The paper presents a solution to binary classification with symmetric label noise (SLN). They show that, in order to obtain consistency (w.r.t. to the 0-1 loss in the "noiseless" case) while using a convex surrogate, one must use the loss $\ell(v,y) = 1 - vy$ -- the "unhinged loss" -- , which is shown to enjoy some useful properties, including robustness to SLN. In a more restricted sense of robustness, it is the only such loss, but in any case it overcomes the limitations of other convex losses for the same problem.

Different implications of using the unhinged loss are discussed; the problem of classification with SLN with the unhinged loss and "linear" classifiers is investigated and solved analytically. The authors also present an empirical evaluation to motivate that their theoretical considerations have practical impact.