Recent empirical work has shown that hierarchical convolutional kernels inspired by convolutional neural networks (CNNs) significantly improve the performance of kernel methods in image classification tasks. A widely accepted explanation for their success is that these architectures encode hypothesis classes that are suitable for natural images. However, understanding the precise interplay between approximation and generalization in convolutional architectures remains a challenge. In this paper, we consider the stylized setting of covariates (image pixels) uniformly distributed on the hypercube, and characterize exactly the RKHS of kernels composed of single layers of convolution, pooling, and downsampling operations. We use this characterization to compute sharp asymptotics of the generalization error for any given function in high-dimension. In particular, we quantify the gain in sample complexity brought by enforcing locality with the convolution operation and approximate translation invariance with average pooling. Notably, these results provide a precise description of how convolution and pooling operations trade off approximation with generalization power in one layer convolutional kernels.
The empirical success of deep convolutional networks on tasks involving high-dimensional data such as images or audio suggests that they can efficiently approximate certain functions that are well-suited for such tasks. In this paper, we study this through the lens of kernel methods, by considering simple hierarchical kernels with two or three convolution and pooling layers, inspired by convolutional kernel networks. These achieve good empirical performance on standard vision datasets, while providing a precise description of their functional space that yields new insights on their inductive b…
In this chapter we review the main literature related to the recent advancement of deep neural-kernel architecture, an approach that seek the synergy between two powerful class of models, i.e. kernel-based models and artificial neural networks. The introduced deep neural-kernel framework is composed of a hybridization of the neural networks architecture and a kernel machine. More precisely, for the kernel counterpart the model is based on Least Squares Support Vector Machines with explicit feature mapping. Here we discuss the use of one form of an explicit feature map obtained by random Fourie…
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…
Convolutional layers in graph neural networks are a fundamental type of layer which output a representation or embedding of each graph vertex. The representation typically encodes information about the vertex in question and its neighbourhood. If one wishes to perform a graph centric task, such as graph classification, this set of vertex representations must be integrated or pooled to form a graph representation. In this article we propose a novel pooling method which maps a set of vertex representations to a function space representation. This method is distinct from existing pooling methods …
Image classification is considered, and a hierarchical max-pooling model with additional local pooling is introduced. Here the additional local pooling enables the hierachical model to combine parts of the image which have a variable relative distance towards each other. Various convolutional neural network image classifiers are introduced and compared in view of their rate of convergence. The finite sample size performance of the estimates is analyzed by applying them to simulated and real data.
Advanced methods of applying deep learning to structured data such as graphs have been proposed in recent years. In particular, studies have focused on generalizing convolutional neural networks to graph data, which includes redefining the convolution and the downsampling (pooling) operations for graphs. The method of generalizing the convolution operation to graphs has been proven to improve performance and is widely used. However, the method of applying downsampling to graphs is still difficult to perform and has room for improvement. In this paper, we propose a graph pooling method based on…
We introduce a simple and effective method for regularizing large convolutional neural networks. We replace the conventional deterministic pooling operations with a stochastic procedure, randomly picking the activation within each pooling region according to a multinomial distribution, given by the activities within the pooling region. The approach is hyper-parameter free and can be combined with other regularization approaches, such as dropout and data augmentation. We achieve state-of-the-art performance on four image datasets, relative to other approaches that do not utilize data augmentati…
Michigan State University（密歇根州立大学）；Pennsylvania State University（宾夕法尼亚州立大学）；IBM T. J. Watson Research Center（IBM T·J·沃森研究中心）
Graph neural networks, which generalize deep neural network models to graph structured data, have attracted increasing attention in recent years. They usually learn node representations by transforming, propagating and aggregating node features and have been proven to improve the performance of many graph related tasks such as node classification and link prediction. To apply graph neural networks for the graph classification task, approaches to generate the \textit{graph representation} from node representations are demanded. A common way is to globally combine the node representations. Howev…
University of Modena and Reggio Emilia（摩德纳-雷焦艾米利亚大学）
