【Paper】CTC Introduce

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 labelling in videos.

2. Question Define

when mapping input sequences $X=[x_1,x_2,\dots ,x_T]$, such as audio, to corresponding output sequences $Y=[y_1,y_2,\dots ,y_U]$, such as transcripts. We want to find an accurate mapping from $X^{\prime }s$ to $Y^{\prime }s$.

• 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 $Y^{\prime }s$, 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 $X$, $Y^{\ast }=argmaxp(Y|X)$；

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

$$Z=[ϵ,y_1,ϵ,y_2,\dots ,ϵ,y_U,ϵ]$$

• 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.

$$\sum _{(X,Y)ϵD}-logP(Y|X)$$

• Inference: (3) don’t take into account the fact that a single output can have many alignments.

$$\begin{gathered} Y^{\ast }=argma{x}_{Y}p(Y|X) \\ {A}^{\ast }=argma{x}_A\prod _{t=1}^T{p}_t(a_t|X) \end{gathered}$$

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.

**From：**https://distill.pub/2017/ctc/