המתח בין הלוגיקה לזיכרון: למידת התנגשויות של סדר גבוה ב-MLPs עם שכבה אחת

תקציר מקורי באנגליתarXiv:2610.00403v1 Announce Type: new Abstract: A network can fit its training examples while failing to recover the rule that generated their labels. We examine this separation in single-hidden-layer multilayer perceptrons (MLPs), using synthetic tasks that control interaction order and the presence of nuisance inputs. We establish elementary benchmark properties: pure parity contains no predictive lower-order marginals, admits an exact Bayes posterior, and can be represented on clean latent inputs by a width-$k$ ReLU network. Experiments then identify distinct optimization outcomes. In a matched order-2--4 sweep, SGD, Adam, and Muon all reach 100\% peak test accuracy at order two; at order three they reach 96.25\%, 50.87\%, and 76.82\%, respectively, while Muon reaches 99.21\% at order f