A comprehensive guide on inferencing in LLMs — Part 1

This will include foundational theory, mathematical underpinnings, inference mechanisms, optimization strategies, open-source and closed-source systems, hardware deployment, and implementation details across different models and platforms.

Introduction

Large Language Model (LLM) inference is the process of using a trained model to generate outputs (tokens) given an input prompt. This guide provides an advanced, one-stop overview of how LLM inference works, from the core math to practical implementations and optimizations.

This is a multi-part series to master LLM inference end-to-end.
Across seven tightly connected chapters, We’ll go from the core math to production-grade serving, with code, diagrams, and trade-off thinking baked in. By the end, you’ll actually understand how to make tokens appear — fast, cheap, and reliably.

We will cover the

• Mathematical foundations of transformer-based LLM inference
• Architecture-specific considerations (GPT, LLaMA, Mistral, Claude, Gemini, etc.)
• Common decoding strategies (greedy, beam, top-$k$, top-$p$), and important performance factors like latency and throughput.
• Practical implementation details with code…