Norm type in cost function of ANN
Reading the article they state that 


  The two vertical lines represent the $L^2$ norm of the error, or what is known as the sum-of-squares error (SSE)


Otherwise known as the Euclidean norm, Euclidean length, $L^2$ distance, $ℓ^2$ distance, $L^2$ norm, $ℓ^2$ norm, $2$-norm, or square norm.

Also speaking from my experience, most of the time when a norm is specified without a subscript then you can generally assume that it is the Euclidean norm.