Search Results for author:
Found 7 papers, 0 papers with code
Topology Reduction in Deep Convolutional Feature Extraction Networks
Finally, for networks based on Weyl-Heisenberg filters, we determine the prototype function bandwidth that minimizes---for fixed network depth $N$---the average number of operationally significant nodes per layer.
Energy Propagation in Deep Convolutional Neural Networks
This paper establishes conditions for energy conservation (and thus for a trivial null-set) for a wide class of deep convolutional neural network-based feature extractors and characterizes corresponding feature map energy decay rates.
Deep Structured Features for Semantic Segmentation
We propose a highly structured neural network architecture for semantic segmentation with an extremely small model size, suitable for low-power embedded and mobile platforms.
Discrete Deep Feature Extraction: A Theory and New Architectures
First steps towards a mathematical theory of deep convolutional neural networks for feature extraction were made---for the continuous-time case---in Mallat, 2012, and Wiatowski and B\"olcskei, 2015.
Deep Convolutional Neural Networks on Cartoon Functions
Wiatowski and B\"olcskei, 2015, proved that deformation stability and vertical translation invariance of deep convolutional neural network-based feature extractors are guaranteed by the network structure per se rather than the specific convolution kernels and non-linearities.
A Mathematical Theory of Deep Convolutional Neural Networks for Feature Extraction
Deep convolutional neural networks have led to breakthrough results in numerous practical machine learning tasks such as classification of images in the ImageNet data set, control-policy-learning to play Atari games or the board game Go, and image captioning.
Deep Convolutional Neural Networks Based on Semi-Discrete Frames
Our generalized feature extractor is proven to be translation-invariant, and we develop deformation stability results for a larger class of deformations than those considered by Mallat.
