void
M2MFstAligner::write_lattice(string lattice)
{
//Write out the entire training set in lattice format
//Perform the union first. This output can then
// be plugged directly in to a counter to obtain expected
// alignment counts for the EM-trained corpus. Yields
// far higher-quality joint n-gram models, which are also
// more robust for smaller training corpora.
//Make sure you call this BEFORE any call to
// write_all_alignments
// as the latter function will override some of the weights
//Chaining the standard Union operation, including using a
// rational FST still performs very poorly in the log semiring.
//Presumably it's running push or something at each step. It
// should be fine to do that just once at the end.
//Rolling our own union turns out to be MUCH faster.
VectorFst<LogArc> ufst;
ufst.AddState();
ufst.SetStart(0);
int total_states = 0;
for (int i = 0; i < fsas.size(); i++) {
TopSort(&fsas[i]);
for (StateIterator<VectorFst<LogArc> > siter(fsas[i]);
!siter.Done(); siter.Next()) {
LogArc::StateId q = siter.Value();
LogArc::StateId r;
if (q == 0)
r = 0;
else
r = ufst.AddState();
for (ArcIterator <VectorFst<LogArc> > aiter(fsas[i], q);
!aiter.Done(); aiter.Next()) {
const LogArc & arc = aiter.Value();
ufst.AddArc(r,
LogArc(arc.ilabel, arc.ilabel, arc.weight,
arc.nextstate + total_states));
}
if (fsas[i].Final(q) != LogWeight::Zero())
ufst.SetFinal(r, LogWeight::One());
}
total_states += fsas[i].NumStates() - 1;
}
//Normalize weights
Push(&ufst, REWEIGHT_TO_INITIAL);
//Write the resulting lattice to disk
ufst.Write(lattice);
//Write the syms table too.
isyms->WriteText("lattice.syms");
return;
}
void
M2MFstAligner::write_model(string _model_file)
{
VectorFst<LogArc> model;
model.AddState();
model.SetStart(0);
model.SetFinal(0, LogWeight::One());
map<LogArc::Label,LogWeight>::iterator it;
for (it = alignment_model.begin(); it != alignment_model.end(); it++)
model.AddArc(0, LogArc((*it).first, (*it).first, (*it).second, 0));
model.SetInputSymbols(isyms);
model.Write(_model_file);
return;
}
/**
* \brief Adds a state.
* \return true if the state requested has already been visited, false otherwise.
*/
inline pair <StateId, bool> add ( typename KenLMModelT::State& m2nextstate,
StateId m1nextstate, Weight m1stateweight ) {
static StateId lm = 0;
getIdx ( m2nextstate );
///New history:
if ( seenlmstates_.find ( history ) == seenlmstates_.end() ) {
seenlmstates_[history] = ++lm;
}
uint64_t compound = m1nextstate * sid + seenlmstates_[history];
LDEBUG ( "compound id=" << compound );
if ( stateexistence_.find ( compound ) == stateexistence_.end() ) {
LDEBUG ( "New State!" );
statemap_[composed_->NumStates()] =
pair<StateId, const typename KenLMModelT::State > ( m1nextstate, m2nextstate );
composed_->AddState();
if ( m1stateweight != mw_ ( ZPosInfinity() ) ) composed_->SetFinal (
composed_->NumStates() - 1, m1stateweight );
stateexistence_[compound] = composed_->NumStates() - 1;
return pair<StateId, bool> ( composed_->NumStates() - 1, false );
}
return pair<StateId, bool> ( stateexistence_[compound], true );
};
void M2MFstAligner::_conditional_max( bool y_given_x ){
/*
Compute the conditional distribution, P(Y|X) using the WFST paradigm.
This is bassed on the approach from Shu and Hetherington 2002.
It is assumed that all WFSTs and operations use the Log semiring.
Given:
FST1 = P(X,Y)
Compute:
FST2 = P(X)
:= Map_inv(Det(RmEps(Proj_i(FST1))))
FST3 = P(Y|X)
:= Compose(FST2,FST1)
Proj_i: project on input labels
RmEps: epsilon removal
Det: determinize
Map_inv: invert weights
Notes: An analogous process may be used to compute P(X|Y). In this
case one would project on OUTPUT labels - Proj_o, and reverse the
composition order to Compose(FST1,FST2).
