VC dimensions of group CNNs are infinite for certain kernels and groups.
problem Estimating the generalization capacity of group convolutional neural networks.
method Identifying precise VC dimension estimates for simple sets of group CNNs.
result Two-parameter families of convolutional neural networks have an infinite VC dimension for infinite groups and certain kernels.
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…
Convolutional neural networks converge quickly with gradient descent.
problem Learning efficient image classifiers with over-parameterized networks.
method Gradient descent for training over-parametrized CNNs with global average-pooling.
result Gradient descent quickly reduces the misclassification risk of CNNs.
Convolutional neural networks improve image classification accuracy.
problem Improving accuracy in image classification.
method Analyzing the convergence rate of misclassification risk for image classifiers.
result A rate of convergence independent of image dimension proves the effectiveness of CNNs.
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…
This work proposes hyperbolic deep convolutional neural networks for better pattern recognition.
problem The limitations of Euclidean deep convolutional neural networks in capturing intricate patterns.
method Developed Hyperbolic DCNN based on Poincaré Disc, analyzing expansive convolution in non-Euclidean space.
result Hyperbolic convolutional architecture outperforms Euclidean ones in pattern recognition tasks.
Proves DCNNs with expansive convolution are strongly universally consistent.
problem Theoretical consistency of deep convolutional neural networks (DCNNs).
method Empirical risk minimization on DCNNs with expansive convolution (with zero-padding).
result DCNNs with expansive convolution are strongly universally consistent.
This research studies affine invariance in continuous-domain convolutional neural networks.
problem Recognizing patterns and features under affine transformations in continuous domains.
method Introduces a new criterion for assessing affine invariance, embeds images into the affine Lie group, and analyzes convolution over this group.
result Extends the scope of geometrical transformations that deep-learning pipelines can handle.
L-CNNs learn gauge invariant quantities on lattices.
problem Learning gauge invariant quantities on lattices.
method Novel convolutional layer preserving gauge equivariance and forming Wilson loops.
result L-CNNs can approximate any gauge covariant function on the lattice.
Convolutional neural networks (CNNs) have achieved breakthrough performances in a wide range of applications including image classification, semantic segmentation, and object detection. Previous research on characterizing the generalization ability of neural networks mostly focuses on fully connected neural networks (F…
L-CNNs maintain gauge symmetry on non-Abelian lattice theories.
problem Applying convolutional neural networks to non-Abelian lattice gauge theories while preserving gauge symmetry.
method Developed a geometric formulation of L-CNNs that are equivariant under global symmetries and gauge transformations.
result Convolutional operations in L-CNNs are a specific case of gauge-equivariant neural networks on SU(N) principal bundles. 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…
Proposes a new convolutional neural network for non-grid data.
problem Limited applicability of standard CNNs to non-grid structured data.
method Introduces Parametric Continuous Convolution (PCC) with learnable kernel functions.
result Significant improvement in point cloud segmentation and lidar motion estimation.
Recently, graph neural networks have been adopted in a wide variety of applications ranging from relational representations to modeling irregular data domains such as point clouds and social graphs. However, the space of graph neural network architectures remains highly fragmented impeding the development of optimized …
Simplicial neural networks extend graph neural networks to handle higher-order interactions.
problem Handling higher-order interactions in complex data structures.
method Define a convolution operation for simplicial complexes and use it to construct convolutional neural networks.
result SNNs effectively impute missing data in coauthorship complexes.
New neural model processes 2D data with long-range dependencies efficiently.
problem Limited receptive field of convolutions for complex 2D tasks.
method Proposes Matrix Shuffle-Exchange network with O(logn) layers and O(n2logn) complexity. result Exceeds convolutional and graph neural network baselines in long-range dependency modeling.
