SONIC: Spectral Oriented Neural Invariant Convolutions

Convolutional Neural Networks (CNNs) rely on fixed-size kernels scanning local patches, which limits their ability to capture global context or long-range dependencies without very deep architectures. Vision Transformers (ViTs), in turn, provide global connectivity but lack spatial inductive bias, depend on explicit positional encodings, and remain tied to the initial patch size. Bridging these limitations requires a representation that is both structured and global. We introduce SONIC (Spectral Oriented Neural Invariant Convolutions), a continuous spectral parameterisation that models convolutional operators using a small set of shared, orientation-selective components. These components define smooth responses across the full frequency domain, yielding global receptive fields and filters that adapt naturally across resolutions. Across synthetic benchmarks, large-scale image classification, and 3D medical datasets, SONIC shows improved robustness to geometric transformations, noise, and resolution shifts, and matches or exceeds convolutional, attention-based, and prior spectral architectures with an order of magnitude fewer parameters. These results demonstrate that continuous, orientation-aware spectral parameterisations provide a principled and scalable alternative to conventional spatial and spectral operators.