Future work:
What we are doing here in terms of *generating* the JOINT fst each
time is really just a dumb hack. We *should* encode the model in an
FST and encode the individual lattices, rather than doing the hacky
manual label encoding that we currently rely on.
*/
//Joint distribution that we start with
VectorFst<LogArc>* joint = new VectorFst<LogArc>();
SymbolTable* misyms = new SymbolTable("misyms");
SymbolTable* mosyms = new SymbolTable("mosyms");
joint->AddState();
joint->AddState();
joint->SetStart(0);
joint->SetFinal(1,LogArc::Weight::One());
map<LogArc::Label,LogWeight>::iterator it;
for( it=prev_alignment_model.begin(); it != prev_alignment_model.end(); it++ ){
string isym = isyms->Find((*it).first);
vector<string> io = tokenize_utf8_string( &isym, &s1s2_sep );
LogArc arc( misyms->AddSymbol(io[0]), mosyms->AddSymbol(io[1]), (*it).second, 1 );
joint->AddArc( 0, arc );
}
//VectorFst<LogArc>* joint = new VectorFst<LogArc>();
//Push<LogArc,REWEIGHT_TO_FINAL>(*_joint, joint, kPushWeights);
//joint->SetFinal(1,LogWeight::One());
joint->Write("m2mjoint.fst");
//BEGIN COMPUTE MARGINAL P(X)
VectorFst<LogArc>* dmarg;
if( y_given_x )
dmarg = new VectorFst<LogArc>(ProjectFst<LogArc>(*joint, PROJECT_INPUT));
else
dmarg = new VectorFst<LogArc>(ProjectFst<LogArc>(*joint, PROJECT_OUTPUT));
RmEpsilon(dmarg);
VectorFst<LogArc>* marg = new VectorFst<LogArc>();
Determinize(*dmarg, marg);
ArcMap(marg, InvertWeightMapper<LogArc>());
if( y_given_x )
ArcSort(marg, OLabelCompare<LogArc>());
else
ArcSort(marg, ILabelCompare<LogArc>());
//END COMPUTE MARGINAL P(X)
marg->Write("marg.fst");
//CONDITIONAL P(Y|X)
VectorFst<LogArc>* cond = new VectorFst<LogArc>();
if( y_given_x )
Compose(*marg, *joint, cond);
else
Compose(*joint, *marg, cond);
//cond now contains the conditional distribution P(Y|X)
cond->Write("cond.fst");
//Now update the model with the new values
for( MutableArcIterator<VectorFst<LogArc> > aiter(cond, 0); !aiter.Done(); aiter.Next() ){
LogArc arc = aiter.Value();
string lab = misyms->Find(arc.ilabel)+"}"+mosyms->Find(arc.olabel);
int labi = isyms->Find(lab);
alignment_model[labi] = arc.weight;
prev_alignment_model[labi] = LogWeight::Zero();
}
delete joint, marg, cond, dmarg;
delete misyms, mosyms;
return;
}
/**
* Create an FST based on an RNN
*/
void FlatBOFstBuilder::convertRNN(CRnnLM & rnnlm, VectorFst<LogArc> &fst) {
queue<NeuronFstHistory> q;
VectorFst<LogArc> new_fst;
NeuronFstHistory fsth(rnnlm.getHiddenLayerSize(),getNumBins());
FstIndex id = 0;
NeuronFstHistory new_fsth(rnnlm.getHiddenLayerSize(),getNumBins());
FstIndex new_id;
NeuronFstHistory min_backoff(rnnlm.getHiddenLayerSize(),getNumBins());
set<NeuronFstHistory>set_min_backoff;
NeuronFstHistory bo_fsth(rnnlm.getHiddenLayerSize(),getNumBins());
bool backoff = false;
vector<FstIndex> deleted;
real p = 0.00;
real p_joint = 0.00;
real entropy = 0.0;
real delta = 0.0;
vector<real> all_prob(rnnlm.getVocabSize());
vector<real> posterior(10);
map< FstIndex,set<FstIndex> > pred;
vector<bool> non_bo_pred(rnnlm.getVocabSize());
vector<int> to_be_added;
vector<int> to_be_removed;
for (int i = 0; i < rnnlm.getVocabSize(); i++) {
to_be_removed.push_back(i);
}
vector<real> to_be_added_prob;
FstIndex n_added = 0;
