CTC_Introduce
LiuDongdong
Connectionist Temporal Classification, an algorithm used to train deep neural networks in speech recognition, handwriting recognition and other sequence problems.
1. Problem
- don’t know the characters in the transcript align to the audio when having a dataset of audio clips and corresponding transcripts.
- people’s rates of speech vary.
- hand-align takes lots of time.
- Speech recognition, handwriting recognition from images, sequences of pen strokes, action labeling in videos.
2. Question Define
when mapping input sequences $X = [x_1, x_2, \ldots, x_T]$,, such as audio, to corresponding output sequences $Y = [y_1, y_2, \ldots, y_U]$, such as transcripts. We want to find an accurate mapping from $X’s$ to $Y’s$.
- Both $X$ and $Y$ can vary in length.
- The ratio of the lengths of $X$ and $Y$ can vary.
- we don’t have an accurate alignment(correspondence of the elements) of $X$ and $Y$.
The CTC algorithm, for a given $X$ it gives us an output distribution over all possible $Y’s$, we can use this distribution either to infer a likely output or to assess the probability of a given output.
- Loss Function: maximize the probability it assigns to the right answer, compute the conditional probability $p(Y|X)$;
- Inference: infer a likely $Y$ given an $X$, $Y^*=argmaxp(Y|X)$；
3. Alignment
- Often, it doesn’t make sense to force every input step to align to some output. In speech recognition, for example, the input can have stretches of silence with no corresponding output.
- We have no way to produce outputs with multiple characters in a row. Consider the alignment [h, h, e, l, l, l, o]. Collapsing repeats will produce “helo” instead of “hello”.
- the allowed alignments between $X$ and $Y$ are monotonic
- the alignment of $X$ to $Y$ is many-to-one.
- the length of $Y$ cannot be greater than the length of $X$.
4. Searching Methods
$$
Z=[ϵ, y_1, ϵ, y_2, …, ϵ, y_U, ϵ]
$$
- Case 1: can’t jump over $z_{s-1}$, the previous token in $Z$.
- Case 2: allowed to skip the previous token in $Z$.
- Loss Function: for a training set D, the model’s parameters are tuned to minimize the negative log-likelihood instead of maximizing the likelihood directly.
$$ \sum_{(X,Y)\epsilon D}-logP(Y|X) $$
- Inference: (3) don’t take into account the fact that a single output can have many alignments.
$$ Y^=argmax_Yp(Y|X)\ A^=argmax_A\prod_{t=1}^Tp_t(a_t|X) $$
5. Properties of CTC
- Conditional Independence
- Alignment Properties
CTC only allows monotonic alignments. In problems such as speech recognition this may be a valid assumption. For other problems like machine translation where a future word in a target sentence can align to an earlier part of the source sentence, this assumption is a deal-breaker.
6. Usage
- Baidu Research has open-sourced warp-ctc. The package is written in C++ and CUDA. The CTC loss function runs on either the CPU or the GPU. Bindings are available for Torch, TensorFlow and PyTorch.
- TensorFlow has built in CTC loss and CTC beam search functions for the CPU.
- Nvidia also provides a GPU implementation of CTC in cuDNN versions 7 and up.
to normalize the $\alpha$’s at each time-step to deal with CTC loss numerically unstable problem.
A common question when using a beam search decoder is the size of the beam to use. There is a trade-off between accuracy and runtime.