hero - Part 1)

Vocabulary and speaking notes for this lesson

Key vocabulary in this video

Phrasal verbs you will hear

Pronunciation to watch

How to practise with this video

Grammar in this video

What is the Shadowing Technique?