Transformers from First Principles
For engineers and researchers who want to derive, implement, and reason about every component of a transformer.
Part of Language AI Handbook. The online chapters are free to read; the PDF edition is yours to keep, with future updates included.
Become a more confident language AI practitioner.
Build the understanding to explain how language models work and make more informed choices about using them. The handbook connects the foundations to the methods behind modern language AI, with explanations you can return to as you learn.
See what you’ll learnWhat you will learn
- Understand Self-Attention.
- Understand Positional Encoding.
- Understand Transformer Blocks.
- Understand Transformer Architectures.
Who this volume is for
- Engineers, researchers, students, AI enthusiasts, linguists, product managers, and anyone interested in understanding or building modern language AI systems, from foundational NLP to advanced large language models.
Prerequisites: Assumes the neural foundations in Volume 4.
Volume 5 PDF edition
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Get all-volume access · $199Reader verdict
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out of 5
12 five-star reader reviews
Genuine feedback, with names abbreviated for privacy.
Meet the community“Really appreciate the way you have explained the concepts. Simple to understand, yet builds up knowledge exponentially, all while reinforcing it with examples repeatedly. I've read the last two chapters `74.Self-attention & 75.Q,K,V` and I've to admit, my concepts have never been clearer. You really are doing an amazing job breaking down maths and complex concepts like a story!”
“I would like to thank you for your work. Specifically, the chapter: 'LIME Explainability: Complete Guide to Local Interpretable Model-Agnostic Explanations' was extremely helpful for me in understanding LIME and communicating to colleagues. Your work is inspiring and valuable. Thank you for doing it.”
“I am enjoying reading your writings. I appreciate the effort you put into it. I want to drop a note of thanks. Thank you!”
“Your writing feels like a treasure trove of great material. So, thank you for compiling everything on your website!”
“I found your book Language AI Handbook's explanations of Transformer architectures and production deployment strategies to be exceptionally clear and insightful”
“Thanks so much for establishing such an amazing community. I appreciate the opportunity to be a learner and a contributor to the community.”
“Thank you Michael. It's top!”
“I came across your collection of online handbooks covering quantitative finance, AI, and machine learning. I wanted to reach out and thank you for making such high-quality material openly available. They are incredibly helpful for my CFA Level II review and for brushing up ahead of ML interviews.”
“I came across one of your books, Language AI Handbook, and man, I'm loving it. I've read many books but have never found such a comprehensive book on large models that covers everything from start to finish with such depth.”
“I just came across your website where your books are available for free to read. Thank you so much for making this available to the public. This will help a lot of people.”
“Thanks for putting cool stuff out into the world.”
“I read a few of your blogs on NLP and oh WOW, they really are something, now I exactly know how all of the terms Entropy, Cross-entropy and how it is connected to Perplexity, will definitely read more of your blogs.”
Read all 12 reader reviews
“I would like to thank you for your work. Specifically, the chapter: 'LIME Explainability: Complete Guide to Local Interpretable Model-Agnostic Explanations' was extremely helpful for me in understanding LIME and communicating to colleagues. Your work is inspiring and valuable. Thank you for doing it.”
“Really appreciate the way you have explained the concepts. Simple to understand, yet builds up knowledge exponentially, all while reinforcing it with examples repeatedly. I've read the last two chapters `74.Self-attention & 75.Q,K,V` and I've to admit, my concepts have never been clearer. You really are doing an amazing job breaking down maths and complex concepts like a story!”
“Thanks so much for establishing such an amazing community. I appreciate the opportunity to be a learner and a contributor to the community.”
“I just came across your website where your books are available for free to read. Thank you so much for making this available to the public. This will help a lot of people.”
“I am enjoying reading your writings. I appreciate the effort you put into it. I want to drop a note of thanks. Thank you!”
“Thank you Michael. It's top!”
“Thanks for putting cool stuff out into the world.”
“I found your book Language AI Handbook's explanations of Transformer architectures and production deployment strategies to be exceptionally clear and insightful”
“Your writing feels like a treasure trove of great material. So, thank you for compiling everything on your website!”
“I came across your collection of online handbooks covering quantitative finance, AI, and machine learning. I wanted to reach out and thank you for making such high-quality material openly available. They are incredibly helpful for my CFA Level II review and for brushing up ahead of ML interviews.”
