详解 DNN 在声学应用中的模型训练

DNN 神经网络 transition-id

2017/07/01 15:58

雷锋网按：本文作者张庆恒，原载于作者个人博客，雷锋网经授权发布。

本文通过简单kaldi源码，分析DNN训练声学模型时神经网络的输入与输出。在进行DNN训练之前需要用到之前GMM-HMM训练的模型，以训练好的mono模型为例，对模型进行维特比alignement（对齐），该部分主要完成了每个语音文件的帧到 transition-id 的映射。

不妨查看对齐后的结果：

$ copy-int-vector "ark:gunzip -c ali.1.gz|" ark,t:- | head -n 1
speaker001_00003 4 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 16 15 15 15 18 890 889 889 889 889 889 889 892 894 893 893 893 86 88 87 90 89 89 89 89 89 89 89 89 89 89 89 89 89 89 194 193 196 195 195 198 197 386 385 385 385 385 385 385 385 385 388 387 387 390 902 901 901 904 903 906 905 905 905 905 905 905 905 905 905 905 905 914 913 913 916 918 917 917 917 917 917 917 752 751 751 751 751 751 754 753 753 753 753 753 753 753 753 756 755 755 926 925 928 927 927 927 927 927 927 927 930 929 929 929 929 929 929 929 929 4 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 16 18

对于一个训练语音文件speaker001_00003，后面的每一个数字标示一个transition-id，同时每个数字对应一个特征向量，对应的向量可以 copy-matrix 查看，可参考特征提取相关内容，链接如下：

http://t.cn/RX2n4Dx

同样查看 transition-id：

$ show-transitions phones.txt final.mdl

Transition-state 1: phone = sil hmm-state = 0 pdf = 0
Transition-id = 1 p = 0.966816 [self-loop]
Transition-id = 2 p = 0.01 [0 -> 1]
Transition-id = 3 p = 0.01 [0 -> 2]
Transition-id = 4 p = 0.013189 [0 -> 3]
Transition-state 2: phone = sil hmm-state = 1 pdf = 1
Transition-id = 5 p = 0.970016 [self-loop]
Transition-id = 6 p = 0.01 [1 -> 2]
Transition-id = 7 p = 0.01 [1 -> 3]
Transition-id = 8 p = 0.01 [1 -> 4]
Transition-state 3: phone = sil hmm-state = 2 pdf = 2
Transition-id = 9 p = 0.01 [2 -> 1]
Transition-id = 10 p = 0.968144 [self-loop]
Transition-id = 11 p = 0.01 [2 -> 3]
Transition-id = 12 p = 0.0118632 [2 -> 4]
Transition-state 4: phone = sil hmm-state = 3 pdf = 3
Transition-id = 13 p = 0.01 [3 -> 1]
Transition-id = 14 p = 0.01 [3 -> 2]
Transition-id = 15 p = 0.932347 [self-loop]
Transition-id = 16 p = 0.0476583 [3 -> 4]
Transition-state 5: phone = sil hmm-state = 4 pdf = 4
Transition-id = 17 p = 0.923332 [self-loop]
Transition-id = 18 p = 0.0766682 [4 -> 5]
Transition-state 6: phone = a1 hmm-state = 0 pdf = 5
Transition-id = 19 p = 0.889764 [self-loop]
Transition-id = 20 p = 0.110236 [0 -> 1]
...

唯一的Transition-state对应唯一的pdf，其下又包括多个 Transition-id，

接下来看神经网络的输入与输出到底是什么。这里以steps/nnet为例。追溯脚本到steps/nnet/train.sh，找到相关的命令：

...
labels_tr="ark:ali-to-pdf $alidir/final.mdl \"ark:gunzip -c $alidir/ali.*.gz |\" ark:- | ali-to-post ark:- ark:- |"

