Low-complexity coding and decoding (LOCOCODE) is a novel approach to sensory coding and unsupervised learning. Unlike previous methods, it explicitly takes into account the information-theoretic complexity of the code generator. It computes lococodes that convey information about the input data and can be computed and decoded by low-complexity mappings. We implement LOCOCODE by training autoassociators with flat minimum search, a recent, general method for discovering low-complexity neural nets. It turns out that this approach can unmix an unknown number of independent data sources by extracting a minimal number of low-complexity features necessary for representing the data. Experiments show that unlike codes obtained with standard autoencoders, lococodes are based on feature detectors, never unstructured, usually sparse, and sometimes factorial or local (depending on statistical properties of the data). Although LOCOCODE is not explicitly designed to enforce sparse or factorial codes, it extracts optimal codes for difficult versions of the “bars” benchmark problem, whereas independent component analysis (ICA) and principal component analysis (PCA) do not. It produces familiar, biologically plausible feature detectors when applied to real-world images and codes with fewer bits per pixel than ICA and PCA. Unlike ICA, it does not need to know the number of independent sources. As a preprocessor for a vowel recognition benchmark problem, it sets the stage for excellent classification performance. Our results reveal an interesting, previously ignored connection between two important fields: regularizer research and ICA-related research. They may represent a first step toward unification of regularization and unsupervised learning.