{
  "id": "sgd-momentum",
  "title": "SGD with momentum",
  "kind": "implement",
  "summary": "One momentum update with the lesson's velocity rule, and a loop that minimizes a quadratic with or without Nesterov lookahead.",
  "difficulty": "easy",
  "tags": ["optimizers", "momentum", "gradient-descent"],
  "lesson": "phases/03-deep-learning-core/06-optimizers",
  "cheatsheet": "deep-learning-training",
  "minutes": 20,
  "entry": ["momentum_step", "minimize_quadratic"],
  "collections": ["optimizers"],
  "time_limit_s": 10,
  "mutants": {
    "ema_velocity": "Scales the gradient by 1 minus beta, so the velocity is an average and not the lesson's sum.",
    "old_velocity_update": "Moves the parameters with the old velocity and not the new velocity.",
    "lookahead_sign": "Computes the Nesterov gradient at x plus lr times beta times v, the wrong side.",
    "grad_sign": "Uses b minus A x as the gradient, so the loop climbs away from the minimum.",
    "in_place_velocity": "Updates the velocity in place with *= and +=, so the caller's velocity array changes."
  }
}