...
feats_tr="ark:copy-feats scp:$dir/train.scp ark:- |"
...
# input-dim,
get_dim_from=$feature_transform
num_fea=$(feat-to-dim "$feats_tr nnet-forward \"$get_dim_from\" ark:- ark:- |" -)
# output-dim,
num_tgt=$(hmm-info --print-args=false $alidir/final.mdl | grep pdfs | awk '{ print $NF }')
...

dnn)
utils/nnet/make_nnet_proto.py $proto_opts \
${bn_dim:+ --bottleneck-dim=$bn_dim} \
$num_fea $num_tgt $hid_layers $hid_dim >$nnet_proto
;;

从上面关键的几个神经网络的训练的准备阶段可以看出，神经网络的输入很清楚是变换后的特征向量（feats_tr），输出是labels_tr，下面单独运行上面的命令，来查看神经网络的输出（target）是什么。labels_tr的生成分两步：

ali-to-pdf：将上面对齐文件中的transition-id转化为对应的pdf-id；
ali-to-post: 根据得到的pdf-id，生成[pdf, post]对，即pdf与其对应的后验概率。

$ ali-to-pdf final.mdl "ark:gunzip -c ali.1.gz|" ark,t:- | head -n 1
speaker001_00003 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 3 3 3 4 440 440 440 440 440 440 440 441 442 442 442 442 38 39 39 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 92 92 93 93 93 94 94 188 188 188 188 188 188 188 188 188 189 189 189 190 446 446 446 447 447 448 448 448 448 448 448 448 448 448 448 448 448 452 452 452 453 454 454 454 454 454 454 454 371 371 371 371 371 371 372 372 372 372 372 372 372 372 372 373 373 373 458 458 459 459 459 459 459 459 459 459 460 460 460 460 460 460 460 460 460 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 4

观察前两帧，结合文章一开始，transition-id 分别为4和1，而对应的pdf均为0。对该结果再进行ali-to-post：

$ ali-to-pdf final.mdl "ark:gunzip -c ali.1.gz|" ark,t:- | head -n 1 | ali-to-post ark,t:- ark,t:-
speaker001_00003 [ 0 1 ] [ 0 1 ] [ 0 1 ] [ 0 1 ] [ 0 1 ] [ 0 1 ] [ 0 1 ] [ 0 1 ] [ 0 1 ] [ 0 1 ] [ 0 1 ] [ 0 1 ] [ 0 1 ] [ 0 1 ] [ 0 1 ] ...... [ 3 1 ] [ 3 1 ] [ 3 1 ] [ 3 1 ] [ 4 1 ] [ 440 1 ] [ 440 1 ] [ 440 1 ] [ 440 1 ] [ 440 1 ] [ 440 1 ] [ 440 1 ] [ 441 1 ] [ 442 1 ] [ 442 1 ] [ 442 1 ] [ 442 1 ] [ 38 1 ] [ 39 1 ] [ 39 1 ] [ 40 1 ] [ 40 1 ] [ 40 1 ] [ 40 1 ] [ 40 1 ] [ 40 1 ] [ 40 1 ] [ 40 1 ] [ 40 1 ] [ 40 1 ] [ 40 1 ] [ 40 1 ] [ 40 1 ] [ 40 1 ] [ 40 1 ] [ 92 1 ] [ 92 1 ]...... [ 0 1 ] [ 0 1 ] [ 0 1 ] [ 0 1 ] [ 3 1 ] [ 4 1 ]

得到pdf-id以及相应的后验概率，这里均为1。

由此得到了训练数据以及对应的target label。进一步来看神经网络的输入与输出的维度，网络结构被utils/nnet/make_nnet_proto.py写到nnet_proto文件中，该Python脚本的两个重要参数 num_fea和num_tgt分别为神经网络的输入与输出的维度。其中num_fea是由feat-to-dim获得：

$ feat-to-dim scp:../tri4b_dnn/train.scp ark,t:- | grep speaker001_00003
speaker001_00003 40

这里为fbank特征，维度为40，而在真正作为神经网络输入时，进一步对特征向量进行的变换，从源码steps/nnet/train.sh也可以看到splice参数（默认值为5），指定了对特征向量的变换：取对应帧前后5帧，拼成一个11帧组成的大向量（维度为440）。该部分特征变换的拓扑也被保存到final.feature_transform:

$ more final.feature_transform
<Nnet>
<Splice> 440 40
[ -5 -4 -3 -2 -1 0 1 2 3 4 5 ]
<!EndOfComponent>
...

