Introduction to LLM
This page provides an easy-to-understand guide on LLMs (Large Language Models) from basics to applications for AI enthusiasts.
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 14 — Token Economics and API Pricing
Fourteenth post of the LLM Primer VI walkthrough. The input-vs-output token asymmetry, the hidden cost of conversation history, and the invisible reasoning tokens that quietly rewrite the daily bill.
2026-05-06
Chapter 1 — The Mechanics of Token Generation
First post of the LLM Primer VI walkthrough. The autoregressive bottleneck, the prefill/decode split, and why a high-end GPU is 99.7% idle while serving a single user.
2026-04-23
Chapter 11 — Attack Surfaces and Protocol Vulnerabilities
Eleventh post of the LLM Primer IV walkthrough. The classical attacks adapted to MCP — Confused Deputy, Token Passthrough, Session Hijacking — the protocol-level flaws around capability escalation and unauthenticated sampling, and the implicit trust propagation that makes context poisoning a structural problem rather than a hygiene one.
2026-04-09
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 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 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
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 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.
2026-02-192.1 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.
2025-09-081.3 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.
2025-09-02