Imposing Star-Shaped Hard Constraints on the Neural Network Output
A problem of imposing hard constraints on the neural network output can be met in many applications. We propose a new method for solving this problem for non-convex constraints that are star-shaped. A region produced by constraints is called star-shaped when there exists an origin in the region from...
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MDPI AG
2024-11-01
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| Series: | Mathematics |
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| author | Andrei Konstantinov Lev Utkin Vladimir Muliukha |
| author_facet | Andrei Konstantinov Lev Utkin Vladimir Muliukha |
| author_sort | Andrei Konstantinov |
| collection | DOAJ |
| description | A problem of imposing hard constraints on the neural network output can be met in many applications. We propose a new method for solving this problem for non-convex constraints that are star-shaped. A region produced by constraints is called star-shaped when there exists an origin in the region from which every point is visible. Two tasks are considered: to generate points inside the region and on the region boundary. The key idea behind the method is to generate a shift of the origin towards a ray parameterized by the additional layer of the neural network. The largest admissible shift is determined by the differentiable Ray marching algorithm. This allows us to generate points which are guaranteed to satisfy the constraints. A more accurate modification of the algorithm is also studied. The proposed method can be regarded as a generalization of the methods for convex constraints. Numerical experiments illustrate the method by solving machine-learning problems. The code implementing the method is publicly available. |
| format | Article |
| id | doaj-art-c62befeacf2d4f34bbad4fa46a61f84c |
| institution | OA Journals |
| issn | 2227-7390 |
| language | English |
| publishDate | 2024-11-01 |
| publisher | MDPI AG |
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| series | Mathematics |
| spelling | doaj-art-c62befeacf2d4f34bbad4fa46a61f84c2025-08-20T01:55:33ZengMDPI AGMathematics2227-73902024-11-011223378810.3390/math12233788Imposing Star-Shaped Hard Constraints on the Neural Network OutputAndrei Konstantinov0Lev Utkin1Vladimir Muliukha2Higher School of Artificial Intelligence Technologies, Peter the Great St. Petersburg Polytechnic University, Polytechnicheskaya, 29, 195251 St. Petersburg, RussiaHigher School of Artificial Intelligence Technologies, Peter the Great St. Petersburg Polytechnic University, Polytechnicheskaya, 29, 195251 St. Petersburg, RussiaHigher School of Artificial Intelligence Technologies, Peter the Great St. Petersburg Polytechnic University, Polytechnicheskaya, 29, 195251 St. Petersburg, RussiaA problem of imposing hard constraints on the neural network output can be met in many applications. We propose a new method for solving this problem for non-convex constraints that are star-shaped. A region produced by constraints is called star-shaped when there exists an origin in the region from which every point is visible. Two tasks are considered: to generate points inside the region and on the region boundary. The key idea behind the method is to generate a shift of the origin towards a ray parameterized by the additional layer of the neural network. The largest admissible shift is determined by the differentiable Ray marching algorithm. This allows us to generate points which are guaranteed to satisfy the constraints. A more accurate modification of the algorithm is also studied. The proposed method can be regarded as a generalization of the methods for convex constraints. Numerical experiments illustrate the method by solving machine-learning problems. The code implementing the method is publicly available.https://www.mdpi.com/2227-7390/12/23/3788neural networkhard constraintsstar-shaped regionRay marchingclassification |
| spellingShingle | Andrei Konstantinov Lev Utkin Vladimir Muliukha Imposing Star-Shaped Hard Constraints on the Neural Network Output Mathematics neural network hard constraints star-shaped region Ray marching classification |
| title | Imposing Star-Shaped Hard Constraints on the Neural Network Output |
| title_full | Imposing Star-Shaped Hard Constraints on the Neural Network Output |
| title_fullStr | Imposing Star-Shaped Hard Constraints on the Neural Network Output |
| title_full_unstemmed | Imposing Star-Shaped Hard Constraints on the Neural Network Output |
| title_short | Imposing Star-Shaped Hard Constraints on the Neural Network Output |
| title_sort | imposing star shaped hard constraints on the neural network output |
| topic | neural network hard constraints star-shaped region Ray marching classification |
| url | https://www.mdpi.com/2227-7390/12/23/3788 |
| work_keys_str_mv | AT andreikonstantinov imposingstarshapedhardconstraintsontheneuralnetworkoutput AT levutkin imposingstarshapedhardconstraintsontheneuralnetworkoutput AT vladimirmuliukha imposingstarshapedhardconstraintsontheneuralnetworkoutput |