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Recent years have seen adversarial losses been applied to many fields. Theirapplications extend beyond the originally proposed generative modeling toconditional generative and discriminative settings. While prior work hasproposed various output activation functions and regularization approaches,some open questions still remain unanswered. In this paper, we aim to study thefollowing two research questions: 1) What types of output activation functionsform a well-behaved adversarial loss? 2) How different combinations of outputactivation functions and regularization approaches perform empirically againstone another? To answer the first question, we adopt the perspective ofvariational divergence minimization and consider an adversarial losswell-behaved if it behaves as a divergence-like measure between the data andmodel distributions. Using a generalized formulation for adversarial losses, wederive the necessary and sufficient conditions of a well-behaved adversarialloss. Our analysis reveals a large class of theoretically valid adversariallosses. For the second question, we propose a simple comparative framework foradversarial losses using discriminative adversarial networks. The proposedframework allows us to efficiently evaluate adversarial losses using a standardevaluation metric such as the classification accuracy. With the proposedframework, we evaluate a comprehensive set of 168 combinations of twelve outputactivation functions and fourteen regularization approaches on the handwrittendigit classification problem to decouple their effects. Our empirical findingssuggest that there is no single winning combination of output activationfunctions and regularization approaches across all settings. Our theoreticaland empirical results may together serve as a reference for choosing ordesigning adversarial losses in future research.

On Output Activation Functions for Adversarial Losses: A Theoretical  Analysis via Variational Divergence Minimization and An Empirical Study on  MNIST Classification