mirror of
https://github.com/tensorflow/haskell.git
synced 2024-11-17 16:39:43 +01:00
40 lines
1.6 KiB
Text
40 lines
1.6 KiB
Text
-- Hoogle documentation, generated by Haddock
|
|
-- See Hoogle, http://www.haskell.org/hoogle/
|
|
|
|
|
|
-- | Friendly layer around TensorFlow bindings.
|
|
--
|
|
-- Please see README.md
|
|
@package tensorflow-nn
|
|
@version 0.1.0.0
|
|
|
|
module TensorFlow.NN
|
|
|
|
-- | Computes sigmoid cross entropy given <tt>logits</tt>.
|
|
--
|
|
-- 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 = targets`. The logistic loss is
|
|
--
|
|
-- z * -log(sigmoid(x)) + (1 - z) * -log(1 - sigmoid(x)) = z * -log(1 <i>
|
|
-- (1 + exp(-x))) + (1 - z) * -log(exp(-x) </i> (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)))
|
|
--
|
|
-- <tt>logits</tt> and <tt>targets</tt> must have the same type and
|
|
-- shape.
|
|
sigmoidCrossEntropyWithLogits :: (MonadBuild m, OneOf '[Float, Double] a, TensorType a, Num a) => Tensor Value a -> Tensor Value a -> m (Tensor Value a)
|