Feedforward neural networks with ReLU activation functions are linear splines
(2017) In Bachelor's Theses in Mathematical Sciences NUMK01 20171Mathematics (Faculty of Engineering)
- Abstract
- In this thesis the approximation properties of feedforward articial
neural networks with one hidden layer and ReLU activation functions are examined. It is shown that functions of these kind are linear splines and the number of spline knots depend on the number of nodes in the network. In fact an upper bound can be derived for the number of knots. Furthermore, the positioning of the knots depend on the optimization of the adjustable parameters of the network. A numerical example is given where the network models are compared to linear interpolating splines with equidistant positioned knots.
Please use this url to cite or link to this publication:
http://lup.lub.lu.se/student-papers/record/8929048
- author
- Hansson, Magnus LU and Olsson, Christoffer LU
- supervisor
-
- Claus Führer LU
- Najmeh Abiri LU
- organization
- course
- NUMK01 20171
- year
- 2017
- type
- M2 - Bachelor Degree
- subject
- publication/series
- Bachelor's Theses in Mathematical Sciences
- report number
- LUNFNA-4017-2017
- ISSN
- 1654-6229
- other publication id
- 2017:K21
- language
- English
- id
- 8929048
- date added to LUP
- 2018-06-07 17:47:42
- date last changed
- 2018-06-07 17:47:42
@misc{8929048, abstract = {{In this thesis the approximation properties of feedforward articial neural networks with one hidden layer and ReLU activation functions are examined. It is shown that functions of these kind are linear splines and the number of spline knots depend on the number of nodes in the network. In fact an upper bound can be derived for the number of knots. Furthermore, the positioning of the knots depend on the optimization of the adjustable parameters of the network. A numerical example is given where the network models are compared to linear interpolating splines with equidistant positioned knots.}}, author = {{Hansson, Magnus and Olsson, Christoffer}}, issn = {{1654-6229}}, language = {{eng}}, note = {{Student Paper}}, series = {{Bachelor's Theses in Mathematical Sciences}}, title = {{Feedforward neural networks with ReLU activation functions are linear splines}}, year = {{2017}}, }