This paper presents a new version of Dropout called Split Dropout (sDropout) and rotational convolution techniques to improve CNNs' performance on image classification. The widely used standard Dropout has advantage of preventing deep neural networks from overfitting by randomly dropping units during training. Our sDropout randomly splits the data into two subsets and keeps both rather than discards one subset. We also introduce two rotational convolution techniques, i.e. rotate-pooling convolution (RPC) and flip-rotate-pooling convolution (FRPC) to boost CNNs' performance on the robustness for rotation transformation. These two techniques encode rotation invariance into the network without adding extra parameters. Experimental evaluations on ImageNet2012 classification task demonstrate that sDropout not only enhances the performance but also converges faster. Additionally, RPC and FRPC make CNNs more robust for rotation transformations. Overall, FRPC together with sDropout bring @math (model of Zeiler and Fergus zeiler2013visualizing , 10-view, top-1) accuracy increase in ImageNet 2012 classification task compared to the original network.
A more direct way to add invariance is Data augmentation. Related work of Sermanet al @cite_5 build a jittered dataset by adding transformed versions of the original training set, including translation, scaling and rotation. There are many more works that transform input data to obtain invariance, e.g. Howard and Andrew G @cite_9 , Dosovitskiy al @cite_14 . But augmenting the training set with rotated versions does not achieve the same effect as ours, as it can not be restricted to upper layers. The rotation invariance in our work is achieved by pooling over systematically transformed versions of filters. It is closely related to the recent work of Gens al @cite_11 , which pools features over symmetry groups within a neural network.
@cite_5 @cite_9 @cite_14 @cite_11
2801243570 2949360407 2340427832 2951770173
Despite breakthroughs in image classification due to the evolution of deep learning and, in particular, convolutional neural networks (CNNs), state-of-the-art models only possess a very limited amount of rotational invariance. Known workarounds include artificial rotations of the training data or ensemble approaches, where several models are evaluated. These approaches either increase the workload of the training or inflate the number of parameters. Further approaches add rotational invariance by globally pooling over rotationally equivariant features. Instead, we propose to incorporate rotational invariance into the feature-extraction part of the CNN directly. This allows to train on unrotated data and perform well on a rotated test set. We use rotational convolutions and introduce a rotational pooling layer that performs a pooling over the back-rotated output feature maps. We show that when training on the original, unrotated MNIST training dataset, but evaluating on rotations of the MNIST test dataset, the error rate can be reduced substantially from 58.20 to 12.20 . Similar results are shown for the CIFAR-10 and CIFAR-100 datasets. In many machine learning tasks it is desirable that a model's prediction transforms in an equivariant way under transformations of its input. Convolutional neural networks (CNNs) implement translational equivariance by construction; for other transformations, however, they are compelled to learn the proper mapping. In this work, we develop Steerable Filter CNNs (SFCNNs) which achieve joint equivariance under translations and rotations by design. The proposed architecture employs steerable filters to efficiently compute orientation dependent responses for many orientations without suffering interpolation artifacts from filter rotation. We utilize group convolutions which guarantee an equivariant mapping. In addition, we generalize He's weight initialization scheme to filters which are defined as a linear combination of a system of atomic filters. Numerical experiments show a substantial enhancement of the sample complexity with a growing number of sampled filter orientations and confirm that the network generalizes learned patterns over orientations. The proposed approach achieves state-of-the-art on the rotated MNIST benchmark and on the ISBI 2012 2D EM segmentation challenge. In this paper we present a deep neural network topology that incorporates a simple to implement transformationinvariant pooling operator (TI-POOLING). This operator is able to efficiently handle prior knowledge on nuisance variations in the data, such as rotation or scale changes. Most current methods usually make use of dataset augmentation to address this issue, but this requires larger number of model parameters and more training data, and results in significantly increased training time and larger chance of under-or overfitting. The main reason for these drawbacks is that that the learned model needs to capture adequate features for all the possible transformations of the input. On the other hand, we formulate features in convolutional neural networks to be transformation-invariant. We achieve that using parallel siamese architectures for the considered transformation set and applying the TI-POOLING operator on their outputs before the fully-connected layers. We show that this topology internally finds the most optimal "canonical" instance of the input image for training and therefore limits the redundancy in learned features. This more efficient use of training data results in better performance on popular benchmark datasets with smaller number of parameters when comparing to standard convolutional neural networks with dataset augmentation and to other baselines. 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.