Equivariance w.r.t. geometric transformations in neural networks improves data efficiency, parameter efficiency and robustness to out-of-domain perspective shifts. When equivariance is not designed into a neural network, the network can still learn equivariant functions from the data. We quantify this learned equivariance, by proposing an improved measure for equivariance. We find evidence for a correlation between learned translation equivariance and validation accuracy on ImageNet. We therefore investigate what can increase the learned equivariance in neural networks, and find that data augmentation, reduced model capacity and inductive bias in the form of convolutions induce higher learned equivariance in neural networks.
Toyota Technological Institute at Chicago（芝加哥丰田技术研究院）；University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）
Designing equivariance as an inductive bias into deep-nets has been a prominent approach to build effective models, e.g., a convolutional neural network incorporates translation equivariance. However, incorporating these inductive biases requires knowledge about the equivariance properties of the data, which may not be available, e.g., when encountering a new domain. To address this, we study how to discover interpretable equivariances from data. Specifically, we formulate this discovery process as an optimization problem over a model's parameter-sharing schemes. We propose to use the partitio…
LEPA: Learning Geometric Equivariance in Satellite Remote Sensing Data with a Predictive Architecture
Jülich Supercomputing Centre (JSC), Forschungszentrum Jülich（茹里希超级计算中心（JSC），茹里希研究中心）；Institute for Visualization and Interactive Systems (VIS), University of Stuttgart（可视化与交互系统研究所（VIS），斯图加特大学）；School of Engineering and Natural Sciences (SENS), University of Iceland（工程与自然科学学院（SENS），爱沙尼亚大学）
Vrije Universiteit Amsterdam（阿姆斯特丹自由大学）；Mitsubishi Electric Research Laboratories（三菱电机研究实验室）
Group Convolutional Neural Networks (G-CNNs) constrain learned features to respect the symmetries in the selected group, and lead to better generalization when these symmetries appear in the data. If this is not the case, however, equivariance leads to overly constrained models and worse performance. Frequently, transformations occurring in data can be better represented by a subset of a group than by a group as a whole, e.g., rotations in $[-90^{\circ}, 90^{\circ}]$. In such cases, a model that respects equivariance $\textit{partially}$ is better suited to represent the data. In addition, rel…
Group Equivariant Convolutions (GConvs) enable convolutional neural networks to be equivariant to various transformation groups, but at an additional parameter and compute cost. We investigate the filter parameters learned by GConvs and find certain conditions under which they become highly redundant. We show that GConvs can be efficiently decomposed into depthwise separable convolutions while preserving equivariance properties and demonstrate improved performance and data efficiency on two datasets. All code is publicly available at github.com/Attila94/SepGrouPy.
Self-supervised representation learning is able to learn semantically meaningful features; however, much of its recent success relies on multiple crops of an image with very few objects. Instead of learning view-invariant representation from simple images, humans learn representations in a complex world with changing scenes by observing object movement, deformation, pose variation, and ego motion. Motivated by this ability, we present a new self-supervised learning representation framework that can be directly deployed on a video stream of complex scenes with many moving objects. Our framework…
Translating or rotating an input image should not affect the results of many computer vision tasks. Convolutional neural networks (CNNs) are already translation equivariant: input image translations produce proportionate feature map translations. This is not the case for rotations. Global rotation equivariance is typically sought through data augmentation, but patch-wise equivariance is more difficult. We present Harmonic Networks or H-Nets, a CNN exhibiting equivariance to patch-wise translation and 360-rotation. We achieve this by replacing regular CNN filters with circular harmonics, return…
Universiteit van Amsterdam（阿姆斯特丹大学）；Vrij Universiteit Amsterdam（阿姆斯特丹自由大学）
Group convolutional neural networks (G-CNNs) have been shown to increase parameter efficiency and model accuracy by incorporating geometric inductive biases. In this work, we investigate the properties of representations learned by regular G-CNNs, and show considerable parameter redundancy in group convolution kernels. This finding motivates further weight-tying by sharing convolution kernels over subgroups. To this end, we introduce convolution kernels that are separable over the subgroup and channel dimensions. In order to obtain equivariance to arbitrary affine Lie groups we provide a conti…
Futurewei Seattle Cloud Lab（未来伟西雅图云实验室）；University of Central Florida（中佛罗里达大学）；Purdue University（普渡大学）
Transformation Equivariant Representations (TERs) aim to capture the intrinsic visual structures that equivary to various transformations by expanding the notion of {\em translation} equivariance underlying the success of Convolutional Neural Networks (CNNs). For this purpose, we present both deterministic AutoEncoding Transformations (AET) and probabilistic AutoEncoding Variational Transformations (AVT) models to learn visual representations from generic groups of transformations. While the AET is trained by directly decoding the transformations from the learned representations, the AVT is tr…
Swansea University（斯旺西大学）；Université de Toulon（土伦大学）；Aix Marseille Univ（艾克斯-马赛大学）；CNRS（法国国家科学研究中心）；Université de Strasbourg（斯特拉斯堡大学）
