Protocol
Multivariable Calculus for Gradients
Build a gradient-check notebook that another learner can apply to a new scalar objective; document nondifferentiable points and when this check cannot certify correctness.
35–60 active hours60–90 min sessionsBeginner
Mastery contract
Core protocol · Standard 1.0 · Build a gradient-check notebook that another learner can apply to a new scalar objective; document nondifferentiable points and when this check cannot certify correctness.
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Reasoning — not yet passed
All 3 derivations have consistent dimensions and correctly identify the dependence on each variable.
Reliable implementation — not yet passed
Analytic and numerical gradients agree to relative error below 1e-5 on the smooth, well-scaled fixtures at a suitable step.
Reproducible experiment — not yet passed
The step-size sweep contains at least 7 values and distinguishes numerical error from a wrong derivative.
Defense and handoff — not yet passed
Explain a saddle point with a Hessian example and defend the gradient checks in a reusable calculus notebook.
All four criteria must pass. Activity completion does not satisfy them.
An independent reviewer reruns your work and varies something you did not rehearse: a fresh input, a different working directory, or a declared edge case.
Pilot decisions are provisional, not external credentials. For an appeal or sensitive artifact, contact your designated pilot operator with the submission ID. Export your assessment history.
What you will do
6 total
Derive gradients for a quadratic, a composition of affine maps and a log-sum-exp; annotate every Jacobian shape and chain-rule multiplication.
Implement central finite differences for scalar gradients and vector Jacobians using NumPy; compare against 3 independently derived formulas.
Sweep the finite-difference step from 1e-2 to 1e-8 on smooth float64 examples; plot relative error and explain truncation versus cancellation.
Debug a missing transpose and an omitted chain-rule factor; demonstrate how a directional derivative isolates each error.
Write a 500–900 word technical report linking the reasoning, code, measurements, and limitations; include the project decision below.
Assess all 4 mastery criteria against saved artifacts, request an independent review, and repeat each failed criterion on a fresh example.
Essentials
A reading session alone never satisfies a mastery criterion.
Store source references, assumptions, and artifact paths beside every result.
Keep an untouched check case that differs from the worked example.
Record all attempts, including failures and results that contradict your prediction.
Use the stated comparison conditions; document every deviation before drawing a conclusion.
Protocol guardrails
Do
- +State the expected result before running the comparison.
- +Keep one minimal reproducible failing case when debugging.
- +Record environment versions and the exact command used.
- +Compare explanations with saved intermediate values.
- +Ask a reviewer to challenge the weakest assumption.
Don't
- ×Do not copy a worked solution and present it as an independent implementation.
- ×Do not tune against held-out evaluation outcomes.
- ×Do not report only the best seed or discard inconvenient runs.
- ×Do not equate elapsed hours or a completed run with a passed assessment.
- ×Do not conceal reduced-scale experiments behind claims about the original full-scale result.
Protocol authorship
Written by NuthinButta as instructional design. The teaching sources are the official references linked in each milestone; the exercises, workload and pass thresholds are ours, not their authors'.