We present a novel and hierarchical approach for supervised classification of signals spanning over a fixed graph, reflecting shared properties of the dataset. To this end, we introduce a Convolutional Cluster Pooling layer exploiting a multi-scale clustering in order to highlight, at different resolutions, locally connected regions on the input graph. Our proposal generalises well-established neural models such as Convolutional Neural Networks (CNNs) on irregular and complex domains, by means of the exploitation of the weight sharing property in a graph-oriented architecture. In this work, su…
We propose a novel graph pooling operation using cliques as the unit pool. As this approach is purely topological, rather than featural, it is more readily interpretable, a better analogue to image coarsening than filtering or pruning techniques, and entirely nonparametric. The operation is implemented within graph convolution network (GCN) and GraphSAGE architectures and tested against standard graph classification benchmarks. In addition, we explore the backwards compatibility of the pooling to regular graphs, demonstrating competitive performance when replacing two-by-two pooling in standar…
We seek to improve deep neural networks by generalizing the pooling operations that play a central role in current architectures. We pursue a careful exploration of approaches to allow pooling to learn and to adapt to complex and variable patterns. The two primary directions lie in (1) learning a pooling function via (two strategies of) combining of max and average pooling, and (2) learning a pooling function in the form of a tree-structured fusion of pooling filters that are themselves learned. In our experiments every generalized pooling operation we explore improves performance when used in…
Massachusetts Institute of Technology（麻省理工学院）；Harvard University（哈佛大学）
Discrete Fourier transforms provide a significant speedup in the computation of convolutions in deep learning. In this work, we demonstrate that, beyond its advantages for efficient computation, the spectral domain also provides a powerful representation in which to model and train convolutional neural networks (CNNs). We employ spectral representations to introduce a number of innovations to CNN design. First, we propose spectral pooling, which performs dimensionality reduction by truncating the representation in the frequency domain. This approach preserves considerably more information per …
The paper discusses a pooling mechanism to induce subsampling in graph structured data and introduces it as a component of a graph convolutional neural network. The pooling mechanism builds on the Non-Negative Matrix Factorization (NMF) of a matrix representing node adjacency and node similarity as adaptively obtained through the vertices embedding learned by the model. Such mechanism is applied to obtain an incrementally coarser graph where nodes are adaptively pooled into communities based on the outcomes of the non-negative factorization. The empirical analysis on graph classification bench…
Shanghai Jiao Tong University（上海交通大学）；École Polytechnique Fédérale de Lausanne (EPFL)（洛桑联邦理工学院）
Graph neural networks have attracted wide attentions to enable representation learning of graph data in recent works. In complement to graph convolution operators, graph pooling is crucial for extracting hierarchical representation of graph data. However, most recent graph pooling methods still fail to efficiently exploit the geometry of graph data. In this paper, we propose a novel graph pooling strategy that leverages node proximity to improve the hierarchical representation learning of graph data with their multi-hop topology. Node proximity is obtained by harmonizing the kernel representat…
The Blavatnik School of Computer Science, Tel Aviv University（特拉维夫大学布拉瓦尼克计算机科学学院）
Max-Pooling operations are a core component of deep learning architectures. In particular, they are part of most convolutional architectures used in machine vision, since pooling is a natural approach to pattern detection problems. However, these architectures are not well understood from a theoretical perspective. For example, we do not understand when they can be globally optimized, and what is the effect of over-parameterization on generalization. Here we perform a theoretical analysis of a convolutional max-pooling architecture, proving that it can be globally optimized, and can generalize…
Ulm University（乌尔姆大学）；Tübingen University（蒂宾根大学）；Masaryk University（马萨里克大学）；University of Catalonia（加泰罗尼亚大学）；University College London（伦敦大学学院）
Proteins perform a large variety of functions in living organisms, thus playing a key role in biology. As of now, available learning algorithms to process protein data do not consider several particularities of such data and/or do not scale well for large protein conformations. To fill this gap, we propose two new learning operations enabling deep 3D analysis of large-scale protein data. First, we introduce a novel convolution operator which considers both, the intrinsic (invariant under protein folding) as well as extrinsic (invariant under bonding) structure, by using $n$-D convolutions defi…
University of Technology Sydney（悉尼科技大学）；Monash University（莫纳什大学）
Graph convolutional networks (GCNs) have recently become one of the most powerful tools for graph analytics tasks in numerous applications, ranging from social networks and natural language processing to bioinformatics and chemoinformatics, thanks to their ability to capture the complex relationships between concepts. At present, the vast majority of GCNs use a neighborhood aggregation framework to learn a continuous and compact vector, then performing a pooling operation to generalize graph embedding for the classification task. These approaches have two disadvantages in the graph classificat…
