I have three vectors $x,y_1,y_2\in\mathbb{R}^{n\times 1}$, where $x=y_1$, $x\perp y_2$. If I use $x$ as input of a 2-layer perceptron, will regressing $y_1$ be easier than $y_2$ (i.e., when fully trained, $\mathcal{L}_{(x,y_1)}<\mathcal{L}_{(x,y_2)}$)? If this is false, how about changing the perceptron to a 2-layer graph neural network (GNN)? I am expecting some rigorous math analysis, but I seem can not figure it out.



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