Title: Learning Graph Decomposition. Abstract: We propose a novel end-to-end trainable framework for the graph decomposition problem. The minimum cost multicut problem is first converted to an unconstrained binary cubic formulation where cycle consistency constraints are incorporated into the objective function. The new optimization problem can be viewed as a Conditional Random Field (CRF) in which the random variables are associated with the binary edge labels of the initial graph and the hard constraints are introduced in the CRF as high-order potentials. The parameters of a standard Neural Network and the fully differentiable CRF can be optimized in an end-to-end manner.  We demonstrate the proposed learning algorithm in the context of clustering of hand written digits, particularly in a setting where no direct supervision for the graph decomposition task is available, and multiple person pose estimation from images in the wild. The experiments validate the effectiveness of our approach both for the feature learning and for the final clustering task.