For continuous/holder function $f$ defined on a compact set K， a fix $L$ and $m_1,m_2,\dots,m_L$, can we find a multilayer Relu fully connected network g with depth $L$ and each $i$-th layer has width $m_i$, so that it approximate f well，I.e. $||f-g||_{C^0(K)}\le C||f||$ ,where $C$ depend on $L，m$ etc.，$||f||$ is an appropriate norm.e.g. lipschetz/hilder constant.
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$\begingroup$ The way this question is phrased doesn't seem right to me. You can take $g$ to be identically zero in which case any $C\geq 1$ works. $\endgroup$– KhashFCommented Nov 22, 2023 at 15:54
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1$\begingroup$ Obviously no. You need to work with a stronger norm on $f$ for such result to hold. $\endgroup$– alesiaCommented Nov 22, 2023 at 19:59
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$\begingroup$ @alesia, yes，it is a misprint.I meant another norm，like lipschetz constant or others. $\endgroup$– Hao YuCommented Nov 23, 2023 at 0:21
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