New graph operations for stochastic processes improve model flexibility.
problem Limited flexibility in graph convolutional networks for stochastic processes.
method Parameterization of graph-dependent linear operations using functional calculus.
result Improved learning flexibility and richer behaviors in graph models.
Study learns convolution operators on compact Abelian groups using regularization.
problem Learning convolution operators on compact Abelian groups.
method Regularization-based approach with ridge regression estimator.
result Characterizes the accuracy of the estimator in terms of finite sample bounds.
New CAOL framework learns diverse convolutional filters for improved signal recovery.
problem Memory limitations in patch-domain approaches for learning kernels from large datasets.
method Convolutional Analysis Operator Learning (CAOL) framework with BPEG-M method.
result CAOL significantly accelerates convergence and improves reconstruction quality.
Characterizes and projects convolutional layers' singular values for improved deep learning performance.
problem Improving deep learning models' performance using convolutional layers.
method Characterizes and projects the singular values of convolutional layers, providing an effective regularizer.
result Improves test error of a deep residual network on CIFAR-10 from 6.2% to 5.3%.
A new framework decouples CNN features into intra-class and semantic differences.
problem Learning visual representations in CNNs is challenging.
method Proposes a decoupled learning framework that models intra-class variation and semantic difference independently.
result Decoupled reparameterization leads to significant performance gains and easier convergence.
Convolution and pooling improve kernel methods in image classification.
problem Understanding the interplay between approximation and generalization in convolutional architectures.
method Characterized RKHS of kernels with convolution, pooling, and downsampling, computed generalization error.
result Convolution and pooling operations trade off approximation with generalization power.
Paper studies a universal logical operator for deep networks, improving interpretability.
problem Learning a universal logical operator for deep convolution networks without manual prescription.
method Exploration of different logical operators (AND, OR, XOR) and learning a universal one.
result Insightful observations lead to a novel logical interpretation of deep convolution networks.
CAOL learns filters from large datasets, and this paper analyzes its performance.
problem Understanding how dataset size impacts CAOL filter updates.
method Analyzes the impact of dataset size on CAOL filter updates using deterministic and probabilistic bounds.
result Empirical evidence suggests that using more training data can improve CAOL performance.
New hypergraph operators improve graph neural networks for higher-order relationships.
problem Learning deep embeddings on high-order graph-structured data.
method Introducing hypergraph convolution and hypergraph attention operators.
result Extensive experimental results show the effectiveness of hypergraph operators.
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.
GCNs improve regression tasks by aggregating neighbor signals.
problem GCNs' statistical properties in regression tasks are poorly understood.
method Examined two GCN convolutions and their impact on learning error.
result GCNs have a bias-variance trade-off that depends on neighborhood size and topology.
Novel volumetric convolution for unit ball improves 3D object recognition.
problem Efficiently convolving functions in a unit ball for deep learning.
method Developed volumetric convolution using Zernike polynomials.
result Improved 3D object recognition through novel convolution.
Paper proposes multiscale self-attentive convolutions for vision and language.
problem Improving language and vision understanding models using self-attention.
method Developed 1D and 2D Self Attentive Convolutions (SAC), multiscale SAC (MSAC).
result MSAC enhances model performance for vision and language tasks.
DSGC unifies graph and grid convolutions.
problem Lack of understanding between graph and grid convolutions.
method Depthwise separable graph convolution.
result DSGC outperforms existing methods on benchmark datasets.
LeanConvNets reduces CNN costs without sacrificing accuracy.
problem High computational cost in fully-coupled CNNs.
method Sparsifying fully-coupled operators in CNNs.
result LeanConvNets achieve similar accuracy to state-of-the-art networks but with lower computational cost.
This paper completes the construction of arbitrary order conformally invariant differential operators in higher spin spaces. Jan Slovák has classified all conformally invariant differential operators on locally conformally flat manifolds. We complete his results in higher spin theory by giving explicit expressions for …
MeshCNN analyzes 3D shapes using edges, overcoming irregularities.
problem Irregularities in mesh representations hinder neural network analysis.
method MeshCNN uses specialized convolution and pooling layers on mesh edges, collapsing them to focus on important features.
result MeshCNN effectively analyzes 3D shapes, learning which edges to collapse.
