  Implicit Neural Representation (INR), which utilizes a neural network to map
coordinate inputs to corresponding attributes, is causing a revolution in the
field of signal processing. However, current INR techniques suffer from the
"frequency"-specified spectral bias and capacity-convergence gap, resulting in
imperfect performance when representing complex signals with multiple
"frequencies". We have identified that both of these two characteristics could
be handled by increasing the utilization of definition domain in current
activation functions, for which we propose the FINER++ framework by extending
existing periodic/non-periodic activation functions to variable-periodic ones.
By initializing the bias of the neural network with different ranges,
sub-functions with various frequencies in the variable-periodic function are
selected for activation. Consequently, the supported frequency set can be
flexibly tuned, leading to improved performance in signal representation. We
demonstrate the generalization and capabilities of FINER++ with different
activation function backbones (Sine, Gauss. and Wavelet) and various tasks (2D
image fitting, 3D signed distance field representation, 5D neural radiance
fields optimization and streamable INR transmission), and we show that it
improves existing INRs. Project page: {https://liuzhen0212.github.io/finerpp/}
