Arc 02 · Software Engineer
Mathematical Machinery for AI Systems
Learn the math as executable engineering machinery: representations, transformations, optimization, uncertainty, and numerical failure.
Exit capability: Reason about model behavior without hiding behind library calls.
- Mapped lessons
- 7
- Published now
- 7
- Full-arc estimate
- ≈13 hours
- Last edited
- 2026-08-14
Lesson sequence
Live units open into complete labs. Planned units stay visible to show the dependency path, but intentionally have no detail route. A withdrawn unit is retained only at its previously advertised URL and is not presented as live.
- 01
Vectors as Representations
LiveConnect coordinates, basis, scale, and information loss to learned representations.
Concept labFoundation80 min estimateArtifact: Representation invariance audit
- 02
Similarity Is a Retrieval Policy
LiveDerive dot product and cosine similarity, then show why normalization changes what a retrieval system rewards.
Failure labFoundation95 min estimateArtifact: Tested similarity audit
- 03
Matrices as Small Programs
LiveRead a matrix as a composition of projection, scaling, rotation, and mixing operations.
Build labFoundation90 min estimateArtifact: Tested linear-map pipeline
- 04
Probability for Decisions, Not Decoration
LiveUse conditional probability, calibration, and expected cost to make model outputs actionable.
Concept labFoundation95 min estimateArtifact: Cost-sensitive decision policy
- 05
Optimization Under Noise
LiveDerive stochastic gradients and distinguish noisy progress from broken learning.
Build labIntermediate100 min estimateArtifact: Noisy optimizer diagnostic
- 06
Numerical Stability Is Part of the Algorithm
LiveBreak softmax, log likelihood, and low-precision reductions, then repair them.
Failure labIntermediate100 min estimateArtifact: Numerical stability harness
- 07
Complexity for Tensor Programs
LiveEstimate FLOPs, memory traffic, activation storage, and asymptotic traps from tensor shapes.
Systems labIntermediate85 min estimateArtifact: Tensor cost estimator