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- W4232647113 abstract "Inspired by the architecture of multilayer feedforward networks on Euclidean spaces, we introduce multilayer functionals: a new parametric family of real valued mappings on arbitrary normed linear spaces. We establish that multilayer functionals on a normed linear space can uniformly approximate on compact sets any continuous functional on the normed linear space. Multilayer functionals are then employed to define multilayer operators: a new parametric family of operators on certain spaces of real valued functions (or sequences) on the real line. We establish that multilayer operators can provide an input-output representation, in a certain sense, for any time-invariant system characterized by a continuous functional. We show that the systems representable by multilayer operators are necessarily stable and continuous, but can be continuous-time or discrete-time, finite or infinite memory, causal or noncausal, and linear or nonlinear. We exemplify the developed theory for multilayer operators by providing explicit representations for two practical classes of systems." @default.
- W4232647113 created "2022-05-12" @default.
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- W4232647113 date "1993-01-01" @default.
- W4232647113 modified "2023-09-26" @default.
- W4232647113 title "Multilayer Functional" @default.
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- W4232647113 doi "https://doi.org/10.1016/s0924-6509(08)70039-4" @default.
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