{
  "schema": "ml-prep/item@1",
  "item": {
    "id": "original-ml-gd",
    "area": "machine-learning",
    "topic": "gradient-descent",
    "origin": "original",
    "title": "Gradient descent on a quadratic",
    "skills": [
      "gradient-update",
      "learning-rate",
      "convergence"
    ],
    "priority": "core",
    "difficulty": "easy",
    "estimated_minutes": 7,
    "prerequisites": [
      "derivatives"
    ],
    "prompt": "For $f(w)=(w-3)^2$, start at $w_0=0$. Compute $w_1$ for learning rates $0.1$ and $1.1$. Explain which update moves toward the minimizer and why overly large learning rates can diverge.\n",
    "answer": "The gradient at $0$ is $-6$. With $\\eta=0.1$, $w_1=0.6$. With $\\eta=1.1$, $w_1=6.6$, overshooting $3$. For this quadratic, convergence requires $0<\\eta<1$; larger steps amplify error.\n",
    "check": {
      "kind": "numeric",
      "id": "original-ml-gd",
      "values": [
        0.6,
        6.6
      ]
    }
  }
}