We present a theoretical investigation into the use of normalised artificial neural network (ANN) outputs in the context of hidden Markov models (HMMs). The work is motivated by the pursuit of a more theoretically rigorous understanding of the Kullback-Liebler (KL)-HMM. Two possible models are considered based respectively on the HMM states storing categorical distributions and Dirichlet distributions. Training and recognition algorithms are derived, and possible relationships with KL-HMM are briefly discussed.