Commit 2470b43b authored by Michael Wimmer's avatar Michael Wimmer
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fix figure link

parent 6972f322
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......@@ -100,7 +100,9 @@ is trained on dimensions $\leq 3$.
Let us look at a simple example. Consider two hybercubes in $d$ dimensions. The two hybercubes have side lengths $L$, so their
volume is $L^d$. We now consider that the two hypercubes are shifted slightly with respect to each other, such that their overlap
in every Cartesian coordinate direction is $\varepsilon L$ with $\varepsilon < 1$, as schematically sketched in 2D below:
![Vanishing overlap in high dimensions](highd-overlap.svg)
![Vanishing overlap in high dimensions](figures/highd-overlap.svg)
We can now compute the ratio of the overlap volume to the volume of the hybercubes and find
$$\frac{(\varepsilon L)^d}{L^d} = \varepsilon^d \xrightarrow{d\rightarrow \infty} 0!$$
So even for a slight shift, the overlap ratio will decrease exponentially with dimension.
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