We introduce Group equivariant Convolutional Neural Networks (G-CNNs), a natural generalization of convolutional neural networks that reduces sample complexity by exploiting symmetries. G-CNNs use G-convolutions, a new type of layer that enjoys a substantially higher degree of weight sharing than regular convolution la…
In this work we propose a novel approach to utilize convolutional neural networks for time series forecasting. The time direction of the sequential data with spatial dimensions D=1,2 is considered democratically as the input of a spatiotemporal (D+1)-dimensional convolutional neural network. Latter then reduces the…
Convolutional networks struggle with repeating patterns in ECGs.
problem Modeling repeating patterns in electrocardiogram signals.
method Demonstrated through ECG examples, highlighting systemic issues in deep learning.
result Counterintuitive effects on generalization in deep networks.
The study examines deep convolutional neural networks and their learning ability.
problem Understanding the learning ability of deep convolutional neural networks (DCNNs).
method Examines DCNNs under both underparameterized and overparameterized settings, using a novel network deepening scheme.
result Establishes the first learning rates of underparameterized DCNNs and shows how adding layers can create interpolating DCNNs with good learning rates.
Combines BERT and graph CNN for improved text classification.
problem Text classification problems
method Combining BERT embedding and graph convolutional neural network
result Graph CNN model performs better than classical models combined with BERT
Deep learning has been widely applied and brought breakthroughs in speech recognition, computer vision, and many other domains. The involved deep neural network architectures and computational issues have been well studied in machine learning. But there lacks a theoretical foundation for understanding the approximation…
In this paper, some patterns of the Neuron Response of deep Convolutional Neural Networks were observed.
Convolutional neural networks predict the analytic rank of elliptic curves accurately.
problem Predicting the analytic rank of elliptic curves over Q.
method Applied one-dimensional convolutional neural networks to Frobenius traces.
result High accuracy predictions for analytic rank across various conductors.
New method tightens Lipschitz bounds for CNNs efficiently.
problem Lipschitz regularization of Convolutional Neural Networks (CNNs).
method Using Toeplitz matrix theory, introduces a tight and computationally efficient upper bound for convolutional layers.
result Developed an algorithm to train Lipschitz regularized CNNs.
A hybrid method improves Convolutional Neural Networks training.
problem Training Convolutional Neural Networks efficiently and avoiding local minima.
method Combines backpropagation with evolutionary strategies.
result Improves accuracy by 0.61% on CIFAR-10 image classification.
In this paper we cast the well-known convolutional neural network in a Gaussian process perspective. In this way we hope to gain additional insights into the performance of convolutional networks, in particular understand under what circumstances they tend to perform well and what assumptions are implicitly made in the…
The paper verifies deep neural networks' ability to approximate functions on spheres.
problem Theoretical verification of deep neural networks' performance on spherical functions.
method Spherical analysis using reproducing kernels and convolutional factorizations.
result Rates of uniform approximation for functions in Sobolev spaces and additive ridge forms.
New method solves PDEs on spheres using physics-informed convolutional neural networks.
problem Solving PDEs on surfaces, especially spheres, with high accuracy and efficiency.
method Physics-informed convolutional neural networks (PICNN) with theoretical analysis and approximation results.
result Established fast convergence rates for PICNN solving PDEs on spheres.
Lie groupoid equivariant neural networks are a new type of neural network.
problem Designing neural networks that respect the structure of Lie groupoids.
method Introducing Lie groupoid equivariant convolutions and layers, and showing their equivalence to Lie algebroid-equivariant networks.
result Lie groupoid equivariant neural networks are equivalent to certain Lie algebroid-equivariant networks.
The fully connected layers of a deep convolutional neural network typically contain over 90% of the network parameters, and consume the majority of the memory required to store the network parameters. Reducing the number of parameters while preserving essentially the same predictive performance is critically important …
L-CNNs preserve gauge symmetry in neural networks.
problem Applying machine learning to lattice gauge theory while preserving gauge symmetry.
method L-CNNs use gauge equivariance to construct a gauge equivariant convolutional layer and bilinear layer.
result L-CNNs achieve higher accuracy in non-linear regression tasks compared to non-equivariant CNNs.
New multigrid approach reduces CNN parameters by focusing on structured convolutions.
problem Redundancy in standard CNNs leads to high parameter count.
method Replace standard convolutions with structured multilevel convolutions.
result Linearly proportional number of parameters to network width, no loss in accuracy.