Robustness to transformation is desirable in many computer vision tasks, given that input data often exhibits pose variance. While translation invariance and equivariance is a documented phenomenon of CNNs, sensitivity to other transformations is typically encouraged through data augmentation. We investigate the modulation of complex valued convolutional weights with learned Gabor filters to enable orientation robustness. The resulting network can generate orientation dependent features free of interpolation with a single set of learnable rotation-governing parameters. By choosing to either re…
Peking University（北京大学）；University of Illinois Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）；HeliXon Research（HeliXon研究院）
Equivariance has been a long-standing concern in various fields ranging from computer vision to physical modeling. Most previous methods struggle with generality, simplicity, and expressiveness -- some are designed ad hoc for specific data types, some are too complex to be accessible, and some sacrifice flexible transformations. In this work, we propose a novel and simple framework to achieve equivariance for point cloud analysis based on the message passing (graph neural network) scheme. We find the equivariant property could be obtained by introducing an orientation for each point to decoupl…
Technical University of Munich（慕尼黑工业大学）；East China Normal University（华东师范大学）
Continual Learning aims to learn multiple incoming new tasks continually, and to keep the performance of learned tasks at a consistent level. However, existing research on continual learning assumes the pose of the object is pre-defined and well-aligned. For practical application, this work focuses on pose-agnostic continual learning tasks, where the object's pose changes dynamically and unpredictably. The point cloud augmentation adopted from past approaches would sharply rise with the task increment in the continual learning process. To address this problem, we inject the equivariance as the…
Pacific Northwest National Laboratory（太平洋西北国家实验室）；University of Washington（华盛顿大学）；Colorado State University（科罗拉多州立大学）；National Geospatial-Intelligence Agency（国家地理空间情报局）
It is often said that a deep learning model is "invariant" to some specific type of transformation. However, what is meant by this statement strongly depends on the context in which it is made. In this paper we explore the nature of invariance and equivariance of deep learning models with the goal of better understanding the ways in which they actually capture these concepts on a formal level. We introduce a family of invariance and equivariance metrics that allows us to quantify these properties in a way that disentangles them from other metrics such as loss or accuracy. We use our metrics to…
Zhejiang University（浙江大学）；Massachusetts General Hospital（麻省总医院）；Harvard Medical School（哈佛医学院）；University of Florida（佛罗里达大学）；Massachusetts General Brigham（麻省总医院布莱根医疗系统）
Deep learning based PET image reconstruction methods have achieved promising results recently. However, most of these methods follow a supervised learning paradigm, which rely heavily on the availability of high-quality training labels. In particular, the long scanning time required and high radiation exposure associated with PET scans make obtaining this labels impractical. In this paper, we propose a dual-domain unsupervised PET image reconstruction method based on learned decent algorithm, which reconstructs high-quality PET images from sinograms without the need for image labels. Specifica…
École Polytechnique Fédérale de Lausanne (EPFL)（洛桑联邦理工学院）；Swiss Data Science Center (SDSC)（瑞士数据科学中心）
Designing a convolution for a spherical neural network requires a delicate tradeoff between efficiency and rotation equivariance. DeepSphere, a method based on a graph representation of the sampled sphere, strikes a controllable balance between these two desiderata. This contribution is twofold. First, we study both theoretically and empirically how equivariance is affected by the underlying graph with respect to the number of vertices and neighbors. Second, we evaluate DeepSphere on relevant problems. Experiments show state-of-the-art performance and demonstrates the efficiency and flexibilit…
Convolutional neural networks are ubiquitous in Machine Learning applications for solving a variety of problems. They however can not be used in their native form when the domain of the data is commonly encountered manifolds such as the sphere, the special orthogonal group, the Grassmanian, the manifold of symmetric positive definite matrices and others. Most recently, generalization of CNNs to data domains such as the 2-sphere has been reported by some research groups, which is referred to as the spherical CNNs (SCNNs). The key property of SCNNs distinct from CNNs is that they exhibit the rot…
Convolutional networks are successful due to their equivariance/invariance under translations. However, rotatable data such as images, volumes, shapes, or point clouds require processing with equivariance/invariance under rotations in cases where the rotational orientation of the coordinate system does not affect the meaning of the data (e.g. object classification). On the other hand, estimation/processing of rotations is necessary in cases where rotations are important (e.g. motion estimation). There has been recent progress in methods and theory in all these regards. Here we provide an overv…
Unitary；VGG, University of Oxford（牛津大学VGG）；University of Edinburgh（爱丁堡大学）
Equivariance to random image transformations is an effective method to learn landmarks of object categories, such as the eyes and the nose in faces, without manual supervision. However, this method does not explicitly guarantee that the learned landmarks are consistent with changes between different instances of the same object, such as different facial identities. In this paper, we develop a new perspective on the equivariance approach by noting that dense landmark detectors can be interpreted as local image descriptors equipped with invariance to intra-category variations. We then propose a …
