Modern approaches for fast retrieval of similar vectors on billion-scaled datasets rely on compressed-domain approaches such as binary sketches or product quantization. These methods minimize a certain loss, typically the mean squared error or other objective functions tailored to the retrieval problem. In this paper, we re-interpret popular methods such as binary hashing or product quantizers as auto-encoders, and point out that they implicitly make suboptimal assumptions on the form of the decoder. We design backward-compatible decoders that improve the reconstruction of the vectors from the same codes, which translates to a better performance in nearest neighbor search. Our method significantly improves over binary hashing methods or product quantization on popular benchmarks.