To date, most state-of-the-art sequence modeling architectures use attention to build generative models for language based tasks. Some of these models use all the available sequence tokens to generate an attention distribution which results in time complexity of $O(n^2)$. Alternatively, they utilize depthwise convolutions with softmax normalized kernels of size $k$ acting as a limited-window self-attention, resulting in time complexity of $O(k{\cdot}n)$. In this paper, we introduce Time-aware Large Kernel (TaLK) Convolutions, a novel adaptive convolution operation that learns to predict the size of a summation kernel instead of using a fixed-sized kernel matrix. This method yields a time complexity of $O(n)$, effectively making the sequence encoding process linear to the number of tokens. We evaluate the proposed method on large-scale standard machine translation, abstractive summarization and language modeling datasets and show that TaLK Convolutions constitute an efficient improvement over other attention/convolution based approaches.
Stanford University（斯坦福大学）；University of California, Berkeley（加州大学伯克利分校）
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 hypercub…
Most methods for time series classification that attain state-of-the-art accuracy have high computational complexity, requiring significant training time even for smaller datasets, and are intractable for larger datasets. Additionally, many existing methods focus on a single type of feature such as shape or frequency. Building on the recent success of convolutional neural networks for time series classification, we show that simple linear classifiers using random convolutional kernels achieve state-of-the-art accuracy with a fraction of the computational expense of existing methods.
Stony Brook University（石溪大学）；The State University of New York Korea（纽约州立大学韩国分校）
We applied pre-defined kernels also known as filters or masks developed for image processing to convolution neural network. Instead of letting neural networks find its own kernels, we used 41 different general-purpose kernels of blurring, edge detecting, sharpening, discrete cosine transformation, etc. for the first layer of the convolution neural networks. This architecture, thus named as general filter convolutional neural network (GFNN), can reduce training time by 30% with a better accuracy compared to the regular convolutional neural network (CNN). GFNN also can be trained to achieve 90% …
Action recognition greatly benefits motion understanding in video analysis. Recurrent networks such as long short-term memory (LSTM) networks are a popular choice for motion-aware sequence learning tasks. Recently, a convolutional extension of LSTM was proposed, in which input-to-hidden and hidden-to-hidden transitions are modeled through convolution with a single kernel. This implies an unavoidable trade-off between effectiveness and efficiency. Herein, we propose a new enhancement to convolutional LSTM networks that supports accommodation of multiple convolutional kernels and layers. This re…
China University of Geosciences（中国地质大学）；University of Kentucky（肯塔基大学）
Convolutional neural network is an important model in deep learning. To avoid exploding/vanishing gradient problems and to improve the generalizability of a neural network, it is desirable to have a convolution operation that nearly preserves the norm, or to have the singular values of the transformation matrix corresponding to a convolutional kernel bounded around $1$. We propose a penalty function that can be used in the optimization of a convolutional neural network to constrain the singular values of the transformation matrix around $1$. We derive an algorithm to carry out the gradient des…
Columbia University（哥伦比亚大学）；Peking University（北京大学）；Deepwise AI Lab（深度智耀人工智能实验室）；The University of Hong Kong（香港大学）
This paper presents a novel network compression framework Kernel Quantization (KQ), targeting to efficiently convert any pre-trained full-precision convolutional neural network (CNN) model into a low-precision version without significant performance loss. Unlike existing methods struggling with weight bit-length, KQ has the potential in improving the compression ratio by considering the convolution kernel as the quantization unit. Inspired by the evolution from weight pruning to filter pruning, we propose to quantize in both kernel and weight level. Instead of representing each weight paramete…
As a popular approach to modeling the dynamics of training overparametrized neural networks (NNs), the neural tangent kernels (NTK) are known to fall behind real-world NNs in generalization ability. This performance gap is in part due to the \textit{label agnostic} nature of the NTK, which renders the resulting kernel not as \textit{locally elastic} as NNs~\citep{he2019local}. In this paper, we introduce a novel approach from the perspective of \emph{label-awareness} to reduce this gap for the NTK. Specifically, we propose two label-aware kernels that are each a superimposition of a label-agno…
