Teach it a rule. Check what it learned.: sources & model

Train a real classifier on editable inspection cards. Reveal a confident mistake, repair a misleading shortcut, and freeze your model before opening its reserved test.

What supports the explanation?

What this model assumes

1. Original synthetic coordinate classifier, not image recognition, a neural network, a foundation model or production inspection software.
2. The guide is known to the lesson author and publicly inspectable. It is simpler to compute the geometric answer directly when that rule is already known.
3. At most 64 training cards, fixed feature maps and 5000 full-batch updates. Bump centers, width and coordinate scaling do not adapt to data.
4. Training examples and the validation grid are designed teaching fixtures. Their percentages are not real-world generalization estimates.
5. The reserved envelope is a pedagogical separation, not secure hidden data. Browser-local exposure memory can be unavailable or cleared.
6. Paired mark reversals and paired training copies share provenance; they do not add independent test evidence.
7. A model score is not a validated probability of correctness, and no fairness or safety conclusion about real people follows from this toy.
8. Independent numeric reproduction, source review and gradient checks do not replace subject, accessibility, device/export or learner review.
9. Exact synthetic geometry: Each dot has integer coordinates u,v from −1000 to 1000; x=u/1000 and y=v/1000. The answer is inside when u²+v²≤490000, including the boundary. The guide radius is 0.7 and both map axes have equal scale. This is invented teaching data, not a production benchmark.
10. The predictor does not receive the answer: The feature vector contains only selected position calculations and possibly a stored visible batch mark. Guide answers are evaluator metadata. Training uses the annotations supplied on training cards, including intentionally wrong ones.
11. One logistic-regression family: The score is σ(w·f), where σ(z)=1/(1+exp(−z)). The main feature choices have 3, 4 or 29 weights. Flexible features add 25 fixed Gaussian bumps centered on a declared grid with width 0.2. These centers and widths are not learned hidden neurons or an infinite kernel.
12. A declared objective: Training minimizes mean binary log loss plus λ/2 times the sum of squared non-intercept weights. The intercept is unpenalized. The workbench reports data loss, penalty and total objective separately. Natural logarithms give nats per example.
13. A genuine simultaneous update: The gradient averages (score−annotation) times each feature, then adds the non-intercept penalty gradient. All coordinates update from the old weight vector. The conservative step η=1/B uses B=Σ||f||²/(4n)+λ, an upper bound derived from σ(1−σ)≤1/4. Validation and reserved labels are absent.
14. A budget is not convergence: Weights start at zero and at most 5000 updates are recorded. Editing examples, features or λ starts a fresh fit. In unregularized separable logistic regression, weights may continue growing as loss approaches zero. A finite update budget does not promise exact convergence or zero loss.
15. Capacity and the target shape: On the symmetric clean grid, the straight model settles at a constant inside score 9/25=0.36. A straight boundary cannot enclose the center while excluding the surrounding outside examples. Running more identical updates cannot add a missing representation.
16. Accuracy and loss can disagree: On the fixed noisy flexible example, λ=0 gives 35/36 validation classifications and mean loss about 0.106845; λ=0.02 gives 36/36 but loss about 0.345015. Regularization improves one criterion here while worsening another. Neither is a universal ranking of model quality.
17. A score is not verified certainty: A fitted score near 0.96 can be wrong on the deliberately noisy fixture. Calibration is about the relationship between predicted probabilities and observed outcomes across suitable data; a confident single prediction does not establish it.
18. Thresholds change decisions: Classify inside when the unrounded score is at least the threshold. Raising the threshold cannot increase true-positive or false-positive counts on fixed data. It leaves weights, scores and log loss unchanged. Exact ties count as inside.
19. Four counts, different questions: Inside is the positive class. TP finds an inside center, FP calls an outside center inside, FN misses an inside center, and TN rejects an outside center. Accuracy divides all correct predictions by all cards; precision divides TP by inside predictions; recall divides TP by actual inside cards. A zero denominator is undefined.
20. Independent fitting is only part of evaluation: Training fits weights; validation guides choices. A reserved set evaluates a frozen choice. Using reserved scores to tune settings compromises their untouched role even when none of those rows enters a gradient. The exposure marker persists locally.
21. A fixed reproducible envelope: The 64 reserved integer-grid positions use a documented 32-bit LCG with coordinate seed 48 and independent mark seed 49, rejecting original training/validation coordinates and duplicates. Their balanced class count happens for this seed; the generator does not enforce it. The code and answers remain inspectable, so this is not a secure exam.
22. Data edits can contaminate a split: Validation and reserved records stay fixed when training is edited. A shared coordinate or lineage is flagged. Changing an ID does not make a copy independent. The original validation grid is deliberately designed, rather than a representative random sample of a factory population.
23. Shortcut, leakage and shift: A pre-existing decoration can support a misleading shortcut without being a future answer leak. Reversing marks changes the input distribution while the geometric rule stays fixed. For a batch-only predictor, the target relationship conditional on its restricted input changes. An inspection-answer field created afterward is excluded for a different reason: it is unavailable at prediction time.
24. A changed specification is another problem: If a shop changes its guide radius from 0.7 to 0.5, the same position (0.6,0) changes answer. That is a new target rule, not just a different mix of positions. Our interactive workbench keeps radius 0.7 fixed; the old weights would not automatically adapt to a new specification.

What has been checked

Analytical reference cases, conservation or transition invariants, finite drawing commands, bounded setup parsing, discovery and route integrity are checked automatically. These checks do not establish anatomical fidelity, learner outcomes or browser/device compatibility. Independent subject review, learner trials, comprehensive accessibility review and browser video encoding checks remain pending.

Each source supports the associated claim. Sources do not certify this implementation or its visuals.

About the cover illustration

Original calculated score map of a genuinely trained synthetic coordinate classifier. The white circle is the separate geometric answer guide; no pixels, people or external dataset were used for training.