Paper introduces non-linear process convolutions for multi-output Gaussian processes.
problem Building accurate covariance functions for multi-output Gaussian processes.
method Volterra series for non-linearity, closed-form expressions for mean and covariance.
result Non-linear model outperforms classical process convolution in synthetic and real datasets.
This article demonstrates that convolutional operation can be converted to matrix multiplication, which has the same calculation way with fully connected layer. The article is helpful for the beginners of the neural network to understand how fully connected layer and the convolutional layer work in the backend. To be c…
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.
Traditional convolutional layers extract features from patches of data by applying a non-linearity on an affine function of the input. We propose a model that enhances this feature extraction process for the case of sequential data, by feeding patches of the data into a recurrent neural network and using the outputs or…
This paper explains a mechanism called phase collapse that improves image classification accuracy.
problem Understanding the role of non-linearities and convolutional filters in image classification.
method Demonstrates phase collapse as a mechanism that eliminates spatial variability and linearly separates classes.
result Phase collapse improves classification accuracy, while thresholding operators degrade performance.
XceptionTime improves hand gesture recognition accuracy using novel deep learning.
problem Improving hand gesture recognition from sparse sEMG signals.
method Depthwise separable convolutions, adaptive pooling, non-linear normalization.
result Significantly improved accuracy (5.71% improvement) in hand gesture recognition.
Deep convolutional networks provide state of the art classifications and regressions results over many high-dimensional problems. We review their architecture, which scatters data with a cascade of linear filter weights and non-linearities. A mathematical framework is introduced to analyze their properties. Computation…
IC-Network improves CNNs by integrating elastic collision units.
problem Designing more effective basic units in neural networks.
method Developed IC layer and IC block units combining the IC structure with convolution operations.
result Significant performance improvements in existing CNNs, reducing top-1 error from 22.85% to 21.49% on imagenet.
Rocket algorithm classifies time-series data efficiently using random projections and natural sparsity.
problem Time-series classification challenges in diverse fields.
method Random convolutional kernels, non-linear transformation, compressed sensing framework.
result Rocket algorithm preserves discriminative patterns in time-series data and expresses inherent sparsity.
New methods improve translation-equivariant neural processes for modeling unknown functions.
problem Modeling unknown latent functions from irregularly sampled measurements.
method Volterra series and set Fourier convolutions to address translation-equivariance and efficiency.
result Improved translation-equivariant neural processes with analytical transparency and linear scalability.
PDE-based G-CNNs add geometric symmetries to CNNs without augmentation.
problem Designing CNNs with built-in symmetries like rotation.
method Formulate CNN layers as PDE solvers on homogeneous spaces.
result PDE-G-CNNs achieve better performance with fewer parameters.
The paper generalizes equivariant neural networks on homogeneous spaces to the non-linear setting.
problem Equivariant neural networks on homogeneous spaces.
method Deriving generalized steerability constraints for non-linear equivariant layers.
result The universality of the derived construction for non-linear equivariant layers.
Improved texture synthesis using wavelet-based statistics with rectifier non-linearity.
problem Improving texture synthesis quality using wavelet representations.
method Proposes a family of statistics based on non-linear wavelet representations with a generalized rectifier non-linearity.
result Significantly improves visual quality of texture synthesis compared to classical wavelet-based models.
Wiatowski and Bölcskei, 2015, proved that deformation stability and vertical translation invariance of deep convolutional neural network-based feature extractors are guaranteed by the network structure per se rather than the specific convolution kernels and non-linearities. While the translation invariance result appli…
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.
Convolutional neural networks can regularize inverse problems without training.
problem Solving inverse problems like image recovery from limited data.
method Fixed or parameterized convolutional networks with few parameters.
result Untrained convolutional networks can recover images from few measurements.
Haar scattering networks improve pattern recognition across various tasks.
problem Improving pattern recognition in diverse tasks like regression and classification.
method Stacking convolutional filters based on Haar wavelets followed by non-linear operators.
result Outperformed best algorithms in 4 out of 18 data classification problems.
ThriftyNet uses a single convolutional layer recursively to maximize parameter usage.
problem Maximizing the use of parameters in deep convolutional neural networks.
method A single convolutional layer is used recursively, with normalization, non-linearities, downsampling, and shortcuts to maintain model expressivity.
result ThriftyNet achieves competitive performance with significantly fewer parameters.
Deep convolutional neural networks have led to breakthrough results in numerous practical machine learning tasks such as classification of images in the ImageNet data set, control-policy-learning to play Atari games or the board game Go, and image captioning. Many of these applications first perform feature extraction …
DISTANA predicts and denoises spatial wave dynamics.
problem Identifying causality in spatially distributed, non-linear dynamical processes.
method Generative, recurrent graph convolution neural network architecture (DISTANA).
result DISTANA outperforms alternative approaches in denoising and predicting complex spatial wave propagation.
Detects memorization in neural networks using non-negative factorization.
problem Identifying memorization in deep neural networks.
method Measures non-linearity using non-negative factorization of activation matrices.
result High non-linearity in deep layers indicates memorization.
