TransitionModel

背景

最近结合kaldi的例子改出来一个语音识别在线服务器，编译通过，对里面的代码进行深入理解下，看到了TransitionModel，它用mdl初始化，是SingleUtteranceNnet2Decoder和OnlineSilenceWeighting这2个类对象构造函数中的参数，这表明 TransitionModel是语音识别的关键输入。下面是一些理论描述，感谢网络上前辈。

理论

kaldi中的HMM模型，实际就是一个TransitionModel对象。这个对象描述了音素的HMM拓扑结构，并保存了pdf-id和transition-id相关的信息，并且可以进行各种变量的转换。
TransitionModel的定义和实现位于transition-model.h和transition-model.cc中。在了解此对象之前，应先阅读和理解hmm-topology相关的内容。
在介绍TransitionModel之前，先介绍一些概念。
                phone:  音素，从1开始编号。可以根据phones.txt映射为具体音素
        HMM-state:  音素HMM模型的状态，从0开始编号
                 pdf-id:  决策树和声学模型中用到的pdf的编号，从0开始
   transition-state:  一个（虚拟的）状态，通过弧跳转到自己或其他状态。某些情况下，可以跟pdf-id一一对应。
  transition-index:  HMM状态中转移的索引，即HmmTopology::HmmState::transitions的索引，从0开始编号
        transition-id:  所有的HMM状态的弧进行编号。从1开始编号。
   
   通常，将phone、HMM-state和pdf-id（包括forward-pdf-id, self-loop-pdf-id）作为一个元组（Tuple），一个元组，可映射为一个transition-state。transition-state加一个具体的transition-index，可以映射出一个transition-id。各种映射关系如下：
   (phone, HMM-state, forward-pdf-id, self-loop-pdf-id) -> transition-state
   (transition-state, transition-index)                 -> transition-id
  
同时也存在着反向的映射关系，即：
                      transition-id -> transition-state
                      transition-id -> transition-index
                   transition-state -> phone
                   transition-state -> HMM-state
                   transition-state -> forward-pdf-id
                   transition-state -> self-loop-pdf-id
kaldi中TransitionModel的定义如下，为了方便阅读和理解，对代码做了修改。

