  The use of Variational Autoencoders in different Machine Learning tasks has
drastically increased in the last years. They have been developed as denoising,
clustering and generative tools, highlighting a large potential in a wide range
of fields. Their embeddings are able to extract relevant information from
highly dimensional inputs, but the converged models can differ significantly
and lead to degeneracy on the latent space. We leverage the relation between
theoretical physics and machine learning to explain this behaviour, and
introduce a new approach to correct for degeneration by using perturbation
theory. The re-formulation of the embedding as multi-dimensional generative
distribution, allows mapping to a new set of functions and their corresponding
energy spectrum. We optimise for a perturbed Hamiltonian, with an additional
energy potential that is related to the unobserved topology of the data. Our
results show the potential of a new theoretical approach that can be used to
interpret the latent space and generative nature of unsupervised learning,
while the energy landscapes defined by the perturbations can be further used
for modelling and dynamical purposes.
