Measuring Understanding Through Discrete Compositional Knowledge Structures in Hierarchical Automata

Quantitative Biology > Neurons and Cognition [Submitted on 2 May 2026 (v1), last revised 30 May 2026 (this version, v2)] Title:Measuring Understanding Through Discrete Compositional Knowledge Structures in Hierarchical Automata View PDFAbstract:How do we measure genuine understanding in artificial cognitive systems? Current approaches face a measurement gap: probabilistic systems refine confidence gradually, practice-based systems compile knowledge through repeated execution, and neural systems distribute understanding across opaque embedding spaces. We propose that making understanding measurable requires architectures where understanding formation produces discrete, inspectable structural signatures. This paper presents hierarchical automata built from finite state machines representing patterns and higher-order automata representing compositions. Constrained inference constructs automata from single observations. Similarity detection clusters related automata, making concept robustness quantifiable. Graph memory makes compositional knowledge directly inspectable. Metacognitive mechanisms enable observable reconfiguration. We demonstrate understanding measurement in a simple geometric domain. Graph evolution tracking reveals five measurable signatures: immediate representation formation, structural knowledge, generalization capacity, compositional awareness, and metacognitive access. These measurements distinguish structural understanding from statistical correlation. Our contribution is a framework for making understanding measurable through discrete compositional knowledge structures. This measurement capability complements perceptual learning in neural systems and task execution in neurosymbolic architectures. Submission history From: Igor Balaz [view email][v1] Sat, 2 May 2026 13:02:34 UTC (438 KB) [v2] Sat, 30 May 2026 19:21:50 UTC (443 KB) References & Citations Loading... Bibliographic and Citation Tools Bibliographic Explorer (What is the Explorer?) Connected Papers (What is Connected Papers?) Litmaps (What is Litmaps?) scite Smart Citations (What are Smart Citations?) Code, Data and Media Associated with this Article alphaXiv (What is alphaXiv?) CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub (What is DagsHub?) Gotit.pub (What is GotitPub?) Hugging Face (What is Huggingface?) ScienceCast (What is ScienceCast?) Demos Recommenders and Search Tools Influence Flower (What are Influence Flowers?) CORE Recommender (What is CORE?) arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.