Hypercubes, Hyperplanes, and Constraint-Induced Complexity Collapse in Atomic Concept Learning

arXiv cs.AIAugust 5, 2026en

arXiv cs.AI

AI Global Wire

arXiv:2608.02930v1 Announce Type: new Abstract: We revisit higher-arity atomic concept learning through the geometry of hypercubes and hyperplanes of ground instances. Our starting point is the observation that the ambient r-dimensional hypercube of ground atoms is not structurally uniform. Its logical complexity is organized by hyperplanes: every hyperplane other than the full diagonal collapses into finitely many elementary-equivalence classes, with a bound independent of the term depth, while the full diagonal is exceptional and its class count grows without bound. This asymmetry is not merely geometric. It reflects the reduction-theoretic structure of the concepts themselves. Building on

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