Machine learning algorithms are typically run on large scale, distributed compute infrastructure that routinely face a number of unavailabilities such as failures and temporary slowdowns. Adding redundant computations using coding-theoretic tools called "codes" is an emerging technique to alleviate the adverse effects of such unavailabilities. A code consists of an encoding function that proactively introduces redundant computation and a decoding function that reconstructs unavailable outputs using the available ones. Past work focuses on using codes to provide resilience for linear computations and specific iterative optimization algorithms. However, computations performed for a variety of applications including inference on state-of-the-art machine learning algorithms, such as neural networks, typically fall outside this realm. In this paper, we propose taking a learning-based approach to designing codes that can handle non-linear computations. We present carefully designed neural network architectures and a training methodology for learning encoding and decoding functions that produce approximate reconstructions of unavailable computation results. We present extensive experimental results demonstrating the effectiveness of the proposed approach: we show that the our learned codes can accurately reconstruct $64 - 98\%$ of the unavailable predictions from neural-network based image classifiers on the MNIST, Fashion-MNIST, and CIFAR-10 datasets. To the best of our knowledge, this work proposes the first learning-based approach for designing codes, and also presents the first coding-theoretic solution that can provide resilience for any non-linear (differentiable) computation. Our results show that learning can be an effective technique for designing codes, and that learned codes are a highly promising approach for bringing the benefits of coding to non-linear computations.