I am familiar with undergrad level linear algebra, but we have not covered neither tensors nor anything more algebraic than a matrix/dot product. I do perfectly understand what an elementwise product means, but I don't have experience with Kronecker product, tensor product etc. So I need some help clarifying the relevant notation and notions.
While reading the paper introducing GLU I've come accross a notation $a\otimes b$ where $a$ and $b$ apparently are two vectors and $\otimes$ is the elementwise product. Yet, from what I recall that $\otimes$ used to denote Kronecker product, which as little as I am familiar with it still differs significantly from the elementwise product. If I google though, I see that $\otimes$ also denotes the tensor product.
I perfectly understand that we only have that many TeX symbols (actually, quite some of them), and if a paper clearly states that $\otimes, \times, \cdot,+, *$ or even $-$ is the elementwise product there, then they have all the rights to use that. Yet, I guess using say $-$ will be very confusing as it usually means subtraction, $+$ addition, $*$ convolution etc.
My question hence is: is $\otimes$ indeed often used in tensor algebra to denote elementwise products?