Quasi-Orthogonality and Polysemy: The Limits of Quantum Analogy in Large Language Models

Karl Svozil

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arXiv · 2504.13824

Quasi-Orthogonality and Polysemy: The Limits of Quantum Analogy in Large Language Models

Karl Svozil

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Abstract

We analyze two geometric aspects of meaning-sensitive behavior in next-token models. First, high-dimensional geometry permits exponentially many nearly orthogonal feature directions at a fixed tolerance, although their residual overlaps limit simultaneous readout. Second, polysemy requires us to distinguish classical convex mixtures of sense vectors, context-dependent occurrence vectors, quantum coherence, and an optional shared-projector incidence construction over sense-labelled bases. For ordinary transformers, the quantum comparisons are structural and deliberately limited.

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Karl Svozil. 2025-04-18. Quasi-Orthogonality and Polysemy: The Limits of Quantum Analogy in Large Language Models. https://arxiv.org/abs/2504.13824

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