InterviewsVector
Capability spine

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
1
Full-arc estimate
≈13 hours
Last edited
2026-08-11

Lesson sequence

Live units open into complete labs. Planned units stay visible to show the dependency path, but intentionally have no detail route.

  1. 01

    Vectors as Representations

    Planned

    Connect coordinates, basis, scale, and information loss to learned representations.

    Concept labFoundation80 min estimate

  2. 02

    Similarity Is a Retrieval Policy

    Live

    Derive dot product and cosine similarity, then show why normalization changes what a retrieval system rewards.

    Failure labFoundation95 min estimateArtifact: Tested similarity audit

  3. 03

    Matrices as Small Programs

    Planned

    Read a matrix as a composition of projection, scaling, rotation, and mixing operations.

    Build labFoundation90 min estimate

  4. 04

    Probability for Decisions, Not Decoration

    Planned

    Use conditional probability, calibration, and expected cost to make model outputs actionable.

    Concept labFoundation95 min estimate

  5. 05

    Optimization Under Noise

    Planned

    Derive stochastic gradients and distinguish noisy progress from broken learning.

    Build labIntermediate100 min estimate

  6. 06

    Numerical Stability Is Part of the Algorithm

    Planned

    Break softmax, log likelihood, and low-precision reductions, then repair them.

    Failure labIntermediate100 min estimate

  7. 07

    Complexity for Tensor Programs

    Planned

    Estimate FLOPs, memory traffic, activation storage, and asymptotic traps from tensor shapes.

    Systems labIntermediate85 min estimate