Re: [Kaldi-users] FST minimization of LMs

[Daniel P. <dp...@gm...>]

> I am trying to decompose weighted acceptors (Language models) . I observe
> this behavior when I compose them to build a new fst. I think I am doing
> something wrong here.
>
> Please be kind enough to clarify me the following.
>
> Given a *weighted acceptor *"*A*",  lets say acceptor "*B*" is created by
> setting all the weights of "A" to *zero *including the final states
> weights.
> is
> *"A compose B"  equivalent to "A"?*
>

If you are in the tropical semiring, then yes, because any path in A is
also in B (with zero cost).  But "A compose B" is a wasteful way of
representing the acceptor because there are multiple alternative paths
through B that will end up multiplying the size, potentially by the n-gram
order minus one.  So it's equivalent in the FST sense, but it's much
larger.

Dan



>
> if the answer is not  equivalent, could you state the reason briefly
>
> Thank you,
>
> Best Regards,
> Lahiru
>
>
> On Fri, Dec 20, 2013 at 3:41 AM, Al Zatv <al...@gm...> wrote:
>
>> Hello! Actually, I don't have such a problem. I think Lahiru Samarakoon,
>> the topic starter, have it:
>> Quote:
>> =====
>>
>> I have my own language model. When I minimize it, actually it increases
>> the number of states and arcs.
>>
>> How can this be possible?
>> I have created the LM in arpa format and used scripts from Kaldi to
>> create the G.fst
>> =====
>>
>> Usually ARPA LMs are acceptors and they are determinized by default, so
>> if Lahiru really observe that min(G.fst) is bigger than G.fst, it is
>> suspicious.
>> 19.12.2013 20:09 пользователь "Michael Riley" <ri...@go...> написал:
>>
>> Not sure what exactly you are doing or what code you are calling but if
>>> you are using the algorithms in OpenFst then
>>> |det(A)| can be > that |A| but |min(det(A))| <= |det(A)| if A is an
>>> acceptor.
>>>
>>> I'd be surprised if there is a bug here (given this condition I believe
>>> is tested on millions of randomly generated machines) but If you have a
>>> counter-example when using unmodified OpenFst as above, then send it to us
>>> along with the precise commands you ran that demonstrate the problem.
>>>
>>> -m
>>>
>>> -m
>>>
>>>
>>> On Thu, Dec 19, 2013 at 2:55 AM, Al Zatv <al...@gm...> wrote:
>>>
>>>> According to this document, size of transducer can be larger than
>>>> original. But ARPA LM is an acceptor, so it must have optimal number of
>>>> states, or I don't misunderstood something?
>>>> 19.12.2013 10:23 пользователь "Michael Riley" <ri...@go...>
>>>> написал:
>>>>
>>>> http://www.openfst.org/twiki/bin/view/FST/MinimizeDoc
>>>>>
>>>>>
>>>>> On Thu, Dec 19, 2013 at 1:13 AM, Lahiru Samarakoon <lah...@gm...
>>>>> > wrote:
>>>>>
>>>>>>
>>>>>> HI All,
>>>>>>
>>>>>> I have my own language model. When I minimize it, actually it
>>>>>> increases the number of states and arcs.
>>>>>>
>>>>>> How can this be possible?
>>>>>> I have created the LM in arpa format and used scripts from Kaldi to
>>>>>> create the G.fst.
>>>>>>
>>>>>> Thank you,
>>>>>>
>>>>>> Best Regards,
>>>>>> Lahiru
>>>>>>
>>>>>>
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