## Chapter 15 — Epsilon is a step on the toy, not a receipt recipe ### Lesson map Lesson 15. Map, example, EX061. ```mermaid flowchart TD W["Printed weights and bias"] --> E["Five eps values, no sixth"] E --> A["Accuracy falls from 0.985 to 0.505"] A --> R["The receipt rule stays prose"] ``` The step moves synthetic points. It does not edit a receipt image. ### Logical drawing ```text weights w=(1.795, 1.756) b=-0.080 eps=0.00 accuracy=0.985 eps=0.25 accuracy=0.950 eps=0.50 accuracy=0.840 eps=0.75 accuracy=0.660 eps=1.00 accuracy=0.505 ``` ### Learning outcomes After this chapter, you should be able to: 1. Read the printed weights, the bias, and the five accuracies. 2. Describe the step as a signed move of size eps on a synthetic point. 3. Keep the €500 review rule out of this print. ### 15.1 Training uses seed 7. The accuracy loop only evaluates. `random.Random(7)` draws two clusters. A point labelled 1 is centred at +1 on both axes. A point labelled 0 is centred at −1. The Gaussian scale is 0.7. Four hundred points train. Two hundred points are held for the accuracy lines. Logistic regression starts at weights `[0, 0]` and bias `0`, runs 200 epochs, and steps by 0.1 times the mean gradient. The printed result of that training is `w=(1.795, 1.756)` and `b=-0.080`. `acc` does not train again. For each test point it computes `p`, then builds a new point by adding `eps * sign((p - y) * w)` on each axis. It scores the new point with the same weights and counts a success when the sigmoid output is at least 0.5 and the label agrees. At eps 0 the added term is zero, so the line is the clean accuracy `0.985`. The later lines are `0.950`, `0.840`, `0.660` and `0.505`. The tuple of eps values has five entries. A sixth eps is not printed. The points are numbers from a generator. They are not pixels, and they are not scanned receipts. The manuscript's decision for ReceiptSort — manual review above €500 or when confidence is low — lives in the adoption prose. It is not a column of this print. Nothing in this chapter is a procedure for altering a real receipt, a real image, or a production classifier. | eps | Printed accuracy | What it is | |---|---|---| | 0.00 | 0.985 | Clean test points | | 0.50 | 0.840 | Midpoint of the five | | 1.00 | 0.505 | Last printed line | | any other | not printed | Not a result | ### 15.2 Worked example | Proposal for the Tallis note | Decision | |---|---| | Quote the five accuracies and the weights | Keep | | Add eps 1.25 because the trend is clear | Refuse | | Turn the sign step into steps for a receipt scan | Refuse | | Leave the €500 review in the adoption plan, as prose | Keep | > **Synthetic case.** ReceiptSort's review rule and this weight vector are different objects. ### Errors and limits A falling accuracy on toy points is a lesson about this classifier. It is not evidence that a client's receipt was altered. ### Apply - **EX061 — Five lines.** What do the weights and the five accuracies say, and what must the note refuse to add? *Rubric:* 3 = w=(1.795, 1.756), b=-0.080, accuracies 0.985 down to 0.505; no sixth eps; the €500 rule stays prose; no receipt procedure;; 2 = the five lines and the refusal;; 1 = one accuracy;; 0 = adds an eps or a procedure. ### Continue studying — lesson 15 (chapter 15 of 20) [← Chapter 14](#ch-14) · [Course chapter index](../SUBJECTS.md) · [Chapter 16 →](#ch-16) Continue to the next authored lesson. ## Worked answers **EX061.** The printed weights are (1.795, 1.756) and the bias is -0.080. The five accuracies run from 0.985 at eps 0.00 to 0.505 at eps 1.00. No sixth eps is printed. The €500 review stays in the adoption prose. The sign step is on synthetic points and is not a receipt procedure.