1,219 research outputs found
Exploiting Cyclic Symmetry in Convolutional Neural Networks
Many classes of images exhibit rotational symmetry. Convolutional neural
networks are sometimes trained using data augmentation to exploit this, but
they are still required to learn the rotation equivariance properties from the
data. Encoding these properties into the network architecture, as we are
already used to doing for translation equivariance by using convolutional
layers, could result in a more efficient use of the parameter budget by
relieving the model from learning them. We introduce four operations which can
be inserted into neural network models as layers, and which can be combined to
make these models partially equivariant to rotations. They also enable
parameter sharing across different orientations. We evaluate the effect of
these architectural modifications on three datasets which exhibit rotational
symmetry and demonstrate improved performance with smaller models.Comment: 10 pages, 6 figures, accepted for publication at ICML 201
Deep Rotation Equivariant Network
Recently, learning equivariant representations has attracted considerable
research attention. Dieleman et al. introduce four operations which can be
inserted into convolutional neural network to learn deep representations
equivariant to rotation. However, feature maps should be copied and rotated
four times in each layer in their approach, which causes much running time and
memory overhead. In order to address this problem, we propose Deep Rotation
Equivariant Network consisting of cycle layers, isotonic layers and decycle
layers. Our proposed layers apply rotation transformation on filters rather
than feature maps, achieving a speed up of more than 2 times with even less
memory overhead. We evaluate DRENs on Rotated MNIST and CIFAR-10 datasets and
demonstrate that it can improve the performance of state-of-the-art
architectures
Searching for Topological Symmetry in Data Haystack
Finding interesting symmetrical topological structures in high-dimensional
systems is an important problem in statistical machine learning. Limited amount
of available high-dimensional data and its sensitivity to noise pose
computational challenges to find symmetry. Our paper presents a new method to
find local symmetries in a low-dimensional 2-D grid structure which is embedded
in high-dimensional structure. To compute the symmetry in a grid structure, we
introduce three legal grid moves (i) Commutation (ii) Cyclic Permutation (iii)
Stabilization on sets of local grid squares, grid blocks. The three grid moves
are legal transformations as they preserve the statistical distribution of
hamming distances in each grid block. We propose and coin the term of grid
symmetry of data on the 2-D data grid as the invariance of statistical
distributions of hamming distance are preserved after a sequence of grid moves.
We have computed and analyzed the grid symmetry of data on multivariate
Gaussian distributions and Gamma distributions with noise
PatchShuffle Regularization
This paper focuses on regularizing the training of the convolutional neural
network (CNN). We propose a new regularization approach named ``PatchShuffle``
that can be adopted in any classification-oriented CNN models. It is easy to
implement: in each mini-batch, images or feature maps are randomly chosen to
undergo a transformation such that pixels within each local patch are shuffled.
Through generating images and feature maps with interior orderless patches,
PatchShuffle creates rich local variations, reduces the risk of network
overfitting, and can be viewed as a beneficial supplement to various kinds of
training regularization techniques, such as weight decay, model ensemble and
dropout. Experiments on four representative classification datasets show that
PatchShuffle improves the generalization ability of CNN especially when the
data is scarce. Moreover, we empirically illustrate that CNN models trained
with PatchShuffle are more robust to noise and local changes in an image
Transformationally Identical and Invariant Convolutional Neural Networks by Combining Symmetric Operations or Input Vectors
Transformationally invariant processors constructed by transformed input
vectors or operators have been suggested and applied to many applications. In
this study, transformationally identical processing based on combining results
of all sub-processes with corresponding transformations at one of the
processing steps or at the beginning step were found to be equivalent for a
given condition. This property can be applied to most convolutional neural
network (CNN) systems. Specifically, a transformationally identical CNN can be
constructed by arranging internally symmetric operations in parallel with the
same transformation family that includes a flatten layer with weights sharing
among their corresponding transformation elements. Other transformationally
identical CNNs can be constructed by averaging transformed input vectors of the
