**Short description**: *CTCLoss* computes the CTC (Connectionist Temporal Classification) Loss.
**Detailed description**:
*CTCLoss* operation is presented in [Connectionist Temporal Classification - Labeling Unsegmented Sequence Data with Recurrent Neural Networks: Graves et al., 2016](http://www.cs.toronto.edu/~graves/icml_2006.pdf)
Briefly, *CTCLoss* operation finds all sequences aligned with a target `labels[i,:]`, computes log-probabilities of the aligned sequences using `logits[i,:,:]`
and computes a negative sum of these log-probabilies.
Input sequences of logits `logits` can have different lengths. The length of each sequence `logits[i,:,:]` equals `logit_length[i]`.
A length of target sequence `labels[i,:]` equals `label_length[i]`. The length of the target sequence must not be greater than the length of corresponding input sequence `logits[i,:,:]`.
Otherwise, the operation behaviour is undefined.
*CTCLoss* calculation scheme:
1. Compute probability of `j`-th character at time step `t` for `i`-th input sequence from `logits` using softmax formula:
The decoding extracts substring of length `label_length[i]` from a target `G`, merges repeated characters in `G` in case *preprocess_collapse_repeated* equal to true and
finds unique elements in the order of character occurrence in case *unique* equal to true.
The decoding merges repeated characters in `S` in case *ctc_merge_repeated* equal to true and removes blank characters represented by `blank_index`.
For example, in case default *ctc_merge_repeated*, *preprocess_collapse_repeated*, *unique* and `blank_index` a target sequence `G=(0,3,2,2,2,2,2,4,3)` of a length `label_length[i]=4` is processed
to `(0,3,2,2)` and a path `S=(0,0,4,3,2,2,4,2,4)` of a length `logit_length[i]=9` is also processed to `(0,3,2,2)`, where `C=5`.
There exist other paths that are also aligned with `G`, for instance, `0,4,3,3,2,4,2,2,2`. Paths checked for alignment with a target `label[:,i]` must be of length `logit_length[i] = L_i`.
Compute probabilities of these aligned paths (alignments) as follows:
**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:
* **Description**: *preprocess_collapse_repeated* is a flag for a preprocessing step before loss calculation, wherein repeated labels in `labels[i,:]` passed to the loss are merged into single labels.
* **Description**: *unique* is a flag to find unique elements for a target `labels[i,:]` before matching with potential alignments. Unique elements in the processed `labels[i,:]` are sorted in the order of their occurrence in original `labels[i,:]`. For example, the processed sequence for `labels[i,:]=(0,1,1,0,1,3,3,2,2,3)` of length `label_length[i]=10` will be `(0,1,3,2)` in case *unique* equal to true.
* **1**: `logits` - Input tensor with a batch of sequences of logits. Type of elements is *T_F*. Shape of the tensor is `[N, T, C]`, where `N` is the batch size, `T` is the maximum sequence length and `C` is the number of classes including the blank. **Required.**
* **2**: `logit_length` - 1D input tensor of type *T1* and of a shape `[N]`. The tensor must consist of non-negative values not greater than `T`. Lengths of input sequences of logits `logits[i,:,:]`. **Required.**
* **3**: `labels` - 2D tensor with shape `[N, T]` of type *T2*. A length of a target sequence `labels[i,:]` is equal to `label_length[i]` and must contain of integers from a range `[0; C-1]` except `blank_index`. **Required.**
* **4**: `label_length` - 1D tensor of type *T1* and of a shape `[N]`. The tensor must consist of non-negative values not greater than `T` and `label_length[i] <= logit_length[i]` for all possible `i`. **Required.**
