Abstract
In many areas of neural computation, like learning, optimization, estimation, and inference, suitable divergences play a key role. In this note, we study the conjecture presented by Amari (2009) and find a counterexample to show that the conjecture does not hold generally. Moreover, we investigate two classes of 
-divergence (Zhang, 2004), weighted f-divergence and weighted 
-divergence, and prove that if a divergence is a weighted f-divergence, as well as a Bregman divergence, then it is a weighted 
-divergence. This result reduces in form to the main theorem established by Amari (2009) when 
.