family at the input layer followed by an ordinary CNN process or by a set of
symmetric operations. Interestingly, we found that both types of
transformationally identical CNN systems are mathematically equivalent by
either applying an averaging operation to corresponding elements of all
sub-channels before the activation function or without using a non-linear
activation function.Comment: 9 pages, 3 figure
Convolutional Networks for Spherical Signals
The success of convolutional networks in learning problems involving planar
signals such as images is due to their ability to exploit the translation
symmetry of the data distribution through weight sharing. Many areas of science
and egineering deal with signals with other symmetries, such as rotation
invariant data on the sphere. Examples include climate and weather science,
astrophysics, and chemistry. In this paper we present spherical convolutional
networks. These networks use convolutions on the sphere and rotation group,
which results in rotational weight sharing and rotation equivariance. Using a
synthetic spherical MNIST dataset, we show that spherical convolutional
networks are very effective at dealing with rotationally invariant
classification problems
Beyond Planar Symmetry: Modeling human perception of reflection and rotation symmetries in the wild
Humans take advantage of real world symmetries for various tasks, yet
capturing their superb symmetry perception mechanism with a computational model
remains elusive. Motivated by a new study demonstrating the extremely high
inter-person accuracy of human perceived symmetries in the wild, we have
constructed the first deep-learning neural network for reflection and rotation
symmetry detection (Sym-NET), trained on photos from MS-COCO (Microsoft-Common
Object in COntext) dataset with nearly 11K consistent symmetry-labels from more
than 400 human observers. We employ novel methods to convert discrete human
labels into symmetry heatmaps, capture symmetry densely in an image and
quantitatively evaluate Sym-NET against multiple existing computer vision
algorithms. On CVPR 2013 symmetry competition testsets and unseen MS-COCO
photos, Sym-NET significantly outperforms all other competitors. Beyond
mathematically well-defined symmetries on a plane, Sym-NET demonstrates
abilities to identify viewpoint-varied 3D symmetries, partially occluded
symmetrical objects, and symmetries at a semantic level.Comment: To appear in the International Conference on Computer Vision (ICCV)
201
Robustness of Rotation-Equivariant Networks to Adversarial Perturbations
Deep neural networks have been shown to be vulnerable to adversarial
examples: very small perturbations of the input having a dramatic impact on the
predictions. A wealth of adversarial attacks and distance metrics to quantify
the similarity between natural and adversarial images have been proposed,
recently enlarging the scope of adversarial examples with geometric
transformations beyond pixel-wise attacks. In this context, we investigate the
robustness to adversarial attacks of new Convolutional Neural Network
architectures providing equivariance to rotations. We found that
rotation-equivariant networks are significantly less vulnerable to
geometric-based attacks than regular networks on the MNIST, CIFAR-10, and
ImageNet datasets.Comment: 4 pages + references; public implementation of Spatially Transformed
Adversarial Examples can be found at https://github.com/rakutentech/stAd
3D G-CNNs for Pulmonary Nodule Detection
Convolutional Neural Networks (CNNs) require a large amount of annotated data
to learn from, which is often difficult to obtain in the medical domain. In
this paper we show that the sample complexity of CNNs can be significantly
improved by using 3D roto-translation group convolutions (G-Convs) instead of
the more conventional translational convolutions. These 3D G-CNNs were applied
to the problem of false positive reduction for pulmonary nodule detection, and
proved to be substantially more effective in terms of performance, sensitivity
to malignant nodules, and speed of convergence compared to a strong and
comparable baseline architecture with regular convolutions, data augmentation
and a similar number of parameters. For every dataset size tested, the G-CNN
achieved a FROC score close to the CNN trained on ten times more data
Equivariance Through Parameter-Sharing
We propose to study equivariance in deep neural networks through parameter
symmetries. In particular, given a group that acts discretely on
the input and output of a standard neural network layer , we show that is equivariant with respect to
-action iff explains the symmetries of the network
parameters . Inspired by this observation, we then propose two
parameter-sharing schemes to induce the desirable symmetry on . Our
procedures for tying the parameters achieve -equivariance and,
under some conditions on the action of , they guarantee
sensitivity to all other permutation groups outside .Comment: icml'1
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