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International audience; This paper presents a new approach for learning transition function in state representation learning (SRL) for control. While state-of-the-art methods use different deterministic neural networks to learn forward and inverse state transition functions independently with auto-supervised learning, we introduce a bidirectional stochastic model to learn both transition functions. We aim at using the uncertainty of the model on its predictions as an intrinsic motivation for exploration to enhance the representation learning. More, using the same model to learn both transition functions allows sharing the parameters, which can reduce their number and should increase the embedding quality of the representation. We use a factored restricted Boltzmann machine (fRBM) based model, enhanced with dedicated structure for learning system dynamics and transitions with shared parameters. The presented work focuses on building the structure of the bidirectional transition model for unsupervised learning. Our fRBM structure is directly inspired from physics interactions between inputs and outputs in reinforcement learning framework. We compare different training algorithms for learning the model that must be able to predict observable random variables to be used in SRL framework. Our structure is not restricted to any type of observable, nevertheless in this paper we focus on learning dynamics from the OpenAI Gym environment Swinging Pendulum. We show that the proposed structure is able to learn bidirectional transition function and performs well in prediction task.