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A CRF-based ASR Toolkit
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CAT: Crf-based Asr Toolkit

CAT provides a complete workflow for CRF-based data-efficient end-to-end speech recognition.


Recent ASR Toolkits based on DNN-HMM hybrid systems like Kaldi and RASR achieve the state-of-the-art performance in terms of recognition accuracy, usually measured by word error rate (WER) or character error rate (CER). In contrast, end-to-end systems[^e2e] (like Eesen and Espnet) put simplicity of the training pipeline at a higher priority and usually are data-hungry. There is still a pronounced gap between attention end-to-end models and hybrid models in terms of recognition accuracy.

CAT aims at combining the advantages of the two kinds of ASR systems. CAT advocates discriminative training in the framework of conditional random field (CRF), particularly with but not limited to connectionist temporal classification (CTC) inspired state topology.

The recently developed CTC-CRF (namely CRF with CTC topology) has achieved superior benchmarking performance with training data ranging from ~100 to ~1000 hours, while being end-to-end with simplified pipeline and being data-efficient in the sense that cheaply available language models (LMs) can be leveraged effectively with or without a pronunciation lexicon.

[^e2e]: End-to-end is in the sense that flat-start training of a single DNN in one stage, without using any previously trained models, forced alignments, or building state-tying decision trees, with or without a pronunciation lexicon.

Please cite CAT using:

  • Hongyu Xiang, Zhijian Ou. CRF-based Single-stage Acoustic Modeling with CTC Topology. ICASSP, Brighton, UK, 2019. pdf

  • Keyu An, Hongyu Xiang. Zhijian Ou. CRF-based ASR Toolkit. arXiv, 2019. pdf

Key Features

  1. CAT contains a full-fledged implementation of CTC-CRF.

    • A non-trivial issue is that the gradient in training CRFs is the difference between empirical expectation and model expectation, which both can be efficiently calculated by the forward-backward algorithm.
    • CAT modifies warp-ctc for fast parallel calculation of the empirical expectation, which resembles the CTC forward-backward calculation.
    • CAT calculates the model expectation using CUDA C/C++ interface, drawing inspiration from Kaldi's implementation of denominator forward-backward calculation.
  2. CAT adopts PyTorch to build DNNs and do automatic gradient computation, and so inherits the power of PyTorch in handling DNNs.

  3. CAT provides a complete workflow for CRF-based end-to-end speech recognition.

    • CAT provides complete training and testing scripts for a number of Chinese and English benchmarks and all the experimental results reported in this paper can be readily reproduced.
    • Detailed documentation and code comments are also provided in CAT, making it easy to get start and obtain state-of-the-art baseline results even for beginners of ASR.
  4. Evaluation results on major benchmarks such as Switchboard and Aishell show that CAT obtains the state-of-the-art results among existing end-to-end models with less parameters, and is competitive compared with the hybrid DNN-HMM models.

  5. Towards flexibility, we show that i-vector based speaker-adapted recognition and latency control mechanism can be explored easily and effectively in CAT.


  • kaldi
  • pytorch 0.4+
  • openfst
  • python 2.7


Step 1. Copy src/kaldi-patch/ to kaldi src/bin, and compile.

Step 2. cd src/ctc_crf/gpu_ctc, change the path to openfst in CMakeLists.txt to your local path and run the commands below:

mkdir build
cd build
cmake ..

Step 3. Carry out Step 2 for the path src/ctc_crf/gpu_den, src/ctc_crf/path_weight, respectively.

Step 4. python in src/ctc_crf. For pytorch version 1.0+, python

Step 5. Change the path to kaldi in egs/wsj/ to your local path, taking WSJ experiment as an example.

Toolkit Workflow

We may have different state topologies in the CRF-based ASR framework. In the following, we take phone-based WSJ experiment as an example to illustrate the step-by-step workflow of running CTC-CRF (namely CRF with CTC topology), which has achieved superior benchmarking performance. Character-based workflow is similar. Scripts from other toolkits are acknowledged.

To begin, go to an example directory under the egs directory, e.g. egs/wsj, and is the top script, which consists of the following steps.

  1. Data preparation
  2. Feature extraction
  3. Denominator LM preparation
  4. Neural network training preparation
  5. Model training
  6. Decoding

Data preparation

1) local/ from Kaldi

Do data preparation. When completed, the folder data/train should contain following files:


2) local/ from Eesen

Download lexicon files and save in folder data/local/dic_phn.

units.txt : used to generate T.fst (a WFST representation of the CTC topology) later.
lexicon.txt : used to generate L.fst (a WFST representation of the lexicon) later.

3) utils/ from Eesen

Compile T.fst and L.fst.

Note that Eesen T.fst (created by utils/ in Eesen) makes mistakes, as described in the CTC-CRF paper. We correct it by a new utils/, which is called by to create the correct T.fst.

4) local/ from Kaldi

Complie G.fst (a WFST representation of the LM used later in ASR decoding) and save in lang_phn_test_{suffix}. The fields in {suffix} could be: tg (3-gram), fg (4-gram), pr (pruned LM), and const (ConstArpa-type LM).

