The hinge loss with G_W(X)=W^T X and a ||W||^2 regularizer gives the linear support vector machine.

Judge as a mathematical fact. True: minimising the hinge loss on a linear score W^T X (using the margin or label formulation in LeCun et al.'s 2006 energy-based learning tutorial) plus an L2 penalty ||W||^2 gives the standard soft-margin linear SVM objective. Mostly true: the equivalence holds up to minor details (a bias term, scaling constants, or a margin parameter). Mixed: it holds only under substantial extra assumptions. Mostly false: the resulting objective differs materially from the SVM. False: the formulation does not correspond to a linear SVM.

Set before the research began.

1. E1 Yann LeCun NYU Courant Institute (talk slides, author's own) Own record

   “Linear Model + Margin Loss + Regularization = SVM”

2. E2 Yann LeCun NYU Courant Institute (talk slides, author's own) Own record

   “Minimize the Regularization term: Make W as short as possible.”

3. E3 Yann LeCun NYU Courant Institute (talk slides, author's own) Own record

   “You get a Support Vector Machine.”

The criteria ask for a judgement on the mathematics. Minimising the hinge loss max(0, m − Y·WᵀX) summed over samples, plus λ||W||², is the soft-margin linear SVM objective up to how the constants are scaled. The match is not exact because G_W(X)=WᵀX has no separate bias term, which the standard SVM includes. Under the criteria that is a minor detail, so the verdict is mostly true rather than true. LeCun's own slides (E1, E2, E3) say the same thing ("Linear Model + Margin Loss + Regularization = SVM"), but they are not independent, so the verdict rests on checking the mathematics, not on the slides.