Introduction to LLM
This page provides an easy-to-understand guide on LLMs (Large Language Models) from basics to applications for AI enthusiasts.
Chapter 11 — Evaluation, Calibration, and Inference
Eleventh post of the LLM Primer II walkthrough. Perplexity, calibration, the error bars that every benchmark score should carry, and the mathematics of measuring hallucination — the chapter where we ask how anyone can measure a machine that can say anything.
2026-03-13
Chapter 10 — Post-Training and Alignment Mathematics
Tenth post of the LLM Primer II walkthrough. The mathematics that civilizes a brilliant but feral next-word predictor into a helpful assistant — supervised fine-tuning, reward modeling, RLHF on a KL leash, and the elegant DPO derivation that collapses the whole pipeline into a single supervised loss.
2026-03-12
Chapter 8 — How Models Learn
Eighth post of the LLM Primer II walkthrough. Why over-parameterized models generalize at all, the implicit bias of gradient-based optimization, the empirical scaling laws that forecast capability before training, and the open mathematical questions that still surround LLM theory.
2026-03-10
Chapter 7 — Efficiency and Transformer Variants
Seventh post of the LLM Primer II walkthrough. The computational complexity of attention, the GPU memory and throughput math that constrains real systems, FlashAttention derived from first principles, and the family of clever variants — multi-query, gated, low-rank — that keep big models running.
2026-03-09
Chapter 6 — Transformer Blocks and Representation Power
Sixth post of the LLM Primer II walkthrough. Feed-forward layers, activation functions, why "attention + FFN" is exactly the right pair, and what mathematical guarantees depth and width give you about expressivity.
2026-03-08
Chapter 2 — LLMs in Context: Concepts and Background
Second post of the LLM Primer II walkthrough. What an LLM actually is, the three things "pretraining, parameters, scale" really stand for, the unusual nature of language as a data source, and why the transformer rewrote the field in a single year.
2026-03-04
Chapter 11 — Cutting-Edge Research: MoE, Reasoning Models, and the New Scaling Axis
Chapter 11 of the LLM Primer I series. The research frontiers that are now production reality — mixture-of-experts, retrieval-augmented memory, native multimodal tokenization, continual learning, and the inference-time scaling paradigm that produced today's reasoning models. The 2026 edition's biggest content addition.
2026-02-28
Chapter 9 — Performance, Scaling, and Costs: The Real Engineering Trade-offs
Chapter 9 of the LLM Primer I series. The operational realities of running LLMs at scale — model size vs capability, the latency–throughput trade-off, cost economics, quantization, and edge deployment. Why frontier-tier models are often the wrong choice even when you can afford them.
2026-02-26
Chapter 4 — The Transformer Architecture: Inside the Engine of Modern AI
Chapter 4 of the LLM Primer I series. A tour of the Transformer block — how self-attention, positional encoding, and stacked layers combine to produce the architecture every modern LLM is built on. Includes a clear explanation of why scaling Transformers works, and what it costs.
2026-02-21
Chapter 3 — Neural Networks for Language: From RNNs to Self-Attention
Chapter 3 of the LLM Primer I series. Why feedforward networks couldn't handle language, how RNNs hit a wall, and what attention changed. A clean conceptual progression through the three neural-network shapes that defined modern NLP — without the math anxiety.
2026-02-20
Chapter 2 — Probability, Tokens, and Text: The Game of Next-Word Guessing
Chapter 2 of the LLM Primer I series. How LLMs convert text into tokens, why language modeling is fundamentally a probability problem, and how the old n-gram approach gave way to neural models that can generalize. Includes plain-English explanations of perplexity and why every token boundary matters.
2026-02-19
Chapter 1 — What Is a Large Language Model? (Beyond the Headlines)
Chapter 1 of the LLM Primer I series. We unpack what 'Large,' 'Language,' and 'Model' actually mean, walk through the move from rule-based systems to neural networks, and address the three biggest misconceptions about how modern LLMs work. A clear, accessible foundation for everything that follows.
2026-02-18
A Chapter-by-Chapter Walkthrough of LLM Primer I — Series Introduction & Index
Introduction and index for the twelve-part chapter-by-chapter walkthrough of LLM Primer I: How Generative AI Works. One post per day, Feb 18 through March 1, 2026. Read them in order or pick the chapter that matters most to you. All twelve are listed and linked here.
