Re: [Kaldi-users] FST minimization of LMs

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

No, they can still be equivalent in the FST sense but be different in that
way.
Dan



On Thu, Dec 19, 2013 at 10:57 PM, Lahiru Samarakoon <lah...@gm...>wrote:

> Please help me with this one last query.
> If the kaldi program "fstisstochastic"  gives significantly different
> values for two fsts, is it safe to say those are not equivalent?
>
> For example,
> fstisstochastic A.fst
> *0.693747*      -0.877091
>
> fstisstochastic B.fst
> *24.1318*      -0.877091
>
> Thanks in advance,
> Lahiru
>
>
> On Fri, Dec 20, 2013 at 1:08 PM, Lahiru Samarakoon <lah...@gm...>wrote:
>
>> Thanks a lot for the clarification Dan.
>>
>>
>> On Fri, Dec 20, 2013 at 1:04 PM, Daniel Povey <dp...@gm...> wrote:
>>
>>> No, because for each path there will be multiple alternatives in B and
>>> the sum of the path weights will be more than one.  I recommend to address
>>> further questions on this topic to www.openfst.org.
>>> Dan
>>>
>>>
>>>
>>> On Thu, Dec 19, 2013 at 8:53 PM, Lahiru Samarakoon <lah...@gm...>wrote:
>>>
>>>> Is this also applies to the log semiring?
>>>> Thanks
>>>> Lahiru
>>>>
>>>>
>>>> On Fri, Dec 20, 2013 at 12:46 PM, Daniel Povey <dp...@gm...>wrote:
>>>>
>>>>>
>>>>> 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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>>>>>
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>>>
>>
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