What Makes the Weights of Implicit Neural Representations Classifiable?

Implicit neural representations (INRs) store an image in the parameters of a small network, and recent work classifies images by reading these parameters. The Meta Weight Transformer (MWT) made such classifiers far more accurate by learning, jointly with a Transformer classifier, how sinusoidal INRs (SIRENs) are fitted. Earlier work relates accuracy to measures of class structure in the parameters, but such measures show what can be read from the parameters, not what a classifier uses. In this paper, we study whether class structure reflects how well MWT classifies, and which inputs its classifier relies on. We first compare nearest-neighbor and nearest-centroid readouts of this structure with the trained classifiers across six MWT training configurations. The readouts are far less accurate and do not rank the configurations by accuracy. Next, we change the inputs of the trained classifiers without retraining them, and find that the classifiers depend heavily on the per-neuron biases, which make up less than 0.4% of their input values. Replacing the biases by their layer means lowers accuracy by 16.3 points on average, whereas the same change to a weight column of the same size lowers it by only 0.3. This dependence centers on a low-dimensional variation of the biases across images, one that closely matches coarse color and brightness statistics. Our results show that, in MWT, the fitted parameters are classifiable in part because their biases carry coarse information about the image.