But what is a GPT? Visual intro to Transformers | Deep learning, chapter 5

Summary

The video script provides an in-depth exploration of Generative Pretrained Transformers (GPT), focusing on their core components and mechanisms. It explains how GPT bots generate new text by predicting the next word in a sequence, using a combination of tokenization, vector representation, attention blocks, and feed-forward layers. The script delves into the concept of word embeddings and how they capture semantic meaning in high-dimensional space. It also touches on the training process, the role of backpropagation, and the importance of matrix multiplication in deep learning. The video aims to demystify the inner workings of GPT models and their applications in AI, such as ChatGPT, and sets the stage for further discussion on the transformative impact of transformers in the field of artificial intelligence.

Takeaways

• 🤖 GPT stands for Generative Pretrained Transformer, highlighting the model's ability to generate new text based on a learning process from massive data.
• 🧠 The Transformer model is a specific kind of neural network architecture that has become central to the recent advancements in AI technology.
• 📈 The model's training involves an attention mechanism that allows the vectors representing tokens to update their values based on their context within the data.
• 🔄 The process of generating text involves predicting the next word based on the current sequence and then feeding it back into the model to continue the prediction.
• 📊 The input data is broken down into tokens and converted into vectors, which are high-dimensional numerical representations of the tokens' meanings.
• 🌐 Vectors in the model's embedding space are designed to have semantic meaning, with directions in the space encoding certain characteristics like gender or nationality.
• 🔢 The model parameters, or weights, are organized into matrices that perform operations like matrix multiplication on the input vectors, allowing the model to process data.
• 🔄 The training process involves backpropagation, a widely used algorithm that adjusts the model's weights to minimize the difference between predicted and actual outputs.
• 📈 The model's context size limits the amount of text it can process at once, which can affect the continuity and coherence of longer conversations or texts.
• 📊 The final step in text generation involves using a matrix to map the last vector in the context to a probability distribution over all possible next tokens, using the Softmax function to normalize these values.

Q & A

What does the acronym GPT stand for?

GPT stands for Generative Pretrained Transformer, which refers to a type of AI model that generates new text based on patterns learned from a large dataset during the pretraining phase.

What is the significance of the term 'Transformer' in GPT?

The term 'Transformer' refers to the underlying architecture of the model, which is a specific kind of neural network that has been central to the advancements in AI, particularly in natural language processing tasks.

How does a Transformer model handle the input data?

The input data is first broken down into tokens, which could be words, parts of words, or other character combinations. Each token is then associated with a vector, a list of numbers that encodes the meaning of that piece of the input.

What is the role of the attention block in a Transformer model?

The attention block allows the vectors (tokens) to communicate with each other, passing information back and forth to update their values based on the context. This helps the model understand the context and relationships between different parts of the input data.

How does a Transformer model generate new text?

The model generates new text by predicting the next token in a sequence based on the input text. It uses a probability distribution over possible next tokens and iteratively feeds the most likely token back into the model to predict the subsequent token, building the text piece by piece.

What is the difference between GPT-2 and GPT-3 mentioned in the script?

GPT-2 and GPT-3 are both Transformer models, but GPT-3 is a much larger version with more parameters. While GPT-2 might generate nonsensical text when given a task, GPT-3, due to its larger size and more extensive training, can produce more coherent and contextually appropriate text.

What is the purpose of the embedding matrix in a Transformer model?

The embedding matrix is used to convert tokens into vectors. Each unique token in the model's vocabulary has a corresponding column in the embedding matrix, and the values in these columns determine the initial vector representation for each token.

How does the softmax function contribute to a Transformer model?

The softmax function is used to convert a list of raw output values (logits) from the model into a probability distribution. This ensures that each value is between 0 and 1 and that the entire list adds up to 1, which is a requirement for probabilities.

What is the concept of 'temperature' in the context of a Transformer model?

Temperature is a parameter used with the softmax function to control the randomness of the text generated by the model. A lower temperature makes the model prefer high-probability tokens, leading to more predictable text, while a higher temperature makes the model more willing to explore lower-probability tokens, potentially leading to more creative but also more nonsensical text.

What is the significance of the context size in a Transformer model?

The context size determines how many tokens the model can consider at once when making predictions. This affects the model's ability to understand and generate text, as a larger context size allows the model to incorporate more surrounding information, which can lead to more coherent and contextually relevant text.

