  The periodic table is a fundamental representation of chemical elements that
plays essential theoretical and practical roles. The research article discusses
the experiences of unsupervised training of neural networks to represent
elements on the 2D latent space based on their electron configurations. To
emphasize chemical properties of the elements, the original data of electron
configurations has been realigned towards valence orbitals. Recognizing seven
shells and four subshells, the input data has been arranged as 7x4 images.
Latent space representation has been performed using a convolutional beta
variational autoencoder (beta-VAE). Despite discrete and sparse input data, the
beta-VAE disentangles elements of different periods, blocks, groups, and types.
The unsupervised representation of elements on the latent space reveals
pairwise symmetries of periods and elements related to the invariance of
quantum numbers of corresponding elements. In addition, it isolates outliers
that turned out to be known cases of Madelung's rule violations for lanthanide
and actinide elements. Considering the generative capabilities of beta-VAE, the
supervised machine learning has been set to find out if there are insightful
patterns distinguishing electron configurations between real elements and
decoded artificial ones. Also, the article addresses the capability of dual
representation by autoencoders. Conventionally, autoencoders represent
observations of input data on the latent space. By transposing and duplicating
original input data, it is possible to represent variables on the latent space
which can lead to the discovery of meaningful patterns among input variables.
Applying that unsupervised learning for transposed data of electron
configurations, the order of input variables that has been arranged by the
encoder on the latent space has turned out to exactly match the sequence of
Madelung's rule.
