  Multidimensional recurrent neural networks (MDRNNs) have shown a remarkable
performance in the area of speech and handwriting recognition. The performance
of an MDRNN is improved by further increasing its depth, and the difficulty of
learning the deeper network is overcome by using Hessian-free (HF)
optimization. Given that connectionist temporal classification (CTC) is
utilized as an objective of learning an MDRNN for sequence labeling, the
non-convexity of CTC poses a problem when applying HF to the network. As a
solution, a convex approximation of CTC is formulated and its relationship with
the EM algorithm and the Fisher information matrix is discussed. An MDRNN up to
a depth of 15 layers is successfully trained using HF, resulting in an improved
performance for sequence labeling.
