  In this study, we address the challenge of using energy-based models to
produce high-quality, label-specific data in complex structured datasets, such
as population genetics, RNA or protein sequences data. Traditional training
methods encounter difficulties due to inefficient Markov chain Monte Carlo
mixing, which affects the diversity of synthetic data and increases generation
times. To address these issues, we use a novel training algorithm that exploits
non-equilibrium effects. This approach, applied on the Restricted Boltzmann
Machine, improves the model's ability to correctly classify samples and
generate high-quality synthetic data in only a few sampling steps. The
effectiveness of this method is demonstrated by its successful application to
four different types of data: handwritten digits, mutations of human genomes
classified by continental origin, functionally characterized sequences of an
enzyme protein family, and homologous RNA sequences from specific taxonomies.