HKConv learns hyperbolic features by aggregating kernel points.
problem Challenges in learning good hyperbolic representations using Euclidean operations.
method Proposes HKConv, a trainable hyperbolic convolution that correlates local features with kernel points and aggregates them.
result HKConv learns expressive local features according to hyperbolic geometry and enjoys equivariance to permutation and invariance to parallel transport.
New PTC convolution preserves properties of Euclidean convolutions on manifolds.
problem Lack of generalizable convolutions on curved domains with desirable properties.
method Parallel transport convolution (PTC) on Riemannian manifolds.
result PTC preserves compactly supported filters and directionality.
A new linear GCN model improves recommendation performance for large graphs.
problem Training difficulties and over-smoothing in GCN-based CF models.
method Proposes a linear residual graph convolutional network (LRGCCF) to address training difficulties and over-smoothing issues.
result The proposed model yields better efficiency and effectiveness on real datasets.
New 3D protein analysis methods improve accuracy.
problem Lack of suitable learning algorithms for protein data.
method Intrinsic-Extrinsic Convolution and Pooling for 3D protein structures.
result Outperforms state-of-the-art methods on protein analysis tasks.
Graph Prolongation Convolutional Networks improve model performance in microtubule bending simulations.
problem Improving prediction accuracy in coarse-grained mechanochemical simulations of microtubule bending.
method Defines a novel ensemble Graph Convolutional Network model using optimized linear projection operators to map between graph scales.
result Graph Prolongation-Convolutional Network outperforms other GCN ensemble models in predicting microtubule bending potential energy.
A new HGNN framework for complex data representation learning.
problem Learning representation for complex data in hypergraph structures.
method Designing hyperedge convolution operations for hypergraph learning.
result HGNN outperforms state-of-the-art methods in citation network and visual object recognition tasks.
We review the properties of transversality of distributions with respect to submersions. This allows us to construct a convolution product for a large class of distributions on Lie groupoids. We get a unital involutive algebra $\cE\_{r,s}'(G,Ω^{1/2})$ enlarging the convolution algebra C∞_c(G,Ω1/2) associate…
New model learns graph features for classification.
problem Graph classification with structural information loss.
method Transform graphs into vertex grids, apply vertex convolution.
result Model preserves structural information on local vertices.
A generative model is developed for deep (multi-layered) convolutional dictionary learning. A novel probabilistic pooling operation is integrated into the deep model, yielding efficient bottom-up (pretraining) and top-down (refinement) probabilistic learning. Experimental results demonstrate powerful capabilities of th…
We present a scalable approach for semi-supervised learning on graph-structured data that is based on an efficient variant of convolutional neural networks which operate directly on graphs. We motivate the choice of our convolutional architecture via a localized first-order approximation of spectral graph convolutions.…
LeanResNet reduces CNN complexity without sacrificing accuracy.
problem High computational cost in CNNs, especially in ResNets.
method Introduces lean convolution operators that reduce parameters and complexity.
result LeanResNet achieves comparable results to other reduced architectures with fewer parameters.
New method learns compressed transforms with flexible displacement operators.
problem Efficiently representing and learning shift-invariant patterns in neural networks.
method Explicitly learns over displacement operators and low-rank components in LDR matrices.
result Reduces sample complexity and improves model accuracy with fewer parameters.
Numerous important problems can be framed as learning from graph data. We propose a framework for learning convolutional neural networks for arbitrary graphs. These graphs may be undirected, directed, and with both discrete and continuous node and edge attributes. Analogous to image-based convolutional networks that op…
New framework for manifold convolutions using toric embeddings.
problem Computational intractability of manifold convolutions.
method Isometric embeddings into tori for global manifold convolutions.
result Global definition of manifold convolutions on finite approximations.
Network deconvolution removes redundant data to improve neural network performance.
problem Redundant data in neural networks makes training challenging.
method Network deconvolution optimally removes pixel-wise and channel-wise correlations before each layer.
result Network deconvolution improves performance across various datasets.
Paper revisits graph-CNNs using Laplace-Beltrami spectral filters and polynomials.
problem Improving spectral graph convolutional neural networks (graph-CNNs).
method Developed Laplace-Beltrami CNN (LB-CNN) by replacing graph Laplacian with LB operator and approximating spectral filters using Chebyshev, Laguerre, and Hermite polynomials.
result Classification accuracy of LB-CNN is not dependent on the type of polynomials or operators.