FstIndex n_processed = 0;
FstIndex next_n_added = 0;
FstIndex next_n_processed = 0;
FstIndex n_backoff = 0;
FstIndex n_only_backoff = 0;
int v = rnnlm.getVocabSize();
int w = 0;
// Initialize
rnnlm.copyHiddenLayerToInput();
// printNeurons(rnnlm.getInputLayer(),0,10);
// Initial state ( 0 | hidden layer after </s>)
printNeurons(rnnlm.getHiddenLayer(),0,10);
fsth.setFstHistory(rnnlm, *dzer);
fsth.setLastWord(0);
q.push(fsth);
addFstState(id, new NeuronFstHistory(fsth), fst);
fst.SetStart(INIT_STATE);
// Final state (don't care about the associated discrete representation)
fst.AddState();
fst.SetFinal(FINAL_STATE, LogWeight::One());
/*posterior.at(INIT_STATE) = MY_LOG_ONE;*/
min_backoff.setLastWord(-1);
computeEntropyAndConditionals(entropy, all_prob, rnnlm, min_backoff);
min_backoff = getBackoff(rnnlm, min_backoff, set_min_backoff, all_prob, to_be_removed);
cout << "MIN BACKOFF " << min_backoff.toString() << endl;
set_min_backoff.insert(min_backoff);
// addFstState(id, min_backoff, fst);
// q.push(min_backoff);
// Estimate number of backoff loop to bound the backoff path length
// float ratioa = 0.0;
// float ratiob = 0.0;
float ratio = 0.0;
// for (int i=0; i < min_backoff.getNumDims(); i++) {
// if (min_backoff.getDim(i) == 1) {
// ratioa++;
// }
// if (fsth.getDim(i) == 1) {
// ratiob++;
// }
// }
// ratioa /= min_backoff.getNumDims();
// ratiob /= min_backoff.getNumDims();
// ratio = (ratioa*(1.0-ratiob))+(ratiob*(1.0-ratioa));
ratio=1.0;
// printf("ratio=%f\t%i BO loops\n", ratio, n_bo_loops);
//foreach state in the queue
while (!q.empty()) {
fsth = q.front();
q.pop();
id = h2state[&fsth];
state2h.push_back(new NeuronFstHistory(fsth));
if (id == FINAL_STATE) { continue; }
dprintf(1,"-- STUDY STATE %li = %s\n", id, fsth.toString().c_str());
/* try { posterior.at(id) = MY_LOG_ONE; }
catch (exception e) {
posterior.resize((int) (posterior.size()*1.5)+1);
posterior.at(id) = MY_LOG_ONE;
}*/
computeEntropyAndConditionals(entropy, all_prob, rnnlm, fsth);
//compute BO in advance and check if it is a min BO node
bo_fsth = getBackoff(rnnlm, fsth, set_min_backoff, all_prob, to_be_removed);
if (bo_fsth == fsth) { bo_fsth = min_backoff; }
//foreach w (ie, foreach word of each class c)
//test if the edge has to kept or removed
backoff = false; //no backoff yet since no edge has been removed
for (w=0; w < rnnlm.getVocabSize(); w++) {
p = all_prob[w];
/*p_joint = exp(-posterior[id]-p);*/
p_joint = exp(-p);
delta = -1.0*p_joint*log2(p_joint);
//accept edge if this leads to a minimum
//relative gain of the entropy
dprintf(2,"P = %e \tP_joint = %e \tH = %e \tDelta =%e \tDelta H = %.6f %%\n",exp(-p), p_joint, entropy, delta, 100.0*delta/entropy);
if (set_min_backoff.find(fsth) != set_min_backoff.end() || (delta > pruning_threshold*entropy)) {
// if ((fsth == min_backoff) || (delta > pruning_threshold*entropy)) {
next_n_added++;
to_be_added.push_back(w);
to_be_added_prob.push_back(p);
dprintf(2,"\tACCEPT [%li] -- %i (%s) / %f --> ...\t(%e > %e)\n", id, w, rnnlm.getWordString(w), p, delta, pruning_threshold*entropy);
// to_be_removed.push_back(w);
}
//backoff
else {
// to_be_removed.push_back(w);
backoff = true;
dprintf(2,"\tPRUNE [%li] -- %i / %f --> ...\n", id, w, p);
