| Texto completo | |
| Autor(es): |
Vital, Wington L.
;
Vieira, Guilherme
;
Valle, Marcos Eduardo
;
Xavier-Junior, JC
;
Rios, RA
Número total de Autores: 5
|
| Tipo de documento: | Artigo Científico |
| Fonte: | INTELLIGENT SYSTEMS, PT II; v. 13654, p. 15-pg., 2022-01-01. |
| Resumo | |
The universal approximation theorem asserts that a single hidden layer neural network approximates continuous functions with any desired precision on compact sets. As an existential result, the universal approximation theorem supports the use of neural networks for various applications, including regression and classification tasks. The universal approximation theorem is not limited to real-valued neural networks but also holds for complex, quaternion, tessarines, and Clifford-valued neural networks. This paper extends the universal approximation theorem for a broad class of hypercomplex-valued neural networks. Precisely, we first introduce the concept of non-degenerate hypercomplex algebra. Complex numbers, quaternions, and tessarines are examples of non-degenerate hypercomplex algebras. Then, we state the universal approximation theorem for hypercomplex-valued neural networks defined on a non-degenerate algebra. (AU) | |
| Processo FAPESP: | 22/01831-2 - Redes neurais artificiais de valor hipercomplexo: além dos números complexos e quaternios |
| Beneficiário: | Marcos Eduardo Ribeiro Do Valle Mesquita |
| Modalidade de apoio: | Auxílio à Pesquisa - Regular |