When seeing a new object, humans can immediately recognize it across different retinal locations: we say that the internal object representation is invariant to translation. It is commonly believed that Convolutional Neural Networks (CNNs) are architecturally invariant to translation thanks to the convolution and/or pooling operations they are endowed with. In fact, several works have found that these networks systematically fail to recognise new objects on untrained locations. In this work we show how, even though CNNs are not 'architecturally invariant' to translation, they can indeed 'learn' to be invariant to translation. We verified that this can be achieved by pretraining on ImageNet, and we found that it is also possible with much simpler datasets in which the items are fully translated across the input canvas. We investigated how this pretraining affected the internal network representations, finding that the invariance was almost always acquired, even though it was some times disrupted by further training due to catastrophic forgetting/interference. These experiments show how pretraining a network on an environment with the right 'latent' characteristics (a more naturalistic environment) can result in the network learning deep perceptual rules which would dramatically improve subsequent generalization.
This paper is focused on studying the view-manifold structure in the feature spaces implied by the different layers of Convolutional Neural Networks (CNN). There are several questions that this paper aims to answer: Does the learned CNN representation achieve viewpoint invariance? How does it achieve viewpoint invariance? Is it achieved by collapsing the view manifolds, or separating them while preserving them? At which layer is view invariance achieved? How can the structure of the view manifold at each layer of a deep convolutional neural network be quantified experimentally? How does fine-t…
Toshiba Infrastructure Systems & Solutions Corporation（东芝基础设施系统与解决方案公司）
This report deals with translation invariance of convolutional neural networks (CNNs) for automatic target recognition (ATR) from synthetic aperture radar (SAR) imagery. In particular, the translation invariance of CNNs for SAR ATR represents the robustness against misalignment of target chips extracted from SAR images. To understand the translation invariance of the CNNs, we trained CNNs which classify the target chips from the MSTAR into the ten classes under the condition of with and without data augmentation, and then visualized the translation invariance of the CNNs. According to our resu…
To tackle increasingly complex tasks, it has become an essential ability of neural networks to learn abstract representations. These task-specific representations and, particularly, the invariances they capture turn neural networks into black box models that lack interpretability. To open such a black box, it is, therefore, crucial to uncover the different semantic concepts a model has learned as well as those that it has learned to be invariant to. We present an approach based on INNs that (i) recovers the task-specific, learned invariances by disentangling the remaining factor of variation i…
A fundamental problem in object recognition is the development of image representations that are invariant to common transformations such as translation, rotation, and small deformations. There are multiple hypotheses regarding the source of translation invariance in CNNs. One idea is that translation invariance is due to the increasing receptive field size of neurons in successive convolution layers. Another possibility is that invariance is due to the pooling operation. We develop a simple a tool, the translation-sensitivity map, which we use to visualize and quantify the translation-invaria…
University of Washington（华盛顿大学）；Purdue University（普渡大学）；University of Massachusetts Amherst（马萨诸塞大学阿默斯特分校）
Incorporating group symmetry directly into the learning process has proved to be an effective guideline for model design. By producing features that are guaranteed to transform covariantly to the group actions on the inputs, group-equivariant convolutional neural networks (G-CNNs) achieve significantly improved generalization performance in learning tasks with intrinsic symmetry. General theory and practical implementation of G-CNNs have been studied for planar images under either rotation or scaling transformation, but only individually. We present, in this paper, a roto-scale-translation equ…
Recently, self-attention (SA) structures became popular in computer vision fields. They have locally independent filters and can use large kernels, which contradicts the previously popular convolutional neural networks (CNNs). CNNs success was attributed to the hard-coded inductive biases of locality and spatial invariance. However, recent studies have shown that inductive biases in CNNs are too restrictive. On the other hand, the relative position encodings, similar to depthwise (DW) convolution, are necessary for the local SA networks, which indicates that the SA structures are not entirely …
