Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: 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.

27
The categories of this paper are: comp-gas
18
The categories of this paper are: econ
11
The categories of this paper are: hep-lat
6
The categories of this paper are: astro-ph
10
The categories of this paper are: q-bio
35
The categories of this paper are: mtrl-th
7
The categories of this paper are: hep-th
26
The categories of this paper are: bayes-an
20
The categories of this paper are: acc-phys
12
The categories of this paper are: nucl-th
21
The categories of this paper are: adap-org
5
The categories of this paper are: gr-qc
19
The categories of this paper are: eess
3
The categories of this paper are: physics
14
The categories of this paper are: math-ph
23
The categories of this paper are: solv-int