New mechanism discovered for feature learning in CNNs.
problem Understanding how CNNs learn features from images.
method Proposed Convolutional Neural Feature Ansatz linking filter covariances to patch-based AGOPs.
result Deep ConvRFM algorithm learns features similar to deep CNNs, improving performance.
In this paper, we introduce Channel-wise recurrent convolutional neural networks (RecNets), a family of novel, compact neural network architectures for computer vision tasks inspired by recurrent neural networks (RNNs). RecNets build upon Channel-wise recurrent convolutional (CRC) layers, a novel type of convolutional …
Convolutional neural networks handle rotated image symmetries without dimensionality issues.
problem Binary image classification with rotational symmetry.
method Least squares plug-in classifiers based on convolutional neural networks under rotationally symmetric assumptions.
result Convolutional neural networks can circumvent the curse of dimensionality in binary image classification with rotational symmetry.
Review of neural network expressivity and architectures.
problem Understanding neural network expressivity across different architectures.
method Comprehensive overview of approximation results for various neural network types.
result Deep neural networks offer advantages over shallow ones for specific function classes.
New method shows fully-connected networks can learn convolutional structures from data.
problem How to learn convolutional structures from translation-invariant data.
method Data-driven emergence of convolutional structure in neural networks.
result Initially fully-connected networks can learn convolutional structures from their inputs.
We establish large deviation principles for convolutional neural networks.
problem Understanding the behavior of convolutional neural networks in the infinite-channel limit.
method We establish large deviation principles for convolutional neural networks under Gaussian prior and posterior distributions.
result We provide a large deviation principle for the sequence of conditional covariance matrices and the posterior distribution.
We propose a new algorithm to learn a one-hidden-layer convolutional neural network where both the convolutional weights and the outputs weights are parameters to be learned. Our algorithm works for a general class of (potentially overlapping) patches, including commonly used structures for computer vision tasks. Our a…
Paper analyzes the free energy of CNNs with skip connections in Bayesian learning.
problem Dependency of CNNs with skip connections on the number of parameters.
method Examines the Bayesian free energy of CNNs with and without skip connections.
result The upper bound of free energy of Bayesian CNN with skip connections does not depend on overparametrization.
This paper describes our UNet based deep convolutional neural network approach on the Traffic4cast challenge 2019. Challenges task is to predict future traffic flow volume, heading and speed on high resolution whole city map. We used UNet based deep convolutional neural network to train predictive model for the short t…
Improved anomaly detection in time series data using kervolutional neural networks.
problem Anomaly detection in time series data.
method Mixed kervolutional and convolutional layers in a temporal auto-encoder.
result The mixed model detects anomalies more sensitively in time series data.
Convolution has been playing a prominent role in various applications in science and engineering for many years. It is the most important operation in convolutional neural networks. There has been a recent growth of interests of research in generalizing convolutions on curved domains such as manifolds and graphs. Howev…
Most of the research in convolutional neural networks has focused on increasing network depth to improve accuracy, resulting in a massive number of parameters which restricts the trained network to platforms with memory and processing constraints. We propose to modify the structure of the Very Deep Convolutional Neural…
The paper explains implicit regularization in hierarchical tensor factorization and deep CNNs.
problem Understanding implicit regularization in complex neural network architectures.
method Theoretical analysis using dynamical systems to overcome challenges in hierarchy.
result Established implicit regularization towards low hierarchical tensor rank, equivalent to locality in CNNs.
New bounds for neural networks ensure robustness and accuracy.
problem Ensuring robustness of neural networks by computing Lipschitz constants.
method Analyzed and proposed new bounds for l1 and l∞ norms, using explicit and implicit methods for convnets. result One of the new bounds is optimal and more accurate than existing ones.
This paper proposes reusing CNN layers to speed up hyperparameters tuning.
problem Time-consuming hyperparameters tuning in CNNs.
method Reuse trained convolutional layers among different trainings.
result Reduces training time and increases accuracy of neural networks.