Details
| Original language | English |
|---|---|
| Pages (from-to) | 931-954 |
| Number of pages | 24 |
| Journal | Journal of Optimization Theory and Applications |
| Volume | 199 |
| Early online date | 25 Oct 2023 |
| Publication status | Published - Dec 2023 |
Abstract
The literature has shown how to optimize and analyze the parameters of different types of neural networks using mixed integer linear programs (MILP). Building on these developments, this work presents an approach to do so for a McCulloch/Pitts and Rosenblatt neurons. As the original formulation involves a step-function, it is not differentiable, but it is possible to optimize the parameters of neurons, and their concatenation as a shallow neural network, by using a mixed integer linear program. The main contribution of this paper is to additionally enforce sparsity constraints on the weights and activations as well as on the amount of used neurons. Several experiments demonstrate that such constraints effectively prevent overfitting in neural networks, and ensure resource optimized models.
Keywords
- Feature selection, Mixed integer linear programming, Neural networks, Resource optimization, Sparse networks
ASJC Scopus subject areas
- Mathematics(all)
- Control and Optimization
- Decision Sciences(all)
- Management Science and Operations Research
- Mathematics(all)
- Applied Mathematics
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In: Journal of Optimization Theory and Applications, Vol. 199, 12.2023, p. 931-954.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Optimization of Sparsity-Constrained Neural Networks as a Mixed Integer Linear Program
T2 - NN2MILP
AU - Rosenhahn, Bodo
N1 - Funding Information: The author received support from Leibniz Universität Hannover, Germany, and thanks the colleagues who provided the datasets used in this manuscript. All datasets are publicly available.
PY - 2023/12
Y1 - 2023/12
N2 - The literature has shown how to optimize and analyze the parameters of different types of neural networks using mixed integer linear programs (MILP). Building on these developments, this work presents an approach to do so for a McCulloch/Pitts and Rosenblatt neurons. As the original formulation involves a step-function, it is not differentiable, but it is possible to optimize the parameters of neurons, and their concatenation as a shallow neural network, by using a mixed integer linear program. The main contribution of this paper is to additionally enforce sparsity constraints on the weights and activations as well as on the amount of used neurons. Several experiments demonstrate that such constraints effectively prevent overfitting in neural networks, and ensure resource optimized models.
AB - The literature has shown how to optimize and analyze the parameters of different types of neural networks using mixed integer linear programs (MILP). Building on these developments, this work presents an approach to do so for a McCulloch/Pitts and Rosenblatt neurons. As the original formulation involves a step-function, it is not differentiable, but it is possible to optimize the parameters of neurons, and their concatenation as a shallow neural network, by using a mixed integer linear program. The main contribution of this paper is to additionally enforce sparsity constraints on the weights and activations as well as on the amount of used neurons. Several experiments demonstrate that such constraints effectively prevent overfitting in neural networks, and ensure resource optimized models.
KW - Feature selection
KW - Mixed integer linear programming
KW - Neural networks
KW - Resource optimization
KW - Sparse networks
UR - http://www.scopus.com/inward/record.url?scp=85174828680&partnerID=8YFLogxK
U2 - 10.1007/s10957-023-02317-x
DO - 10.1007/s10957-023-02317-x
M3 - Article
AN - SCOPUS:85174828680
VL - 199
SP - 931
EP - 954
JO - Journal of Optimization Theory and Applications
JF - Journal of Optimization Theory and Applications
SN - 0022-3239
ER -