Introduction to LLM
This page provides an easy-to-understand guide on LLMs (Large Language Models) from basics to applications for AI enthusiasts.
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.
2025-09-08Chapter 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
5.3 Real-Time Deployment Challenges
A preview from Chapter 5.3: Explore latency, scalability, and optimization techniques for deploying large language models in real-time applications.
2024-10-01
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
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
3.0 How to Train Large Language Models (LLMs): Data Preparation, Steps, and Fine-Tuning
Learn the key techniques for training Large Language Models (LLMs), including data preprocessing, forward and backward propagation, fine-tuning, and transfer learning. Optimize your model’s performance with efficient training methods.
2024-09-11