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<section id="lodr-for-rnn-transducer">
<span id="lodr"></span><h1>LODR for RNN Transducer<a class="headerlink" href="#lodr-for-rnn-transducer" title="Permalink to this heading"></a></h1>
<p>As a type of E2E model, neural transducers are usually considered as having an internal
language model, which learns the language level information on the training corpus.
In real-life scenario, there is often a mismatch between the training corpus and the target corpus space.
This mismatch can be a problem when decoding for neural transducer models with language models as its internal
language can act “against” the external LM. In this tutorial, we show how to use
<a class="reference external" href="https://arxiv.org/abs/2203.16776">Low-order Density Ratio</a> to alleviate this effect to further improve the performance
of langugae model integration.</p>
<div class="admonition note">
<p class="admonition-title">Note</p>
<p>This tutorial is based on the recipe
<a class="reference external" href="https://github.com/k2-fsa/icefall/tree/master/egs/librispeech/ASR/pruned_transducer_stateless7_streaming">pruned_transducer_stateless7_streaming</a>,
which is a streaming transducer model trained on <a class="reference external" href="https://www.openslr.org/12">LibriSpeech</a>.
However, you can easily apply LODR to other recipes.
If you encounter any problems, please open an issue here <a class="reference external" href="https://github.com/k2-fsa/icefall/issues">icefall</a>.</p>
</div>
<div class="admonition note">
<p class="admonition-title">Note</p>
<p>For simplicity, the training and testing corpus in this tutorial are the same (<a class="reference external" href="https://www.openslr.org/12">LibriSpeech</a>). However,
you can change the testing set to any other domains (e.g <a class="reference external" href="https://github.com/SpeechColab/GigaSpeech">GigaSpeech</a>) and prepare the language models
using that corpus.</p>
</div>
<p>First, let’s have a look at some background information. As the predecessor of LODR, Density Ratio (DR) is first proposed <a class="reference external" href="https://arxiv.org/abs/2002.11268">here</a>
to address the language information mismatch between the training
corpus (source domain) and the testing corpus (target domain). Assuming that the source domain and the test domain
are acoustically similar, DR derives the following formula for decoding with Bayes’ theorem:</p>
<div class="math notranslate nohighlight">
\[\text{score}\left(y_u|\mathit{x},y\right) =
\log p\left(y_u|\mathit{x},y_{1:u-1}\right) +
\lambda_1 \log p_{\text{Target LM}}\left(y_u|\mathit{x},y_{1:u-1}\right) -
\lambda_2 \log p_{\text{Source LM}}\left(y_u|\mathit{x},y_{1:u-1}\right)\]</div>
<p>where <span class="math notranslate nohighlight">\(\lambda_1\)</span> and <span class="math notranslate nohighlight">\(\lambda_2\)</span> are the weights of LM scores for target domain and source domain respectively.
Here, the source domain LM is trained on the training corpus. The only difference in the above formula compared to
shallow fusion is the subtraction of the source domain LM.</p>
<p>Some works treat the predictor and the joiner of the neural transducer as its internal LM. However, the LM is
considered to be weak and can only capture low-level language information. Therefore, <a class="reference external" href="https://arxiv.org/abs/2203.16776">LODR</a> proposed to use
a low-order n-gram LM as an approximation of the ILM of the neural transducer. This leads to the following formula
during decoding for transducer model:</p>
<div class="math notranslate nohighlight">
\[\text{score}\left(y_u|\mathit{x},y\right) =
\log p_{rnnt}\left(y_u|\mathit{x},y_{1:u-1}\right) +
\lambda_1 \log p_{\text{Target LM}}\left(y_u|\mathit{x},y_{1:u-1}\right) -
\lambda_2 \log p_{\text{bi-gram}}\left(y_u|\mathit{x},y_{1:u-1}\right)\]</div>
<p>In LODR, an additional bi-gram LM estimated on the source domain (e.g training corpus) is required. Compared to DR,
the only difference lies in the choice of source domain LM. According to the original <a class="reference external" href="https://arxiv.org/abs/2203.16776">paper</a>,
LODR achieves similar performance compared to DR in both intra-domain and cross-domain settings.
