Controlling Logical Collapse in LLMs via Algebraic Ontology Projection over F2
Do large language models internally encode ontological relations in a formally verifiable algebraic structure? We introduce Algebraic Ontology Projection (AOP), which projects LLM hidden states into the Galois Field F2 under Liskov Substitution Principle constraints, using only 42 relational pairs as algebraic keys. AOP achieves up to 93.33% zero-shot inclusion accuracy on unseen concept pairs (Gemma-2 Instruct with optimized prompt), with consistent 86.67% accuracy observed across multiple model families -- with no model tuning, but through prompt alone. This algebraic structure is strongly layer-dependent. We introduce Semantic Crystallisation (SC), a metric that quantifies F2 constrain...
| Authors | Hisashi Miyashita, Mgnite Inc |
|---|---|
| Primary category | cs.LG |
| Published | 13 May 2026 |
| Last updated at source | 13 May 2026 |
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