Diffraction drastically limits the bit density in optical data storage. To increase the storage density, alternative strategies involving supplementary recording dimensions and robust readout schemes must be explored. Here, we propose to encode multiple bits of information in the geometry of subwavelength dielectric nanostructures. A crucial problem in high-density information storage concepts is the robustness of the information readout with respect to fabrication errors and experimental noise. Using a machine-learning-based approach in which the scattering spectra are analysed by an artificial neural network, we achieve quasi-error-free readout of sequences of up to 9 bits, encoded in top-down fabricated silicon nanostructures. We demonstrate that probing few wavelengths instead of the entire spectrum is sufficient for robust information retrieval and that the readout can be further simplified, exploiting the RGB values from microscopy images. Our work paves the way towards high-density optical information storage using planar silicon nanostructures, compatible with mass-production-ready complementary metal–oxide–semiconductor technology.