The generalized perceptron loss is always positive because its second term is a lower bound on its first term.

Use the generalized perceptron loss as defined in the 2006 source (LeCun et al., 'A Tutorial on Energy-Based Learning'): the energy of the correct answer minus the minimum energy over all answers. 'Positive' is read in its loose sense of non-negative. TRUE: under that definition, the second term (the minimum over all Y, which includes the correct answer) is always less than or equal to the first term, so the loss can never be negative. Cases where the loss equals zero do not count against the claim. MOSTLY TRUE: the loss is non-negative only under a mild condition in the definition (for example, that the minimum is taken over a set that includes the correct answer), and the source states that condition elsewhere. MOSTLY FALSE: the loss is non-negative only under significant extra assumptions that the source does not state. FALSE: under the source's definition the loss can be negative, because the second term is not a lower bound on the first.

Set before the research began.

1. E1 A tutorial on energy-based - Yann LeCun Yann LeCun (yann.lecun.com) · 19 August 2006 Own record

   “the learning procedure must shape the energy surface so that the desired value of Y has lower energy than all other (undesired) values.”

The resolution criteria fix the loss as the energy of the correct answer minus the minimum energy over all answers. The 2006 tutorial (E2) treats the desired value of Y as one of the values of Y that the energy is compared over, so the minimum is taken over a set that includes the correct answer. A minimum over a set that includes the correct answer can never exceed that answer's energy, so the second term is a lower bound on the first and the loss is never negative. Under the criteria, cases where the loss is zero do not count against the claim.