AI Systems · intro
ML Math Foundations
Vectors, matrices, dot products, matmul, shapes.
Mental model
Three lenses keep coming back: linear algebra describes the data (vectors and matrices), calculus describes learning (gradients), probability describes uncertainty. Pick the lens that matches the question.
How to study ML Math Foundations
Begin by restating the mental model in your own words, then connect it to a concrete system you have built or operated. Name the mechanism, the constraint it addresses, and the trade-off it introduces. Use Math Notes for ML (Alisa Wuffles), Neural Networks: Zero to Hero (Karpathy), Essence of Linear Algebra (3Blue1Brown) to check details, but close the source before writing your explanation. Retrieval is the learning step; rereading is only preparation.
Next, compare ML Math Foundations with Gradient Descent, Vectors & Vector Spaces, Matrices & Linear Transformations, Derivatives & Gradients. Ask what changes in correctness, latency, resource use, operability, and failure recovery. Complete Dot product and matmul shapes and preserve the command, input, output, and one failed attempt as evidence. Finish by explaining the idea without jargon to someone who has not studied the track.
Proof of understanding
- Explain the mechanism from first principles and identify the state it reads or changes.
- Give one situation where the concept is the right choice and one where it is not.
- Predict a realistic failure mode before running the drill, then compare the prediction with evidence.
- Connect the result to a roadmap or build artifact instead of treating the concept as isolated trivia.
Learn from primary sources
Practice and explain it back
Dot product and matmul shapes
Vectors a=[1,2,3], b=[4,5,6]. Compute dot(a,b). Matrices A (2×3) and B (3×2): is A·B valid? What is the output shape?
Expected evidence: dot=32; A·B is 2×2.
Open the interactive drill →Review prompts
- A matmul fails with a shape error. What does reading the shapes tell you about what the layer is actually doing?
Build evidence
Synthesize: AI Models & Training
Move from transformer foundations through pre-training, fine-tuning, post-training, compression, and evaluation. Produce one working system, benchmark, or evidence-backed design that integrates the path.
- Implements or precisely models the core mechanisms from all three milestones
- Includes at least one injected failure or adversarial case and demonstrates recovery
- Reports quality, latency, resource, reliability, or usability measurements relevant to the domain
- Ships a concise architecture note explaining decisions, trade-offs, and remaining risks