Comparison of ReLU and linear saturated activation functions in neural network for universal approximation Article Swipe
Dominik Štursa
,
Petr Doležel
·
YOU?
·
· 2019
· Open Access
·
· DOI: https://doi.org/10.1109/pc.2019.8815057
YOU?
·
· 2019
· Open Access
·
· DOI: https://doi.org/10.1109/pc.2019.8815057
Activation functions used in hidden layers directly affect the possibilities for describing nonlinear systems using a feedforward neural network. Furthermore, linear based activation functions are less computationally demanding than their nonlinear alternatives. In addition, feedforward neural networks with linear based activation functions can be advantageously used for control of nonlinear systems, as shown in previous authors' publications. This paper aims to compare two types of linear based functions - symmetric linear saturated function and the rectifier linear unit (ReLU) function as activation functions of the feedforward neural network used for a nonlinear system approximation. Topologies with one hidden layer and the combination of defined quantities of hidden layer neurons in the feedforward neural network are used. Strict criteria are applied for the conditions of the experiments; specifically, the Levenberg-Marquardt algorithm is applied as a training algorithm and the Nguyen-Widrow algorithm is used for the weights and biases initialization. Three benchmark systems are then selected as nonlinear plants for approximation, which should serve as a repeatable source of data for testing. The training data are acquired by the computation of the output as a reaction to a specified colored input signal. The comparison is based on the convergence speed of the training for a fixed value of the error function, and also on the performance over a constant number of epochs. At the end of the experiments, only small differences between the performance of both applied activation functions are observed. Although the symmetric linear saturated activation function provides the lesser median of the final error function value across the all tested numbers of neurons in topologies, the ReLU function seems to be also capable of use as the activation function for nonlinear system modeling.
Related Topics
Concepts
Activation function
Feedforward neural network
Artificial neural network
Rectifier (neural networks)
Initialization
Computer science
Nonlinear system
Feed forward
Control theory (sociology)
Algorithm
Function approximation
Mathematics
Time delay neural network
Artificial intelligence
Stochastic neural network
Engineering
Programming language
Physics
Quantum mechanics
Control engineering
Control (management)
Metadata
- Type
- article
- Language
- en
- Landing Page
- https://doi.org/10.1109/pc.2019.8815057
- OA Status
- green
- Cited By
- 47
- References
- 13
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W2971145620
All OpenAlex metadata
Raw OpenAlex JSON
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https://openalex.org/W2971145620Canonical identifier for this work in OpenAlex
- DOI
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https://doi.org/10.1109/pc.2019.8815057Digital Object Identifier
- Title
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Comparison of ReLU and linear saturated activation functions in neural network for universal approximationWork title
- Type
-
articleOpenAlex work type
- Language
-
enPrimary language
- Publication year
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2019Year of publication
- Publication date
-
2019-06-01Full publication date if available
- Authors
-
Dominik Štursa, Petr DoleželList of authors in order
- Landing page
-
https://doi.org/10.1109/pc.2019.8815057Publisher landing page
- Open access
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YesWhether a free full text is available
- OA status
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greenOpen access status per OpenAlex
- OA URL
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https://hdl.handle.net/10195/75129Direct OA link when available
- Concepts
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Activation function, Feedforward neural network, Artificial neural network, Rectifier (neural networks), Initialization, Computer science, Nonlinear system, Feed forward, Control theory (sociology), Algorithm, Function approximation, Mathematics, Time delay neural network, Artificial intelligence, Stochastic neural network, Engineering, Programming language, Physics, Quantum mechanics, Control engineering, Control (management)Top concepts (fields/topics) attached by OpenAlex
- Cited by
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47Total citation count in OpenAlex
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2025: 4, 2024: 10, 2023: 5, 2022: 14, 2021: 7Per-year citation counts (last 5 years)
- References (count)
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13Number of works referenced by this work
- Related works (count)
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10Other works algorithmically related by OpenAlex
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| abstract_inverted_index.for | 10, 46, 89, 120, 142, 157, 168, 201, 279 |
| abstract_inverted_index.one | 96 |
| abstract_inverted_index.the | 8, 74, 84, 100, 110, 121, 124, 127, 137, 143, 176, 179, 195, 199, 206, 212, 221, 224, 230, 240, 247, 251, 257, 265, 276 |
| abstract_inverted_index.two | 62 |
| abstract_inverted_index.use | 274 |
| abstract_inverted_index.ReLU | 266 |
| abstract_inverted_index.This | 57 |
| abstract_inverted_index.aims | 59 |
| abstract_inverted_index.also | 210, 271 |
