Making sense of show-alignments using shot-transitions

[Kaldi_new_uSER]

While running Librispeech training script, I am looking at 0.mdl and the alignment files created initially.

Then I do 

show-alignments data/lang_nosp/phones.txt exp/mono/0.mdl ark,t:align.1.ali > 1

For the first line in output I see

103-1240-0015  [ 4 1 16 15 18 17 ] [ 1118 1117 1120 1119 1122 1121 ] ...  

In order to understand which transitions are [ 4 1 16 15 18 17 ] referring to, I run following command

show-transitions data/lang_nosp/phones.txt exp/mono/0.mdl > 2

Inside 2 I find following information 

Transition-state 1: phone = SIL hmm-state = 0 pdf = 0

 Transition-id = 1 p = 0.25 [self-loop]

 Transition-id = 2 p = 0.25 [0 -> 1]

 Transition-id = 3 p = 0.25 [0 -> 2]

 Transition-id = 4 p = 0.25 [0 -> 3]

Transition-state 2: phone = SIL hmm-state = 1 pdf = 1

 Transition-id = 5 p = 0.25 [self-loop]

 Transition-id = 6 p = 0.25 [1 -> 2]

 Transition-id = 7 p = 0.25 [1 -> 3]

 Transition-id = 8 p = 0.25 [1 -> 4]

Transition-state 3: phone = SIL hmm-state = 2 pdf = 2

 Transition-id = 9 p = 0.25 [2 -> 1]

 Transition-id = 10 p = 0.25 [self-loop]

 Transition-id = 11 p = 0.25 [2 -> 3]

 Transition-id = 12 p = 0.25 [2 -> 4]

Transition-state 4: phone = SIL hmm-state = 3 pdf = 3

 Transition-id = 13 p = 0.25 [3 -> 1]

 Transition-id = 14 p = 0.25 [3 -> 2]

 Transition-id = 15 p = 0.25 [self-loop]

 Transition-id = 16 p = 0.25 [3 -> 4]

Transition-state 5: phone = SIL hmm-state = 4 pdf = 4

 Transition-id = 17 p = 0.75 [self-loop]

 Transition-id = 18 p = 0.25 [4 -> 5]

That means, [ 4 1 16 15 18 17 ] translates to following transitions within HMM states of SIL

[0 -> 3] [0 -> 0] [3 -> 4] [3 -> 4] [4 -> 5] [4 -> 4]

I am confused by these transitions. If first transition is 0 -> 3 then next transition must start at 3, rather than 0! Please help me understand.  

[Daniel Povey]

It had to do with 'reordering', and the option 'reorder=true'.  You can use these as search terms, there is documentation about it.

We should never have designed it this way, we should have used an arc-based formalism that would be more compatible with FSTs, and not the standard state-based one.  But it would require a redesign of too many things to fix this now.

Dan

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[Kaldi_new_uSER]

Thanks, I got it.

So the actual transitions are

[0 -> 0] [0 -> 3] [3 -> 3] [3 -> 4] [4 -> 4] [4 -> 5]

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