Phase Structure in Rotary Attention: A Spectral Framework for Semantic Continuity and Execution-Boundary Governance

• URL: http://arxiv.org/abs/2607.25507v1
• Date: Tue, 28 Jul 2026 09:41:05 GMT
• Title: Phase Structure in Rotary Attention: A Spectral Framework for Semantic Continuity and Execution-Boundary Governance
• Abstract summary: This paper develops a bounded spectral framework for examining rotary phase alignment, hidden-state continuity, and semantic drift.<n>It first identifies ordered hidden-state sequences, rather than vocabulary indices, as valid domains for spectral decomposition.<n>It then derives the Rotary Position Embedding (RoPE) attention score as a sum of magnitude-weighted cosine terms and proves a local stability lemma.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Transformer language models are usually analyzed through vector geometry, yet ordered context and rotary position encoding introduce explicit phase structure into query-key interactions. This paper develops a bounded spectral framework for examining rotary phase alignment, hidden-state continuity, and semantic drift without treating language models as literal physical wave systems. It first identifies ordered hidden-state sequences, rather than vocabulary indices, as valid domains for spectral decomposition. It then derives the Rotary Position Embedding (RoPE) attention score as a sum of magnitude-weighted cosine terms and proves a local stability lemma: uniformly bounded phase displacement limits degradation of the corresponding pre-softmax score. To extend phase analysis beyond native RoPE coordinates, the paper defines complex modal coordinates over fixed orthonormal direction pairs and introduces a weighted coherence functional for hidden-state trajectories. These constructions support a strict distinction between representational continuity and execution-boundary admissibility. Internal coherence may describe preservation of task-relevant relations, but it cannot authorize a consequential transition. Positioned against existing geometric, spectral, phase-modulation, representation-analysis, and mechanistic-interpretability accounts, the framework contributes a theoretical and methodological program for determining when spectral structure explains continuity and when governance must remain an external predicate over execution.

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