Expanding the receptive field to capture large-scale context is key to obtaining good performance in dense prediction tasks, such as human pose estimation. While many state-of-the-art fully-convolutional architectures enlarge the receptive field by reducing resolution using strided convolution or pooling layers, the most straightforward strategy is adopting large filters. This, however, is costly because of the quadratic increase in the number of parameters and multiply-add operations. In this work, we explore using learnable box filters to allow for convolution with arbitrarily large kernel s…
Vrije Universiteit Amsterdam（阿姆斯特丹自由大学）；Delft University of Technology（代尔夫特理工大学）；University of Amsterdam（阿姆斯特丹大学）
When designing Convolutional Neural Networks (CNNs), one must select the size\break of the convolutional kernels before training. Recent works show CNNs benefit from different kernel sizes at different layers, but exploring all possible combinations is unfeasible in practice. A more efficient approach is to learn the kernel size during training. However, existing works that learn the kernel size have a limited bandwidth. These approaches scale kernels by dilation, and thus the detail they can describe is limited. In this work, we propose FlexConv, a novel convolutional operation with which hig…
A novel algorithm is proposed to solve the sample-based optimal transport problem. An adversarial formulation of the push-forward condition uses a test function built as a convolution between an adaptive kernel and an evolving probability distribution $ν$ over a latent variable $b$. Approximating this convolution by its simulation over evolving samples $b^i(t)$ of $ν$, the parameterization of the test function reduces to determining the flow of these samples. This flow, discretized over discrete time steps $t_n$, is built from the composition of elementary maps. The optimal transport also foll…
Shenzhen Institutes of Advanced Technology, Chinese Academy of Sciences（中国科学院深圳先进技术研究院）；Shenzhen College of Advanced Technology, University of Chinese Academy of Sciences（中国科学院大学深圳先进技术学院）；Institute for Computing and Information Sciences, Radboud University（拉德堡德大学计算与信息科学研究所）；Faculty of Management, Science and Technology, Open University of The Netherlands（荷兰开放大学管理、科学与技术学院）
Multi-output Gaussian processes (MOGPs) are an extension of Gaussian Processes (GPs) for predicting multiple output variables (also called channels, tasks) simultaneously. In this paper we use the convolution theorem to design a new kernel for MOGPs, by modeling cross channel dependencies through cross convolution of time and phase delayed components in the spectral domain. The resulting kernel is called Multi-Output Convolution Spectral Mixture (MOCSM) kernel. Results of extensive experiments on synthetic and real-life datasets demonstrate the advantages of the proposed kernel and its state o…
We present a novel deep learning architecture in which the convolution operation leverages heterogeneous kernels. The proposed HetConv (Heterogeneous Kernel-Based Convolution) reduces the computation (FLOPs) and the number of parameters as compared to standard convolution operation while still maintaining representational efficiency. To show the effectiveness of our proposed convolution, we present extensive experimental results on the standard convolutional neural network (CNN) architectures such as VGG \cite{vgg2014very} and ResNet \cite{resnet}. We find that after replacing the standard con…
Vrije Universiteit Amsterdam（阿姆斯特丹自由大学）；University of Amsterdam（阿姆斯特丹大学）
Conventional neural architectures for sequential data present important limitations. Recurrent networks suffer from exploding and vanishing gradients, small effective memory horizons, and must be trained sequentially. Convolutional networks are unable to handle sequences of unknown size and their memory horizon must be defined a priori. In this work, we show that all these problems can be solved by formulating convolutional kernels in CNNs as continuous functions. The resulting Continuous Kernel Convolution (CKConv) allows us to model arbitrarily long sequences in a parallel manner, within a s…
College of Computer and Information Science, Southwest University（西南大学计算机与信息科学学院）；Chongqing University of Posts and Telecommunications（重庆邮电大学）
