1,724 research outputs found
Group Invariance, Stability to Deformations, and Complexity of Deep Convolutional Representations
The success of deep convolutional architectures is often attributed in part
to their ability to learn multiscale and invariant representations of natural
signals. However, a precise study of these properties and how they affect
learning guarantees is still missing. In this paper, we consider deep
convolutional representations of signals; we study their invariance to
translations and to more general groups of transformations, their stability to
the action of diffeomorphisms, and their ability to preserve signal
information. This analysis is carried by introducing a multilayer kernel based
on convolutional kernel networks and by studying the geometry induced by the
kernel mapping. We then characterize the corresponding reproducing kernel
Hilbert space (RKHS), showing that it contains a large class of convolutional
neural networks with homogeneous activation functions. This analysis allows us
to separate data representation from learning, and to provide a canonical
measure of model complexity, the RKHS norm, which controls both stability and
generalization of any learned model. In addition to models in the constructed
RKHS, our stability analysis also applies to convolutional networks with
generic activations such as rectified linear units, and we discuss its
relationship with recent generalization bounds based on spectral norms
Fast object detection in compressed JPEG Images
Object detection in still images has drawn a lot of attention over past few
years, and with the advent of Deep Learning impressive performances have been
achieved with numerous industrial applications. Most of these deep learning
models rely on RGB images to localize and identify objects in the image.
However in some application scenarii, images are compressed either for storage
savings or fast transmission. Therefore a time consuming image decompression
step is compulsory in order to apply the aforementioned deep models. To
alleviate this drawback, we propose a fast deep architecture for object
detection in JPEG images, one of the most widespread compression format. We
train a neural network to detect objects based on the blockwise DCT (discrete
cosine transform) coefficients {issued from} the JPEG compression algorithm. We
modify the well-known Single Shot multibox Detector (SSD) by replacing its
first layers with one convolutional layer dedicated to process the DCT inputs.
Experimental evaluations on PASCAL VOC and industrial dataset comprising images
of road traffic surveillance show that the model is about faster than
regular SSD with promising detection performances. To the best of our
knowledge, this paper is the first to address detection in compressed JPEG
images
CayleyNets: Graph Convolutional Neural Networks with Complex Rational Spectral Filters
The rise of graph-structured data such as social networks, regulatory
networks, citation graphs, and functional brain networks, in combination with
resounding success of deep learning in various applications, has brought the
interest in generalizing deep learning models to non-Euclidean domains. In this
paper, we introduce a new spectral domain convolutional architecture for deep
learning on graphs. The core ingredient of our model is a new class of
parametric rational complex functions (Cayley polynomials) allowing to
efficiently compute spectral filters on graphs that specialize on frequency
bands of interest. Our model generates rich spectral filters that are localized
in space, scales linearly with the size of the input data for
sparsely-connected graphs, and can handle different constructions of Laplacian
operators. Extensive experimental results show the superior performance of our
approach, in comparison to other spectral domain convolutional architectures,
on spectral image classification, community detection, vertex classification
and matrix completion tasks
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