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Novel view synthesis has recently been revolutionized by learning neural radiance fields directly from sparse observations. However, rendering images with this new paradigm is slow due to the fact that an accurate quadrature of the volume rendering equation requires a large number of samples for each ray. Previous work has mainly focused on speeding up the network evaluations that are associated with each sample point, e.g., via caching of radiance values into explicit spatial data structures, but this comes at the expense of model compactness. In this paper, we propose a novel dual-network architecture that takes an orthogonal direction by learning how to best reduce the number of required sample points. To this end, we split our network into a sampling and shading network that are jointly trained. Our training scheme employs fixed sample positions along each ray, and incrementally introduces sparsity throughout training to achieve high quality even at low sample counts. After fine-tuning with the target number of samples, the resulting compact neural representation can be rendered in real-time. Our experiments demonstrate that our approach outperforms concurrent compact neural representations in terms of quality and frame rate and performs on par with highly efficient hybrid representations. Code and supplementary material is available at https://thomasneff.github.io/adanerf.