Function MinOrMaxGrad

tensorflow/cc/gradients/math_grad.cc:798–860

REGISTER_GRADIENT_OP("Lgamma", LgammaGrad);

Status MinOrMaxGrad(const Scope& scope, const Operation& op,
                    const std::vector<Output>& grad_inputs,
                    std::vector<Output>* grad_outputs) {
  // The partial derivative for any input along a "reduced" dimension
  // is 1 when it is the min (or max) and 0 everywhere else. So the
  // gradient calculation is identical for both operators.
  //
  // There's a special case for propagating gradients when there are
  // multiple minima (or maxima) - we choose to divide the gradient
  // equally among all matching inputs.
  //
  // Please note this comment
  // https://github.com/tensorflow/tensorflow/issues/4886#issuecomment-256836063
  // for details.

  // Running example:
  // input: [[5, 5, 5],
  //         [1, 2, -3]]
  // reduction_indices: [1]
  auto input = op.input(0);
  auto reduction_indices = op.input(1);

  // [2, 3]
  auto input_shape = Shape(scope, input);

  // [2, 1]
  auto output_shape_kept_dims =
      ReducedShapeHelper(scope, input_shape, reduction_indices);

  // for op=min (say)
  // output = [5, -3]
  // y = [[5],
  //      [-3]]
  auto y = Reshape(scope, op.output(0), output_shape_kept_dims);

  // reshape([g1, g2], [2, 1]) = [[g1],
  //                              [g2]]
  auto grad = Reshape(scope, grad_inputs[0], output_shape_kept_dims);

  // indicators = equal(y, input)
  //  = equal([[5],   [[5, 5, 5],
  //           [-3]],  [1, 2, -3]])
  //  = [[1, 1, 1],
  //     [0, 0, 1]]
  auto indicators = Cast(scope, Equal(scope, y, input), grad_inputs[0].type());

  // [[3],
  //  [1]]
  auto num_selected = Reshape(scope, Sum(scope, indicators, reduction_indices),
                              output_shape_kept_dims);

  // [[1/3, 1/3, 1/3],
  //  [0, 0, 1]]
  auto scale = Div(scope, indicators, num_selected);

  // [[g1/3, g1/3, g1/3],
  //  [0, 0, g2]]
  grad_outputs->push_back(Mul(scope, scale, grad));