Approximation capability of two hidden layer feedforward neural networks with fixed weights
Copyright policy )Approximation capability of two hidden layer feedforward neural networks with fixed weights
We algorithmically construct a two hidden layer feedforward neural network (TLFN) model with the weights fixed as the unit coordinate vectors of the $d$-dimensional Euclidean space and having $3d+2$ number of hidden neurons in total, which can approximate any continuous $d$-variable function with an arbitrary precision. This result, in particular, shows an advantage of the TLFN model over the single hidden layer feedforward neural network (SLFN) model, since SLFNs with fixed weights do not have the capability of approximating multivariate functions.
13 pages, 3 figures; this article uses the algorithm from arXiv:1708.06219; for associated SageMath worksheet, see https://sites.google.com/site/njguliyev/papers/tlfn
- Institute of Mathematics and Mechanics Azerbaijan
- Azerbaijan National Academy of Sciences Azerbaijan
FOS: Computer and information sciences, Computer Science - Information Theory, multilayer feedforward neural network, [INFO.INFO-NE] Computer Science [cs]/Neural and Evolutionary Computing [cs.NE], 41A30, 41A63, 65D15, 68T05, 92B20, hidden layer, [MATH.MATH-IT] Mathematics [math]/Information Theory [math.IT], C.1.3, FOS: Mathematics, C.1.3; F.1.1; I.2.6; I.5.1, activation function, Mathematics - Numerical Analysis, Neural and Evolutionary Computing (cs.NE), I.5.1, I.2.6, Information Theory (cs.IT), Computer Science - Neural and Evolutionary Computing, weight, Numerical Analysis (math.NA), [MATH.MATH-NA] Mathematics [math]/Numerical Analysis [math.NA], sigmoidal function, the Kolmogorov superposition theorem, [INFO.INFO-IT] Computer Science [cs]/Information Theory [cs.IT], F.1.1
FOS: Computer and information sciences, Computer Science - Information Theory, multilayer feedforward neural network, [INFO.INFO-NE] Computer Science [cs]/Neural and Evolutionary Computing [cs.NE], 41A30, 41A63, 65D15, 68T05, 92B20, hidden layer, [MATH.MATH-IT] Mathematics [math]/Information Theory [math.IT], C.1.3, FOS: Mathematics, C.1.3; F.1.1; I.2.6; I.5.1, activation function, Mathematics - Numerical Analysis, Neural and Evolutionary Computing (cs.NE), I.5.1, I.2.6, Information Theory (cs.IT), Computer Science - Neural and Evolutionary Computing, weight, Numerical Analysis (math.NA), [MATH.MATH-NA] Mathematics [math]/Numerical Analysis [math.NA], sigmoidal function, the Kolmogorov superposition theorem, [INFO.INFO-IT] Computer Science [cs]/Information Theory [cs.IT], F.1.1
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