Connectionist Temporal Classification: Labelling Unsegmented Sequence Data with Recurrent Neural Networks

3.2 Constructing the Classifier

1. What is best path decoding in CTC, and its weakness?
   Take the most active output at every time step and collapse: \(h(\mathbf{x}) \approx \mathcal{B}(\pi^*)\), \(\pi^* = \arg\max_\pi p(\pi \mid \mathbf{x})\). It is trivial to compute but not guaranteed to find the most probable labelling, since that probability is spread over many paths.
   • Graves et al., 2006, Connectionist Temporal Classification (Proceedings of the 23rd International Conference on Machine Learning (ICML 2006)), §3.2, pp. 371–372
2. How does prefix search decoding work in CTC?
   A modified forward-backward algorithm computes the probability of extensions of labelling prefixes; the most probable remaining prefix is always expanded, until one complete labelling beats every remaining prefix. It finds the best labelling given enough time, but can take exponential time; in practice the output was split at points where blank probability exceeds a threshold, and each section decoded separately.
   • Graves et al., 2006, Connectionist Temporal Classification (Proceedings of the 23rd International Conference on Machine Learning (ICML 2006)), §3.2, pp. 371–372