As a bi-gram is much faster to evaluate, LODR is usually much faster.</p>
<p>Now, we will show you how to use LODR in <code class="docutils literal notranslate"><span class="pre">icefall</span></code>.
For illustration purpose, we will use a pre-trained ASR model from this <a class="reference external" href="https://huggingface.co/Zengwei/icefall-asr-librispeech-pruned-transducer-stateless7-streaming-2022-12-29">link</a>.
If you want to train your model from scratch, please have a look at <a class="reference internal" href="../recipes/Non-streaming-ASR/librispeech/pruned_transducer_stateless.html#non-streaming-librispeech-pruned-transducer-stateless"><span class="std std-ref">Pruned transducer statelessX</span></a>.
The testing scenario here is intra-domain (we decode the model trained on <a class="reference external" href="https://www.openslr.org/12">LibriSpeech</a> on <a class="reference external" href="https://www.openslr.org/12">LibriSpeech</a> testing sets).</p>
<p>As the initial step, let’s download the pre-trained model.</p>
<div class="highlight-bash notranslate"><div class="highlight"><pre><span></span>$<span class="w"> </span><span class="nv">GIT_LFS_SKIP_SMUDGE</span><span class="o">=</span><span class="m">1</span><span class="w"> </span>git<span class="w"> </span>clone<span class="w"> </span>https://huggingface.co/Zengwei/icefall-asr-librispeech-pruned-transducer-stateless7-streaming-2022-12-29
$<span class="w"> </span><span class="nb">cd</span><span class="w"> </span>icefall-asr-librispeech-pruned-transducer-stateless7-streaming-2022-12-29/exp
$<span class="w"> </span>git<span class="w"> </span>lfs<span class="w"> </span>pull<span class="w"> </span>--include<span class="w"> </span><span class="s2">&quot;pretrained.pt&quot;</span>
$<span class="w"> </span>ln<span class="w"> </span>-s<span class="w"> </span>pretrained.pt<span class="w"> </span>epoch-99.pt<span class="w"> </span><span class="c1"># create a symbolic link so that the checkpoint can be loaded</span>
$<span class="w"> </span><span class="nb">cd</span><span class="w"> </span>../data/lang_bpe_500
$<span class="w"> </span>git<span class="w"> </span>lfs<span class="w"> </span>pull<span class="w"> </span>--include<span class="w"> </span>bpe.model
$<span class="w"> </span><span class="nb">cd</span><span class="w"> </span>../../..
</pre></div>
</div>
<p>To test the model, let’s have a look at the decoding results <strong>without</strong> using LM. This can be done via the following command:</p>
<div class="highlight-bash notranslate"><div class="highlight"><pre><span></span>$<span class="w"> </span><span class="nv">exp_dir</span><span class="o">=</span>./icefall-asr-librispeech-pruned-transducer-stateless7-streaming-2022-12-29/exp/
$<span class="w"> </span>./pruned_transducer_stateless7_streaming/decode.py<span class="w"> </span><span class="se">\</span>
<span class="w"> </span>--epoch<span class="w"> </span><span class="m">99</span><span class="w"> </span><span class="se">\</span>
<span class="w"> </span>--avg<span class="w"> </span><span class="m">1</span><span class="w"> </span><span class="se">\</span>
<span class="w"> </span>--use-averaged-model<span class="w"> </span>False<span class="w"> </span><span class="se">\</span>
<span class="w"> </span>--exp-dir<span class="w"> </span><span class="nv">$exp_dir</span><span class="w"> </span><span class="se">\</span>
<span class="w"> </span>--bpe-model<span class="w"> </span>./icefall-asr-librispeech-pruned-transducer-stateless7-streaming-2022-12-29/data/lang_bpe_500/bpe.model<span class="w"> </span><span class="se">\</span>
<span class="w"> </span>--max-duration<span class="w"> </span><span class="m">600</span><span class="w"> </span><span class="se">\</span>
<span class="w"> </span>--decode-chunk-len<span class="w"> </span><span class="m">32</span><span class="w"> </span><span class="se">\</span>
<span class="w"> </span>--decoding-method<span class="w"> </span>modified_beam_search
</pre></div>
</div>
<p>The following WERs are achieved on test-clean and test-other:</p>
<div class="highlight-text notranslate"><div class="highlight"><pre><span></span>$ For test-clean, WER of different settings are:
$ beam_size_4 3.11 best for test-clean
$ For test-other, WER of different settings are:
$ beam_size_4 7.93 best for test-other
</pre></div>
</div>
<p>Then, we download the external language model and bi-gram LM that are necessary for LODR.
