  Hidden Markov Model (HMM) is often regarded as the dynamical model of choice
in many fields and applications. It is also at the heart of most
state-of-the-art speech recognition systems since the 70's. However, from
Gaussian mixture models HMMs (GMM-HMM) to deep neural network HMMs (DNN-HMM),
the underlying Markovian chain of state-of-the-art models did not changed much.
The "left-to-right" topology is mostly always employed because very few other
alternatives exist. In this paper, we propose that finely-tuned HMM topologies
are essential for precise temporal modelling and that this approach should be
investigated in state-of-the-art HMM system. As such, we propose a
proof-of-concept framework for learning efficient topologies by pruning down
complex generic models. Speech recognition experiments that were conducted
indicate that complex time dependencies can be better learned by this approach
than with classical "left-to-right" models.