}
//print
if (next_n_processed % 100000 == 0) {
fprintf(stderr, "\rH=%.5f / N proc'd=%li / N added=%li (%.5f %%) / N bo=%li (%.5f %%) / %li/%li Nodes (%2.1f %%) / N min BO=%i", entropy, n_processed, n_added, ((float) n_added/ (float)n_processed)*100.0, n_backoff, ((float) n_backoff/ (float)n_added)*100.0, id, id+q.size(), 100.0 - (float) (100.0*id/(id+q.size())), (int) set_min_backoff.size());
}
next_n_processed++;
// }
}
//Set a part of the new FST history
new_fsth.setFstHistory(rnnlm, *dzer);
//if at least one word is backing off
if (backoff) {
n_backoff++;
if (to_be_added.size() == 0) {
n_only_backoff++;
}
if (addFstState(new_id, new NeuronFstHistory(bo_fsth), fst)) {
q.push(bo_fsth);
try { non_bo_pred.at(new_id) = false; }
catch (exception e) {
non_bo_pred.resize(new_id+(int) (non_bo_pred.size()*0.5)+1);
non_bo_pred.at(new_id) = false;
}
}
dprintf(1,"BACKOFF\t[%li]\t(%s)\n-------\t[%li]\t(%s)\n", id, fsth.toString().c_str(), new_id, bo_fsth.toString().c_str());
fst.AddArc(id, LogArc(EPSILON, EPSILON, LogWeight::Zero(), new_id));
addPred(pred, new_id, id);
}
vector<real>::iterator it_p = to_be_added_prob.begin();
for (vector<int>::iterator it = to_be_added.begin(); it != to_be_added.end(); ++it) {
w = *it;
p = *it_p;
if (w == 0) {
fst.AddArc(id, LogArc(FstWord(w),FstWord(w),p,FINAL_STATE));
dprintf(1,"EDGE [%li] (%s)\n---- %i (%s) / %f -->\n---- [%li] FINAL STATE)\n\n", id, fsth.toString().c_str(), FstWord(w), rnnlm.getWordString(w), p, FINAL_STATE);
}
//accept edge
else {
new_fsth.setLastWord(w);
//if sw not in the memory
//then add a new state for sw in the FST and push sw in the queue
if (addFstState(new_id, new NeuronFstHistory(new_fsth), fst)) {
q.push(new_fsth);
try { non_bo_pred.at(new_id) = true; }
catch (exception e) {
non_bo_pred.resize(new_id+(int) (non_bo_pred.size()*0.5)+1);
non_bo_pred.at(new_id) = true;
}
}
else { /* already exists */ }
//add the edge in the FST
non_bo_pred.at(new_id) = true;
fst.AddArc(id, LogArc(FstWord(w),FstWord(w),p,new_id));
dprintf(1,"EDGE [%li] (%s)\n---- %i (%s) / %f -->\n---- [%li] (%s)\n\n", id, fsth.toString().c_str(), FstWord(w), rnnlm.getWordString(w), p, new_id, new_fsth.toString().c_str());
// posterior.at(new_id) += posterior[id]*p;
}
/*if (posterior[id]+p < LogWeight::Zero().Value()) {
p_joint = exp(-posterior[id]-p);
entropy -= p_joint*log2(p_joint);
}*/
++it_p;
}
n_added = next_n_added;
n_processed = next_n_processed;
//reset queues
to_be_added.clear();
to_be_added_prob.clear();
// to_be_removed.clear();
}
cout << endl;
//compute backoff weights
deleted = compactBackoffNodes(fst, pred, non_bo_pred);
computeAllBackoff(fst, pred);
//remove useless nodes
removeStates(fst, new_fst, deleted);
fst.DeleteStates();
fst = new_fst;
//Fill the table of symbols
SymbolTable dic("dictionnary");
dic.AddSymbol("*", 0);
for (int i=0; i<rnnlm.getVocabSize(); i++) {
dic.AddSymbol(string(rnnlm.getWordString(i)), i+1);
}
fst.SetInputSymbols(&dic);
fst.SetOutputSymbols(&dic);
//printf("H=%.5f / N proc'd=%li / N added=%li (%.5f %%) %li/%li Nodes (%2.1f %%)\n", entropy, n_processed, n_added, ((float) n_added/ (float)n_processed)*100.0, id, id+q.size(), 100.0 - (float) (100.0*id/(id+q.size())));
cout << "END" << endl;
}