{
  "schema": "ml-prep/item@1",
  "item": {
    "id": "pml-book1-ex13.1",
    "area": "machine-learning",
    "topic": "neural-networks",
    "origin": "external",
    "title": "Backpropagation for a multilayer perceptron",
    "skills": [
      "forward-pass",
      "activations",
      "chain-rule",
      "backpropagation"
    ],
    "priority": "core",
    "difficulty": "hard",
    "estimated_minutes": 20,
    "prerequisites": [
      "softmax",
      "cross-entropy",
      "matrix-calculus",
      "relu"
    ],
    "source_id": "pml-book1-2022",
    "locator": {
      "document": "PML Book 1 online draft (2025-04-18), Chapter 13 exercises",
      "label": "Exercise 13.1",
      "page_label": "title on book p. 463 (PDF p. 493); task continues on book p. 465 (PDF p. 495)",
      "solution_pages": "30"
    },
    "links": {
      "problem": "https://github.com/probml/pml-book/releases/download/2025-04-18/book1.pdf#page=493",
      "solution": "https://probml.github.io/pml-book/solns-public.pdf#page=30"
    },
    "selection_note": "Derives layer errors, parameter gradients, and the input gradient for a one-hidden-layer classifier.",
    "source_caveat": "A full-page figure separates the title from the task; the public solution manual predates the dated book draft.",
    "answer_status": "official-solution"
  }
}