How does the unembedding matrix work in a Transformer model?

The unembedding matrix is used at the end of the model to map the final vector back into the vocabulary space. It transforms the context-rich vector into a list of values, one for each token in the vocabulary, which are then turned into a probability distribution using the softmax function to predict the next token.

Outlines

00:00

🤖 Introduction to GPT and Transformers

This paragraph introduces the concept of Generative Pretrained Transformers (GPT), explaining that these are AI models capable of generating new text based on patterns learned from vast amounts of data. It outlines the process of training a model on general data and then fine-tuning it for specific tasks. The core invention of transformers, a type of neural network, is highlighted as the driving force behind the current AI advancements. The video's aim is to visually explain the inner workings of a transformer, following the data flow and its step-by-step transformation. The versatility of transformer models is exemplified by their applications in various AI tools that emerged in 2022, such as Dolly and Midjourney, which can generate images from text descriptions. The original purpose of the transformer, developed by Google in 2017, was for text translation, but the variant discussed here focuses on predicting the next text chunk in a passage given some input text. The process of generating longer text by feeding the model an initial snippet and repeatedly sampling from the prediction distribution is described, along with the author's astonishment at the capabilities of these AI models.

05:02

🧠 High-Level Overview of Data Flow in Transformers

This paragraph provides a high-level overview of the data flow within a transformer model. It explains the process starting with the input being broken into tokens, which are then associated with vectors that encode their meanings. These vectors pass through attention blocks, allowing them to update their values based on the context provided by other vectors. The attention block is crucial for understanding how the meanings of words change depending on their context. Following the attention blocks, the vectors go through a multi-layer perceptron or feed-forward layer, where they are updated based on a set of questions and answers. The paragraph also touches on the complexity of understanding the matrices involved in these operations and sets the stage for a deeper dive into the mechanics of transformers.

10:04

📈 Deep Learning and Model Parameters

This paragraph delves into the specifics of deep learning models, emphasizing the role of parameters, often referred to as weights, in these models. It explains that these weights interact with the data through weighted sums, which are typically packaged as matrix vector products. The paragraph clarifies that the model's weights are the learned elements responsible for its behavior, while the data being processed represents the specific input for a given run. The importance of formatting the input as an array of real numbers and the progression of data through distinct layers is highlighted. The paragraph also introduces the concept of backpropagation, the training algorithm that enables these models to scale well, and the necessity for models to follow a specific format for effective training.

15:08

🔤 Tokenization and Embedding in Transformers

This paragraph focuses on the initial step of text processing in transformers, which involves breaking up the input text into tokens and converting these tokens into vectors. The model's predefined vocabulary and the use of an embedding matrix to determine the vector representation of each word are discussed. The concept of word embeddings as points in a high-dimensional space is introduced, along with the idea that these embeddings can carry semantic meaning based on their positions in the space. The paragraph provides examples of how vectors can represent relationships between words and how they can be manipulated to find embeddings for related words. The dimensionality of the embeddings and the role of the embedding matrix as the first set of weights in the model are also explained.

20:09

🗣️ Context and Prediction in Transformer Models

This paragraph discusses the limitations of transformer models in handling long conversations due to their fixed context size. It explains how the model's context size, set at 2048 for GPT-3, dictates the amount of text it can consider when predicting the next word. The paragraph then describes the final steps of the prediction process, which involves using a matrix to map the last vector in the context to a list of values for each possible next token. The Softmax function is introduced as the method for normalizing these values into a probability distribution, with the potential to adjust the distribution using a temperature parameter. The paragraph also touches on the concept of logits and how they relate to the raw, unnormalized outputs of the model.

25:11

🚀 Setting the Stage for Understanding Attention Mechanism

In this final paragraph, the author emphasizes the importance of understanding the foundational concepts laid out in the previous sections for grasping the attention mechanism, a key component of transformer models. The attention mechanism will be the focus of the next chapter, and the author encourages viewers to join in for a deeper understanding of this aspect of AI. The author also mentions the availability of a draft for Patreon supporters and provides information on how the public can access the upcoming content.

Keywords

💡Generative Pretrained Transformer (GPT)

GPT is a type of artificial intelligence model that generates new text based on patterns it has learned from a large dataset. The 'Generative' aspect means it creates new content, while 'Pretrained' indicates that the model has undergone initial learning from massive amounts of data. 'Transformer' refers to the specific architecture of the model, which is central to its functioning. In the video, GPT is the focus, with an aim to explain its inner workings and its role in the current AI boom.

