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In this technical report we describe some properties of f-divergences and f-GAN training. We present an elementary derivation of the f-divergence lower bounds which form the basis of f-GAN training. We derive informative but perhaps underappreciated properties of f-divergences and f-GAN training, including a gradient matching property and the fact that all f-divergences agree up to an overall scale factor on the divergence between nearby distributions. We provide detailed expressions forarXiv:2009.00757v1 fatcat:xh3mkhck3vbuzgo6nmjzxtvybq