{
  "id": "softmax-cross-entropy",
  "title": "Stable softmax and cross-entropy",
  "kind": "implement",
  "summary": "Batched softmax, mean cross-entropy and its gradient, without overflow for large logits.",
  "difficulty": "easy",
  "tags": ["softmax", "loss-functions", "gradients", "numerical-stability"],
  "lesson": "phases/03-deep-learning-core/05-loss-functions",
  "cheatsheet": "deep-learning-training",
  "minutes": 20,
  "entry": ["softmax", "cross_entropy", "cross_entropy_grad"],
  "collections": ["deep-learning-core"],
  "time_limit_s": 10,
  "mutants": {
    "global_max": "Takes the maximum and the sum over the whole batch, not over each row.",
    "grad_missing_onehot": "Returns softmax divided by N and forgets to subtract the one-hot target.",
    "in_place_shift": "Subtracts the maximum in place, so the caller's logits change.",
    "no_max_shift": "Calls np.exp on the raw logits, so large logits overflow to infinity.",
    "sum_not_mean": "Sums the example losses and gradients and does not divide by N."
  }
}