In this paper we challenge the common assumption that convolutional layers in modern CNNs are translation invariant. We show that CNNs can and will exploit the absolute spatial location by learning filters that respond exclusively to particular absolute locations by exploiting image boundary effects. Because modern CNNs filters have a huge receptive field, these boundary effects operate even far from the image boundary, allowing the network to exploit absolute spatial location all over the image. We give a simple solution to remove spatial location encoding which improves translation invarianc…
Tolerance to image variations (e.g. translation, scale, pose, illumination) is an important desired property of any object recognition system, be it human or machine. Moving towards increasingly bigger datasets has been trending in computer vision specially with the emergence of highly popular deep learning models. While being very useful for learning invariance to object inter- and intra-class shape variability, these large-scale wild datasets are not very useful for learning invariance to other parameters forcing researchers to resort to other tricks for training a model. In this work, we in…
Beihang University（北京航空航天大学）；Shanghai Aerospace Control Technology Institute（上海航天控制技术研究所）；Peking Union Medical College Hospital（北京协和医院）；Chinese Academy of Medical Sciences and Peking Union Medical College（中国医学科学院北京协和医学院）
The computer-aided diagnosis (CAD) system can provide a reference basis for the clinical diagnosis of skin diseases. Convolutional neural networks (CNNs) can not only extract visual elements such as colors and shapes but also semantic features. As such they have made great improvements in many tasks of dermoscopy images. The imaging of dermoscopy has no principal orientation, indicating that there are a large number of skin lesion rotations in the datasets. However, CNNs lack rotation invariance, which is bound to affect the robustness of CNNs against rotations. To tackle this issue, we propos…
We address the problem that state-of-the-art Convolution Neural Networks (CNN) classifiers are not invariant to small shifts. The problem can be solved by the removal of sub-sampling operations such as stride and max pooling, but at a cost of severely degraded training and test efficiency. We present a novel usage of Gaussian-Hermite basis to efficiently approximate arbitrary filters within the CNN framework to obtain translation invariance. This is shown to be invariant to small shifts, and preserves the efficiency of training. Further, to improve efficiency in memory usage as well as computa…
The convolutional layers of standard convolutional neural networks (CNNs) are equivariant to translation. However, the convolution and fully-connected layers are not equivariant or invariant to other affine geometric transformations. Recently, a new class of CNNs is proposed in which the conventional layers of CNNs are replaced with equivariant convolution, pooling, and batch-normalization layers. The final classification layer in equivariant neural networks is invariant to different affine geometric transformations such as rotation, reflection and translation, and the scalar value is obtained…
Humans can identify objects following various spatial transformations such as scale and viewpoint. This extends to novel objects, after a single presentation at a single pose, sometimes referred to as online invariance. CNNs have been proposed as a compelling model of human vision, but their ability to identify objects across transformations is typically tested on held-out samples of trained categories after extensive data augmentation. This paper assesses whether standard CNNs can support human-like online invariance by training models to recognize images of synthetic 3D objects that undergo …
As object recognition becomes an increasingly common ML task, and recent research demonstrating CNNs vulnerability to attacks and small image perturbations necessitate fully understanding the foundations of object recognition. We focus on understanding the mechanisms behind how neural networks generalize to spatial transformations of complex objects. While humans excel at discriminating between objects shown at new positions, orientations, and scales, past results demonstrate that this may be limited to familiar objects - humans demonstrate low tolerance of spatial-variances for purposefully c…
University of Applied Sciences Western Switzerland (HES-SO)（瑞士西部应用科学大学）；Harvard School of Engineering and Applied Sciences（哈佛大学工程与应用科学学院）；Centre Hospitalier Universitaire Vaudois (CHUV)（沃州大学中心医院）；Hopitaux Universitaires de Genève (HUG)（日内瓦大学医院）
Locally Rotation Invariant (LRI) image analysis was shown to be fundamental in many applications and in particular in medical imaging where local structures of tissues occur at arbitrary rotations. LRI constituted the cornerstone of several breakthroughs in texture analysis, including Local Binary Patterns (LBP), Maximum Response 8 (MR8) and steerable filterbanks. Whereas globally rotation invariant Convolutional Neural Networks (CNN) were recently proposed, LRI was very little investigated in the context of deep learning. LRI designs allow learning filters accounting for all orientations, whi…
