Binary softmax decision boundary In this paper, in figure 4:



the decision boundaries are shown for different $W1$ and $W2$s. If the softmax classification forces either $W_1.x &gt; W_2.x$ or $W_1.x &lt; W_2.x$ for class 1 and class 2 respectively, then the decision boundary is $(W1-W2).x = 0$ which means that that the decision boundary is perpendicular to $W1-W2$. However in this figure only in the case where $||W1|| = ||W2||$ this is visually correct. In other cases, this is not the case. If one draws $W1-W2$, it won't be perpendicular to the decision boundary. 

Am I thinking right?
Yes you are right. But I think the authors only want to emphasize that if $||1|| &gt; ||2||$, the decision boundary will be closer to $2$ and vice versa.