The deep convolutional neural networks (CNNs)-based single image dehazing methods have achieved significant success. The previous methods are devoted to improving the network's performance by increasing the network's depth and width. The current methods focus on increasing the convolutional kernel size to enhance its performance by benefiting from the larger receptive field. However, directly increasing the size of the convolutional kernel introduces a massive amount of computational overhead and parameters. Thus, a novel Large Kernel Convolution Dehaze Block (LKD Block) consisting of the Deco…
Intel Labs China（英特尔中国研究院）；The Chinese University of Hong Kong（香港中文大学）
Learning a single static convolutional kernel in each convolutional layer is the common training paradigm of modern Convolutional Neural Networks (CNNs). Instead, recent research in dynamic convolution shows that learning a linear combination of $n$ convolutional kernels weighted with their input-dependent attentions can significantly improve the accuracy of light-weight CNNs, while maintaining efficient inference. However, we observe that existing works endow convolutional kernels with the dynamic property through one dimension (regarding the convolutional kernel number) of the kernel space, …
LIGM, Ecole des Ponts（巴黎桥路学院LIGM实验室）；Univ Gustave Eiffel（古斯塔夫·埃菲尔大学）；CNRS（法国国家科学研究中心）
Recent state-of-the-art methods for point cloud processing are based on the notion of point convolution, for which several approaches have been proposed. In this paper, inspired by discrete convolution in image processing, we provide a formulation to relate and analyze a number of point convolution methods. We also propose our own convolution variant, that separates the estimation of geometry-less kernel weights and their alignment to the spatial support of features. Additionally, we define a point sampling strategy for convolution that is both effective and fast. Finally, using our convolutio…
Convolution is a fundamental operation in many applications, such as computer vision, natural language processing, image processing, etc. Recent successes of convolutional neural networks in various deep learning applications put even higher demand on fast convolution. The high computation throughput and memory bandwidth of graphics processing units (GPUs) make GPUs a natural choice for accelerating convolution operations. However, maximally exploiting the available memory bandwidth of GPUs for convolution is a challenging task. This paper introduces a general model to address the mismatch bet…
We demonstrate a simple connection between dictionary methods for time series classification, which involve extracting and counting symbolic patterns in time series, and methods based on transforming input time series using convolutional kernels, namely ROCKET and its variants. We show that by adjusting a single hyperparameter it is possible to move by degrees between models resembling dictionary methods and models resembling ROCKET. We present HYDRA, a simple, fast, and accurate dictionary method for time series classification using competing convolutional kernels, combining key aspects of bo…
Group equivariant convolutional networks (GCNNs) endow classical convolutional networks with additional symmetry priors, which can lead to a considerably improved performance. Recent advances in the theoretical description of GCNNs revealed that such models can generally be understood as performing convolutions with G-steerable kernels, that is, kernels that satisfy an equivariance constraint themselves. While the G-steerability constraint has been derived, it has to date only been solved for specific use cases - a general characterization of G-steerable kernel spaces is still missing. This wo…
Tsinghua University（清华大学）；Peng Cheng Laboratory（鹏城实验室）；Tencent AI LAB（腾讯人工智能实验室）
Kernels on discrete structures evaluate pairwise similarities between objects which capture semantics and inherent topology information. Existing kernels on discrete structures are only developed by topology information(such as adjacency matrix of graphs), without considering original attributes of objects. This paper proposes a two-phase paradigm to aggregate comprehensive information on discrete structures leading to a Discount Markov Diffusion Learnable Kernel (DMDLK). Specifically, based on the underlying projection of DMDLK, we design a Simple Hypergraph Kernel Convolution (SHKC) for hidd…
This paper describes maxDNN, a computationally efficient convolution kernel for deep learning with the NVIDIA Maxwell GPU. maxDNN reaches 96.3% computational efficiency on typical deep learning network architectures. The design combines ideas from cuda-convnet2 with the Maxas SGEMM assembly code. We only address forward propagation (FPROP) operation of the network, but we believe that the same techniques used here will be effective for backward propagation (BPROP) as well.
