Arbitrary nonlinearity is sufficient to represent all functions by neural networks: A theorem
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Summary
It is proved that if the authors have neurons implementing arbitrary linear functions and a neuron implementing one (arbitrary but smooth) nonlinear function g(x), then for every continuous function f(x1, …, xm) of arbitrarily many variables and for arbitrary e > 0 they can construct a network that consists of g-neurons and linear neurons and computes f with precision e.
- Type
- article
- Published
- 1991-06-01
- Cited by
- 166
- References
- 10
- OpenAlex
- https://openalex.org/W1988358579
- Semantic Scholar
- https://api.semanticscholar.org/CorpusID:20840813
Keywords
Artificial neural network, Nonlinear system, Construct (python library), Function (biology), Mathematics
References
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- Multilayer feedforward networks are universal approximators
- Parallel distributed processing: explorations in the microstructure of cognition, vol. 1: foundations
- Kolmogorov''s Mapping Neural Network Existence Theorem
- Group-theoretic approach to intractable problems
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