Task Specific Adversarial Cost Function

The cost function used to train a generative model should fit the purpose of the model. If the model is intended for tasks such as generating perceptually correct samples, it is beneficial to maximise the likelihood of a sample drawn from the model, Q, coming from the same distribution as the training data, P. This is equivalent to minimising the Kullback-Leibler (KL) distance, KL[Q||P]. However, if the model is intended for tasks such as retrieval or classification it is beneficial to maximise the likelihood that a sample drawn from the training data is captured by the model, equivalent to minimising KL[P||Q]. The cost function used in adversarial training optimises the Jensen-Shannon entropy which can be seen as an even interpolation between KL[Q||P] and KL[P||Q]. Here, we propose an alternative adversarial cost function which allows easy tuning of the model for either task. Our task specific cost function is evaluated on a dataset of hand-written characters in the following tasks: Generation, retrieval and one-shot learning.