Introduction to LLM
This page provides an easy-to-understand guide on LLMs (Large Language Models) from basics to applications for AI enthusiasts.
Chapter 15 — Building a Secure AI Organization
Fifteenth post of the LLM Primer VII walkthrough. Security culture for AI teams, red teams and internal audits, vendor risk (SOC 2, ISO 42001), and the emerging AI BOM.
2026-05-24
Chapter 12 — Access Control and Identity
Twelfth post of the LLM Primer VII walkthrough. OAuth 2.0 + PKCE, ABAC vs ReBAC (Zanzibar), multi-tenant isolation, and token-bucket rate limits for LLM APIs.
2026-05-21
Chapter 11 — Observability, Logging, and Incident Response
Eleventh post of the LLM Primer VII walkthrough. Structured LLM logging with PII redaction, OpenTelemetry GenAI conventions, and the NIST SP 800-61 IR cycle adapted for probabilistic systems.
2026-05-20
Chapter 8 — Adversarial Attacks on Models
Eighth post of the LLM Primer VII walkthrough. Adversarial examples in NLP (HotFlip, TextFooler), model extraction (Tramèr et al., Carlini et al.), and the defensive strategies for API-boundary abuse.
2026-05-17
Chapter 6 — Retrieval-Augmented Generation Risks
Sixth post of the LLM Primer VII walkthrough. Trust boundaries in RAG, malicious document injection, PoisonedRAG and BadRAG, and monitoring retrieval flows for the attacker's fingerprints.
2026-05-15
Chapter 2 — Threat Modeling for LLM Systems
Second post of the LLM Primer VII walkthrough. Adapting STRIDE, PASTA, and attack trees to LLM systems — model, prompt, data, and infrastructure as assets, and MITRE ATLAS as the LLM-specific adversary catalog.
2026-05-11
LLM Primer VII — Series Introduction & Index
Kicking off the chapter-by-chapter walkthrough of Book VII in the LLM Primer series — AI Security. Why in LLM systems code and data are the same string, and the schedule for the seventeen posts that follow, May 10 through May 26. This is the series finale.
2026-05-09
Chapter 15 — Serverless APIs vs Dedicated Infrastructure
Fifteenth post of the LLM Primer VI walkthrough. The breakeven math between serverless APIs and dedicated infrastructure, the hidden platform-engineering overhead each side takes on, and microVM sandboxes for agent code execution.
2026-05-07
Chapter 13 — Autoscaling and Cold-Start Mitigation
Thirteenth post of the LLM Primer VI walkthrough. Why standard HPA fails for LLM serving, KEDA for TTFT-aware scaling, Knative scale-to-zero, and CRIU / CUDA graph caching for sub-5-second cold starts.
2026-05-05
Chapter 10 — The LLM Engine Layer
Tenth post of the LLM Primer VI walkthrough. vLLM as the safe default, TensorRT-LLM for peak NVIDIA-only throughput, SGLang for structured and agentic outputs, and TGI/Ollama for the rest.
2026-05-02
Chapter 8 — Next-Generation KV Cache Management
Eighth post of the LLM Primer VI walkthrough. PagedAttention, KV eviction algorithms (H2O, InfiniGen), and prefix caching for multi-turn conversations and multi-agent RAG.
2026-04-30
Chapter 3 — Data Center GPUs for Generative AI
Third post of the LLM Primer VI walkthrough. The NVIDIA lineup (H100, H200, B200, L40S) vs AMD MI300X — and why HBM bandwidth matters more than FLOPs for decoding.
2026-04-25
LLM Primer VI — Series Introduction & Index
Kicking off the chapter-by-chapter walkthrough of Book VI in the LLM Primer series — Scaling AI Systems. Why inference is the discipline that decides whether an LLM app survives real users, and the schedule for the sixteen posts that follow, April 23 through May 8.
2026-04-22
Chapter 6 — AI Observability and Tracing
Sixth post of the LLM Primer V walkthrough. OpenTelemetry GenAI conventions, span design for LLM apps, cost tracking, and the loop back into the evaluation harness.
2026-04-19
Chapter 5 — Evaluating LLM Applications
Fifth post of the LLM Primer V walkthrough. The offline-online eval distinction, LLM-as-judge patterns, the RAG Triad, and trajectory tests for agents.
2026-04-18
LLM Primer V — Series Introduction & Index
Kicking off the chapter-by-chapter walkthrough of Book V in the LLM Primer series — Building Real-World LLM Applications. Why AI engineering is a discipline of its own, who this book is for, and the schedule for the eight posts that follow, April 14 through April 21.
2026-04-13
LLM Primer IV — Series Introduction & Index
Kicking off the chapter-by-chapter walkthrough of Book IV in the LLM Primer series — Designing AI Cognition with MCP. Why agents need a protocol layer to scale past demoware, who this book is for, and the schedule for the fourteen posts that follow, March 30 through April 12.
2026-03-29
LLM Primer III — Series Introduction & Index
Kicking off the chapter-by-chapter walkthrough of Book III in the LLM Primer series — Enhancing Enterprise AI with RAG. Why retrieval-augmented generation looks simple from the outside and is a stack of disciplines underneath, who this book is for, and the schedule for the eleven posts that follow, March 18 through March 28.
2026-03-17
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 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 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 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.
2026-02-172.1 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.
2025-09-04Chapter 1 — Mathematical Intuition for Language Models
An accessible introduction to Chapter 1 of Understanding LLMs Through Math. Learn how mathematical notation, probability, entropy, and information theory form the core intuition behind modern Large Language Models. This chapter builds the foundation for understanding how LLMs generate text and quantify uncertainty.
2025-09-03Part 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.
2025-09-02Understanding LLMs – A Mathematical Approach to the Engine Behind AI
A preview from Chapter 7.4: Discover why large language models inherit bias, the real-world risks, strategies for mitigation, and the growing role of AI governance.
2025-09-01
7.4 Data Ethics and Bias in Large Language Models
A preview from Chapter 7.4: Discover why large language models inherit bias, the real-world risks, strategies for mitigation, and the growing role of AI governance.
2024-10-09
7.0 Future Outlook and Challenges
A preview from Chapter 7: Explore the future of large language models—ethics, efficiency, multimodal AI, and responsible governance beyond scaling.
2024-10-06
6.2 Simple Python Experiments with LLMs
A preview from Chapter 6.2: Learn how to run large language models with Hugging Face, OpenAI, Google Cloud, and Azure using just Python and a few lines of code.
2024-10-05