Depthwise convolution is becoming increasingly popular in modern efficient ConvNets, but its kernel size is often overlooked. In this paper, we systematically study the impact of different kernel sizes, and observe that combining the benefits of multiple kernel sizes can lead to better accuracy and efficiency. Based on this observation, we propose a new mixed depthwise convolution (MixConv), which naturally mixes up multiple kernel sizes in a single convolution. As a simple drop-in replacement of vanilla depthwise convolution, our MixConv improves the accuracy and efficiency for existing Mobil…
University of Toronto（多伦多大学）；Concordia University（康考迪亚大学）
Random convolution kernel transform (Rocket) is a fast, efficient, and novel approach for time series feature extraction using a large number of independent randomly initialized 1-D convolution kernels of different configurations. The output of the convolution operation on each time series is represented by a partial positive value (PPV). A concatenation of PPVs from all kernels is the input feature vector to a Ridge regression classifier. Unlike typical deep learning models, the kernels are not trained and there is no weighted/trainable connection between kernels or concatenated features and …
University of Louisiana at Lafayette（路易斯安那大学拉斐特分校）
Transpose convolution has shown prominence in many deep learning applications. However, transpose convolution layers are computationally intensive due to the increased feature map size due to adding zeros after each element in each row and column. Thus, convolution operation on the expanded input feature map leads to poor utilization of hardware resources. The main reason for unnecessary multiplication operations is zeros at predefined positions in the input feature map. We propose an algorithmic-level optimization technique for the effective transpose convolution implementation to solve these…
Beijing National Research Center for Information Science and Technology (BNRist)（北京信息科学与技术国家研究中心）；School of Software, Tsinghua University（清华大学软件学院）；Department of Automation, Tsinghua University（清华大学自动化系）；Institute for Brain and Cognitive Sciences, Tsinghua University（清华大学脑与认知科学研究所）；WMG Data Science, University of Warwick（华威大学WMG数据科学部）
As designing appropriate Convolutional Neural Network (CNN) architecture in the context of a given application usually involves heavy human works or numerous GPU hours, the research community is soliciting the architecture-neutral CNN structures, which can be easily plugged into multiple mature architectures to improve the performance on our real-world applications. We propose Asymmetric Convolution Block (ACB), an architecture-neutral structure as a CNN building block, which uses 1D asymmetric convolutions to strengthen the square convolution kernels. For an off-the-shelf architecture, we rep…
We propose a novel approach for designing kernels for support vector machines (SVMs) when the class label is linked to the observation through a latent state and the likelihood function of the observation given the state (the sensing model) is available. We show that the Bayes-optimum decision boundary is a hyperplane under a mapping defined by the likelihood function. Combining this with the maximum margin principle yields kernels for SVMs that leverage knowledge of the sensing model in an optimal way. We derive the optimum kernel for the bag-of-words (BoWs) sensing model and demonstrate its …
Time series classification with random convolution kernels: pooling operators and input representations matter
Univ. Artois, UR 4025, Laboratoire Systèmes Electrotechniques et Environnement (LSEE)（阿劳斯堡大学，UR 4025，电力系统与环境实验室）；Univ. Artois, UR 3926, Laboratoire de Génie Informatique et d’Automatique de l’Artois (LGI2A)（阿劳斯堡大学，UR 3926，阿劳斯堡信息与自动化实验室）
Irish Centre for Maternal and Child Health Research (INFANT)（爱尔兰母婴健康研究中心（INFANT））；University College Cork（科克大学）
Linear classifiers with random convolution kernels are computationally efficient methods that need no design or domain knowledge. Unlike deep neural networks, there is no need to hand-craft a network architecture; the kernels are randomly generated and only the linear classifier needs training. A recently proposed method, RandOm Convolutional KErnel Transforms (ROCKETs), has shown high accuracy across a range of time-series data sets. Here we propose a multi-scale version of this method, using both high- and low-frequency components. We apply our methods to inter-burst detection in a cohort of…
Recent advances in optimization methods used for training convolutional neural networks (CNNs) with kernels, which are normalized according to particular constraints, have shown remarkable success. This work introduces an approach for training CNNs using ensembles of joint spaces of kernels constructed using different constraints. For this purpose, we address a problem of optimization on ensembles of products of submanifolds (PEMs) of convolution kernels. To this end, we first propose three strategies to construct ensembles of PEMs in CNNs. Next, we expound their geometric properties (metric a…