Note that the bi-gram is estimated on the LibriSpeech 960 hours’ text.</p>
<div class="highlight-bash notranslate"><div class="highlight"><pre><span></span>$<span class="w"> </span><span class="c1"># download the external LM</span>
$<span class="w"> </span><span class="nv">GIT_LFS_SKIP_SMUDGE</span><span class="o">=</span><span class="m">1</span><span class="w"> </span>git<span class="w"> </span>clone<span class="w"> </span>https://huggingface.co/ezerhouni/icefall-librispeech-rnn-lm
$<span class="w"> </span><span class="c1"># create a symbolic link so that the checkpoint can be loaded</span>
$<span class="w"> </span><span class="nb">pushd</span><span class="w"> </span>icefall-librispeech-rnn-lm/exp
$<span class="w"> </span>git<span class="w"> </span>lfs<span class="w"> </span>pull<span class="w"> </span>--include<span class="w"> </span><span class="s2">&quot;pretrained.pt&quot;</span>
$<span class="w"> </span>ln<span class="w"> </span>-s<span class="w"> </span>pretrained.pt<span class="w"> </span>epoch-99.pt
$<span class="w"> </span><span class="nb">popd</span>
$
$<span class="w"> </span><span class="c1"># download the bi-gram</span>
$<span class="w"> </span>git<span class="w"> </span>lfs<span class="w"> </span>install
$<span class="w"> </span>git<span class="w"> </span>clone<span class="w"> </span>https://huggingface.co/marcoyang/librispeech_bigram
$<span class="w"> </span><span class="nb">pushd</span><span class="w"> </span>data/lang_bpe_500
$<span class="w"> </span>ln<span class="w"> </span>-s<span class="w"> </span>../../librispeech_bigram/2gram.fst.txt<span class="w"> </span>.
$<span class="w"> </span><span class="nb">popd</span>
</pre></div>
</div>
<p>Then, we perform LODR decoding by setting <code class="docutils literal notranslate"><span class="pre">--decoding-method</span></code> to <code class="docutils literal notranslate"><span class="pre">modified_beam_search_lm_LODR</span></code>:</p>
<div class="highlight-bash notranslate"><div class="highlight"><pre><span></span>$<span class="w"> </span><span class="nv">exp_dir</span><span class="o">=</span>./icefall-asr-librispeech-pruned-transducer-stateless7-streaming-2022-12-29/exp
$<span class="w"> </span><span class="nv">lm_dir</span><span class="o">=</span>./icefall-librispeech-rnn-lm/exp
$<span class="w"> </span><span class="nv">lm_scale</span><span class="o">=</span><span class="m">0</span>.42
$<span class="w"> </span><span class="nv">LODR_scale</span><span class="o">=</span>-0.24
$<span class="w"> </span>./pruned_transducer_stateless7_streaming/decode.py<span class="w"> </span><span class="se">\</span>
<span class="w"> </span>--epoch<span class="w"> </span><span class="m">99</span><span class="w"> </span><span class="se">\</span>
<span class="w"> </span>--avg<span class="w"> </span><span class="m">1</span><span class="w"> </span><span class="se">\</span>
<span class="w"> </span>--use-averaged-model<span class="w"> </span>False<span class="w"> </span><span class="se">\</span>
<span class="w"> </span>--beam-size<span class="w"> </span><span class="m">4</span><span class="w"> </span><span class="se">\</span>
<span class="w"> </span>--exp-dir<span class="w"> </span><span class="nv">$exp_dir</span><span class="w"> </span><span class="se">\</span>
<span class="w"> </span>--max-duration<span class="w"> </span><span class="m">600</span><span class="w"> </span><span class="se">\</span>
<span class="w"> </span>--decode-chunk-len<span class="w"> </span><span class="m">32</span><span class="w"> </span><span class="se">\</span>
<span class="w"> </span>--decoding-method<span class="w"> </span>modified_beam_search_LODR<span class="w"> </span><span class="se">\</span>
<span class="w"> </span>--bpe-model<span class="w"> </span>./icefall-asr-librispeech-pruned-transducer-stateless7-streaming-2022-12-29/data/lang_bpe_500/bpe.model<span class="w"> </span><span class="se">\</span>
