Learnable Spectral Activations

Tamir Shor, Or Litany, Alex Bronstein

Implicit neural representations (INRs) are shaped by the spectral structure induced by their input encodings and activation functions. Existing methods improve fitting primarily by modifying which frequencies are available to the network, through coordinate encodings or periodic nonlinearities. However, frequency access is not the only bottleneck: signals with localized or spatially varying structure require the network to efficiently compose frequencies into multi-harmonic internal responses. We introduce learnable spectral activations (LSA), which replace fixed neuron-level nonlinearities with a residual truncated Fourier series whose harmonic amplitudes are learned during training. LSA does not expand the asymptotic function class. Instead, it changes the factorization of the representation: linear weights select features while activation coefficients control spectral shaping, and the two are updated by separate gradients. Because the activation output is affine in the coefficients given fixed pre-activations, spectral tuning becomes a more direct subproblem compared to architectures where it is entangled with feature selection. Empirically, this factorization concentrates…