Matches in SemOpenAlex for { <https://semopenalex.org/work/W4386942885> ?p ?o ?g. }
Showing items 1 to 57 of
57
with 100 items per page.
- W4386942885 abstract "The universal approximation property of width-bounded networks has been studied as a dual of the classical universal approximation theorem for depth-bounded ones. There were several attempts to characterize the minimum width $w_{min}$ enabling the universal approximation property; however, only a few of them found the exact values. In this work, we show that the minimum width for the universal approximation of $L^p$ functions from $[0,1]^{d_x}$ to $mathbb R^{d_y}$ is exactly $max{d_x,d_y,2}$ if an activation function is ReLU-Like (e.g., ReLU, GELU, Softplus). Compared to the known result $w_{min}=max{d_x+1,d_y}$ when the domain is ${mathbb R^{d_x}}$, our result first shows that approximation on a compact domain requires smaller width than on ${mathbb R^{d_x}}$. We next prove a lower bound on $w_{min}$ for uniform approximation using general activation functions including ReLU: $w_{min}ge d_y+1$ if $d_x<d_yle2d_x$. Together with our first result, this shows a dichotomy between $L^p$ and uniform approximations for general activation functions and input/output dimensions." @default.
- W4386942885 created "2023-09-22" @default.
- W4386942885 creator A5004627880 @default.
- W4386942885 creator A5045935665 @default.
- W4386942885 creator A5078305669 @default.
- W4386942885 date "2023-09-19" @default.
- W4386942885 modified "2023-10-18" @default.
- W4386942885 title "Minimum width for universal approximation using ReLU networks on compact domain" @default.
- W4386942885 doi "https://doi.org/10.48550/arxiv.2309.10402" @default.
- W4386942885 hasPublicationYear "2023" @default.
- W4386942885 type Work @default.
- W4386942885 citedByCount "0" @default.
- W4386942885 crossrefType "posted-content" @default.
- W4386942885 hasAuthorship W4386942885A5004627880 @default.
- W4386942885 hasAuthorship W4386942885A5045935665 @default.
- W4386942885 hasAuthorship W4386942885A5078305669 @default.
- W4386942885 hasBestOaLocation W43869428851 @default.
- W4386942885 hasConcept C114614502 @default.
- W4386942885 hasConcept C117148685 @default.
- W4386942885 hasConcept C118615104 @default.
- W4386942885 hasConcept C121332964 @default.
- W4386942885 hasConcept C134306372 @default.
- W4386942885 hasConcept C14036430 @default.
- W4386942885 hasConcept C148764684 @default.
- W4386942885 hasConcept C33923547 @default.
- W4386942885 hasConcept C34388435 @default.
- W4386942885 hasConcept C36503486 @default.
- W4386942885 hasConcept C78458016 @default.
- W4386942885 hasConcept C86803240 @default.
- W4386942885 hasConceptScore W4386942885C114614502 @default.
- W4386942885 hasConceptScore W4386942885C117148685 @default.
- W4386942885 hasConceptScore W4386942885C118615104 @default.
- W4386942885 hasConceptScore W4386942885C121332964 @default.
- W4386942885 hasConceptScore W4386942885C134306372 @default.
- W4386942885 hasConceptScore W4386942885C14036430 @default.
- W4386942885 hasConceptScore W4386942885C148764684 @default.
- W4386942885 hasConceptScore W4386942885C33923547 @default.
- W4386942885 hasConceptScore W4386942885C34388435 @default.
- W4386942885 hasConceptScore W4386942885C36503486 @default.
- W4386942885 hasConceptScore W4386942885C78458016 @default.
- W4386942885 hasConceptScore W4386942885C86803240 @default.
- W4386942885 hasLocation W43869428851 @default.
- W4386942885 hasOpenAccess W4386942885 @default.
- W4386942885 hasPrimaryLocation W43869428851 @default.
- W4386942885 hasRelatedWork W1598979804 @default.
- W4386942885 hasRelatedWork W1978042415 @default.
- W4386942885 hasRelatedWork W2018828049 @default.
- W4386942885 hasRelatedWork W2042726902 @default.
- W4386942885 hasRelatedWork W2046712581 @default.
- W4386942885 hasRelatedWork W2136053165 @default.
- W4386942885 hasRelatedWork W2370340664 @default.
- W4386942885 hasRelatedWork W2951043270 @default.
- W4386942885 hasRelatedWork W3102909640 @default.
- W4386942885 hasRelatedWork W4294364856 @default.
- W4386942885 isParatext "false" @default.
- W4386942885 isRetracted "false" @default.
- W4386942885 workType "article" @default.