5) local/ from Eesen

Compose T.fstL.fstG.fst into TLG.fst, which is placed in folder lang_phn_test_{suffix}.

Summary of Data preparation: TLG

Feature extraction

1) utils/ from Kaldi

Split train set and dev set in folder data. There are two options to split, according to speakers or utterances respectively, configured by --cv-spk-percent or --cv-utt-percent respectively.

2) utils/data/ from kaldi

3-fold data augmentation by perturbing the speaking speed of the original training speech data. The augmented data are postfixed with sp, so as to be differentiated from the original data.

3) steps/ from kaldi

Extract filter bank features, and place in folder fbank.

4) steps/ from Kaldi

Compute the mean and variance of features for feature normalization.

Denominator LM preparation

1) utils/ from Eesen

The training transcripts are saved in text file. Based on lexicon, convert word sequences in text file to label sequences and place in text_number file. For example,


will be converted to

38 59 35 32 67 46 41 24 9 34 41 45 37 48 19 68 4 70 55 4 56 59 10 67 9 45 4 56 43 38 47 23 9 57 59 56 40

2) chain-est-phone-lm from Kaldi

Sort the training transcripts in text_number file according to head labels in label sequences, remove identical label sequences, and obtain unique_text_number file.

Based on unique_text_number file, train a phone-based language model phone_lm.fst and place in folder data/den_meta.

3) utils/

Create the correct T_den.fst.

4) fstcompose from Kaldi

Compose phone_lm.fst and T_den.fst to den_lm.fst, and place in folder data/den_meta.

Summary of Denominator LM preparation: den

Neural network training preparation

For train set, dev set and test set, do the following steps respectively.

1) apply-cmvn from Kaldi

Apply feature normalization to the input feature sequence, write to feats.scp.

2) add-deltas from Kaldi

Calculate the delta features for the input feature sequence.

3) subsample-feats from Kaldi

Sub-sample the input feature sequence (default sampling rate: 3).

4) path_weight/build/path_weight

Note that the potential function (as shown in the CTC-CRF paper)


consists of the denominator LM weight for each training utterance, in addition to the log-softmax weights from the bottom neural neural network. We need to calculate and save the weight for the label sequence, by the following steps:

  • Construct a linearFST for each label sequence in text_number file;
  • Compose the linearFST with phone_lm.fst to obtain ofst.
  • Calculate the path weight from ofst.

5) utils/

Save features, text_number, and the corresponding path weights into folder data\hdf5(in the format of hdf5 file). This file is used as the input of neural network training.

Model training

1) speech_recognition_wsj()

The main function.

2) Settings

feature_size the dimension of the input feature (default :120)
hdim the number of units in each hidden layer
K number of neural network output layer. K=#phone+1 for phone-based model (#char+1 for char-based model.)
n_layers number of recurrent layers
dropout dropout ratio (we adopt 0.5 for all our experiments)
optimizer default: Adam
lr the learning rate

3) Neural network definition

The definition of our neural network is in The default model is BLSTM.

4) Loss function

The output of BLSTM is passed through a fully-conneted network (input dim=hdim*2, output dim=K) and a log-softmax layer, which is then used together with the labels to calculate the following loss[^loss] --- Eq (4) in the CAT paper, by class CTC_CRF_LOSS in


[^loss]: As convention, loss is the negative of log-likelihood.

Note that in the python code, the path weights are not included in the loss for back-propagation because they behave as constants during back-propagation, so we call the loss partial_loss for sake of clarity.

The loss function is defined by class CTC_CRF_LOSS in, which calls two functions --- gpu_ctc (for the numerator costs_ctc calculation) and gpu_den (for the denominator costs_alpha_den calculation, including weights for all possible paths). Both functions are implemented with CUDA. The interface definitions for the two functions are in src\ctc_crf\binding.cpp and src\ctc_crf\binding.h, and the implementations are in src\ctc_crf\gpu_den and src\ctc_crf\gpu_ctc. For the numerator calculation, we borrowed some codes from warp-ctc

costs_ctc and costs_alpha_den are used to calculate the partial_loss as follows:

(- costs_ctc + costs_alpha_den) - lamb * costs_ctc

where lamb is the weight for the CTC Loss, which is employed to stabilize the training.



Do inference over the test set, using the trained model. The outputs of the network are saved in the format of ark files in folder decode_{}/ark.


Consists of two steps : latgen-faster and

  • latgen-faster from Eesen

    • Generating lattices, by using TLG.fst and the outputs of the network (decode.{}.ark). Lattices are saved as lat.gz file in exp/decode_${dataset}/lattice_$lmtype.
  • from Eesen

    • lattice-scale: Scale the lattice with different acoustic scales.
    • lattice-best-path: Find the best path in the generated lattice.
    • compute-wer: Compute the WER.

3) from Kaldi

Rescore the lattice with ConstArpa-type language model.

4) from Kaldi

Rescore the lattice with fst-type language model.

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