what is the meaning of $\mathbb{R}^{768\times (768 * 2)}$?

Hi I'm an undergraduate student interested in Machine Learning. I was reading a paper from ICLR 2020 and came a cross a weird looking vector dimensions.

Can anyone tell me what this means??

$\mathbb{R}^{768\times (768 * 2)}$

Does this mean that in python numpy array the shape would probably be (2, 768, 768) ?? I remember reading that the numpy array dimensions are reversed from the actual vector dimensions representations. And the vector I asked about shows up in page 4.

Topic matrix matrix-factorisation machine-learning

Category Data Science

1
answered at

$\mathbb{R}^{m\times n}$ refers to the real-valued matrices of dimension $m$ by $n$.

$\mathbb{R}$ refers to real values (-$\infty$ to +$\infty$).

See here for an example, https://en.wikipedia.org/wiki/Matrix_(mathematics)#Notation

1
answered at

To my knowledge, that notation refers to a matrix which is of shape 768 by 1536. I am guessing the 2 is there to highlight that the dimension increase is proportional to the 768 (whether that is the input shape to a layer in a neural network, for example).

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