SHARING TAILS OF TREES

• Assume a bigram language model.
  
  
• A linear tail in a lexical tree is defined as a subpath ending in a leaf node and going through states with a unique successor (also called a single-word subpath).
  
  
• LM factorization pushes forward the LM probability to the last arc of the linear tail.
  
  
• We can optimize a tree to take advantage of shared-tail optimization. Consider this tree before optimization:
  
  
  
  and this tree after shared-tail optimization:
  
  
  
  
• What are the advantages of this approach?