{
  "id": "mlp-backprop",
  "title": "Backpropagation through a two-layer MLP",
  "kind": "implement",
  "summary": "Forward pass with a cache and a backward pass that returns the gradient of every weight and bias of a two-layer sigmoid network.",
  "difficulty": "hard",
  "tags": ["backpropagation", "gradients", "mlp", "chain-rule"],
  "lesson": "phases/03-deep-learning-core/03-backpropagation",
  "cheatsheet": "neural-net-basics",
  "minutes": 40,
  "entry": ["mlp_forward", "mse_loss", "mlp_backward"],
  "collections": ["deep-learning-core"],
  "time_limit_s": 10,
  "mutants": {
    "divide_by_batch_only": "Divides the loss gradient by N, not by N times n_out, so the gradient is too large when n_out is more than 1.",
    "extra_activation_factor": "Multiplies the gradient that flows back through W2 by a1 one extra time.",
    "mean_bias_grad": "Takes the mean of the hidden bias gradient over the batch, not the sum.",
    "missing_factor_two": "Drops the factor 2 from the derivative of the squared error.",
    "no_hidden_sigmoid_grad": "Forgets the sigmoid derivative of the hidden layer."
  }
}