Generative Adversarial Networks (GANs) are a powerful class of generative models. Despite their successes, the most appropriate choice of a GAN network architecture is still not well understood. GAN models for image synthesis have adopted a deep convolutional network architecture, which eliminates or minimizes the use of fully connected and pooling layers in favor of convolution layers in the generator and discriminator of GANs. In this paper, we demonstrate that a convolution network architecture utilizing deep fully connected layers and pooling layers can be more effective than the tradition…
Recent studies have demonstrated the power of recurrent neural networks for machine translation, image captioning and speech recognition. For the task of capturing temporal structure in video, however, there still remain numerous open research questions. Current research suggests using a simple temporal feature pooling strategy to take into account the temporal aspect of video. We demonstrate that this method is not sufficient for gesture recognition, where temporal information is more discriminative compared to general video classification tasks. We explore deep architectures for gesture reco…
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…
In modern computer vision tasks, convolutional neural networks (CNNs) are indispensable for image classification tasks due to their efficiency and effectiveness. Part of their superiority compared to other architectures, comes from the fact that a single, local filter is shared across the entire image. However, there are scenarios where we may need to treat spatial locations in non-uniform manner. We see this in nature when considering how humans have evolved foveation to process different areas in their field of vision with varying levels of detail. In this paper we propose a way to enable CN…
University of Kent（肯特大学）；University of Oxford（牛津大学）
Acoustic scenes are rich and redundant in their content. In this work, we present a spatio-temporal attention pooling layer coupled with a convolutional recurrent neural network to learn from patterns that are discriminative while suppressing those that are irrelevant for acoustic scene classification. The convolutional layers in this network learn invariant features from time-frequency input. The bidirectional recurrent layers are then able to encode the temporal dynamics of the resulting convolutional features. Afterwards, a two-dimensional attention mask is formed via the outer product of t…
Princeton University（普林斯顿大学）；University of Technology Sydney（悉尼科技大学）；Max Planck Institute for Mathematics in the Sciences（马克斯·普朗克数学科学研究所）；University of New South Wales（新南威尔士大学）；Zhejiang Normal University（浙江师范大学）；University of Cambridge（剑桥大学）
Graph neural networks (GNNs) extends the functionality of traditional neural networks to graph-structured data. Similar to CNNs, an optimized design of graph convolution and pooling is key to success. Borrowing ideas from physics, we propose a path integral based graph neural networks (PAN) for classification and regression tasks on graphs. Specifically, we consider a convolution operation that involves every path linking the message sender and receiver with learnable weights depending on the path length, which corresponds to the maximal entropy random walk. It generalizes the graph Laplacian …
Polygonal meshes provide an efficient representation for 3D shapes. They explicitly capture both shape surface and topology, and leverage non-uniformity to represent large flat regions as well as sharp, intricate features. This non-uniformity and irregularity, however, inhibits mesh analysis efforts using neural networks that combine convolution and pooling operations. In this paper, we utilize the unique properties of the mesh for a direct analysis of 3D shapes using MeshCNN, a convolutional neural network designed specifically for triangular meshes. Analogous to classic CNNs, MeshCNN combine…
Tianjin University（天津大学）；Dalian University of Technology（大连理工大学）；Harbin Institute of Technology（哈尔滨工业大学）；The Hong Kong Polytechnic University（香港理工大学）
Compared with global average pooling in existing deep convolutional neural networks (CNNs), global covariance pooling can capture richer statistics of deep features, having potential for improving representation and generalization abilities of deep CNNs. However, integration of global covariance pooling into deep CNNs brings two challenges: (1) robust covariance estimation given deep features of high dimension and small sample size; (2) appropriate usage of geometry of covariances. To address these challenges, we propose a global Matrix Power Normalized COVariance (MPN-COV) Pooling. Our MPN-CO…
The current methodology in tackling Acoustic Scene Classification (ASC) task can be described in two steps, preprocessing of the audio waveform into log-mel spectrogram and then using it as the input representation for Convolutional Neural Network (CNN). This paradigm shift occurs after DCASE 2016 where this framework model achieves the state-of-the-art result in ASC tasks on the (ESC-50) dataset and achieved an accuracy of 64.5%, which constitute to 20.5% improvement over the baseline model, and DCASE 2016 dataset with an accuracy of 90.0% (development) and 86.2% (evaluation), which constitut…
