The decoder is a differentiable function of the coordinate, so the field it decodes can be differentiated exactly. Pick a formula, type one, or paint or upload a field: it is encoded as one embedding, and the gradient of its decoding û, ∂û/∂x1 and ∂û/∂x2, is compared with the true one, the formula's own gradient or the central differences of the field's pixels.
Checking the server…The input is one embedding, which captures only its lowest frequencies, and so does its gradient; the presets are functions it captures with their gradient within 4% relative L2 error. The reference of a field is the central difference of its pixels, an approximation itself.