后面在进行神经网络的训练时会使用该拓扑对特征向量进行变换，最终的神经网络输入维度为440。

而num_tgt的维度则是通过hmm-info获得：

$ hmm-info final.mdl
number of phones 218
number of pdfs 1026
number of transition-ids 2834
number of transition-states 1413

$ hmm-info final.mdl | grep pdfs | awk '{ print $NF }'
1026

因此，看到神经网络的输出维度为1026，这时查看nnet_proto：

<AffineTransform> <InputDim> 440 <OutputDim> 1024 <BiasMean> -2.000000 <BiasRange> 4.000000 <ParamStddev> 0.037344 <MaxNorm> 0.000000
<Sigmoid> <InputDim> 1024 <OutputDim> 1024
<AffineTransform> <InputDim> 1024 <OutputDim> 1024 <BiasMean> -2.000000 <BiasRange> 4.000000 <ParamStddev> 0.109375 <MaxNorm> 0.000000
<Sigmoid> <InputDim> 1024 <OutputDim> 1024
<AffineTransform> <InputDim> 1024 <OutputDim> 1024 <BiasMean> -2.000000 <BiasRange> 4.000000 <ParamStddev> 0.109375 <MaxNorm> 0.000000
<Sigmoid> <InputDim> 1024 <OutputDim> 1024
<AffineTransform> <InputDim> 1024 <OutputDim> 1024 <BiasMean> -2.000000 <BiasRange> 4.000000 <ParamStddev> 0.109375 <MaxNorm> 0.000000
<Sigmoid> <InputDim> 1024 <OutputDim> 1024
<AffineTransform> <InputDim> 1024 <OutputDim> 1026 <BiasMean> 0.000000 <BiasRange> 0.000000 <ParamStddev> 0.109322 <LearnRateCoef> 1.000000 <BiasLearnRateCoef> 0.100000
<Softmax> <InputDim> 1026 <OutputDim> 1026

这里可以看到神经网络的输入维度有40变为440，输出为pdf的个数（对应HMM状态的个数）。

如果继续追查代码，最后可以找到单次神经网络的训练实现，kaldi/src/nnetbin/nnet-train-frmshuff.cc：

Perform one iteration (epoch) of Neural Network training with mini-batch Stochastic Gradient Descent. The training targets are usually pdf-posteriors, prepared by ali-to-post.

继续分析代码，可以看到几个关键步骤：

解析训练参数，配置网络
读取特征向量和target label，输入为Matrix< BaseFloat >类型，输出为Posterior类型，即<pdf-id, posterior>对。

// get feature / target pair,
Matrix<BaseFloat> mat = feature_reader.Value();
Posterior targets = targets_reader.Value(utt);

随机打乱训练数据，作为神经网络输入与期望输出：

const CuMatrixBase<BaseFloat>& nnet_in = feature_randomizer.Value();
const Posterior& nnet_tgt = targets_randomizer.Value();
const Vector<BaseFloat>& frm_weights = weights_randomizer.Value();

前向传播，计算估计值nnet_out

// forward pass,
nnet.Propagate(nnet_in, &nnet_out);

计算cost，这里支持交叉熵和平方差和multitask。结果为obj_diff

// evaluate objective function we've chosen,
if (objective_function == "xent") {
// gradients re-scaled by weights in Eval,
xent.Eval(frm_weights, nnet_out, nnet_tgt, &obj_diff);
} else if (objective_function == "mse") {
// gradients re-scaled by weights in Eval,
mse.Eval(frm_weights, nnet_out, nnet_tgt, &obj_diff);
}
...