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 — 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 2 — The KV Cache Challenge
Second post of the LLM Primer VI walkthrough. The KV cache formula, the attention-variant trade-offs (MHA vs GQA vs MQA), and the memory-fragmentation problem PagedAttention solves.
2026-04-24
Chapter 9 — Managing the Attention Budget
Ninth post of the LLM Primer IV walkthrough. Context rot, the lost-in-the-middle cliff, tool-loadout rot, and the three architectural answers — MCP, RAG, fine-tuning — to the question of where a model's missing knowledge actually belongs.
2026-04-07
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 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 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 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.
2026-02-20Chapter 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.
2025-09-071.1 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.
2025-09-03
2.2 Understanding the Attention Mechanism in Large Language Models (LLMs)
Learn about the core attention mechanism that powers Large Language Models (LLMs). Discover the concepts of self-attention, scaled dot-product attention, and multi-head attention, and how they contribute to NLP tasks.
2024-09-09
2.1 Transformer Model Explained: Core Architecture of Large Language Models (LLM)
Discover the Transformer model, the backbone of modern Large Language Models (LLM) like GPT and BERT. Learn about its efficient encoder-decoder architecture, self-attention mechanism, and how it revolutionized Natural Language Processing (NLP).
2024-09-07
2.0 The Basics of Large Language Models (LLMs): Transformer Architecture and Key Models
Learn about the foundational elements of Large Language Models (LLMs), including the transformer architecture and attention mechanism. Explore key LLMs like BERT, GPT, and T5, and their applications in NLP.
2024-09-06