arXiv research

Convolutional Neural Networks, as most artificial neural networks, are commonly viewed as methods different in essence from kernel-based methods. We provide a systematic translation of Convolutional Neural Networks (ConvNets) into their kernel-based counterparts, Convolutional Kernel Networks (CKNs), and demonstrate th…

Convolution and pooling improve kernel methods in image classification.

Graph convolutional kernel networks generalize CNNs to graph data.

VC dimensions of group CNNs are infinite for certain kernels and groups.

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 la…

Kernel Quantization improves CNN compression without sacrificing performance.

Deep convolutional networks can be understood through kernel methods, providing insights into their inductive bias.

We present a practical way of introducing convolutional structure into Gaussian processes, making them more suited to high-dimensional inputs like images. The main contribution of our work is the construction of an inter-domain inducing point approximation that is well-tailored to the convolutional kernel. This allows …

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 convoluti…

Unified theory for adaptive image convolutions using metric perspectives.

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 corresp…

This work studies nonnegativity-preserving kernels for stochastic equations and their applications.

Convolutional neural network is a very important model of deep learning. It can help avoid the exploding/vanishing gradient problem and improve the generalizability of a neural network if the singular values of the Jacobian of a layer are bounded around $1$ in the training process. We propose a new penalty function for…

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 t…

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…

The paper proposes an ensemble of convolution-based methods for fault detection in gearboxes.

Locality helps in learning from high-dimensional data.

S4 model improves long sequence modeling efficiency.

We describe convolutional networks using harmonic functions.

In this paper, we introduce a new image representation based on a multilayer kernel machine. Unlike traditional kernel methods where data representation is decoupled from the prediction task, we learn how to shape the kernel with supervision. We proceed by first proposing improvements of the recently-introduced convolu…

New unsupervised learning technique learns independent kernels for better machine learning tasks.

3D convolutional neural networks are difficult to train because they are parameter-expensive and data-hungry. To solve these problems we propose a simple technique for learning 3D convolutional kernels efficiently requiring less training data. We achieve this by factorizing the 3D kernel along the temporal dimension, r…

We give a short proof of a strong version of the short time asymptotic expansion of heat kernels associated to Laplace type operators acting on sections of vector bundles over compact Riemannian manifolds, including exponential decay of the difference of the approximate heat kernel and the true heat kernel. We use this…

Deep Gaussian processes (DGPs) provide a Bayesian non-parametric alternative to standard parametric deep learning models. A DGP is formed by stacking multiple GPs resulting in a well-regularized composition of functions. The Bayesian framework that equips the model with attractive properties, such as implicit capacity …

Although the convolutional neural networks (CNNs) have become popular for various image processing and computer vision task recently, it remains a challenging problem to reduce the storage cost of the parameters for resource-limited platforms. In the previous studies, tensor decomposition (TD) has achieved promising co…

Convolutional DKMs improve kernel methods on MNIST, CIFAR-10, and CIFAR-100.

A novel kernel-based support vector machine (SVM) for graph classification is proposed. The SVM feature space mapping consists of a sequence of graph convolutional layers, which generates a vector space representation for each vertex, followed by a pooling layer which generates a reproducing kernel Hilbert space (RKHS)…

HKConv learns hyperbolic features by aggregating kernel points.

We show that the output of a (residual) convolutional neural network (CNN) with an appropriate prior over the weights and biases is a Gaussian process (GP) in the limit of infinitely many convolutional filters, extending similar results for dense networks. For a CNN, the equivalent kernel can be computed exactly and, u…

The success of deep convolutional architectures is often attributed in part to their ability to learn multiscale and invariant representations of natural signals. However, a precise study of these properties and how they affect learning guarantees is still missing. In this paper, we consider deep convolutional represen…

Recent research shows that for training with $\ell_2$ loss, convolutional neural networks (CNNs) whose width (number of channels in convolutional layers) goes to infinity correspond to regression with respect to the CNN Gaussian Process kernel (CNN-GP) if only the last layer is trained, and correspond to regression wit…

Recently, non-stationary spectral kernels have drawn much attention, owing to its powerful feature representation ability in revealing long-range correlations and input-dependent characteristics. However, non-stationary spectral kernels are still shallow models, thus they are deficient to learn both hierarchical featur…

In this paper, we firstly introduce a method to efficiently implement large-scale high-dimensional convolution with realistic memristor-based circuit components. An experiment verified simulator is adapted for accurate prediction of analog crossbar behavior. An improved conversion algorithm is developed to convert conv…

Vanilla convolutional neural networks are known to provide superior performance not only in image recognition tasks but also in natural language processing and time series analysis. One of the strengths of convolutional layers is the ability to learn features about spatial relations in the input domain using various pa…

New mechanism discovered for feature learning in CNNs.

In this paper we study the problem of learning the weights of a deep convolutional neural network. We consider a network where convolutions are carried out over non-overlapping patches with a single kernel in each layer. We develop an algorithm for simultaneously learning all the kernels from the training data. Our app…

Convolutional operator learning is gaining attention in many signal processing and computer vision applications. Learning kernels has mostly relied on so-called patch-domain approaches that extract and store many overlapping patches across training signals. Due to memory demands, patch-domain methods have limitations w…

A CNN-based method detects and counts corn kernels from images.

Study learns convolution operators on compact Abelian groups using regularization.

We introduce the convolutional spectral kernel (CSK), a novel family of non-stationary, nonparametric covariance kernels for Gaussian process (GP) models, derived from the convolution between two imaginary radial basis functions. We present a principled framework to interpret CSK, as well as other deep probabilistic mo…

Study shows deterministic equivalent for neural network kernel convergence.

Bayesian convolutional deep sets improve ambiguity in stationary process modeling.

We introduce a guide to help deep learning practitioners understand and manipulate convolutional neural network architectures. The guide clarifies the relationship between various properties (input shape, kernel shape, zero padding, strides and output shape) of convolutional, pooling and transposed convolutional layers…

Proposes a new CNN for meshes that can handle orientation.

We present a convolutional network that is equivariant to rigid body motions. The model uses scalar-, vector-, and tensor fields over 3D Euclidean space to represent data, and equivariant convolutions to map between such representations. These SE(3)-equivariant convolutions utilize kernels which are parameterized as a …

Improved deep kernel machine achieves 94.5% test accuracy on CIFAR-10.

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. …

Regularization techniques are widely used to improve the generality, robustness, and efficiency of deep convolutional neural networks (DCNNs). In this paper, we propose a novel approach of regulating DCNN convolutional kernels by a structured filter bank. Comparing with the existing regularization methods, such as $\el…