WaveKernel: Continuous Kernel Synthesis via Optical Wave Propagation

Continuous-time models aim to learn discretization-consistent signal representations, with their expressive properties significantly influenced by the functional parameterization of local temporal operators. Prior approaches largely rely on predefined basis functions or neural networks, leaving the effective parameterization of continuous kernels an important open challenge. We propose WaveKernel, a continuous convolution operator that synthesizes kernels by evaluating the optical field generated by a slab-type diffractive model at continuous spatial positions. Learnable amplitude–phase modulation units jointly shape the spatial profile of the optical field, thereby defining a continuous kernel expanded in a basis of optical impulse responses. By introducing a structured inductive bias derived from optical wave propagation and mapping relative temporal coordinates onto continuous spatial positions for kernel evaluation, the proposed parameterization allows the same learned coefficients to be evaluated across different sampling rates. Integrated into a shared time-series architecture, WaveKernel improves seven-rate mean accuracy over spline-based continuous convolution on three sleep-staging benchmarks, while maintaining stable performance across the evaluated sampling rates.