For a long time, additive quantizers, such as product quantization, have been considered the gold standard in terms of accuracy and efficiency. Recently, scalar quantization has re-emerged from the depths of history with a new wave of data-agnostic techniques. Inscribed in this general framework, we turn our attention to data-driven methods, showing that new highs in recall and speed can be achieved by reducing the number of dimensions while increasing the bitrate per dimension. Critically, this dimensionality reduction needs to be learned from data to be successful. We present ASH (Asymmetric Scalar Hashing), a data-driven encoder-decoder framework that applies dimensionality reduction to database vectors via a learned orthonormal projection, followed by scalar quantization, while keeping queries in their original form. This asymmetric design enables higher accuracy than the best additive and scalar quantizers at iso-compression, while admitting highly efficient similarity computations via SIMD operations. ASH has short learning and encoding times, making it attractive for real-world deployment. Extensive experiments on a variety of datasets demonstrate that ASH achieves state-of-the-art ANN recall and speeds across all compression regimes.