LLMs Explained

How Large Language Models Learn, Think and Generate

Introduction: The Black Box on Your Screen

1. The Question Everyone Is Asking
2. What This Book Will Explain
3. A First-Pass Tour: From Prompt to Response

Chapter 1: The Fundamental Idea - Predicting the Next Token

1. Autocomplete with Ambition
2. Why Prediction Requires “Understanding”
3. The Training Objective in Plain Language
4. From One Word at a Time to Coherent Thought
5. More Challenging Prediction Tasks

Chapter 2: From Text to Numbers - Tokenization and Preprocessing

1. Why Models Cannot Read Words
2. Building a Vocabulary: Tokens vs. Words
3. Byte-Pair Encoding and Subword Strategies
4. Data Collection: Where the Training Corpus Comes From
5. Tokenization Edge Cases and Their Consequences
6. The Impact of Sequence Length on Training

Chapter 3: Embeddings - Meaning as Vectors

1. The Embedding Layer: A Lookup Table with Power
2. Semantic Geometry: Why Similar Words Are Nearby
3. Positional Encodings: Giving the Model a Sense of Order
4. What an Embedding Vector Actually Contains
5. Embeddings in Context: From Static to Dynamic Representations
6. The Mathematics of Cosine Similarity
7. Embedding Dimensionality and Capacity

Chapter 4: The Transformer Architecture - An Overview

1. Before Transformers: Why RNNs Could Not Scale
2. The Big Picture: Layers, Blocks and Data Flow
3. Feed-Forward Networks: The Hidden Computation
4. Residual Connections and Layer Normalization
5. Encoder, Decoder and Decoder-Only Architectures
6. Parameter Counts and Model Sizing
7. The Complete Forward Pass: A Numerical Example

Chapter 5: Self-Attention - The Heart of the Transformer

1. What Does It Mean for One Token to Attend to Another?
2. Queries, Keys and Values: The Attention Mechanism
3. Softmax: Turning Scores into Weights
4. Multi-Head Attention: Different Perspectives on the Same Text
5. Tensor Shapes and Dimensionality Tracking
6. Computational Complexity: The Quadratic Bottleneck
7. Attention Patterns: What the Weights Reveal

Chapter 6: Training Mechanics - Loss, Gradients and Descent

1. Measuring Failure: The Cross-Entropy Loss Function
2. Backpropagation: How Errors Flow Backward
3. Gradient Descent: Nudging Parameters in the Right Direction
4. Adam and the Art of Optimization
5. Tracing Gradients Through a Transformer Block
6. Learning Rate Schedules: Warmup and Cosine Decay
7. Gradient Clipping and Training Stability
8. The Loss Landscape and Optimization Dynamics

Chapter 7: Pretraining - Learning from the Entire Internet

1. The Pretraining Loop: One Step at a Time
2. What the Model Learns: Patterns, Facts and Structure
3. Scaling Laws: Why Bigger Is Better (and Why)
4. Emergent Abilities: When More Parameters Change Everything
5. Distributed Training: Parallelism at Scale
6. Phases of Learning During Pretraining
7. Data Quality Versus Quantity

Chapter 8: Knowledge Representation - What Lives in the Weights?

1. Parameters as Compressed Knowledge
2. Finding Facts Inside Neural Networks
3. Knowledge Neurons and Factual Localization
4. The Superposition Hypothesis: More Features Than Dimensions
5. Sparse Autoencoders: Disentangling Features
6. Feed-Forward Networks as Key-Value Memories
7. Induction Heads: The Circuit Behind In-Context Learning
8. The Limits of Current Understanding
9. The Geometry of Reasoning: How Chains of Thought Emerge
10. What Models Do Not Know (and Why They Hallucinate)

Chapter 9: Instruction Tuning - Teaching the Model to Obey

1. From Completion Engine to Assistant
2. Supervised Fine-Tuning: Learning from Examples
3. Reinforcement Learning from Human Feedback
4. Reward Model Training: From Preferences to Scores
5. PPO Optimization: Reinforcement Learning in Practice
6. Direct Preference Optimization: A Simpler Alternative
7. The Trade-Off Between Capability and Alignment

Chapter 10: Inference - How a Response Is Generated, Token by Token

1. The Inference Loop: One Token at a Time
2. KV Caching: Avoiding Redundant Computation
3. Temperature and Sampling: Controlling Creativity
4. Greedy Decoding, Beam Search and Their Trade-offs
5. Context Windows and Computational Cost
6. Prefill Versus Decode: Two Different Computational Regimes
7. KV Cache Memory: The Hidden Cost
8. Speculative Decoding: Generating Multiple Tokens Per Step
9. Repetition Penalties and Generation Controls

Chapter 11: Reasoning and Emergent Capabilities

1. Did We Train Models to Reason? (No. So How?)
2. In-Context Learning: Prompting as Programming
3. Chain-of-Thought: Making Reasoning Visible
4. The Boundary Between Pattern Matching and Reasoning
5. The Emergence Debate: Real Phenomenon or Measurement Artifact?
6. Systematic Evaluation of Reasoning Capabilities
7. What In-Context Learning Reveals About Model Capabilities

Conclusion: What We Know, What We Do Not

1. The Complete Picture: From Tokens to Intelligence-Like Behavior
2. What LLMs Achieved (and How)
3. Open Questions and Honest Uncertainties

References