FM-SIREN & FM-FINER: Nyquist-Informed Frequency Multiplier for Implicit Neural Representation with Periodic Activation
This work addresses a specific bottleneck in implicit neural representations for researchers and practitioners, offering an incremental improvement over existing methods.
The paper tackled the problem of hidden feature redundancy in periodic activation-based implicit neural representation networks, such as SIREN and FINER, by proposing FM-SIREN and FM-FINER, which assign Nyquist-informed, neuron-specific frequency multipliers to reduce redundancy by nearly 50% and improve signal reconstruction across tasks like audio, image, shape fitting, and NeRF synthesis.
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 fitting 1D audio, 2D image and 3D shape, and synthesis of neural radiance fields (NeRF), outperforming their baseline counterparts while maintaining efficiency.