SigmoidCrossEntropyWithLogits

public class SigmoidCrossEntropyWithLogits

Public Constructors

SigmoidCrossEntropyWithLogits()

Public Methods

static <T extends TNumber> Operand<T>
sigmoidCrossEntropyWithLogits(Scope scope, Operand<T> labels, Operand<T> logits)
Computes sigmoid cross entropy given logits.

Inherited Methods

Public Constructors

public SigmoidCrossEntropyWithLogits ()

Public Methods

public static Operand<T> sigmoidCrossEntropyWithLogits (Scope scope, Operand<T> labels, Operand<T> logits)

Computes sigmoid cross entropy given logits.

Measures the probability error in discrete classification tasks in which each class is independent and not mutually exclusive. For instance, one could perform multilabel classification where a picture can contain both an elephant and a dog at the same time.

For brevity, let x = logits, z = labels. The logistic loss in pseudo-code is 

 z * -log(sigmoid(x)) + (1 - z) * -log(1 - sigmoid(x))
  = z * -log(1 / (1 + exp(-x))) + (1 - z) * -log(exp(-x) / (1 + exp(-x)))
  = z * log(1 + exp(-x)) + (1 - z) * (-log(exp(-x)) + log(1 + exp(-x)))
  = z * log(1 + exp(-x)) + (1 - z) * (x + log(1 + exp(-x))
  = (1 - z) * x + log(1 + exp(-x))
  = x - x * z + log(1 + exp(-x))

For x < 0, to avoid overflow in exp(-x), we reformulate the above 

 x - x * z + log(1 + exp(-x))
  = log(exp(x)) - x * z + log(1 + exp(-x))
  = - x * z + log(1 + exp(x))

Hence, to ensure stability and avoid overflow, the implementation uses this equivalent formulation 

   max(x, 0) - x * z + log(1 + exp(-abs(x)))

logits and labels must have the same type and shape.

Parameters
scope The TensorFlow scope
labels the labels
logits the logits of type float32 or float64
Returns
  • the component-wise logistic losses.
Throws
IllegalArgumentException if logits' and labels' do not have the same shape