ChatGPT is an LLM. LLMs can be used to answer questions and generate emails, marketing materials, blogs, video scripts, code, and even books that look a lot like they’ve been written by humans. However, you probably want to know about the technology.

Let’s start with what an LLM is.

LLMs are deep learning models, specifically, transformer networks or just “transformers.” Transformers certainly have transformed our culture!

An LLM is trained on huge amounts of text data, petabytes (thousands of terabytes) of data, and predicts the next word or words. Due to the way LLMs operate, they are not perfect at outputting text; they can give alternative facts, facts that are “hallucinated.”

ChatGPT is, as of the time of writing, the most popular and famous LLM, created and managed by OpenAI. OpenAI is a charity and a capped-profit organization based in San Francisco [OpenAI_LP, OpenAIStructure].

ChatGPT is now widely...

Earlier neural networks with their ability to read sentences and predict the next word could only read one word at a time and were called recurrent neural networks, (RNNs). RNNs attempted to mimic human-like sequential processing of words and sentences but faced challenges in handling long-term dependencies between words and sentences due to very limited memory capacity.

In 1925, the groundwork was laid by Wilhelm Lenz and Ernst Ising with their non-learning Ising model, considered an early RNN architecture [Brush, Gemini].

In 1972, Shun’ichi Amari made this architecture adaptive, paving the way for learning RNNs. This work was later popularized by John Hopfield in 1982 [Amari, Gemini].

Due to this, there has been a fair amount of research to find ways to stretch this memory to include more text to get more context. RNNs are transformers. There are other transformers, including LSTMs, which are long short-term memory neural networks that are based on...

There are many LLMs today and they can be put into a family tree; see Figure 1.1. The figure shows the evolution from word2vec to the most advanced LLMs in 2023: GPT-4 and Gemini [Bard].

Figure 1.1: Family tree of LLMs from word2vec to GPT-4 and Bard, from Yang2023 with permission

So, that’s all of them but, for now, we’ll look at the earlier LLMs that lead to the most advanced technologies today. We’ll start with GPT.

GPT lineage

The development of GPT is a constantly changing and iterative process, with each new model building upon the strengths and weaknesses of its ancestors. The GPT series, initiated by OpenAI, has undergone a great deal of evolution, leading to advancements in natural language processing (NLP) and understanding.

GPT-3, the third iteration, brought a significant leap in terms of size and complexity, with an impressive 175 billion parameters. This allowed it to generate pretty human-like text...

After the explosive take-off of ChatGPT in late 2022, with 1 million active users in 5 days and 100 million active users in January 2023 (about 2 months), 2023 was a pretty hot year for LLMs, AI research, and the use of AI in general.

Most tech companies have worked on their own LLMs or transformer models to use and make publicly available. Many companies, organizations, and individuals (students included) have used LLMs for a multitude of tasks. OpenAI keeps updating its GPT family and Google keeps updating its Bard version. Bard became Gemini in February 2024, so all references to Bard have changed to Gemini. Many companies use ChatGPT or GPT-4 as the core of their offering, just creating a wrapper and selling it.

This might change as OpenAI keeps adding modalities (speech, image, etc.) to the GPTs and even a new marketplace platform where users can create and sell their own GPT agents right on OpenAI servers. This was launched in early January 2024 to...

Moving on to the general transformers, Figure 1.8 shows the structure of a Transformer:

Figure 1.8: Architecture of a Transformer: an encoder for the inputs and a decoder for the outputs (reproduced from Zahere)

You can see that it has an encoder and a decoder. The encoder learns the patterns in the data and the decoder tries to recreate them.

The encoder has multiple neural network layers. In transformers, each layer uses self-attention, allowing the encoder to understand how the different parts of the sentence fit together and understand the context.

Here is a quick version of the transformer process:

1. Encoder network:

   Uses multiple layers of neural networks.

   Each layer employs self-attention to understand relationships between sentence parts and context.

   Creates a compressed representation of the input.

2. Decoder network:

   Utilizes the encoder’s representation for generating new outputs.

   Employs multiple layers...

Getting into the mathematical center of LLMs can be a bit of work, but understanding their core principles reveals a lot about how the most powerful and widely used AIs today function. So, if you want to make these AI models and research them, the mathematics is very interesting:

• Foundations in linear algebra: The bedrock of LLMs lies in linear algebra, where matrices and vectors rule. Words are mapped to high-dimensional vectors, capturing their meanings and relationships within a vast semantic space. Each word is a point in a multi-dimensional space, with related words clustering closer together.
• Backpropagation and optimization: Training LLMs requires massive datasets and sophisticated optimization algorithms. One powerful tool is backpropagation, a mathematical technique that calculates the error gradient – how much each parameter in the model contributes to the overall deviation from the desired output. By iteratively adjusting...

The LLM revolution is reaching its virtual tentacles into every corner of life, from writing your college essay to generating personalized Coca-Cola ads and customer services. Here’s a quick peek into just 16 diverse applications:

• DIYVA: Designs stunning visuals and logos, making even the artistically challenged look like Picassos (https://diyva.life/).
• LimeWire: Conjures up unique AI-generated artwork, turning your wildest creative visions into reality. Start here: https://limewire.com/studio?referrer=ml736b1k7k.
• Coca-Cola: Creates targeted ad campaigns, crafting personalized marketing messages for each individual Coke-sipper (https://www.coca-cola.com/gb/en).
• Slack: Transcribes meetings and automatically summarizes key points, saving you precious time and attention (https://slack.com/intl/en-gb).
• Octopus Energy: Predicts your energy usage and suggests personalized plans, optimizing your home’s power with LLM intelligence...

In this chapter, we covered what ChatGPT is and what LLMs in general are, the origins of some widely used LLMs such as BERT, the GPT family, LlaMDA, LlaMA, and modern LLMs such as GPT-4 and Gemini. We looked at some architecture of LLMs and transformers. We had a go at fully processing a sentence in the way an LLM model would: tokenizing, Word2Vec contextual embedding, and more. We also touched on the types of mathematics involved and the applications of this fantastic technology deployed by companies.

Hopefully, you now understand the nature of LLMs such as ChatGPT/Gemini; understand the architectures of LLMs; understand some mathematics of LLMs; and are enlightened about competition in the field and how to teach LLMs to others.

In Chapter 2, we will look at the advantages of coding with LLMs, planning your LLM-powered coding, doing some coding with LLMs, and making it work for you.

• Amari: “Learning Patterns and Pattern Sequences by Self-Organizing Nets of Threshold Elements”, S. I. Amari https://ieeexplore.ieee.org/document/1672070 in IEEE Transactions on Computers, vol. C-21, no. 11, pp. 1197-1206, Nov. 1972, doi: 10.1109/T-C.1972.223477

  keywords: {Associative memory, brain model, concept formation, logic nets of threshold elements, self-organization, sequential recalling, stability of state transition}

• AnswerIQ: “25+ Google Bard Statistics 2024 (Usage, Traffic & Cost)”, Paul Rogers: https://www.answeriq.com/google-bard-statistics/ 6th Jan 2024
• Brownlee_LLMs: “What are Large Language Models”, Adrian Tam: https://machinelearningmastery.com/what-are-large-language-models/
• Brownlee_BLEU: “A Gentle Introduction to Calculating the BLEU Score for Text in Python”, Jason Brownlee, https://machinelearningmastery.com/calculate-bleu-score-for-text-python/
• Brush: “History...