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This research proposes the Lattice Representation Hypothesis, suggesting that large language models utilize a symbolic backbone grounded in embedding geometry to perform logical operations. By unifying linear representation theories with Formal Concept Analysis, the study demonstrates how continuous vector spaces can encode discrete conceptual hierarchies and enable principled reasoning through geometric intersections and unions. Empirical validation on WordNet sub-hierarchies confirms that LLM embeddings naturally structure concept lattices, bridging the gap between neural geometry and symbolic abstraction for more robust AI systems.

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The Lattice Representation Hypothesis of Large Language Models

arXivJuly 28, 20261 min read

arXiv:2603.01227v3 Announce Type: replace Abstract: We propose the Lattice Representation Hypothesis of large language models: a symbolic backbone that grounds conceptual hierarchies and logical operations in embedding geometry. Our framework unifies the Linear Representation Hypothesis with Formal Concept Analysis (FCA), showing that linear attribute directions with separating thresholds induce a concept lattice via half-space intersections. This geometry enables symbolic reasoning through geometric meet (intersection) and join (union) operations, and admits a canonical form when attribute directions are linearly independent. Experiments on WordNet sub-hierarchies provide empirical evidence that LLM embeddings encode concept lattices and their logical structure, revealing a principled bridge between continuous geometry and symbolic abstraction. Datasets and code are open available at https://github.com/xiongbo010/lattice-representation-hypothesis.

Abstract:We propose the Lattice Representation Hypothesis of large language models: a symbolic backbone that grounds conceptual hierarchies and logical operations in embedding geometry. Our framework unifies the Linear Representation Hypothesis with Formal Concept Analysis (FCA), showing that linear attribute directions with separating thresholds induce a concept lattice via half-space intersections. This geometry enables symbolic reasoning through geometric meet (intersection) and join (union) operations, and admits a canonical form when attribute directions are linearly independent. Experiments on WordNet sub-hierarchies provide empirical evidence that LLM embeddings encode concept lattices and their logical structure, revealing a principled bridge between continuous geometry and symbolic abstraction. Datasets and code are open available at this https URL.

Artificial Intelligence (cs.AI)

arXiv:2603.01227 [cs.AI]

(or arXiv:2603.01227v3 [cs.AI] for this version)

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