Turn attention equations, tensor shapes, and implementation details into reliable LLM engineering decisions
Explain how self-attention performs content-dependent weighted averaging and identify what it cannot express without positional information.
Derive single-head QKV attention, track tensor shapes end to end, and justify the inverse-square-root key-dimension scaling.
Analyze how causal masking restricts the attention matrix, enforces next-token prediction constraints, and prevents future-token leakage.
Explain how per-head projections and concatenation factorize representation into subspaces and create distinct capacity and failure modes.
Diagnose saturation, overflow, underflow, and precision problems, then apply stable softmax and masking formulations.
Map framework attention code to its mathematics and shapes, and specify unit checks for masking, shape, and positional bugs.
4 sections · 9 lessons
Explain attention as content-dependent mixing, derive QKV projections and tensor shapes, and connect scaling to stable single-head computation.
2 lessonsAnalyze causal masking, multi-head subspace factorization, and positional schemes as structural choices that determine what attention can represent.
3 lessonsDiagnose softmax pathologies, quantify compute and memory costs, and evaluate KV caching and efficiency tactics under practical constraints.
2 lessonsTrace framework attention code back to its equations and shapes, then use targeted checks and an end-to-end mental model to find bugs and guide optimization.
2 lessonsSelf-attention is content-dependent mixing: it combines token representations according to relationships computed from the sequence, while positional information determines what order the mechanism can distinguish. This course develops a precise mental model of transformer attention, from QKV projections and causal masking through multi-head structure, numerical behavior, efficiency tradeoffs, and reference implementations. It is designed for ML engineers who need to reason about attention mathematically, diagnose implementation bugs, and make defensible choices when debugging or optimizing real LLM systems.
The course covers content-dependent mixing, QKV projections, tensor shapes, causal masking, multi-head subspaces, absolute and relative positional information, softmax stability, attention FLOPs and memory, KV caching, framework implementations, and unit checks.
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Something to operate in every section.
Three findings from decades of learning research shaped how every Fenzo lesson is built.
Average pass rate · Freeman et al., PNAS 2014
What the science says
Students in lecture-only classes are 1.5× more likely to fail.
How Fenzo does it
Every Fenzo lesson is interactive. No passive reading or watching, ever.
You work through itAI does it for you
Skill retention over time · with vs. without practice
What the science says
Offloading thinking to AI erodes the very skills you’re trying to build.
How Fenzo does it
Fenzo makes you do the thinking — guided, but never done for you.
Retrieval practiceRe-reading
Long-term recall · retrieval vs. re-reading
What the science says
Recalling information beats re-reading it for building durable understanding.
How Fenzo does it
Lessons weave in quizzes and recall prompts, so it sticks.