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41 lines
1.6 KiB
Plaintext
41 lines
1.6 KiB
Plaintext
-- Hoogle documentation, generated by Haddock
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-- See Hoogle, http://www.haskell.org/hoogle/
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-- | Friendly layer around TensorFlow bindings.
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--
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-- Please see README.md
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@package tensorflow-nn
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@version 0.1.0.0
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module TensorFlow.NN
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-- | Computes sigmoid cross entropy given <tt>logits</tt>.
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--
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-- Measures the probability error in discrete classification tasks in
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-- which each class is independent and not mutually exclusive. For
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-- instance, one could perform multilabel classification where a picture
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-- can contain both an elephant and a dog at the same time.
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--
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-- For brevity, let `x = logits`, `z = targets`. The logistic loss is
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--
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-- z * -log(sigmoid(x)) + (1 - z) * -log(1 - sigmoid(x)) = z * -log(1 <i>
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-- (1 + exp(-x))) + (1 - z) * -log(exp(-x) </i> (1 + exp(-x))) = z *
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-- log(1 + exp(-x)) + (1 - z) * (-log(exp(-x)) + log(1 + exp(-x))) = z *
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-- log(1 + exp(-x)) + (1 - z) * (x + log(1 + exp(-x)) = (1 - z) * x +
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-- log(1 + exp(-x)) = x - x * z + log(1 + exp(-x))
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--
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-- For x < 0, to avoid overflow in exp(-x), we reformulate the above
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--
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-- x - x * z + log(1 + exp(-x)) = log(exp(x)) - x * z + log(1 + exp(-x))
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-- = - x * z + log(1 + exp(x))
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--
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-- Hence, to ensure stability and avoid overflow, the implementation uses
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-- this equivalent formulation
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--
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-- max(x, 0) - x * z + log(1 + exp(-abs(x)))
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--
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-- <tt>logits</tt> and <tt>targets</tt> must have the same type and
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-- shape.
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sigmoidCrossEntropyWithLogits :: (OneOf '[Float, Double] a, TensorType a, Num a) => Tensor Value a -> Tensor Value a -> Build (Tensor Value a)
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