2,980 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
A Kernel Perspective for Regularizing Deep Neural Networks
We propose a new point of view for regularizing deep neural networks by using
the norm of a reproducing kernel Hilbert space (RKHS). Even though this norm
cannot be computed, it admits upper and lower approximations leading to various
practical strategies. Specifically, this perspective (i) provides a common
umbrella for many existing regularization principles, including spectral norm
and gradient penalties, or adversarial training, (ii) leads to new effective
regularization penalties, and (iii) suggests hybrid strategies combining lower
and upper bounds to get better approximations of the RKHS norm. We
experimentally show this approach to be effective when learning on small
datasets, or to obtain adversarially robust models.Comment: ICM
Geometric deep learning: going beyond Euclidean data
Many scientific fields study data with an underlying structure that is a
non-Euclidean space. Some examples include social networks in computational
social sciences, sensor networks in communications, functional networks in
brain imaging, regulatory networks in genetics, and meshed surfaces in computer
graphics. In many applications, such geometric data are large and complex (in
the case of social networks, on the scale of billions), and are natural targets
for machine learning techniques. In particular, we would like to use deep
neural networks, which have recently proven to be powerful tools for a broad
range of problems from computer vision, natural language processing, and audio
analysis. However, these tools have been most successful on data with an
underlying Euclidean or grid-like structure, and in cases where the invariances
of these structures are built into networks used to model them. Geometric deep
learning is an umbrella term for emerging techniques attempting to generalize
(structured) deep neural models to non-Euclidean domains such as graphs and
manifolds. The purpose of this paper is to overview different examples of
geometric deep learning problems and present available solutions, key
difficulties, applications, and future research directions in this nascent
field
On the Inductive Bias of Neural Tangent Kernels
State-of-the-art neural networks are heavily over-parameterized, making the
optimization algorithm a crucial ingredient for learning predictive models with
good generalization properties. A recent line of work has shown that in a
certain over-parameterized regime, the learning dynamics of gradient descent
are governed by a certain kernel obtained at initialization, called the neural
tangent kernel. We study the inductive bias of learning in such a regime by
analyzing this kernel and the corresponding function space (RKHS). In
particular, we study smoothness, approximation, and stability properties of
functions with finite norm, including stability to image deformations in the
case of convolutional networks, and compare to other known kernels for similar
architectures.Comment: NeurIPS 201
DeepOrgan: Multi-level Deep Convolutional Networks for Automated Pancreas Segmentation
Automatic organ segmentation is an important yet challenging problem for
medical image analysis. The pancreas is an abdominal organ with very high
anatomical variability. This inhibits previous segmentation methods from
achieving high accuracies, especially compared to other organs such as the
liver, heart or kidneys. In this paper, we present a probabilistic bottom-up
approach for pancreas segmentation in abdominal computed tomography (CT) scans,
using multi-level deep convolutional networks (ConvNets). We propose and
evaluate several variations of deep ConvNets in the context of hierarchical,
coarse-to-fine classification on image patches and regions, i.e. superpixels.
We first present a dense labeling of local image patches via
and nearest neighbor fusion. Then we describe a regional
ConvNet () that samples a set of bounding boxes around
each image superpixel at different scales of contexts in a "zoom-out" fashion.
Our ConvNets learn to assign class probabilities for each superpixel region of
being pancreas. Last, we study a stacked leveraging
the joint space of CT intensities and the dense
probability maps. Both 3D Gaussian smoothing and 2D conditional random fields
are exploited as structured predictions for post-processing. We evaluate on CT
images of 82 patients in 4-fold cross-validation. We achieve a Dice Similarity
Coefficient of 83.66.3% in training and 71.810.7% in testing.Comment: To be presented at MICCAI 2015 - 18th International Conference on
Medical Computing and Computer Assisted Interventions, Munich, German
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