Solving ARC visual analogies with neural embeddings and vector
  arithmetic: A generalized method
Luca H. Thoms Karel A. Veldkamp Hannes Rosenbusch Claire E. Stevenson
Analogical reasoning derives information from known relations and generalizes
this information to similar yet unfamiliar situations. One of the first
generalized ways in which deep learning models were able to solve verbal
analogies was through vector arithmetic of word embeddings, essentially
relating words that were mapped to a vector space (e.g., king - man + woman =
__?). In comparison, most attempts to solve visual analogies are still
predominantly task-specific and less generalizable. This project focuses on
visual analogical reasoning and applies the initial generalized mechanism used
to solve verbal analogies to the visual realm. Taking the Abstraction and
Reasoning Corpus (ARC) as an example to investigate visual analogy solving, we
use a variational autoencoder (VAE) to transform ARC items into low-dimensional
latent vectors, analogous to the word embeddings used in the verbal approaches.
Through simple vector arithmetic, underlying rules of ARC items are discovered
and used to solve them. Results indicate that the approach works well on simple
items with fewer dimensions (i.e., few colors used, uniform shapes), similar
input-to-output examples, and high reconstruction accuracy on the VAE.
Predictions on more complex items showed stronger deviations from expected
outputs, although, predictions still often approximated parts of the item's
rule set. Error patterns indicated that the model works as intended. On the
official ARC paradigm, the model achieved a score of 2% (cf. current world
record is 21%) and on ConceptARC it scored 8.8%. Although the methodology
proposed involves basic dimensionality reduction techniques and standard vector
arithmetic, this approach demonstrates promising outcomes on ARC and can easily
be generalized to other abstract visual reasoning tasks.