💡Transformer

A Transformer is a class of neural network architecture that is particularly effective for processing sequential data, such as text. It relies on 'attention mechanisms' to weigh the importance of different parts of the input data when generating each output element. The script emphasizes the Transformer as the key innovation that has driven the development of models like GPT, which have revolutionized the field of AI.

💡Attention Block

An Attention Block is a crucial component of the Transformer architecture. It allows the model to dynamically focus on different parts of the input when generating each output, effectively giving it the ability to understand context. In the video, the attention block is described as what enables the model to update the meanings of words based on their context within a sentence or a passage.

💡Word Embeddings

Word Embeddings are a critical concept in natural language processing where words are represented as vectors in a high-dimensional space. Each vector captures the semantic meaning of the word and its relationship to other words. The video explains that during the training process, the model learns to embed words in such a way that words with similar meanings are closer in this space.

💡Context Size

The Context Size refers to the amount of surrounding text that the model can take into account when making predictions. For GPT-3, this is 2048 tokens. This limit affects how much information the model can use at once and thus impacts its ability to understand and generate text, especially in long conversations.

💡Softmax Function

The Softmax Function is used to convert a list of raw output scores from a neural network into a probability distribution. It ensures that all outputs are between 0 and 1 and that they sum up to 1, which is a requirement for probabilities. In the video, Softmax is described as essential for turning the model's output into a distribution that can be interpreted as the likelihood of each possible next word.

💡Unembedding Matrix

The Unembedding Matrix is a weight matrix used in the Transformer model to map the final vector back to the vocabulary space. It is trained during the model's learning process to associate each vector with the correct word or token in the vocabulary. This is a crucial step in generating text, as it allows the model to make predictions about what word should come next.

💡Backpropagation

Backpropagation is the training algorithm used for teaching neural networks, including Transformers. It involves calculating the gradient of the loss function with respect to the model's parameters and using these gradients to update the parameters. This process is repeated many times with different training examples to improve the model's performance.

💡Dot Product

The Dot Product is a mathematical operation that measures the similarity between two vectors. In the context of the video, dot products are used to understand how well two word embeddings align with each other, which can reveal semantic relationships. A positive dot product indicates similarity, while a negative one suggests dissimilarity.

💡Temperature

Temperature is a hyperparameter used with the Softmax function to control the randomness or 'creativity' of the model's predictions. A higher temperature makes the distribution more uniform, allowing for less predictable words, while a lower temperature makes the distribution sharper, favoring the most likely words.

💡Logits

Logits are the raw, unnormalized output values from a neural network before they are passed through a function like Softmax to produce a probability distribution. In the context of the video, logits represent the model's initial predictions for the next word in a sequence before they are normalized to sum up to 1.

Highlights

GPT stands for Generative Pretrained Transformer, representing a type of AI model that generates new text based on patterns learned from massive data sets.

Transformers are a specific kind of neural network architecture that has become the core invention underlying the current boom in AI advancements.

The transformer model is capable of fine-tuning for specific tasks beyond its initial training, providing flexibility in application across various domains.

The process of generating text with a transformer involves breaking input into tokens, encoding these tokens into vectors, and using these vectors to predict the next sequence of text.

The attention mechanism within the transformer model allows for the model to weigh the relevance of different parts of the input data, improving the contextual understanding and prediction accuracy.

The use of a multi-layer perceptron or feed-forward layer in the transformer model plays a role in interpreting and updating the contextual meaning of the input data.

The training of transformer models involves backpropagation, an algorithm that adjusts the model's parameters to better match the training data.

GPT-3, a large variant of the transformer model, has 175 billion parameters, showcasing the scale and complexity of modern deep learning models.

Word embeddings in transformers are high-dimensional vectors that capture the semantic meaning of words and their relationships within a text.

The concept of context size in transformers limits the amount of text the model can consider at one time, affecting the model's ability to maintain long-term conversations.

The unembedding matrix in the transformer model is used to map the final vector back into the vocabulary space, allowing for the prediction of the next word.

Softmax is a function used in neural networks, including transformers, to convert raw output values into a probability distribution.

The use of temperature in the softmax function can adjust the creativity of the text generation, balancing between predictable and novel outputs.

