The Wave Optics of Semantic Computation: Complex Transformers, Phase Interference, and Readout Capacity Limits

Abstract

Timo Aukusti Laine

We establish a first-principles field theory of semantic computation that grounds language representations in physical wave mechanics, demonstrating that complex-valued vectors define an autonomous classical wave theory. We structure semantic computation into three exact mathematical levels: Level 1 (standard real transformers operating as phase- restricted subspaces), Level 2 (complex transformers operating strictly as classical wave optics governed by Poincare polarization kinematics and an explicit layer-wise coherence budget), and Level 3 (quantum semantic fields obtained through canonical quantization of the Level 2 phase space without approximation). Level 2 provides a self-contained physical framework that maps natively onto passive, room-temperature photonic integrated circuits (PICs). By formalizing this structure, we derive exact readout capacity bounds across all levels and decompose LLM hallucinations into an unremovable readout capacity floor forced by vocabulary scaling, an architectural gap caused by real-space phase restrictions, and an empirical gap reducible by training. Canonical quantization to Level 3 yields non-classical limits, including a semantic zero-point energy and an entropic attention bandwidth relation. Empirically evaluating Level 2 on FB15k-237 knowledge graph completion across ten random seeds confirms that complex wave transformers consistently outperform matched real baselines in accuracy, Mean Reciprocal Rank, and hallucination reduction while utilizing 4.6% fewer total parameters, proving phase interference to be a parameter-efficient, physically grounded inductive bias for sequence modeling.

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