Protocol
Numerical Stability and Computational Cost
Produce a numerical reliability report for a small solver and probability routine; define failure reporting instead of silently returning NaN or false convergence.
25–45 active hours60–90 min sessionsBeginner
Mastery contract
Core protocol · Standard 1.0 · Produce a numerical reliability report for a small solver and probability routine; define failure reporting instead of silently returning NaN or false convergence.
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Reasoning — not yet passed
Explain conditioning versus algorithmic stability and derive the log-sum-exp shift exactly.
Reliable implementation — not yet passed
Stable functions stay finite for logits near ±1000 and agree with a trusted reference on ordinary inputs.
Reproducible experiment — not yet passed
Report both residual and solution error across the 3 cases and explain at least one disagreement.
Defense and handoff — not yet passed
Defend a precision and stopping policy using measured accuracy, memory and computation costs.
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 shift-invariant log-sum-exp and estimate matrix multiplication and solver memory costs for stated dimensions.
Implement stable softmax and log-sum-exp without calling their library equivalents; implement a residual-based stopping rule for an iterative linear solver.
Compare float32 and float64 on 3 ill-conditioned or extreme-magnitude cases; log relative errors, nonfinite counts and solver residuals.
Debug exp overflow and a convergence check that stops on a tiny parameter change despite a large residual.
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'.