{
  "lesson": "44-cosine-lr-warmup",
  "title": "Cosine LR with Linear Warmup",
  "questions": [
    {
      "stage": "pre",
      "question": "Why does the cosine-with-warmup schedule start at zero rather than at lr_max?",
      "options": [
        "Random tradition",
        "Because lr_max is illegal at step zero",
        "The first thousand updates are noisy; a linear ramp from zero to lr_max gives the optimizer a small effective step size while running estimates stabilise",
        "Because Adam requires it"
      ],
      "correct": 2,
      "explanation": "Warmup keeps brittle early updates small; the model otherwise either diverges or plateaus."
    },
    {
      "stage": "check",
      "question": "Why is the schedule implemented as a single function over step rather than three glued segments?",
      "options": [
        "A glued schedule loses one boundary the first time lr_max is changed; the single function evaluates the same closed-form expression and preserves continuity at warmup and total endpoints",
        "Linters require it",
        "Random",
        "Single functions are smaller"
      ],
      "correct": 0,
      "explanation": "Continuity at lr(warmup_steps) and lr(total_steps) follows from the closed form."
    },
    {
      "stage": "check",
      "question": "What happens for step > total_steps in the schedule?",
      "options": [
        "It returns nan",
        "It throws an exception",
        "It wraps around",
        "It pins at lr_min; the schedule does not extrapolate, and trainers that need to extend training change total_steps explicitly"
      ],
      "correct": 3,
      "explanation": "A pinned floor keeps an overshooting trainer in a documented state instead of crashing."
    },
    {
      "stage": "check",
      "question": "Why log gradient L2 norm next to the learning rate?",
      "options": [
        "Tradition",
        "The norm is the other half of training health: a divergent run spikes its norm before the loss; a too-aggressive peak shows up as a norm that stays high after warmup",
        "It looks pretty",
        "Adam requires it"
      ],
      "correct": 1,
      "explanation": "Co-logging makes pathological schedules visible at run time, not after the fact."
    },
    {
      "stage": "post",
      "question": "Why configure warmup_steps as a fraction of total_steps in production?",
      "options": [
        "Fractions are cleaner",
        "A fixed warmup count that suits a 20k-step run is essentially no warmup in a 200M-step run; the fraction (typical 1-3 percent) scales with training duration",
        "Hardware requirement",
        "Random preference"
      ],
      "correct": 1,
      "explanation": "Absolute warmup counts misbehave across training-duration scales."
    },
    {
      "stage": "post",
      "question": "Why is a non-zero lr_min typical in production?",
      "options": [
        "A floor near 10 percent of lr_max keeps the optimizer learning during the long tail; an lr_min of zero produces a curve that looks good and a model that has not finished training",
        "Numerical stability",
        "Backward compatibility",
        "Adam requires non-zero"
      ],
      "correct": 0,
      "explanation": "The tail of the schedule is where late-stage refinements land; zeroing it wastes that signal."
    }
  ]
}