Reading the latest "author2vec" paper (Author2vec publication), I stumbled upon equations (1):
$h_C^{(x)}=v_u \odot v_p$
and (5): for the sake of this question consider it exactly as (1),
where they use a point within a circle ($\odot$) to represent the angle between the embedding vectors.
I'm familiar with the arccos way to get the angle between vectors (solving theta from the dot product definition), but I have never seen this notation to represent it before. I've googled it and found nothing.
Could anyone give some info about this notation? Specifically, if it actually represents the angle between vectors.
As JMoravitz stated in the comments, "$\odot$ is commonly used as a placeholder symbol for operations which are uncommon and are often defined in context". In this case, they (authors of the paper) define the operator in the preceding paragraph as the angle between the vectors, so in this context $\odot$ refers to this operation.