Phase Structure in Continuous Wave Fields Enables Speech Classification Without Backpropagation

Abstract Physical neural networks promise energy-efficient computation by exploiting the intrinsic dynamics of physical substrates, but existing implementations rely on discrete elements or restrict learning to digital readout layers. Here we demonstrate that a continuous Landau-Ginzburg wave field, operating in the underdamped regime, generates phase structure sufficient for classifying spoken words at 74.1% accuracy on a 10-class spoken command recognition task (Google Speech Commands V2) — using only a linear readout and no backpropagation through the physical dynamics. Systematic ablation across ten conditions reveals a three-tier hierarchy of contributions. First, operating in the underdamped regime accounts for ~20 percentage points (pp): a from-scratch baseline trained with EP but initialized in the overdamped regime (γ/ω = 1.0) reaches only 53%, while theoretically-motivated underdamped initialization (γ/ω < 0.05) yields 74.1% (EP fine-tuning contributed an additional 0.81 pp; ablation 7). Second, within the architecture, readout design is decisive: explicit phase extraction — cosine and sine of the phase angle, amplitude, and amplitude gradient — contributes 7.8 points over implicit complex-component encoding, revealing that linear readouts cannot exploit phase information unless it is explicitly projected into trigonometric form. Third, individual physics components — cross-phase modulation, spatial parameter grids, evanescent coupling, and EP fine-tuning of material parameters — each contribute less than 1 percentage point individually, indicating that the underdamped LG regime is robust to specific parameter choices once the architecture is correctly designed. Notably, Equilibrium Propagation drives the lateral inhibition strength toward opposite optima depending on the readout — higher under amplitude measurement (D → 0.27), lower under phase-sensitive measurement (D → 0.025) — demonstrating that EP co-adapts the physical substrate to the measurement apparatus. Every learned parameter in principle maps directly to fabrication specifications for photonic or acoustic hardware.