Does the Implicit-Regularizer View of Kolmogorov–Arnold Networks Survive Real Photometric Noise? A Heteroscedastic Stress-Test on SDSS DR17 and DESI DR1

This paper stress-tests whether the implicit-regularizer view of Kolmogorov-Arnold Networks (KAN 2.0) survives real, heteroscedastic per-object photometric noise rather than the synthetic uniform-SNR noise used in prior work. Using real per-object uncertainties for 73,302 SDSS DR17 objects (PSF magnitude errors) and 99,999 DESI DR1 objects (inverse-variance-derived errors), the author re-runs the equal-baseline comparison between KAN, a weight-decay-regularized MLP (MLP-Reg), an unregularized MLP, and XGBoost under three settings: uncertainties as input features, per-object real-noise injection scaled by a factor alpha, and magnitude-binned degradation. The equal-baseline equivalence holds under realistic noise (alpha <= 2) on both surveys, with KAN and the regularized MLP agreeing to within a few tenths of a percentage point and the regularized MLP marginally ahead. A genuine KAN architectural advantage emerges only on SDSS under extreme, strongly heteroscedastic multi-band noise (+4.4 +/- 1.7 p.p. at alpha=10, p=0.004, robust across five seeds) and is absent on DESI. A band-ablation isolates the cause: the edge is driven entirely by the strongly heteroscedastic high-sigma u band, vanishing when u is excluded, and the g,r,z subset reproduces the DESI null on the same SDSS objects. Per class the edge is almost entirely a quasar effect (+13.3 p.p. in QSO F1). A direct measurement of the input-to-logit Jacobian explains the contrast: both weight decay and the KAN architecture suppress the Jacobian norm by roughly an order of magnitude relative to an unregularized MLP, and KAN's mean Jacobian is about 45% lower than the accuracy-matched regularized MLP, the mechanistic signature of its extreme-noise edge. Appending per-object uncertainties as input features does not help classification for any model. Real photometric noise therefore refines the implicit-regularizer account rather than overturning it: regularization, not architecture, drives KAN's noise robustness at realistic levels, while the strongly heteroscedastic extreme reveals a genuine architectural difference exactly where a lower average Jacobian predicts it.