### Web: http://arxiv.org/abs/2206.07199

June 16, 2022, 1:10 a.m. | Alireza Fathollah Pour, Hassan Ashtiani

We observe that given two (compatible) classes of functions $\mathcal{F}$ and
$\mathcal{H}$ with small capacity as measured by their uniform covering
numbers, the capacity of the composition class $\mathcal{H} \circ \mathcal{F}$
can become prohibitively large or even unbounded. We then show that adding a
small amount of Gaussian noise to the output of $\mathcal{F}$ before composing
it with $\mathcal{H}$ can effectively control the capacity of $\mathcal{H} \circ \mathcal{F}$, offering a general recipe for modular design. To prove our
results, we …

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