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Fix a specification for CTCLoss operation (#1786)

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Roman Kazantsev
2020-08-18 13:47:59 +03:00
committed by GitHub
parent 1cb1f13eaa
commit b01112bcbc
1 changed files with 9 additions and 3 deletions
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12
docs/ops/sequence/CTCLoss_4.md
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@@ -39,12 +39,18 @@ Compute probabilities of these aligned paths (alignments) as follows:
p(S) = \prod_{t=1}^{L_i} p_{i,t,ct}
\f]
3. Finally, compute negative sum of log-probabilities of all found alignments:
3. Finally, compute negative log of summed up probabilities of all found alignments:
\f[
CTCLoss = \minus \sum_{S} \ln p(S)
CTCLoss = \minus \ln \sum_{S} p(S)
\f]
**Note**: This calculation scheme does not provide steps for optimal implementation and primarily serves for better explanation.
**Note 1**: This calculation scheme does not provide steps for optimal implementation and primarily serves for better explanation.
**Note 2**: This is recommended to compute a log-probability \f$ \ln p(S)\f$ for an aligned path as a sum of log-softmax of input logits. It helps to avoid underflow and overflow during calculation.
Having log-probabilities for aligned paths, log of summed up probabilities for these paths can be computed as follows:
\f[
\ln(a + b) = \ln(a) + \ln(1 + \exp(\ln(b) - \ln(a)))
\f]
**Attributes**