To perform well on unseen and potentially out-of-distribution samples, it is desirable for machine learning models to have a predictable response with respect to transformations affecting the factors of variation of the input. Here, we study the relative importance of several types of inductive biases towards such predictable behavior: the choice of data, their augmentations, and model architectures. Invariance is commonly achieved through hand-engineered data augmentation, but do standard data augmentations address transformations that explain variations in real data? While prior work has foc…
Being able to adequately process and combine data arising from different sites is crucial in neuroimaging, but is difficult, owing to site, sequence and acquisition-parameter dependent biases. It is important therefore to design algorithms that are not only robust to images of differing contrasts, but also be able to generalise well to unseen ones, with a quantifiable measure of uncertainty. In this paper we demonstrate the efficacy of a physics-informed, uncertainty-aware, segmentation network that employs augmentation-time MR simulations and homogeneous batch feature stratification to achiev…
Convolutional Neural Networks (CNNs) are commonly assumed to be invariant to small image transformations: either because of the convolutional architecture or because they were trained using data augmentation. Recently, several authors have shown that this is not the case: small translations or rescalings of the input image can drastically change the network's prediction. In this paper, we quantify this phenomena and ask why neither the convolutional architecture nor data augmentation are sufficient to achieve the desired invariance. Specifically, we show that the convolutional architecture doe…
GRASP Laboratory, University of Pennsylvania（宾夕法尼亚大学GRASP实验室）
Convolutional neural networks (CNNs) are inherently equivariant to translation. Efforts to embed other forms of equivariance have concentrated solely on rotation. We expand the notion of equivariance in CNNs through the Polar Transformer Network (PTN). PTN combines ideas from the Spatial Transformer Network (STN) and canonical coordinate representations. The result is a network invariant to translation and equivariant to both rotation and scale. PTN is trained end-to-end and composed of three distinct stages: a polar origin predictor, the newly introduced polar transformer module and a classif…
Convolutional neural networks (CNN) are now being widely used for classifying and detecting pulmonary abnormalities in chest radiographs. Two complementary generalization properties of CNNs, translation invariance and equivariance, are particularly useful in detecting manifested abnormalities associated with pulmonary disease, regardless of their spatial locations within the image. However, these properties also come with the loss of exact spatial information and global relative positions of abnormalities detected in local regions. Global relative positions of such abnormalities may help disti…
University of Electronic Science and Technology of China（电子科技大学）
Convolutional Neural Networks (CNNs) perform very well in image classification and object detection in recent years, but even the most advanced models have limited rotation invariance. Known solutions include the enhancement of training data and the increase of rotation invariance by globally merging the rotation equivariant features. These methods either increase the workload of training or increase the number of model parameters. To address this problem, this paper proposes a module that can be inserted into the existing networks, and directly incorporates the rotation invariance into the fe…
University of Amsterdam（阿姆斯特丹大学）；University of Heidelberg（海德堡大学）
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 int…
Many of our core assumptions about how neural networks operate remain empirically untested. One common assumption is that convolutional neural networks need to be stable to small translations and deformations to solve image recognition tasks. For many years, this stability was baked into CNN architectures by incorporating interleaved pooling layers. Recently, however, interleaved pooling has largely been abandoned. This raises a number of questions: Are our intuitions about deformation stability right at all? Is it important? Is pooling necessary for deformation invariance? If not, how is defo…
Rotation invariance and translation invariance have great values in image recognition tasks. In this paper, we bring a new architecture in convolutional neural network (CNN) named cyclic convolutional layer to achieve rotation invariance in 2-D symbol recognition. We can also get the position and orientation of the 2-D symbol by the network to achieve detection purpose for multiple non-overlap target. Last but not least, this architecture can achieve one-shot learning in some cases using those invariance.
