[AI from Scratch] Episode 311: Connectionist Temporal Classification (CTC) — Maintaining Label Alignment in Speech Recognition

Recap and Today’s Theme

Hello! In the previous episode, we discussed Hidden Markov Models (HMMs), a classical approach to speech recognition. While HMMs decompose speech into phonemes, they face limitations when capturing the complex and long-term dependencies in speech data.

In this episode, we’ll dive into Connectionist Temporal Classification (CTC), a method that plays a critical role in modern speech recognition systems. CTC, combined with deep learning models, is an efficient approach to converting speech to text while maintaining label alignment. We’ll explore how CTC works and its implementation in speech recognition.

What is Connectionist Temporal Classification (CTC)?

Connectionist Temporal Classification (CTC) is a technique used in tasks such as speech recognition and handwriting recognition, where the input and output sequence lengths do not match. CTC is often used with deep learning models, particularly Recurrent Neural Networks (RNNs) or Long Short-Term Memory (LSTM) networks, to predict labels (e.g., characters or words) across an entire sequence.

Purpose of CTC

CTC is designed to handle the mismatch between the length of input sequences (e.g., speech signal samples) and output sequences (e.g., text transcription). In speech recognition, the audio signal consists of many samples, while the output text is much shorter. CTC learns to map the input sequence to the output labels effectively, even when the lengths differ significantly.

How Does CTC Work?

CTC introduces a blank (blank) label between the input and output sequences, allowing flexible alignment between them. This blank label enables the model to map input time steps where no meaningful output (e.g., no word) occurs.

1. Introducing the Blank Label

CTC adds a special blank symbol to the label set, representing steps in the input sequence where no output is produced. This allows the model to handle the mismatch between the input and output lengths without forcing an immediate mapping.

2. Removing Duplicates and Blanks

While the network outputs a label for each time step (including blanks), the final text sequence is obtained by removing duplicates and eliminating blanks from the sequence.

For example, consider the following output from a network:

Network output: ['b', '-', '-', 'a', 'a', '-', 't', '-', 't']

After applying the CTC decoding rules, the final output becomes:

CTC decoded result: ['b', 'a', 't']

This method reduces the sequence length and retrieves meaningful text from the predictions.

3. CTC Loss Function

CTC uses a specialized CTC loss function to evaluate how well the predicted sequence aligns with the true label sequence. The loss function computes the probability that the predicted sequence matches the true sequence, even when the input and output lengths differ. This enables end-to-end learning, where the model is trained directly on the raw input (speech) to output text.

The key properties of CTC loss are:

• Handles varying input-output lengths: It maps long input sequences (e.g., speech signals) to shorter output sequences (e.g., text labels).
• End-to-end learning: The network can learn to predict text directly from audio features, simplifying the speech recognition system.

Example of CTC in Python

CTC can be implemented using deep learning frameworks such as TensorFlow or PyTorch. Below is a simple example using TensorFlow to calculate CTC loss.

1. Installing Required Libraries

pip install tensorflow

2. Example of CTC Implementation

Here’s how you can implement CTC using TensorFlow’s built-in functions:

import tensorflow as tf

# Dummy data (audio features)
batch_size = 2
timesteps = 50  # Length of the audio feature sequence
input_dim = 13  # Number of MFCC features
inputs = tf.random.normal([batch_size, timesteps, input_dim])

# Dummy labels (ground truth text labels)
labels = tf.sparse.from_dense([[1, 2, 3], [1, 2]])

# Length of each sequence in the batch
input_lengths = tf.constant([50, 50], dtype=tf.int32)
label_lengths = tf.constant([3, 2], dtype=tf.int32)

# Calculate the CTC loss
ctc_loss = tf.nn.ctc_loss(
    labels=labels,
    logits=inputs,
    label_length=label_lengths,
    logit_length=input_lengths,
    logits_time_major=False
)

# Compute the average loss
loss = tf.reduce_mean(ctc_loss)
print(f'CTC Loss: {loss}')

• tf.nn.ctc_loss(): Computes the CTC loss, which measures how well the network’s output aligns with the ground truth.
• labels: The ground truth labels are provided as sparse tensors.
• inputs: The network’s output (logits) based on the input audio features.
• logits_time_major: Specifies the shape of the output tensor. By default, it expects the format (batch, time, features).

In this code, the CTC loss function evaluates how well the model’s predicted sequence matches the true labels. By minimizing this loss, the model improves its ability to generate accurate text from input speech.

Benefits and Limitations of CTC

Benefits

• Flexibility: CTC can handle sequences with mismatched input and output lengths, making it suitable for tasks like speech recognition and handwriting recognition.
• End-to-End Learning: CTC allows models to predict text labels directly from audio features, simplifying the design of speech recognition systems.

Limitations

• Handling Long-Term Dependencies: CTC may struggle to capture long-term dependencies in the input data. For this reason, architectures such as LSTM and Transformers are often used alongside CTC.
• Real-Time Processing: Since CTC requires looking at the entire input sequence to generate the best label alignment, it may not be well-suited for real-time applications.

Summary

In this episode, we covered Connectionist Temporal Classification (CTC), a method used to align input and output sequences of different lengths in speech recognition. CTC is a powerful tool that enables end-to-end learning for converting speech to text, and it is widely used in modern speech recognition systems. In the next episode, we’ll delve into DeepSpeech, a speech recognition model that leverages CTC for accurate and efficient speech-to-text conversion.

Next Episode Preview

In the next episode, we’ll explore DeepSpeech, a deep learning-based speech recognition model that combines CTC with neural networks. Learn how DeepSpeech achieves high accuracy in speech recognition tasks.

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Notes

• Blank Label: A special symbol in CTC that represents no output at a given time step.
• CTC Loss: A loss function used to align input and output sequences in tasks such as speech recognition. 【113†source】