Convolutional Neural Networks have become the standard for image classification tasks, however, these architectures are not invariant to translations of the input image. This lack of invariance is attributed to the use of stride which ignores the sampling theorem, and fully connected layers which lack spatial reasoning. We show that stride can greatly benefit translation invariance given that it is combined with sufficient similarity between neighbouring pixels, a characteristic which we refer to as local homogeneity. We also observe that this characteristic is dataset-specific and dictates the relationship between pooling kernel size and stride required for translation invariance. Furthermore we find that a trade-off exists between generalization and translation invariance in the case of pooling kernel size, as larger kernel sizes lead to better invariance but poorer generalization. Finally we explore the efficacy of other solutions proposed, namely global average pooling, anti-aliasing, and data augmentation, both empirically and through the lens of local homogeneity.
Since their inception, CNNs have utilized some type of striding operator to reduce the overlap of receptive fields and spatial dimensions. Although having clear heuristic motivations (i.e. lowering the number of parameters to learn) the mathematical role of striding within CNN learning remains unclear. This paper offers a novel and mathematical rigorous perspective on the role of the striding operator within modern CNNs. Specifically, we demonstrate theoretically that one can always represent a CNN that incorporates striding with an equivalent non-striding CNN which has more filters and smalle…
Although Convolutional Neural Networks (CNNs) are widely used, their translation invariance (ability to deal with translated inputs) is still subject to some controversy. We explore this question using translation-sensitivity maps to quantify how sensitive a standard CNN is to a translated input. We propose the use of Cosine Similarity as sensitivity metric over Euclidean Distance, and discuss the importance of restricting the dimensionality of either of these metrics when comparing architectures. Our main focus is to investigate the effect of different architectural components of a standard C…
SKL of Computer Architecture, Institute of Computing Technology, CAS（中国科学院计算技术研究所计算机体系结构国家重点实验室）；University of Chinese Academy of Sciences（中国科学院大学）；Cambricon Tech. Ltd（寒武纪科技有限公司）；Institute of Brain-Intelligence Technology, Zhangjiang Laboratory（张江实验室脑智科技研究所）；Shanghai Research Center for Brian Science and Brain-Inspired Instelligence（上海脑科学与脑启发智能研究中心）；CAS Center for Excellence in Brain Science and Intelligence Technology（中国科学院脑科学与智能技术卓越创新中心）
Winograd's minimal filtering algorithm has been widely used in Convolutional Neural Networks (CNNs) to reduce the number of multiplications for faster processing. However, it is only effective on convolutions with kernel size as 3x3 and stride as 1, because it suffers from significantly increased FLOPs and numerical accuracy problem for kernel size larger than 3x3 and fails on convolution with stride larger than 1. In this paper, we propose a novel Decomposable Winograd Method (DWM), which breaks through the limitation of original Winograd's minimal filtering algorithm to a wide and general co…
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…
Institute for Theoretical Physics, TU Wien（维也纳工业大学理论物理研究所）
In these proceedings we present lattice gauge equivariant convolutional neural networks (L-CNNs) which are able to process data from lattice gauge theory simulations while exactly preserving gauge symmetry. We review aspects of the architecture and show how L-CNNs can represent a large class of gauge invariant and equivariant functions on the lattice. We compare the performance of L-CNNs and non-equivariant networks using a non-linear regression problem and demonstrate how gauge invariance is broken for non-equivariant models.
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…
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 (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…
Deep convolutional neural networks (CNNs) have been shown to be able to fit a random labeling over data while still being able to generalize well for normal labels. Describing CNN capacity through a posteriori measures of complexity has been recently proposed to tackle this apparent paradox. These complexity measures are usually validated by showing that they correlate empirically with GE; being empirically larger for networks trained on random vs normal labels. Focusing on the case of spectral complexity we investigate theoretically and empirically the insensitivity of the complexity measure …
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…
Recent studies have put into question the commonly assumed shift invariance property of convolutional networks, showing that small shifts in the input can affect the output predictions substantially. In this paper, we analyze the benefits of addressing lack of shift invariance in CNN-based sound event classification. Specifically, we evaluate two pooling methods to improve shift invariance in CNNs, based on low-pass filtering and adaptive sampling of incoming feature maps. These methods are implemented via small architectural modifications inserted into the pooling layers of CNNs. We evaluate …
Subsampling is used in convolutional neural networks (CNNs) in the form of pooling or strided convolutions, to reduce the spatial dimensions of feature maps and to allow the receptive fields to grow exponentially with depth. However, it is known that such subsampling operations are not translation equivariant, unlike convolutions that are translation equivariant. Here, we first introduce translation equivariant subsampling/upsampling layers that can be used to construct exact translation equivariant CNNs. We then generalise these layers beyond translations to general groups, thus proposing gro…
