Differentiable Weighted Finite-State Transducers

E B. (2) The primary difference between ASG and CTC is the inclusion of a blank token, b, represented by the graph in figure 3a. Constructing CTC amounts to including the blank token graph when constructing the full token graph T. The intersection T Y then results in the CTC alignment graph (Figure 1b). Note, this version of CTC does not force transitions on b between repeats tokens. This requires remembering the previous state and hence is more involved (see Appendix A.1 for details). A benefit of constructing sequence-level criteria by composing operations on simpler graphs is the access to a large design space of loss functions with which we can encode useful priors. For example we could construct a "spike" CTC, a "duration-limited" CTC, or an "equally spaced" CTC by substituting the appropriate token graphs into equation 2 (see Appendix A.2 for details).