The video aims to provide a visually-driven explanation of the inner workings of transformers, making the complex mechanisms of AI more accessible.

The potential applications of transformers span across various fields such as language translation, audio processing, and image generation, revolutionizing the way AI interacts with and understands different types of data.

The video series is designed to delve deeper into the mechanics of deep learning and transformers, providing both foundational knowledge and advanced insights into the field.

Transcripts

The initials GPT stand for Generative Pretrained Transformer.

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

Pretrained 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 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 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.

The story just doesn't 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 pi creature would live in a land of math and

computation.

This 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 chatbots 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 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 feed-forward 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 the 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 multi-layer perceptron blocks,

until 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, all possible little chunks of text 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 of 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 ChatGPT 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 step of training that's required to make this work well,

but at a high level this is the 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 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 perceptron 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 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 the same training algorithm, called backpropagation,

and the context I want you to have as we go in is that in order for this training

algorithm to work well at scale, these models have to follow a certain specific format.

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 arbitrary.

First, whatever model you're making, the input

has to be formatted as an array of real numbers.

This could 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.

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

distinct layers, 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.

For example, the final layer in our text processing model is a list of

numbers representing the probability distribution for all possible next tokens.

In deep learning, these model parameters are almost always referred to as weights,

and this is because a key feature of these models is that the only way these

parameters interact with the data being processed is through weighted sums.

You also sprinkle some non-linear functions throughout,

but they won't depend on parameters.

Typically though, instead of seeing the weighted sums all naked

and written out explicitly like this, you'll instead find them

packaged together as various components in a matrix vector product.

It amounts to saying the same thing, if you think back to how matrix vector

multiplication works, each component in the output looks like a weighted sum.

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

about matrices that are filled with tunable parameters that

transform vectors that are drawn from the data being processed.

For example, those 175 billion weights in GPT-3 are

organized into just under 28,000 distinct matrices.

Those matrices in turn fall into eight different categories,

and what you and I are going to do is step through each one of those categories to

understand what that type does.

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

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

Even if nowadays there are bigger and better models,

this one has a certain charm as the large-language model to really capture the world's

attention outside of ML communities.

Also, practically speaking, companies tend to keep much tighter

lips around the specific numbers for more modern networks.

I just want to set the scene going in, 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.

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, which I'll always color in blue or red,

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

The weights are the actual brains, they are the things learned during training,

and they determine how it behaves.

The data being processed simply encodes whatever specific input is

fed into the model for a given run, like an example snippet of text.

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.

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,

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

Because we humans think in words, this will just make it much

easier to reference little examples and clarify each step.

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, has a single column for each one of these words.

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

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.

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,

and it sets the foundation for everything that follows,

so let's take a moment to get familiar with it.

We often call this embedding a word, which invites you to think of

these vectors very geometrically as points in some high dimensional space.

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.

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.

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

and project all the points onto that slice, for the sake of animating word

embeddings that a simple model is giving me, I'm going to do an analogous

thing by choosing a three-dimensional slice through this very high dimensional space,

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

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

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,

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

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.

It's not a transformer, but it's enough to illustrate the

idea that directions in the space can carry semantic meaning.

A very classic example of this is how if you take the difference between the vectors

for woman and man, something you would visualize as a little vector connecting the tip

of one to the tip of the other, it's very similar to the difference between king and

queen.

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

you could find it by taking king, adding this woman-man direction,

and searching for the embeddings closest to that point.

At least, kind of.

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,

presumably because the way queen is used in training data is not merely a feminine

version of king.

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

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

choose embeddings such that one direction in this space encodes gender information.

Another example is that if you take the embedding of Italy,

and you subtract the embedding of Germany, and add that to the embedding of Hitler,

you get something very close to the embedding of Mussolini.

It's as if the model learned to associate some directions with Italian-ness,

and others with WWII axis leaders.

Maybe my favorite example in this vein is how in some models,

if you take the difference between Germany and Japan, and add it to sushi,

you end up very close to bratwurst.

Also in playing this game of finding nearest neighbors,

I was pleased to see how close Kat was to both beast and monster.

One bit of mathematical intuition that's helpful to have in mind,

especially for the next chapter, is how the dot product of two

vectors can be thought of as a way to measure how well they align.

Computationally, dot products involve multiplying all the

corresponding components and then adding the results, which is good,

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

Geometrically, the dot product is positive when vectors point in similar directions,

it's zero if they're perpendicular, and it's negative whenever

they point in opposite directions.

