  Analogical Reasoning problems challenge both connectionist and symbolic AI
systems as these entail a combination of background knowledge, reasoning and
pattern recognition. While symbolic systems ingest explicit domain knowledge
and perform deductive reasoning, they are sensitive to noise and require inputs
be mapped to preset symbolic features. Connectionist systems on the other hand
can directly ingest rich input spaces such as images, text or speech and
recognize pattern even with noisy inputs. However, connectionist models
struggle to include explicit domain knowledge for deductive reasoning. In this
paper, we propose a framework that combines the pattern recognition abilities
of neural networks with symbolic reasoning and background knowledge for solving
a class of Analogical Reasoning problems where the set of attributes and
possible relations across them are known apriori. We take inspiration from the
'neural algorithmic reasoning' approach [DeepMind 2020] and use
problem-specific background knowledge by (i) learning a distributed
representation based on a symbolic model of the problem (ii) training
neural-network transformations reflective of the relations involved in the
problem and finally (iii) training a neural network encoder from images to the
distributed representation in (i). These three elements enable us to perform
search-based reasoning using neural networks as elementary functions
manipulating distributed representations. We test this on visual analogy
problems in RAVENs Progressive Matrices, and achieve accuracy competitive with
human performance and, in certain cases, superior to initial end-to-end
neural-network based approaches. While recent neural models trained at scale
yield SOTA, our novel neuro-symbolic reasoning approach is a promising
direction for this problem, and is arguably more general, especially for
problems where domain knowledge is available.
