We study here a way to approximate information retrieval metrics through a softmax-based approximation of the rank indicator function. Indeed, this latter function is a key component in the design of information retrieval metrics, as well as in the design of the ranking and sorting functions. Obtaining a good approximation for it thus opens the door to differentiable approximations of many evaluation measures that can in turn be used in neural end-to-end approaches. We first prove theoretically

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... that the approximations proposed are of good quality, prior to validate them experimentally on both learning to rank and text-based information retrieval tasks.