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

and you hypothesize that the embedding of cats minus cat might represent a sort of

plurality direction in this space.

To test this, I'm going to take this vector and compute its dot

product against the embeddings of certain singular nouns,

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

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.

It's also fun how if you take this dot product with the embeddings of the words 1,

2, 3, and so on, they give increasing values, so it's as if we can

quantitatively measure how plural the model finds a given word.

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

This embedding matrix, whose columns tell us what happens to each word,

is the first pile of weights in our model.

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.

The embedding dimension is 12,288, and multiplying

those tells us this consists of about 617 million weights.

Let's go ahead and add this to a running tally,

remembering that by the end we should count up to 175 billion.

In the case of transformers, you really want to think of the vectors

in this embedding space as not merely representing individual words.

For one thing, they also encode information about the position of that word,

which we'll talk about later, but more importantly,

you should think of them as having the capacity to soak in context.

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,

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

Think about your own understanding of a given word.

The meaning of that word is clearly informed by the surroundings,

and sometimes this includes context from a long distance away,

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.

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, so initially each one can only encode

the meaning of a single word without any input from its surroundings.

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 and specific than what mere individual words could represent.

The network can only process a fixed number of vectors at a time,

known as its context size.

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,

each of which has 12,000 dimensions.

This context size limits how much text the transformer can

incorporate when it's making a prediction of the next word.

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.

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.

Remember, the desired output is a probability

distribution over all tokens that might come next.

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,

and also if you give me some leeway by letting me pretend that tokens simply

look like full words, then a well-trained network that had built up knowledge

of Harry Potter would presumably assign a high number to the word Snape.

This involves two different steps.

The first one is to use another matrix that maps the very last vector in

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

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

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

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 there are thousands of

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

This has to do with the fact that in the training process it turns out to be

much more efficient if you use each one of those vectors in the final layer

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

There's a lot more to be said about training later on,

but I just want to call that out right now.

This matrix is called the Unembedding matrix and we give it the label WU.

Again, like all the weight matrices we see, its entries begin at random,

but they are learned during the training process.

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.

It's very similar to the embedding matrix, just with the order swapped,

so it adds another 617 million parameters to the network,

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

a small but not wholly insignificant fraction of the 175 billion

we'll end up with in total.

As the last mini-lesson for this chapter, I want to talk more about this softmax

function, since it makes another appearance for us once we dive into the attention blocks.

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

However, if you're playing the learning game where everything you do looks like

matrix-vector multiplication, the outputs you get by default don't abide by this at all.

The values are often negative, or much bigger than 1,

and they almost certainly don't add up to 1.

Softmax is the standard way to turn an arbitrary list of numbers

into a valid distribution in such a way that the largest values end up closest to 1,

and the smaller values end up very close to 0.

That's all you really need to know.

But if you're curious, the way 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,

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.

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,

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

input.

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,

and everything changes continuously as you continuously vary the inputs.

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

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.

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,

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, where in the extreme, setting t equal to zero means all of the weight

goes to maximum value.

For example, I'll have GPT-3 generate a story with the seed text,

once upon a time there was A, but I'll use different temperatures in each case.

Temperature zero means that it always goes with the most predictable word,

and what you get ends up being a trite derivative of Goldilocks.

A higher temperature gives it a chance to choose less likely words,

but it comes with a risk.

In this case, the story starts out more originally,

about a young web artist from South Korea, but it quickly degenerates into nonsense.

Technically speaking, the API doesn't actually let you pick a temperature bigger than 2.

There's no mathematical reason for this, it's just an arbitrary constraint imposed

to keep their tool from being seen generating things that are too nonsensical.

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,

and then I tweak the probabilities based on an exponent of 1 5th.

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,

or some people say logits, some people say logits, I'm gonna say logits.

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, machine learning people would refer to the components in that raw,

unnormalized output as the logits for the next word prediction.

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.

You see, if you have a strong intuition for word embeddings, for softmax,

for how dot products measure similarity, and also the underlying premise that

most of the calculations have to look like matrix multiplication with matrices

full of tunable parameters, then understanding the attention mechanism,

this cornerstone piece in the whole modern boom in AI, should be relatively smooth.

For that, come join me in the next chapter.

As I'm publishing this, a draft of that next chapter

is available for review by Patreon supporters.

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.

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.