Optical information encoded in holograms is transferred by means of ultrashort laser filaments propagating in highly nonlinear and turbulent media. After propagation, the initial optical information is completely scrambled and cannot be retrieved by any experimental or physical modeling system. Yet, we demonstrate that neural networks trained on experimental data provide a robust way to fully recover the original hologram images. Remarkably, our approach demonstrates the ability to decode intricate spatial information, marking a significant advancement in information retrieval from chaotic media, with applications in secure free-space optical communications and cryptography.