Sitzmann et al.'s 2020 SIREN paper represents images, video, sound, and PDE solutions as continuous differentiable functions parameterized by neural networks with periodic activations, not as discrete grids of samples

The 2020 paper "Implicit Neural Representations with Periodic Activation Functions" (SIREN), by Vincent Sitzmann and colleagues at Stanford, proposes representing a signal — an image, an audio clip, a video, or the solution of a partial differential equation — as a continuous, differentiable function whose parameters are the weights of a small neural network. Rather than storing a signal as a discrete array of samples (pixels, audio samples, voxels), the network maps coordinates to values, so the representation is defined everywhere and can be differentiated analytically. SIREN's specific contribution is the use of periodic (sinusoidal) activation functions, which the authors argue make such networks "ideally suited for representing complex natural signals and their derivatives."

This is a foundational statement of the implicit neural representation (INR) idea that also underpins neural radiance fields (NeRF) and much of modern neural rendering: the model is the signal. The claim recorded here is narrow — what SIREN represents and how — and rests on the paper's own arXiv abstract (Tier 1).

The historically interesting angle, treated separately and as an explicitly unsourced synthesis, is that this "signal as a compact function instead of a sample grid" premise was also the founding pitch of 1980s–1990s fractal image compression — a lineage no source in the capture actually draws (claim-fractal-compression-to-implicit-neural-representations-bridge). As a signal-compression idea, INR also sits near the vault's image-compression cluster (claim-djvu-1998-paper-coauthored-by-lecun-and-bengio).