Deep Convolutional Neural Networks Based on Semi-Discrete Frames
Deep convolutional neural networks have led to breakthrough results in practical feature extraction applications. The mathematical analysis of these networks was pioneered by Mallat, 2012. Specifically, Mallat considered so-called scattering networks based on identical semi-discrete wavelet frames in each network layer, and proved translation-invariance as well as deformation stability of the resulting feature extractor. The purpose of this paper is to develop Mallat's theory further by allowing for different and, most importantly, general semi-discrete frames (such as, e.g., Gabor frames, wavelets, curvelets, shearlets, ridgelets) in distinct network layers. This allows to extract wider classes of features than point singularities resolved by the wavelet transform. 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. For Mallat's wavelet-based feature extractor, we get rid of a number of technical conditions. The mathematical engine behind our results is continuous frame theory, which allows us to completely detach the invariance and deformation stability proofs from the particular algebraic structure of the underlying frames.
Code (0)
등록된 구현이 없습니다.
Tasks
TranslationSimilar Papers 제목 키워드 기반
Attentioned Convolutional LSTM InpaintingNetwork for Anomaly Detection in Videos
We propose a semi-supervised model for detecting anomalies in videos inspiredby the Video Pixel Network [van den Oord et al., 2016]. VPN is a probabilisticgenerative model based on a deep neural network that estimates th…
Anomaly DetectionCommon Sense ReasoningDecoderSemi-Automated Annotation of Discrete States in Large Video Datasets
We propose a framework for semi-automated annotation of video frames where the video is of an object that at any point in time can be labeled as being in one of a finite number of discrete states. A Hidden Markov Model (…
Anomaly Detection in Video Data Based on Probabilistic Latent Space Models
This paper proposes a method for detecting anomalies in video data. A Variational Autoencoder (VAE) is used for reducing the dimensionality of video frames, generating latent space information that is comparable to low-d…
Anomaly DetectionAutonomous VehiclesTaylorSwiftNet: Taylor Driven Temporal Modeling for Swift Future Frame Prediction
While recurrent neural networks (RNNs) demonstrate outstanding capabilities for future video frame prediction, they model dynamics in a discrete time space, i.e., they predict the frames sequentially with a fixed tempora…
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 t…
Atari GamesImage CaptioningTranslation