In this paper, we describe the infinite replicated Softmax model (iRSM) as an adaptive topic model, utilizing the combination of the infinite restricted Boltzmann machine (iRBM) and the replicated Softmax model (RSM). In our approach, the iRBM extends the RBM by enabling its hidden layer to adapt to the data at hand, while the RSM allows for modeling low-dimensional latent semantic representation from a corpus. The combination of the two results is a method that is able to self-adapt to the number of topics within the document corpus and hence, renders manual identification of the correct number of topics superfluous. We propose a hybrid training approach to effectively improve the performance of the iRSM. An empirical evaluation is performed on a standard data set and the results are compared to the results of a baseline topic model. The results show that the iRSM adapts its hidden layer size to the data and when trained in the proposed hybrid manner outperforms the base RSM model.