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 …
Harbin Institute of Technology（哈尔滨工业大学）；Peking University（北京大学）
In most convolution neural networks (CNNs), downsampling hidden layers is adopted for increasing computation efficiency and the receptive field size. Such operation is commonly so-called pooling. Maximation and averaging over sliding windows (max/average pooling), and plain downsampling in the form of strided convolution are popular pooling methods. Since the pooling is a lossy procedure, a motivation of our work is to design a new pooling approach for less lossy in the dimensionality reduction. Inspired by the Fourier spectral pooling(FSP) proposed by Rippel et. al. [1], we present the Hartle…
Most modern convolutional neural networks (CNNs) used for object recognition are built using the same principles: Alternating convolution and max-pooling layers followed by a small number of fully connected layers. We re-evaluate the state of the art for object recognition from small images with convolutional networks, questioning the necessity of different components in the pipeline. We find that max-pooling can simply be replaced by a convolutional layer with increased stride without loss in accuracy on several image recognition benchmarks. Following this finding -- and building on other rec…
Korea Advanced Institute of Science and Technology（韩国科学技术院）；Mokwon University（牧园大学）
Convolutional neural networks (CNNs) with convolutional and pooling operations along the frequency axis have been proposed to attain invariance to frequency shifts of features. However, this is inappropriate with regard to the fact that acoustic features vary in frequency. In this paper, we contend that convolution along the time axis is more effective. We also propose the addition of an intermap pooling (IMP) layer to deep CNNs. In this layer, filters in each group extract common but spectrally variant features, then the layer pools the feature maps of each group. As a result, the proposed IM…
Within the world of machine learning there exists a wide range of different methods with respective advantages and applications. This paper seeks to present and discuss one such method, namely Convolutional Neural Networks (CNNs). CNNs are deep neural networks that use a special linear operation called convolution. This operation represents a key and distinctive element of CNNs, and will therefore be the focus of this method paper. The discussion starts with the theoretical foundations that underlie convolutions and CNNs. Then, the discussion proceeds to discuss some improvements and augmentat…
Binghamton University（宾汉姆顿大学）；IBM T.J. Watson Research Center（IBM T.J. 沃森研究中心）；University of California, San Diego（加州大学圣地亚哥分校）
Feature pooling layers (e.g., max pooling) in convolutional neural networks (CNNs) serve the dual purpose of providing increasingly abstract representations as well as yielding computational savings in subsequent convolutional layers. We view the pooling operation in CNNs as a two-step procedure: first, a pooling window (e.g., $2\times 2$) slides over the feature map with stride one which leaves the spatial resolution intact, and second, downsampling is performed by selecting one pixel from each non-overlapping pooling window in an often uniform and deterministic (e.g., top-left) manner. Our s…
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…
Chennai Mathematical Institute（金奈数学研究所）；Microsoft Research（微软研究院）
Convolutional neural networks or standard CNNs (StdCNNs) are translation-equivariant models that achieve translation invariance when trained on data augmented with sufficient translations. Recent work on equivariant models for a given group of transformations (e.g., rotations) has lead to group-equivariant convolutional neural networks (GCNNs). GCNNs trained on data augmented with sufficient rotations achieve rotation invariance. Recent work by authors arXiv:2002.11318 studies a trade-off between invariance and robustness to adversarial attacks. In another related work arXiv:2005.08632, given …
Partial differential equation (PDE) models and their associated variational energy formulations are often rotationally invariant by design. This ensures that a rotation of the input results in a corresponding rotation of the output, which is desirable in applications such as image analysis. Convolutional neural networks (CNNs) do not share this property, and existing remedies are often complex. The goal of our paper is to investigate how diffusion and variational models achieve rotation invariance and transfer these ideas to neural networks. As a core novelty we propose activation functions wh…
Handong Global University（韩东国际大学）；Dept. of Information and Communication Engineering（信息与通信工程系）
Convolutional neural networks (CNNs) have achieved remarkable performance in many applications, especially in image recognition tasks. As a crucial component of CNNs, sub-sampling plays an important role for efficient training or invariance property, and max-pooling and arithmetic average-pooling are commonly used sub-sampling methods. In addition to the two pooling methods, however, there could be many other pooling types, such as geometric average, harmonic average, and so on. Since it is not easy for algorithms to find the best pooling method, usually the pooling types are assumed a priorit…
TU Darmstadt（达姆施塔特工业大学）；NEC Laboratories Europe（欧洲NEC实验室）；Oculus Research（Oculus研究院）
Most convolutional neural networks use some method for gradually downscaling the size of the hidden layers. This is commonly referred to as pooling, and is applied to reduce the number of parameters, improve invariance to certain distortions, and increase the receptive field size. Since pooling by nature is a lossy process, it is crucial that each such layer maintains the portion of the activations that is most important for the network's discriminability. Yet, simple maximization or averaging over blocks, max or average pooling, or plain downsampling in the form of strided convolutions are th…
