CTCLoss#
Versioned name: CTCLoss-4
Category: Sequence processing
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
CTCLoss estimates likelihood that a target labels[i,:]
can occur (or is real) for given input sequence of logits logits[i,:,:]
. 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-probabilities.
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:
Compute probability of
j
-th character at time stept
fori
-th input sequence fromlogits
using softmax formula:
For a given
i
-th target fromlabels[i,:]
find all aligned paths. A pathS = (c1,c2,...,cT)
is aligned with a targetG=(g1,g2,...,gT)
if both chains are equal after decoding. The decoding extracts substring of lengthlabel_length[i]
from a targetG
, merges repeated characters inG
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 inS
in case ctc_merge_repeated equal to true and removes blank characters represented byblank_index
. By default,blank_index
is equal toC-1
, whereC
is a number of classes including the blank. For example, in case default ctc_merge_repeated, preprocess_collapse_repeated, unique andblank_index
a target sequenceG=(0,3,2,2,2,2,2,4,3)
of a lengthlabel_length[i]=4
is processed to(0,3,2,2)
and a pathS=(0,0,4,3,2,2,4,2,4)
of a lengthlogit_length[i]=9
is also processed to(0,3,2,2)
, whereC=5
. There exist other paths that are also aligned withG
, for instance,0,4,3,3,2,4,2,2,2
. Paths checked for alignment with a targetlabel[:,i]
must be of lengthlogit_length[i] = L_i
. Compute probabilities of these aligned paths (alignments) as follows:
Finally, compute negative log of summed up probabilities of all found alignments:
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 \(\ln p(S)\) 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:
Attributes
preprocess_collapse_repeated
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.Range of values: true or false
Type:
boolean
Default value: false
Required: no
ctc_merge_repeated
Description: ctc_merge_repeated is a flag for merging repeated characters in a potential alignment during the CTC loss calculation.
Range of values: true or false
Type:
boolean
Default value: true
Required: no
unique
Description: unique is a flag to find unique elements for a target
labels[i,:]
before matching with potential alignments. Unique elements in the processedlabels[i,:]
are sorted in the order of their occurrence in originallabels[i,:]
. For example, the processed sequence forlabels[i,:]=(0,1,1,0,1,3,3,2,2,3)
of lengthlabel_length[i]=10
will be(0,1,3,2)
in case unique equal to true.Range of values: true or false
Type:
boolean
Default value: false
Required: no
Inputs
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]
, whereN
is the batch size,T
is the maximum sequence length andC
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 thanT
. Lengths of input sequences of logitslogits[i,:,:]
. Required.3:
labels
- 2D tensor with shape[N, T]
of type T2. A length of a target sequencelabels[i,:]
is equal tolabel_length[i]
and must contain of integers from a range[0; C-1]
exceptblank_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 thanT
andlabel_length[i] <= logit_length[i]
for all possiblei
. Required.5:
blank_index
- Scalar of type T2. Set the class index to use for the blank label. Default value isC-1
. Optional.
Output
1: Output tensor with shape
[N]
, negative sum of log-probabilities of alignments. Type of elements is T_F.
Types
T_F: any supported floating-point type.
T1, T2:
int32
orint64
.
Example
<layer ... type="CTCLoss" ...>
<input>
<port id="0">
<dim>8</dim>
<dim>20</dim>
<dim>128</dim>
</port>
<port id="1">
<dim>8</dim>
</port>
<port id="2">
<dim>8</dim>
<dim>20</dim>
</port>
<port id="3">
<dim>8</dim>
</port>
<port id="4"> <!-- blank_index value is: 120 -->
</input>
<output>
<port id="0">
<dim>8</dim>
</port>
</output>
</layer>