Title: FM-SIREN & FM-FINER: Nyquist-Informed Frequency Multiplier for Implicit Neural Representation with Periodic Activation
Primary area: unsupervised, self-supervised, semi-supervised, and supervised representation learning
Keywords: Implicit Neural Representation; Nyquist Sampling; Frequency Features

Abstract: Existing periodic activation-based implicit neural representation (INR) networks, such as SIREN and FINER, suffer from hidden feature redundancy, where neurons within a layer capture overlapping frequency components due to the use of a fixed frequency multiplier. This redundancy limits the expressive capacity of multilayer perceptrons (MLPs). Drawing inspiration from classical signal processing methods such as the Discrete Sine Transform (DST), we propose FM-SIREN and FM-FINER, which assign Nyquist-informed, neuron-specific frequency multipliers to periodic activations. Unlike existing approaches, our design introduces frequency diversity without requiring hyperparameter tuning or additional network depth. This simple yet principled modification reduces the redundancy of features by nearly 50% and consistently improves signal reconstruction across diverse INR tasks, including 1D audio, 2D image regression, 3D shape fitting, and neural radiance field (NeRF) synthesis, outperforming their baseline counterparts while maintaining efficiency.