  Neural-symbolic approaches to machine learning incorporate the advantages
from both connectionist and symbolic methods. Typically, these models employ a
first module based on a neural architecture to extract features from complex
data. Then, these features are processed as symbols by a symbolic engine that
provides reasoning, concept structures, composability, better generalization
and out-of-distribution learning among other possibilities. However, neural
approaches to the grounding of symbols in sensory data, albeit powerful, still
require heavy training and tedious labeling for the most part. This paper
presents a new symbolic-only method for the generation of hierarchical concept
structures from complex spatial sensory data. The approach is based on
Bateson's notion of difference as the key to the genesis of an idea or a
concept. Following his suggestion, the model extracts atomic features from raw
data by computing elemental sequential comparisons in a stream of multivariate
numerical values. Higher-level constructs are built from these features by
subjecting them to further comparisons in a recursive process. At any stage in
the recursion, a concept structure may be obtained from these constructs and
features by means of Formal Concept Analysis. Results show that the model is
able to produce fairly rich yet human-readable conceptual representations
without training. Additionally, the concept structures obtained through the
model (i) present high composability, which potentially enables the generation
of 'unseen' concepts, (ii) allow formal reasoning, and (iii) have inherent
abilities for generalization and out-of-distribution learning. Consequently,
this method may offer an interesting angle to current neural-symbolic research.
Future work is required to develop a training methodology so that the model can
be tested against a larger dataset.
