Beyond Point Samples: Acquisition Modeling as a Separate Axis for Implicit Neural Representations

Implicit neural representations (INRs) provide continuous representations of signals, yet recovering a continuous field from discrete measurements depends on both the representation and the process by which measurements constrain it. This relationship is specified by the acquisition model, which maps the continuous field to discrete observations. However, INR reconstruction has largely treated this measurement process as fixed. Most INR work has focused on representation design, while the measurement constraint itself is usually kept fixed as pointwise supervision. Here we isolate the effect of acquisition choice by holding the representation fixed and varying only the acquisition model. We find that acquisition choice materially changes the recovered continuous field, with increasingly pronounced effects as reconstruction relies increasingly on interpolation between sparse observations. Spatial acquisition improves continuous-field recovery overall, but its effect is spatially nonuniform, with larger reductions around boundaries, thin structures, and regions of rapid spatial variation, while point acquisition can remain locally preferable. Acquisition choice also changes the spectral structure of reconstruction error, particularly at intermediate and higher spatial frequencies. These results motivate treating the acquisition model as an explicit part of INR reconstruction rather than a fixed supervision choice.