  Implicit Neural Representations (INR) use multilayer perceptrons to represent
high-frequency functions in low-dimensional problem domains. Recently these
representations achieved state-of-the-art results on tasks related to complex
3D objects and scenes. A core problem is the representation of highly detailed
signals, which is tackled using networks with periodic activation functions
(SIRENs) or applying Fourier mappings to the input. This work analyzes the
connection between the two methods and shows that a Fourier mapped perceptron
is structurally like one hidden layer SIREN. Furthermore, we identify the
relationship between the previously proposed Fourier mapping and the general
d-dimensional Fourier series, leading to an integer lattice mapping. Moreover,
we modify a progressive training strategy to work on arbitrary Fourier mappings
and show that it improves the generalization of the interpolation task. Lastly,
we compare the different mappings on the image regression and novel view
synthesis tasks. We confirm the previous finding that the main contributor to
the mapping performance is the size of the embedding and standard deviation of
its elements.
