Spectral Gating via Damped Oscillations for Adaptive Implicit Neural Representations

Implicit Neural Representations (INRs) have been provensuccessful in encoding continuous signals through coordinate-based net-works, yet facing a spectral dilemma: periodic activations capture finedetails but act as all-pass filters that memorise noise, while spatiallycompact activations regularise effectively but suffer from low-frequencybias. Existing attempts to resolve this trade-off introduce computationaloverhead or tuning frailty. We propose to model each neuron’s activationas the steady-state response of a sinusoidally-forced damped harmonicoscillator, whose amplitude naturally governs the network’s spectral se-lectivity during training. By jointly optimising the oscillator parametersalongside the network weights, our method adapts to the target signal’sspectral content without explicit regularisation. Initialised in the stop-band, the network exhibits a coarse-to-fine learning curriculum that pro-gressively expands its spectral gate, capturing low-frequency structuresfirst and high-frequency details only when justified by the reconstructionobjective. Comprehensive experiments show that our approach consis-tently achieves state-of-the-art or competitive results against establishedINRs, while requiring no task-specific tuning of any hyperparameters.Project Page available at https://alex-costanzino.github.io/fdho/.