“I read a few of your blogs on NLP and oh WOW, they really are something, now I exactly know how all of the terms Entropy, Cross-entropy and how it is connected to Perplexity, will definitely read more of your blogs.”
“I came across one of your books, Language AI Handbook, and man, I'm loving it. I've read many books but have never found such a comprehensive book on large models that covers everything from start to finish with such depth.”
Exact contents
27 chapters across 4 parts
Every linked chapter is free to read online.
Part XIII: Self-Attention
- 01Self-Attention Concept
Covers cross-attention vs self-attention, self-attention motivation, all-pairs interaction, self-attention for representation learning, self-attention computational pattern.
- 02Query, Key, Value
Covers QKV intuition (database lookup), projection matrices Wq, Wk, Wv, query-key matching, value retrieval, QKV dimensions and shapes, QKV as learned transformations.
- 03Scaled Dot-Product Attention
Covers dot product for similarity, softmax for normalization, scaling factor derivation (1/√dk), attention output computation, attention in matrix form, attention implementation.
- 04Attention Masking
Covers padding masks, causal (look-ahead) masks, combining multiple masks, mask shapes and broadcasting, efficient masking implementation, custom attention patterns.
- 05Multi-Head Attention
Covers multiple attention heads motivation, head dimension splitting, parallel attention computation, output concatenation and projection, head specialization, multi-head vs single head.
- 06Attention Complexity
Covers O(n²) attention complexity, memory requirements, attention bottleneck in long sequences, FLOPs computation, attention vs RNN complexity, practical scaling limits.
Part XIV: Positional Encoding
- 01Position Problem
Covers transformer position blindness, why position matters for language, position information requirements, position encoding vs position embedding, absolute vs relative position.
- 02Sinusoidal Position Encoding
Covers sinusoidal formula derivation, wavelength intuition, position encoding visualization, extrapolation properties, sinusoidal encoding implementation, learned vs sinusoidal trade-offs.
- 03Learned Position Embeddings
Covers position embedding table, position embedding training, maximum sequence length, learned embedding extrapolation, position embedding analysis, GPT-style position embeddings.
- 04Relative Position Encoding
Covers relative position motivation, relative attention formulation, clipping relative positions, relative position in self-attention, Shaw et al. relative positions, relative bias implementation.
- 05Rotary Position Embedding (RoPE)
Covers RoPE intuition, rotation matrix formulation, RoPE in complex numbers, relative position through rotation, RoPE implementation, RoPE frequency patterns.
- 06ALiBi
Covers ALiBi motivation, linear bias by distance, head-specific slopes, ALiBi extrapolation properties, ALiBi simplicity advantages, ALiBi vs RoPE comparison.
- 07Position Encoding Comparison
Covers extrapolation benchmarks, training efficiency comparison, implementation complexity, position encoding for long context, hybrid approaches, current best practices.
Part XV: Transformer Blocks
- 01Residual Connections
Covers residual connection formulation, gradient highway interpretation, residual scaling, residual connections in transformers, pre-norm vs post-norm residuals.
- 02Layer Normalization
Covers layer norm vs batch norm, layer norm formula, learnable affine parameters, layer norm placement, layer norm gradient flow, layer norm implementation.
- 03RMSNorm
Covers RMSNorm derivation, removing mean centering, RMSNorm efficiency, RMSNorm vs LayerNorm performance, RMSNorm in modern architectures.
- 04Pre-Norm vs Post-Norm
Covers original transformer (post-norm), pre-norm formulation, training stability comparison, gradient flow differences, when to use each, modern consensus.
- 05Feed-Forward Networks
Covers FFN architecture, hidden dimension expansion, FFN as two linear layers, position independence, FFN parameter count, FFN computational cost.
- 06FFN Activation Functions
Covers ReLU in original transformer, GELU adoption, GELU approximations, SiLU/Swish in modern models, activation function comparison.
- 07Gated Linear Units
Covers GLU formulation, gating mechanism, SwiGLU derivation, GeGLU variant, GLU parameter efficiency, GLU in modern architectures.
- 08Transformer Block Assembly
Covers standard block structure, component ordering, block implementation, block initialization, forward pass walkthrough, block hyperparameters.
