The Phasor Transformer: Resolving Attention Bottlenecks on the Unit Circle

Transformer models have redefined sequence learning, yet dot-product self-attention introduces a quadratic token-mixing bottleneck for long-context time-series. We introduce the \textbf{Phasor Transformer} block, a phase-native alternative representing sequence states on the unit-circle manifold $S^1$. Each block combines lightweight trainable phase-shifts with parameter-free Discrete Fourier Transform (DFT) token coupling, achieving global $\mathcal{O}(N\log N)$ mixing without explicit attention maps. Stacking these blocks defines the \textbf{Large Phasor Model (LPM)}. We validate LPM on autoregressive time-series prediction over synthetic multi-frequency benchmarks. Operating with a highly compact parameter budget, LPM learns stable global dynamics and achieves competitive forecasting behavior compared to conventional self-attention baselines. Our results establish an explicit efficiency-performance frontier, demonstrating that large-model scaling for time-series can emerge from geometry-constrained phase computation with deterministic global coupling, offering a practical path toward scalable temporal modeling in oscillatory domains.