2026-02-17
The LLM Primer Series — A Field Guide to Generative AI, Built One Volume at a Time
The LLM Primer Series — a seven-volume field guide to generative AI by Sho Shimoda. Each volume covers a different layer of working with large language models, from foundations to scaling to security. This is the landing page: an overview of the whole series, plus the live chapter-by-chapter walkthrough of the first volume.
2026-02-152.1 What Is a Large Language Model?
A clear and in-depth explanation of what Large Language Models (LLMs) are. Learn how LLMs map token sequences to probability distributions, why next-token prediction unlocks general intelligence, and what makes a model “large.” This section builds the foundation for understanding pretraining, parameters, and scaling laws.
2025-09-08Chapter 2 — LLMs in Context: Concepts and Background
An accessible introduction to Chapter 2 of Understanding LLMs Through Math. Explore what Large Language Models are, why pretraining and parameters matter, how scaling laws shape model performance, and why Transformers revolutionized NLP. This chapter provides essential context before diving deeper into the mechanics of modern LLMs.
2025-09-071.3 Entropy and Information: Quantifying Uncertainty
A clear, intuitive exploration of entropy, information, and uncertainty in Large Language Models. Learn how information theory shapes next-token prediction, why entropy matters for creativity and coherence, and how cross-entropy connects probability to learning. This section concludes Chapter 1 and prepares readers for the conceptual foundations in Chapter 2.
2025-09-061.2 Basics of Probability for Language Generation
An intuitive, beginner-friendly guide to probability in Large Language Models. Learn how LLMs represent uncertainty, compute conditional probabilities, apply the chain rule, and generate text through sampling. This chapter builds the mathematical foundation for entropy and information theory in Section 1.3.
2025-09-051.1 Getting Comfortable with Mathematical Notation
A clear and accessible guide to understanding the mathematical notation used in Large Language Models. Learn how tokens, sequences, functions, and conditional probability expressions form the foundation of LLM reasoning. This chapter prepares readers for probability, entropy, and information theory in later sections.
2025-09-04Part I — Mathematical Foundations for Understanding LLMs
A clear and intuitive introduction to the mathematical foundations behind Large Language Models (LLMs). This section explains probability, entropy, embeddings, and the essential concepts that allow modern AI systems to think, reason, and generate language. Learn why mathematics is the timeless core of all LLMs and prepare for Chapter 1: Mathematical Intuition for Language Models.
2025-09-02
4.4 How LLMs Write Code: The Rise of AI-Powered Programming Assistants
Explore how large language models (LLMs) generate and complete code from natural-language prompts, and what it means for the future of software development.
2024-09-27
2.1 Transformer Model Explained: Core Architecture of Large Language Models (LLM)
Discover the Transformer model, the backbone of modern Large Language Models (LLM) like GPT and BERT. Learn about its efficient encoder-decoder architecture, self-attention mechanism, and how it revolutionized Natural Language Processing (NLP).
2024-09-07
2.0 The Basics of Large Language Models (LLMs): Transformer Architecture and Key Models
Learn about the foundational elements of Large Language Models (LLMs), including the transformer architecture and attention mechanism. Explore key LLMs like BERT, GPT, and T5, and their applications in NLP.
2024-09-06
1.3 Differences Between Large Language Models (LLMs) and Traditional Machine Learning
Understand the key differences between Large Language Models (LLMs) and traditional machine learning models. Explore how LLMs utilize transformer architecture, offer scalability, and leverage transfer learning for versatile NLP tasks.
2024-09-05
1.2 The Role of Large Language Models (LLMs) in Natural Language Processing (NLP)
Discover the impact of Large Language Models (LLMs) on natural language processing tasks. Learn how LLMs excel in text generation, question answering, translation, summarization, and even code generation.
2024-09-04
1.1 Understanding Large Language Models (LLMs): Definition, Training, and Scalability Explained
Explore the fundamentals of Large Language Models (LLMs), including their structure, training techniques like pre-training and fine-tuning, and the importance of scalability. Discover how LLMs like GPT and BERT work to perform NLP tasks like text generation and translation.
2024-09-03
1.0 What is an LLM? A Guide to Large Language Models in NLP
Discover the basics of Large Language Models (LLMs) in natural language processing (NLP). Learn how LLMs like GPT and BERT are trained, their roles, and how they differ from traditional machine learning models.
2024-09-02
A Guide to LLMs (Large Language Models): Understanding the Foundations of Generative AI
Learn about large language models (LLMs), including GPT, BERT, and T5, their functionality, training processes, and practical applications in NLP. This guide provides insights for engineers interested in leveraging LLMs in various fields.
2024-09-01