Part XVI: Transformer Architectures
- 01Encoder Architecture
Covers encoder-only design, bidirectional self-attention, encoder for understanding tasks, encoder output usage, BERT-style encoder, encoder layer stacking.
- 02Decoder Architecture
Covers decoder-only design, causal masking requirement, autoregressive generation, decoder for generation tasks, GPT-style decoder, decoder layer stacking.
- 03Encoder-Decoder Architecture
Covers encoder-decoder interaction, cross-attention mechanism, encoder-decoder for seq2seq, T5-style architecture, information flow, when to use encoder-decoder.
- 04Cross-Attention
Covers cross-attention formulation, KV from encoder, Q from decoder, cross-attention masking, cross-attention placement, cross-attention implementation.
- 05Weight Tying
Covers input-output embedding tying, encoder-decoder tying, parameter reduction, weight tying effects on training, when to tie weights.
- 06Architecture Hyperparameters
Covers depth vs width trade-offs, number of heads selection, hidden dimension ratios, FFN expansion ratio, total parameter calculation, architecture search.
Choose the edition that fits your next step
Volume 5: Transformers from First Principles
860 pages focused on this subject, with future updates included.
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Get all-volume accessExplore the other volumes
Volume 1 · 570 pages
Language Data and Classical NLP
Text as Data · Classical Text Representations · Distributional Semantics
Volume 2 · 790 pages
Embeddings, Tokenization, and Sequence Labeling
Word Embeddings · Subword Tokenization · Sequence Labeling
Volume 3 · Coming soon
Linguistic Structure and Meaning
Morphology · Syntax · Semantics · Discourse · Dialogue
Volume 4 · 920 pages
Neural NLP and Sequence Models
Neural Network Foundations · Recurrent Neural Networks · Sequence-to-Sequence
Volume 6 · 510 pages
Efficient, Long-Context, and Alternative Architectures
Efficient Attention · Long Context
Volume 7 · 760 pages
Pre-training Data and Scaling
Data Curation · Pre-training Objectives · Scaling Laws
Volume 8 · 440 pages
Encoder, Multilingual, and Translation Models
BERT and Variants · Encoder-Decoder Models
Volume 9 · 730 pages
Decoder Language Models and Capabilities
GPT Architecture · Modern Decoder Models · Emergent Capabilities
Volume 10 · 920 pages
Large-Scale Training and Sparse Models
Training Infrastructure · Training Optimization · Mixture of Experts
Volume 11 · 730 pages
Fine-tuning and Efficient Adaptation
Fine-tuning Fundamentals · Parameter-Efficient Fine-tuning · Instruction Tuning
Volume 12 · 510 pages
Alignment, Preferences, and Oversight
Alignment and RLHF
Volume 13 · 220 pages
Reasoning and Verifiable Learning
Reasoning
Volume 14 · 640 pages
Efficient Inference and On-Device Models
Model Compression · Inference Optimization
Volume 15 · 600 pages
Retrieval, Knowledge, and Memory
Retrieval-Augmented Generation · Continual Learning
Volume 16 · 510 pages
Agents and AI Coding Systems
Code Generation · Tool Use and Agents
Volume 17 · 540 pages
Speech, Multimodal, and Embodied Language
Multimodal Models · Speech and Audio
Volume 18 · 950 pages
Evaluation, Factuality, and Reliability
Evaluation Fundamentals · Benchmark Evaluation · Human and Model Evaluation · Hallucination and Factuality
Volume 19 · 760 pages
Responsible, Secure, and Interpretable Language AI
Bias and Fairness · Interpretability · Safety and Security
Volume 20 · 510 pages
Applications, Production, and Compound AI Systems
LLM Applications · Production Systems
Author and edition details
About the author and this edition
Michael Brenndoerfer
Michael has spent more than a decade working across software engineering, data, AI, and business. He writes to understand difficult ideas more deeply and to share what he learns in a clear, practical way.
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- First edition
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- Last reviewed
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Library access includes every future volume and update. When a volume changes, its updated PDF appears in My books at no extra cost.
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Edition 2026.08.0
Initial volume-library release with 19 written PDFs, a Volume 3 placeholder, and no combined edition.