Recent attempts for unsupervised landmark learning leverage synthesized image pairs that are similar in appearance but different in poses. These methods learn landmarks by encouraging the consistency between the original images and the images reconstructed from swapped appearances and poses. While synthesized image pairs are created by applying pre-defined transformations, they can not fully reflect the real variances in both appearances and poses. In this paper, we aim to open the possibility of learning landmarks on unpaired data (i.e. unaligned image pairs) sampled from a natural image coll…
We propose a framework for learning neural scene representations directly from images, without 3D supervision. Our key insight is that 3D structure can be imposed by ensuring that the learned representation transforms like a real 3D scene. Specifically, we introduce a loss which enforces equivariance of the scene representation with respect to 3D transformations. Our formulation allows us to infer and render scenes in real time while achieving comparable results to models requiring minutes for inference. In addition, we introduce two challenging new datasets for scene representation and neural…
ETH Zurich（苏黎世联邦理工学院）；Max Planck ETH Center for Learning Systems（马克斯·普朗克-苏黎世联邦理工学习系统中心）
Learning-based 3D reconstruction using implicit neural representations has shown promising progress not only at the object level but also in more complicated scenes. In this paper, we propose Dynamic Plane Convolutional Occupancy Networks, a novel implicit representation pushing further the quality of 3D surface reconstruction. The input noisy point clouds are encoded into per-point features that are projected onto multiple 2D dynamic planes. A fully-connected network learns to predict plane parameters that best describe the shapes of objects or scenes. To further exploit translational equivar…
Guangdong Polytechnic Normal University（广东技术师范大学）；University of Technology Sydney（悉尼科技大学）
In this work, we investigate the following: 1) how the routing affects the CapsNet model fitting; 2) how the representation using capsules helps discover global structures in data distribution, and; 3) how the learned data representation adapts and generalizes to new tasks. Our investigation yielded the results some of which have been mentioned in the original paper of CapsNet, they are: 1) the routing operation determines the certainty with which a layer of capsules pass information to the layer above and the appropriate level of certainty is related to the model fitness; 2) in a designed exp…
Google Research（谷歌研究院）；Mila（米拉研究所）；MIT CSAIL（麻省理工学院计算机科学与人工智能实验室）；Brown University（布朗大学）
Pre-trained deep image representations are useful for post-training tasks such as classification through transfer learning, image retrieval, and object detection. Data augmentations are a crucial aspect of pre-training robust representations in both supervised and self-supervised settings. Data augmentations explicitly or implicitly promote invariance in the embedding space to the input image transformations. This invariance reduces generalization to those downstream tasks which rely on sensitivity to these particular data augmentations. In this paper, we propose a method of learning represent…
Benefit from flexible network designs and end-to-end joint optimization approach, learned image compression (LIC) has demonstrated excellent coding performance and practical feasibility in recent years. However, existing compression models suffer from serious multi-generation loss, which always occurs during image editing and transcoding. During the process of repeatedly encoding and decoding, the quality of the image will rapidly degrade, resulting in various types of distortion, which significantly limits the practical application of LIC. In this paper, a thorough analysis is carried out to …
Technical University of Munich (TUM)（慕尼黑工业大学）；Kyung Hee University（庆熙大学）；University of Munich (LMU)（慕尼黑大学）
One challenging property lurking in medical datasets is the imbalanced data distribution, where the frequency of the samples between the different classes is not balanced. Training a model on an imbalanced dataset can introduce unique challenges to the learning problem where a model is biased towards the highly frequent class. Many methods are proposed to tackle the distributional differences and the imbalanced problem. However, the impact of these approaches on the learned features is not well studied. In this paper, we look deeper into the internal units of neural networks to observe how han…
Simon Fraser University（西蒙弗雷泽大学）；Google Inc.（谷歌公司）；Tencent Technologies（腾讯科技）
Learned image compression has recently shown the potential to outperform the standard codecs. State-of-the-art rate-distortion (R-D) performance has been achieved by context-adaptive entropy coding approaches in which hyperprior and autoregressive models are jointly utilized to effectively capture the spatial dependencies in the latent representations. However, the latents are feature maps of the same spatial resolution in previous works, which contain some redundancies that affect the R-D performance. In this paper, we propose the first learned multi-frequency image compression and entropy co…
Imperial College London（帝国理工学院）；FaceSoft Ltd（FaceSoft有限公司）；University of Oulu（奥卢大学）
Automatic facial behavior analysis has a long history of studies in the intersection of computer vision, physiology and psychology. However it is only recently, with the collection of large-scale datasets and powerful machine learning methods such as deep neural networks, that automatic facial behavior analysis started to thrive. Three of its iconic tasks are automatic recognition of basic expressions (e.g. happy, sad, surprised), estimation of continuous emotions (e.g., valence and arousal), and detection of facial action units (activations of e.g. upper/inner eyebrows, nose wrinkles). Up unt…