Proposes a new pooling operator for CNNs to handle spatially varying information.
problem Need to treat spatial locations in non-uniform manner for better image classification.
method Introduces an extended pooling operator that can learn different weights for each pixel location.
result The proposed pooling operator improves generalization and robustness in image classification tasks.
Local convolutions bias neural networks towards high-frequency adversarial examples.
problem High-frequency adversarial examples in neural networks.
method Analysis of different linear and nonlinear architectures, focusing on the impact of local convolution operations.
result Local convolutions induce an implicit bias towards high frequency features, leading to high-frequency adversarial examples.
BankGCN improves graph convolution networks by handling multi-channel signals with adaptive filter banks.
problem Handling multi-channel graph signals with limited architectures.
method BankGCN decomposes multi-channel signals into subspaces and uses adapted filters for each subspace.
result BankGCN achieves excellent performance in graph classification on benchmark datasets.
BiGraphNet generalizes graph neural networks for more efficient operations.
problem Fragmented graph neural network architectures hinder optimization.
method Explicitly separates input and output nodes, enabling new efficient operations.
result BiGraphNet accelerates and scales computations in hierarchical networks.
Self-attention can replace convolutional layers in vision tasks.
problem The supremacy of convolutional layers in vision tasks.
method Analysis and experiments with self-attention layers compared to convolutional layers.
result Self-attention layers can perform as well as convolutional layers and learn to do so.
SphereConv improves deep learning by learning angular representations on hyperspheres.
problem Challenges in training deep CNNs due to increased depth and larger parameter space.
method Introduces hyperspherical convolution (SphereConv) and deep hyperspherical convolution networks (SphereNet) to learn angular representations on hyperspheres.
result SphereNet effectively encodes discriminative representation and alleviates training difficulty.
We introduce a convolutional neural network that operates directly on graphs. These networks allow end-to-end learning of prediction pipelines whose inputs are graphs of arbitrary size and shape. The architecture we present generalizes standard molecular feature extraction methods based on circular fingerprints. We sho…
Cross-GCN models cross features in GCN for better performance.
problem GCN's lack of cross feature modeling limits its effectiveness.
method Introduces Cross-feature Graph Convolution (Cross-GCN) to model cross features explicitly.
result Explicit cross feature modeling improves GCN's performance on tasks requiring cross features.
Develops BASGCN for graph classification with improved feature learning.
problem Graph classification with information loss and imprecise representation.
method Transforms graphs into grid structures and defines a new spatial graph convolution operation.
result Reduces information loss and improves feature representation compared to existing models.
Defines a new algebra for singular foliations, extending Schwartz kernels.
problem Extending Schwartz kernel operators to singular foliations.
method Defines convolution algebra of transverse distributions, proves representation as operators on spaces of functions.
result Generalizes Schwartz kernel operators to singular foliations.
Dual-Primal Graph CNN learns vertex and edge features on graphs.
problem Learning features on non-Euclidean structured data like graphs.
method Alternates graph convolutional operations on graph and its dual.
result State-of-the-art results on various graph benchmarks.
TransGCN combines GCNs with transformation assumptions for better link prediction in KGs.
problem Link prediction in knowledge graphs for understanding graph structure.
method Unified GCN framework with simultaneous learning of entity and relation embeddings, using transformation assumptions.
result TransGCN outperforms state-of-the-art models on FB15K-237 and WN18RR.
New online method learns from all images, supports incomplete data.
problem High memory usage and limited training data in batch methods.
method Online convolutional dictionary learning with spatial mask support.
result Improved performance and better scalability with training set size.
Proposes a method to constrain singular values of convolutional kernels in neural networks.
problem Avoiding exploding/vanishing gradient problems and improving generalizability in neural networks.
method Introduces a penalty function to constrain singular values of convolutional kernels around 1, and derives an algorithm for optimization.
result Demonstrates the effectiveness of the method through numerical examples.
LGCL uses learnable filters to apply CNNs on graphs.
problem Applying CNNs to generic graphs like networks.
method Learnable graph convolutional layer (LGCL) and sub-graph training.
result LGCL achieves better performance on various graph datasets.