Web20 de dez. de 2013 · Instead of just counting the number of the linear regions, this paper studies their local properties, such as the inspheres, the directions of the corresponding … WebFor piecewise linear neural networks (PLNNs), the number of linear regions is a natural measure of their expressive power since it characterizes the number of linear pieces …
On the number of linear regions of deep neural networks
Web8 de jul. de 2024 · We present a framework to derive upper bounds on the number of regions that feed-forward neural networks with ReLU activation functions are affine linear on. It is based on an inductive analysis that keeps track of the number of such regions per dimensionality of their images within the layers. More precisely, the information about the … Web12 de nov. de 2024 · For piecewise linear neural networks (PLNNs), the number of linear regions is a natural measure of their expressive power since it characterizes the number of linear pieces available to model complex patterns. In this article, we theoretically analyze the expressive power of PLNNs by counting and bounding the number of linear regions. shane the perfect match
Unboundedness of Linear Regions of Deep ReLU Neural Networks
Web13 de out. de 2024 · Figures from the annual Scottish Household Survey reveal that the number of people doing regular exercise in the most deprived communities was 18 per cent lower than those in the wealthiest areas ... Web16 de nov. de 2024 · Others proved that an upper bound to the number of linear regions scales exponentially with network depth but polynomially with width [12], [13], ... Web20 de dez. de 2013 · This paper offers a framework for comparing deep and shallow models that belong to the family of piecewise linear functions based on computational geometry and looks at a deep rectifier multi-layer perceptron (MLP) with linear outputs units and compares it with a single layer version of the model. Abstract: This paper explores the complexity of … shane theriot wiki