Introduction to LLM

This page provides an easy-to-understand guide on LLMs (Large Language Models) from basics to applications for AI enthusiasts.

Total of 62 articles available. | Currently on page 1 of 2.

Chapter 14 — Practical Knowledge for Engineers

Twelfth post — the closing chapter of the LLM Primer II walkthrough. How to keep deepening your understanding after the book ends, the tools and libraries that turn the math into shipping work, and the bridge to the other books in the LLM Primer series.

2026-03-16

Chapter 13 — Limitations, Risks, and Open Challenges

Eleventh post of the LLM Primer II walkthrough. The honest chapter — the compute and energy ceilings that constrain the field, the biases that scale with the data, and the ethical and societal questions that math alone cannot answer.

2026-03-15

Chapter 12 — Real-World Applications of LLMs

Twelfth post of the LLM Primer II walkthrough. Text generation, summarization, QA, translation, reasoning — and the constrained decoding, agent loops, and multimodal generalization that turn one next-token machine into a dozen kinds of product.

2026-03-14

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 9 — Training at Scale

Ninth post of the LLM Primer II walkthrough. How data preprocessing quietly shapes everything that follows, the mathematics of mini-batch learning and parallelism, and the surprisingly subtle question of how to keep a training run numerically stable across thousands of GPUs.

2026-03-11

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 5 — Position, Order, and Sequence Structure

Fifth post of the LLM Primer II walkthrough. How transformers acquire a sense of order — from the original sinusoidal encoding to relative position to RoPE — and a striking final view that ties the whole apparatus to Fourier analysis.

2026-03-07

Chapter 4 — Attention: The Core Mechanism

Fourth post of the LLM Primer II walkthrough. Self-attention derived from intuition, the geometry of queries/keys/values, multi-head structure and normalization, softmax in detail with its temperature knob, and a striking final move: attention seen as a kernel method.

2026-03-06

Chapter 3 — Mathematical Tools for Language Models

Third post of the LLM Primer II walkthrough. The probability and statistics you actually need for language modeling, the slice of linear algebra that matters, and embeddings as the first place those two tools meet inside an LLM.

2026-03-05

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 1 — Mathematical Intuition for Language Models

First post of the LLM Primer II walkthrough. Mathematical notation without intimidation, probability for language generation explained from scratch, and entropy as a way to measure uncertainty — the trio that makes the rest of the book readable.

2026-03-03

LLM Primer II — Language Models Through Mathematics: Series Introduction & Index

Kicking off the chapter-by-chapter walkthrough of Book II in the LLM Primer series — Language Models Through Mathematics. How the book is organized, what each chapter delivers, and the schedule for the fourteen posts that follow, March 3 through March 16.

2026-03-02

Chapter 12 — Building Your Own LLM System: From Datasets to Production

Chapter 12 of the LLM Primer I series. The final chapter. What it actually takes to build an LLM-powered system end to end — dataset licensing, training pipelines, evaluation frameworks, the integrated application stack, and the case-study patterns that distinguish successful deployments from failed pilots.

2026-03-01

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 10 — Safety, Ethics, & Trust: Beyond the Marketing

Chapter 10 of the LLM Primer I series. The honest picture of LLM safety — why hallucinations happen mechanistically, where bias actually lives, how layered guardrails work, and why governance is the institutional layer that technical controls can't replace. For practitioners who need to ship safely.

2026-02-27

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 8 — Using LLMs in Applications: Chatbots, Code, Extraction, and Agents

Chapter 8 of the LLM Primer I series. The application patterns that actually ship in production — chatbots, summarization, code assistants, structured extraction, and the rise of agentic systems where the model drives a tool-use loop. Plus the benchmarks every engineer should recognize by name.

2026-02-25

Chapter 7 — Beyond Next-Token Prediction: Embeddings, Retrieval, and Multimodality

Chapter 7 of the LLM Primer I series. The capabilities that turn a next-token predictor into something much more — embeddings, semantic search, retrieval-augmented generation, and the move into multimodal inputs. How RAG actually keeps an LLM grounded in real documents instead of confabulating.

2026-02-24

Chapter 6 — Fine-Tuning & Adaptation: From Raw Model to Helpful Assistant

Chapter 6 of the LLM Primer I series. The full adaptation stack — from cheap prompt-based steering to parameter-efficient fine-tuning to full alignment with RLHF and its modern successors like DPO. Why post-training is now where closed-model APIs actually differentiate.

2026-02-23

Chapter 5 — Training Large Models: What Actually Goes Into a Frontier Model

Chapter 5 of the LLM Primer I series. How frontier LLMs are actually trained — the data pipeline, the loss function, the months of GPU time, and why "training" is now an industrial-scale engineering problem more than a research problem. Demystifies what those hundred-million-dollar training runs are paying for.

2026-02-22

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.

2026-02-15

2.1 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.

2025-09-08

Chapter 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.

2025-09-07

1.3 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.

2025-09-06

1.2 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.

2025-09-05

1.1 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.

2025-09-04

Part 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

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