Lesson 0011 · Homework 1 overview
Four required problems, one optional bonus, all built from pieces you've already met. This lesson is the map — it doesn't teach anything new by itself, it shows you where each problem sits relative to lessons 0001–0010, so nothing on the page feels unfamiliar before you open it.
Every problem hands you a fitted score and asks two things: compute a small quantity from it, then explain what that quantity does — and does not — establish about the real-world decision. That's the x → f^_D → s → δ → a pipeline from Lesson 0001, wearing different clothes each time.
| Problem | New skill | Already known from | Lesson |
|---|---|---|---|
| 1 — thresholds & capacity | Confusion matrix, TPR/FPR at a chosen threshold; a capacity constraint changing δ without retraining; validation splits that respect grouped data | 0001 (pipeline, δ), 0003 (confusion matrix, TPR/FPR) | 0012 |
| 2 — logistic regression by hand | Log loss, its gradient, one gradient-descent update, L2 regularization | 0002 (softmax family), 0006 (gradient descent teased, not yet computed) | 0013 |
| 3 — softmax & deployment | Multiclass log loss vs. classification error; a confidence threshold that routes to a human | 0002 (softmax, argmax), 0003 (evaluation), 0001 (δ) | 0014 |
| 4 — regularization geometry | L1 vs. L2 penalty arithmetic and geometry; shortcut features and audits | 0003 (group fairness / spurious patterns), 0006 (weights, blame) | 0015 |
| Bonus — ReLU gate | Two ReLUs composing into |x| | 0005 (ReLU as an activation), 0006 (why smoothness matters) | 0016 |
Homework 1 introduces a small batch of new symbols on top of the ones in the notation decoder. None of them are conceptually new — they're the same "estimate vs. truth," "which batch of data," and "map a raw score to something usable" ideas, just written for this specific setting.
| Symbol | Read it as | You've essentially seen this as... |
|---|---|---|
t | "the cutoff on the score" — same t as Lesson 0003's threshold | δ_t(s), Lesson 0003 |
σ(z) = 1/(1+e−z) | "squash any real number into (0,1)" — the sigmoid | Same job as softmax's normalization, but for two classes instead of many |
L(β), L′(β) | "how wrong the current guess is" and "which way to move β to reduce that" | Lesson 0006's "nudge" and "blame," made numeric |
β(0), β(1) | the parenthesized superscript is a step count, not a power — "β after step 0," "after step 1" | Same labeling trick as f^_D's subscript D — it just says which version |
λ | "how hard to punish big coefficients" — a knob you set, not something the data fits | New this homework — see Lesson 0013 |
‖β‖₁, ‖β‖₂² | "total size of the coefficients," two different ways of measuring "total" | New this homework — see Lesson 0015 |
Lesson 0012 uses Problem 1's own numbers directly — but the widget there is interactive, not a worked answer: it shows the real 8 scores and labels and lets you drag the threshold yourself, so you compute TP/FP/FN/TN and TPR/FPR firsthand rather than reading them off the page. Lessons 0013–0016 still use different numbers than the actual homework — same structure, different data — for the same reason the syllabus gives: GenAI tools can't do the assignment's central reasoning for you, so those lessons build the skill on a parallel example, and you apply it yourself to Homework 1's actual tables.