In-situ graph reasoning and knowledge expansion using Graph-PReFLexOR
Authors: name: Markus J. Buehler

The pursuit of automated scientific discovery has fueled progress from
symbolic logic to modern AI, forging new frontiers in reasoning and pattern
recognition. Transformers function as potential systems, where every possible
relationship remains latent potentiality until tasks impose constraints, akin
to measurement. Yet, refining their sampling requires more than probabilistic
selection: solutions must conform to specific structures or rules, ensuring
consistency and the invocation of general principles. We present
Graph-PReFLexOR (Graph-based Preference-based Recursive Language Modeling for
Exploratory Optimization of Reasoning), a framework that combines graph
reasoning with symbolic abstraction to dynamically expand domain knowledge.
Inspired by reinforcement learning, Graph-PReFLexOR defines reasoning as a
structured mapping, where tasks yield knowledge graphs, abstract patterns, and
ultimately, final answers. Inspired by category theory, it encodes concepts as
nodes and their relationships as edges, supporting hierarchical inference and
adaptive learning through isomorphic representations. Demonstrations include
hypothesis generation, materials design, and creative reasoning, such as
discovering relationships between mythological concepts like 'thin places' with
materials science. We propose a 'knowledge garden growth' strategy that
integrates insights across domains, promoting interdisciplinary connections.
Results with a 3-billion-parameter Graph-PReFLexOR model show superior
reasoning depth and adaptability, underscoring the potential for transparent,
multidisciplinary AI-driven discovery. It lays the groundwork for general
autonomous reasoning solutions.