| abstract_inverted_index.both | 233 |
| abstract_inverted_index.data | 167, 172 |
| abstract_inverted_index.less | 25 |
| abstract_inverted_index.only | 226 |
| abstract_inverted_index.over | 214 |
| abstract_inverted_index.than | 28 |
| abstract_inverted_index.then | 152 |
| abstract_inverted_index.unit | 77 |
| abstract_inverted_index.used | 2, 45, 88, 141 |
| abstract_inverted_index.with | 37, 95 |
| abstract_inverted_index.Three | 148 |
| abstract_inverted_index.based | 21, 39, 66, 193 |
| abstract_inverted_index.error | 207, 253 |
| abstract_inverted_index.final | 252 |
| abstract_inverted_index.fixed | 203 |
| abstract_inverted_index.input | 188 |
| abstract_inverted_index.layer | 98, 107 |
| abstract_inverted_index.paper | 58 |
| abstract_inverted_index.seems | 268 |
| abstract_inverted_index.serve | 161 |
| abstract_inverted_index.shown | 52 |
| abstract_inverted_index.small | 227 |
| abstract_inverted_index.speed | 197 |
| abstract_inverted_index.their | 29 |
| abstract_inverted_index.types | 63 |
| abstract_inverted_index.used. | 115 |
| abstract_inverted_index.using | 14 |
| abstract_inverted_index.value | 204, 255 |
| abstract_inverted_index.which | 159 |
| abstract_inverted_index.(ReLU) | 78 |
| abstract_inverted_index.Strict | 116 |
| abstract_inverted_index.across | 256 |
| abstract_inverted_index.affect | 7 |
| abstract_inverted_index.biases | 146 |
| abstract_inverted_index.hidden | 4, 97, 106 |
| abstract_inverted_index.layers | 5 |
| abstract_inverted_index.lesser | 248 |
| abstract_inverted_index.linear | 20, 38, 65, 70, 76, 242 |
| abstract_inverted_index.median | 249 |
| abstract_inverted_index.neural | 17, 35, 86, 112 |
| abstract_inverted_index.number | 217 |
| abstract_inverted_index.output | 180 |
| abstract_inverted_index.plants | 156 |
| abstract_inverted_index.should | 160 |
| abstract_inverted_index.source | 165 |
| abstract_inverted_index.system | 92, 281 |
| abstract_inverted_index.tested | 259 |
| abstract_inverted_index.applied | 119, 131, 234 |
| abstract_inverted_index.between | 229 |
| abstract_inverted_index.capable | 272 |
| abstract_inverted_index.colored | 187 |
| abstract_inverted_index.compare | 61 |
| abstract_inverted_index.control | 47 |
| abstract_inverted_index.defined | 103 |
| abstract_inverted_index.epochs. | 219 |
| abstract_inverted_index.network | 87, 113 |
| abstract_inverted_index.neurons | 108, 262 |
| abstract_inverted_index.numbers | 260 |
| abstract_inverted_index.signal. | 189 |
| abstract_inverted_index.systems | 13, 150 |
| abstract_inverted_index.weights | 144 |
| abstract_inverted_index.Although | 239 |
| abstract_inverted_index.acquired | 174 |
| abstract_inverted_index.constant | 216 |
| abstract_inverted_index.criteria | 117 |
| abstract_inverted_index.directly | 6 |
| abstract_inverted_index.function | 72, 79, 245, 254, 267, 278 |
| abstract_inverted_index.network. | 18 |
| abstract_inverted_index.networks | 36 |
| abstract_inverted_index.previous | 54 |
| abstract_inverted_index.provides | 246 |
| abstract_inverted_index.reaction | 183 |
| abstract_inverted_index.selected | 153 |
| abstract_inverted_index.systems, | 50 |
| abstract_inverted_index.testing. | 169 |
| abstract_inverted_index.training | 134, 171, 200 |
| abstract_inverted_index.addition, | 33 |
| abstract_inverted_index.algorithm | 129, 135, 139 |
| abstract_inverted_index.benchmark | 149 |
| abstract_inverted_index.demanding | 27 |
| abstract_inverted_index.function, | 208 |
| abstract_inverted_index.functions | 1, 23, 41, 67, 82, 236 |
| abstract_inverted_index.modeling. | 282 |
| abstract_inverted_index.nonlinear | 12, 30, 49, 91, 155, 280 |
| abstract_inverted_index.observed. | 238 |
| abstract_inverted_index.rectifier | 75 |
| abstract_inverted_index.saturated | 71, 243 |
| abstract_inverted_index.specified | 186 |
| abstract_inverted_index.symmetric | 69, 241 |
| abstract_inverted_index.Activation | 0 |
| abstract_inverted_index.Topologies | 94 |
| abstract_inverted_index.activation | 22, 40, 81, 235, 244, 277 |
| abstract_inverted_index.comparison | 191 |
| abstract_inverted_index.conditions | 122 |
| abstract_inverted_index.describing | 11 |
| abstract_inverted_index.quantities | 104 |
| abstract_inverted_index.repeatable | 164 |
| abstract_inverted_index.combination | 101 |
| abstract_inverted_index.computation | 177 |
| abstract_inverted_index.convergence | 196 |
| abstract_inverted_index.differences | 228 |
| abstract_inverted_index.feedforward | 16, 34, 85, 111 |
| abstract_inverted_index.performance | 213, 231 |
| abstract_inverted_index.topologies, | 264 |
| abstract_inverted_index.Furthermore, | 19 |
| abstract_inverted_index.experiments, | 225 |
| abstract_inverted_index.experiments; | 125 |
| abstract_inverted_index.Nguyen-Widrow | 138 |
| abstract_inverted_index.alternatives. | 31 |
| abstract_inverted_index.possibilities | 9 |
| abstract_inverted_index.publications. | 56 |
| abstract_inverted_index.specifically, | 126 |
| abstract_inverted_index.advantageously | 44 |
| abstract_inverted_index.approximation, | 158 |
| abstract_inverted_index.approximation. | 93 |
| abstract_inverted_index.computationally | 26 |
| abstract_inverted_index.initialization. | 147 |
| abstract_inverted_index.authors' | 55 |
| abstract_inverted_index.Levenberg-Marquardt | 128 |
| cited_by_percentile_year.max | 99 |
| cited_by_percentile_year.min | 90 |
| countries_distinct_count | 1 |
| institutions_distinct_count | 2 |
| citation_normalized_percentile.value | 0.95104075 |
| citation_normalized_percentile.is_in_top_1_percent | False |
| citation_normalized_percentile.is_in_top_10_percent | True |