Convolutional Neural Networks (CNNs) define an exceptionally powerful class of models for image classification, but the theoretical background and the understanding of how invariances to certain transformations are learned is limited. In a large scale screening with images modified by different affine and nonaffine transformations of varying magnitude, we analyzed the behavior of the CNN architectures AlexNet and ResNet. If the magnitude of different transformations does not exceed a class- and transformation dependent threshold, both architectures show invariant behavior. In this work we furt…
The University of Kansas（堪萨斯大学）；Mitsubishi Electric Research Laboratories (MERL)（三菱电机研究实验室）
In this paper we propose integrating a priori knowledge into both design and training of convolutional neural networks (CNNs) to learn object representations that are invariant to affine transformations (i.e., translation, scale, rotation). Accordingly we propose a novel multi-scale maxout CNN and train it end-to-end with a novel rotation-invariant regularizer. This regularizer aims to enforce the weights in each 2D spatial filter to approximate circular patterns. In this way, we manage to handle affine transformations in training using convolution, multi-scale maxout, and circular filters. Em…
Taras Shevchenko National University of Kyiv（基辅塔拉斯·舍甫琴科国立大学）
At this work we introduce horizontally symmetric convolutional kernels for CNNs which make the network output invariant to horizontal flips of the image. We also study other types of symmetric kernels which lead to vertical flip invariance, and approximate rotational invariance. We show that usage of such kernels acts as regularizer, and improves generalization of the convolutional neural networks at the cost of more complicated training process.
Convolutional Neural Networks (CNNs) are extremely efficient, since they exploit the inherent translation-invariance of natural images. However, translation is just one of a myriad of useful spatial transformations. Can the same efficiency be attained when considering other spatial invariances? Such generalized convolutions have been considered in the past, but at a high computational cost. We present a construction that is simple and exact, yet has the same computational complexity that standard convolutions enjoy. It consists of a constant image warp followed by a simple convolution, which a…
We propose a framework for rotation and translation covariant deep learning using $SE(2)$ group convolutions. The group product of the special Euclidean motion group $SE(2)$ describes how a concatenation of two roto-translations results in a net roto-translation. We encode this geometric structure into convolutional neural networks (CNNs) via $SE(2)$ group convolutional layers, which fit into the standard 2D CNN framework, and which allow to generically deal with rotated input samples without the need for data augmentation. We introduce three layers: a lifting layer which lifts a 2D (vector va…
University of Bristol（布里斯托尔大学）；Department of Psychology（心理学系）
When seeing a new object, humans can immediately recognize it across different retinal locations: the internal object representation is invariant to translation. It is commonly believed that Convolutional Neural Networks (CNNs) are architecturally invariant to translation thanks to the convolution and/or pooling operations they are endowed with. In fact, several studies have found that these networks systematically fail to recognise new objects on untrained locations. In this work, we test a wide variety of CNNs architectures showing how, apart from DenseNet-121, none of the models tested was …
Deep convolutional neural networks (CNNs) are broadly considered to be state-of-the-art generic end-to-end image classification systems. However, they are known to underperform when training data are limited and thus require data augmentation strategies that render the method computationally expensive and not always effective. Rather than using a data augmentation strategy to encode invariances as typically done in machine learning, here we propose to mathematically augment a nearest subspace classification model in sliced-Wasserstein space by exploiting certain mathematical properties of the …
University of Science and Technology of China（中国科学技术大学）；University of Technology Sydney（悉尼科技大学）
Convolutional Neural Networks (CNNs) have demonstrated state-of-the-art performance on many visual recognition tasks. However, the combination of convolution and pooling operations only shows invariance to small local location changes in meaningful objects in input. Sometimes, such networks are trained using data augmentation to encode this invariance into the parameters, which restricts the capacity of the model to learn the content of these objects. A more efficient use of the parameter budget is to encode rotation or translation invariance into the model architecture, which relieves the mod…
