In contrast to softmax loss, which can be viewed as a probabilistic version of zero-one loss, risk defines a probabilistic version of the translation error (Smith and Eisner 2006;Zens, Hasan, and Ney 2007;Li and Eisner 2009;He and Deng 2012).
risk is based on the expected error incurred by a probabilistic model parameterized by w. This combines the advantages of the probabilistic model in softmax loss with the direct consideration of translation accuracy afforded by using error directly.