Introduction to LLM
This page provides an easy-to-understand guide on LLMs (Large Language Models) from basics to applications for AI enthusiasts.
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 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 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
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 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 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.
2026-02-19Chapter 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
7.3 Integrating Multimodal Models
A preview from Chapter 7.3: Discover how multimodal models fuse text, images, audio, and video to unlock richer AI capabilities beyond text-only LLMs.
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
4.2 Enhancing Customer Support with LLM-Based Question Answering Systems
Discover how Question Answering Systems powered by Large Language Models (LLMs) are transforming customer support, search engines, and specialized fields with high accuracy and flexibility.
2024-09-17
3.2 LLM Training Steps: Forward Propagation, Backward Propagation, and Optimization
Explore the key steps in training Large Language Models (LLMs), including initialization, forward propagation, loss calculation, backward propagation, and hyperparameter tuning. Learn how these processes help optimize model performance.
2024-09-13