<span class="w"> </span>--use-shallow-fusion<span class="w"> </span><span class="m">1</span><span class="w"> </span><span class="se">\</span>
<span class="w"> </span>--lm-type<span class="w"> </span>rnn<span class="w"> </span><span class="se">\</span>
<span class="w"> </span>--lm-exp-dir<span class="w"> </span><span class="nv">$lm_dir</span><span class="w"> </span><span class="se">\</span>
<span class="w"> </span>--lm-epoch<span class="w"> </span><span class="m">99</span><span class="w"> </span><span class="se">\</span>
<span class="w"> </span>--lm-scale<span class="w"> </span><span class="nv">$lm_scale</span><span class="w"> </span><span class="se">\</span>
<span class="w"> </span>--lm-avg<span class="w"> </span><span class="m">1</span><span class="w"> </span><span class="se">\</span>
<span class="w"> </span>--rnn-lm-embedding-dim<span class="w"> </span><span class="m">2048</span><span class="w"> </span><span class="se">\</span>
<span class="w"> </span>--rnn-lm-hidden-dim<span class="w"> </span><span class="m">2048</span><span class="w"> </span><span class="se">\</span>
<span class="w"> </span>--rnn-lm-num-layers<span class="w"> </span><span class="m">3</span><span class="w"> </span><span class="se">\</span>
<span class="w"> </span>--lm-vocab-size<span class="w"> </span><span class="m">500</span><span class="w"> </span><span class="se">\</span>
<span class="w"> </span>--tokens-ngram<span class="w"> </span><span class="m">2</span><span class="w"> </span><span class="se">\</span>
<span class="w"> </span>--ngram-lm-scale<span class="w"> </span><span class="nv">$LODR_scale</span>
</pre></div>
</div>
<p>There are two extra arguments that need to be given when doing LODR. <code class="docutils literal notranslate"><span class="pre">--tokens-ngram</span></code> specifies the order of n-gram. As we
are using a bi-gram, we set it to 2. <code class="docutils literal notranslate"><span class="pre">--ngram-lm-scale</span></code> is the scale of the bi-gram, it should be a negative number
as we are subtracting the bi-gram’s score during decoding.</p>
<p>The decoding results obtained with the above command are shown below:</p>
<div class="highlight-text notranslate"><div class="highlight"><pre><span></span>$ For test-clean, WER of different settings are:
$ beam_size_4 2.61 best for test-clean
$ For test-other, WER of different settings are:
$ beam_size_4 6.74 best for test-other
</pre></div>
</div>
<p>Recall that the lowest WER we obtained in <a class="reference internal" href="shallow-fusion.html#shallow-fusion"><span class="std std-ref">Shallow fusion for Transducer</span></a> with beam size of 4 is <code class="docutils literal notranslate"><span class="pre">2.77/7.08</span></code>, LODR
indeed <strong>further improves</strong> the WER. We can do even better if we increase <code class="docutils literal notranslate"><span class="pre">--beam-size</span></code>:</p>
<table class="docutils align-default" id="id1">
<caption><span class="caption-number">Table 2 </span><span class="caption-text">WER of LODR with different beam sizes</span><a class="headerlink" href="#id1" title="Permalink to this table"></a></caption>
<colgroup>
<col style="width: 25.0%" />
<col style="width: 25.0%" />
<col style="width: 50.0%" />
</colgroup>
<thead>
<tr class="row-odd"><th class="head"><p>Beam size</p></th>
<th class="head"><p>test-clean</p></th>
<th class="head"><p>test-other</p></th>
</tr>
</thead>
<tbody>
<tr class="row-even"><td><p>4</p></td>
<td><p>2.61</p></td>
<td><p>6.74</p></td>
</tr>
<tr class="row-odd"><td><p>8</p></td>
<td><p>2.45</p></td>
<td><p>6.38</p></td>
</tr>
<tr class="row-even"><td><p>12</p></td>
<td><p>2.4</p></td>
<td><p>6.23</p></td>
</tr>
</tbody>
</table>
</section>
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