1. class TransitionModel {
2.  
3.  public:
4.  
5.   TransitionModel() { }
6.  
7.   void Read(std::istream &is, bool binary);
8.   void Write(std::ostream &os, bool binary) const;
9.  
10.   /// return reference to HMM-topology object.
11.   const HmmTopology &GetTopo() const { return topo_; }
12.  
13.   /// \name Integer mapping functions
14.   /// @{
15.  
16.   int32 TupleToTransitionState(int32 phone, int32 hmm_state, int32 pdf, int32 self_loop_pdf) const;
17.   int32 PairToTransitionId(int32 trans_state, int32 trans_index) const;
18.   int32 TransitionIdToTransitionState(int32 trans_id) const;  //return id2state_[trans_id];
19.   int32 TransitionIdToTransitionIndex(int32 trans_id) const;
20.   int32 TransitionStateToPhone(int32 trans_state) const;  //return tuples_[trans_state-1].phone;
21.   int32 TransitionStateToHmmState(int32 trans_state) const;
22.   int32 TransitionStateToForwardPdfClass(int32 trans_state) const;
23.   int32 TransitionStateToSelfLoopPdfClass(int32 trans_state) const;
24.   int32 TransitionStateToForwardPdf(int32 trans_state) const;
25.   int32 TransitionStateToSelfLoopPdf(int32 trans_state) const;
26.   int32 SelfLoopOf(int32 trans_state) const;  // returns the self-loop transition-id, or zero if
27.   // this state doesn't have a self-loop.
28.  
29.   inline int32 TransitionIdToPdf(int32 trans_id) const;  //return id2pdf_id_[trans_id];
30.   int32 TransitionIdToPhone(int32 trans_id) const;  //return tuples_[id2state_[trans_id]-1].phone;
31.   int32 TransitionIdToPdfClass(int32 trans_id) const;
32.   int32 TransitionIdToHmmState(int32 trans_id) const;
33.  
34.  
35.  
36.   /// Returns the total number of transition-ids (note, these are one-based).
37.   inline int32 NumTransitionIds() const { return id2state_.size()-1; }
38.  
39.   /// Returns the number of transition-indices for a particular transition-state.
40.   /// Note: "Indices" is the plural of "index".   Index is not the same as "id",
41.   /// here.  A transition-index is a zero-based offset into the transitions
42.   /// out of a particular transition state.
43.   int32 NumTransitionIndices(int32 trans_state){
44.                 return state2id_[trans_state+1]-state2id_[trans_state];
45.   }
46.  
47.   /// Returns the total number of transition-states (note, these are one-based).
48.   int32 NumTransitionStates() const { return tuples_.size(); }
49.  
50.   // NumPdfs() actually returns the highest-numbered pdf we ever saw, plus one.
51.   // In normal cases this should equal the number of pdfs in the system, but if you
52.   // initialized this object with fewer than all the phones, and it happens that
53.   // an unseen phone has the highest-numbered pdf, this might be different.
54.   int32 NumPdfs() const { return num_pdfs_; }
55.  
56.   BaseFloat GetTransitionLogProb(int32 trans_id){
57.                 return log_probs_(trans_id);
58.   }
59.  
60.  
61.  private:
62.  
63.   struct Tuple {
64.     int32 phone;
65.     int32 hmm_state;
66.     int32 forward_pdf;
67.     int32 self_loop_pdf;
68.     Tuple() { }
69.     Tuple(int32 phone, int32 hmm_state, int32 forward_pdf, int32 self_loop_pdf):
70.       phone(phone), hmm_state(hmm_state), forward_pdf(forward_pdf), self_loop_pdf(self_loop_pdf) { }
71.   };
72.  
73.   HmmTopology topo_;
74.  
75.   /// Triples indexed by transition state minus one;
76.   /// the triples are in sorted order which allows us to do the reverse mapping from
77.   /// triple to transition state
78.   std::vector<Tuple> tuples_;
79.  
80.   /// Gives the first transition_id of each transition-state; indexed by
81.   /// the transition-state.  Array indexed 1..num-transition-states+1 (the last one
82.   /// is needed so we can know the num-transitions of the last transition-state.
83.   std::vector<int32> state2id_;
84.  
85.   /// For each transition-id, the corresponding transition
86.   /// state (indexed by transition-id).
87.   std::vector<int32> id2state_;
88.  
89.   std::vector<int32> id2pdf_id_;
90.  
91.   /// For each transition-id, the corresponding log-prob.  Indexed by transition-id.
92.   Vector<BaseFloat> log_probs_;
93.  
94.   /// For each transition-state, the log of (1 - self-loop-prob).  Indexed by
95.   /// transition-state.
96.   Vector<BaseFloat> non_self_loop_log_probs_;
97.  
98.   /// This is actually one plus the highest-numbered pdf we ever got back from the
99.   /// tree (but the tree numbers pdfs contiguously from zero so this is the number
100.   /// of pdfs).
101.   int32 num_pdfs_;
103. };

实际写入模型文件（如final.mdl）中的HMM模型就是一个TransitionModel对象。但是写入到文件中的，并不是所有成员变量。只是写入了topo_、tuples_和log_probs_这三项。其他项，都是在后来计算出来的。下面的表格，也对几个成员变量，做了汇总介绍。

表格中，“tr_state”表示transition-state。

相关工具

查看模型transition信息

show-transitions phones.txt final.mdl

可视化tree，dot命令，详细查询graphviz

# -Gsize指定大小，-T指定保存类型，可以是png, jpg, pdf等
draw-tree phones.txt tree | dot -Gsize=80,100 -Tpng > tree.png
draw-tree phones.txt tree | dot -Tpdf > tree.pdf

GMM模型转文本格式

# 输出到标准输出
gmm-copy --binary=false final.mdl -

Tree转文本格式

# 输出到标准输出
eg: copy-tree --binary=false tree -

调试跟踪

有些特殊情况可以带if语句的日志输出来判断，毕竟工具看的结果是已经运行后的结果，运行状态看不到。