Language as a Wave Phenomenon: Semantic Phase Locking and Interference in Neural Networks

Abstract

In standard Transformer architectures, semantic importance is often conflated with activation magnitude, obscuring the geometric structure of latent representations. To disentangle these factors, we introduce PRISM, a complex-valued architecture designed to isolate the computational role of phase. By enforcing a strict unit-norm constraint (|z| = 1) and replacing attention with gated harmonic convolutions, the model is compelled to utilize subtractive interference in the frequency domain to suppress noise, rather than relying on magnitude-based gating. We utilize this constrained regime to demonstrate that a hybrid architecture—fusing phase-based routing with standard attention—achieves superior parameter efficiency and representation quality compared to unconstrained baselines. Mechanistically, we identify geometric phase clustering, where tokens naturally self-organize to resolve semantic ambiguities. This establishes an O(N log N) reasoning framework based on spectral interference, providing an algorithmic existence proof that subtractive logic is a logical primitive for deep reasoning.