On the number of regions of piecewise linear neural networks
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Publication:6145187
DOI10.1016/j.cam.2023.115667arXiv2206.08615MaRDI QIDQ6145187
Michael Unser, Arian Etemadi, Alexis Goujon
Publication date: 30 January 2024
Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2206.08615
splinesexpressivityactivation functionsdeep learningconvex partitionscontinuous and piecewise-linear functions
Numerical computation using splines (65D07) Artificial neural networks and deep learning (68T07) Spline approximation (41A15)
Cites Work
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- A representation method for PWL functions oriented to parallel processing
- Region configurations for realizability of lattice piecewise-linear models.
- Spaces of convex \(n\)-partitions
- Deep vs. shallow networks: An approximation theory perspective
- Learning Deep Architectures for AI
- Generalization of Hinging Hyperplanes
- Facing up to arrangements: face-count formulas for partitions of space by hyperplanes
- A Framework for the Construction of Upper Bounds on the Number of Affine Linear Regions of ReLU Feed-Forward Neural Networks
- Sharp Bounds for the Number of Regions of Maxout Networks and Vertices of Minkowski Sums
- Stable parameterization of continuous and piecewise-linear functions
- Approximation of Lipschitz Functions Using Deep Spline Neural Networks
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