Chalmers University of Technology（查尔姆斯理工大学）；Umeå University（于默奥大学）
We characterize the class of image plane transformations which realize rigid camera motions and call these transformations `rigidity preserving'. In particular, 2D translations of pinhole images are not rigidity preserving. Hence, when using CNNs for 3D inference tasks, it can be beneficial to modify the inductive bias from equivariance towards translations to equivariance towards rigidity preserving transformations. We investigate how equivariance with respect to rigidity preserving transformations can be approximated in CNNs, and test our ideas on both 6D object pose estimation and visual lo…
Efficient Rotation Invariance in Deep Neural Networks through Artificial Mental Rotation
ZHAW Centre for Artificial Intelligence（苏黎世应用科学大学人工智能中心）；University of Lugano（卢加诺大学）；European Centre for Living Technology（欧洲生命技术中心）；The Swiss AI Lab IDSIA（瑞士人工智能实验室 IDSIA）；King Abdullah University of Science and Technology (KAUST)（阿卜杜拉国王科技大学）
The translational equivariant nature of Convolutional Neural Networks (CNNs) is a reason for its great success in computer vision. However, networks do not enjoy more general equivariance properties such as rotation or scaling, ultimately limiting their generalization performance. To address this limitation, we devise a method that endows CNNs with simultaneous equivariance with respect to translation, rotation, and scaling. Our approach defines a convolution-like operation and ensures equivariance based on our proposed scalable Fourier-Argand representation. The method maintains similar effic…
Poznan University of Technology（波兹南理工大学）；IDSIA Dalle Molle Institute for Artificial Intelligence Research（达勒·莫勒人工智能研究所）
Achieving superhuman playing level by AlphaGo corroborated the capabilities of convolutional neural architectures (CNNs) for capturing complex spatial patterns. This result was to a great extent due to several analogies between Go board states and 2D images CNNs have been designed for, in particular translational invariance and a relatively large board. In this paper, we verify whether CNN-based move predictors prove effective for Othello, a game with significantly different characteristics, including a much smaller board size and complete lack of translational invariance. We compare several C…
Revisiting Data Augmentation for Rotational Invariance in Convolutional Neural Networks
Instituto de Investigación en Informática LIDI, Facultad de Informática, Universidad Nacional de La Plata（拉普拉塔国立大学信息学院LIDI信息学研究所）；Universitat Rovira i Virgili（罗维拉-依维尔基里大学）
In this work, we focus on using convolution neural networks (CNN) to perform object recognition on the event data. In object recognition, it is important for a neural network to be robust to the variations of the data during testing. For traditional cameras, translations are well handled because CNNs are naturally equivariant to translations. However, because event cameras record the change of light intensity of an image, the geometric shape of event volumes will not only depend on the objects but also on their relative motions with respect to the camera. The deformation of the events caused b…
Eindhoven University of Technology（埃因霍温理工大学）；University of Amsterdam（阿姆斯特丹大学）
We present a PDE-based framework that generalizes Group equivariant Convolutional Neural Networks (G-CNNs). In this framework, a network layer is seen as a set of PDE-solvers where geometrically meaningful PDE-coefficients become the layer's trainable weights. Formulating our PDEs on homogeneous spaces allows these networks to be designed with built-in symmetries such as rotation in addition to the standard translation equivariance of CNNs. Having all the desired symmetries included in the design obviates the need to include them by means of costly techniques such as data augmentation. We will…
Australian Institute for Machine Learning（澳大利亚机器学习研究所）；University of Adelaide（阿德莱德大学）
Although provably robust to translational perturbations, convolutional neural networks (CNNs) are known to suffer from extreme performance degradation when presented at test time with more general geometric transformations of inputs. Recently, this limitation has motivated a shift in focus from CNNs to Capsule Networks (CapsNets). However, CapsNets suffer from admitting relatively few theoretical guarantees of invariance. We introduce a rigourous mathematical framework to permit invariance to any Lie group of warps, exclusively using convolutions (over Lie groups), without the need for capsule…
