  Integer sequences are of central importance to the modeling of concepts
admitting complete finitary descriptions. We introduce a novel view on the
learning of such concepts and lay down a set of benchmarking tasks aimed at
conceptual understanding by machine learning models. These tasks indirectly
assess model ability to abstract, and challenge them to reason both
interpolatively and extrapolatively from the knowledge gained by observing
representative examples. To further aid research in knowledge representation
and reasoning, we present FACT, the Finitary Abstraction Comprehension Toolkit.
The toolkit surrounds a large dataset of integer sequences comprising both
organic and synthetic entries, a library for data pre-processing and
generation, a set of model performance evaluation tools, and a collection of
baseline model implementations, enabling the making of the future advancements
with ease.