New methods for geometric deep learning on manifolds.
problem Efficiently incorporating rotational effects and sampling on manifolds.
method Horizontal frame bundle flows and non-linear bridge sampling schemes.
result Efficient manifold convolution layers with weighted diffusion mean.
GraphAIR improves graph representation learning by capturing non-linear interactions.
problem Challenges in capturing non-linear interactions in graph data.
method Integrates neighborhood aggregation and interaction modeling.
result Demonstrates improved performance on node classification and link prediction tasks.
Convolutional neural networks learn phase-dependent frequency representations.
problem Capturing phase dependence in frequency representations for better signal analysis.
method Convolutional neural networks learn filters with different phases, which rectify to phase-dependent descriptors.
result Phase harmonics correlations can compressively represent signals with sparse wavelet coefficients.
Knowledge graphs are graphical representations of large databases of facts, which typically suffer from incompleteness. Inferring missing relations (links) between entities (nodes) is the task of link prediction. A recent state-of-the-art approach to link prediction, ConvE, implements a convolutional neural network to …
In this article, we follow the study of quadratic backward SDEs with jumps,that is to say for which the generator has quadratic growth in the variables (z; u), started in our accompanying paper [15]. Relying on the existence and uniqueness result of [15], we define the corresponding g-expectations and study some of the…
Enhances DenseNets with multi-scale convolutions and stochastic feature reuse.
problem Overfitting in DenseNets with dense feature reuse.
method Multi-scale Convolution Aggregation module and Stochastic Feature Reuse.
result Significant improvement in model accuracy with fewer parameters.
Layer-wise relevance propagation (LRP) is a recently proposed technique for explaining predictions of complex non-linear classifiers in terms of input variables. In this paper, we apply LRP for the first time to natural language processing (NLP). More precisely, we use it to explain the predictions of a convolutional n…
Steerable E(3) Graph Neural Networks incorporate geometric and physical covariant information.
problem Incorporating covariant information like position, force, velocity, or spin in graph neural networks.
method Steerable E(3) Equivariant Graph Neural Networks (SEGNNs) that use steerable MLPs to incorporate geometric and physical covariant information.
result SEGNNs improve upon classic linear point convolutions and recent equivariant graph networks that send invariant messages.
Unified framework for convolution and attention models.
problem Complex neural network structures and their parameter control.
method Unified framework for convolution and attention models.
result Attention models are a special case of convolution with adaptive structure.
First steps towards a mathematical theory of deep convolutional neural networks for feature extraction were made---for the continuous-time case---in Mallat, 2012, and Wiatowski and Bölcskei, 2015. This paper considers the discrete case, introduces new convolutional neural network architectures, and proposes a mathemati…
Paper investigates Lipschitz constants of self-attention modules in neural networks.
problem Lipschitz constants of self-attention modules in neural networks.
method Proved standard dot-product self-attention is not Lipschitz for unbounded input domain. Proposed L2 self-attention that is Lipschitz. Derived upper bound on L2 self-attention's Lipschitz constant.
result Proved standard self-attention is not Lipschitz for unbounded input domain and proposed an alternative L2 self-attention that is Lipschitz.
Proposes Neural Random Subspace for deep learning.
problem Combining random subspace method with deep learning.
method Neural Random Subspace (NRS) integrating deep learning and random subspace.
result Achieves superior performance on 35 datasets and improves recognition tasks.
Study of Dirac equation with non-local nonlinearity on spheres.
problem Conformally invariant Dirac equation with non-local nonlinearity.
method Investigation of compactness, bubbling, and energy quantization of energy functional; characterization of ground state solutions; proof of Aubin-type inequality and Brezis-Nirenberg type result.
result Existence of solutions to the conformal Einstein-Dirac problem in dimension 4.
Graph convolutions can enhance high frequencies, leading to over-sharpening.
problem Graph convolutions suffer from over-smoothing and poor performance on heterophilic graphs.
method Rigorously prove that linear graph convolutions minimize a generalized Dirichlet energy, showing that weight matrices induce edge-wise attraction or repulsion.
result Graph convolutions can enhance high frequencies, leading to over-sharpening instead of over-smoothing.
3D-TGCN learns road graphs from time series similarity for spatio-temporal traffic forecasting.
problem Challenging spatio-temporal prediction in traffic networks due to dependency and dynamics.
method Proposes 3D-TGCN with novel components: spatial information-free road graph and 3D graph convolution.
result 3D-TGCN outperforms state-of-the-art baselines in traffic forecasting.
The widespread availability of electronic health records (EHRs) promises to usher in the era of personalized medicine. However, the problem of extracting useful clinical representations from longitudinal EHR data remains challenging. In this paper, we explore deep neural network models with learned medical feature embe…
A framework for designing and evaluating new GCN variants.
problem Designing and evaluating new graph convolutional network (GCN) variants.
method Propose a framework to compose networks using building blocks of GCN.
result Several newly composed variants are useful alternatives and competitive with original GCNs.
Transforms improve CNNs' invariance to image transformations.
problem Current CNN models lack robustness to spatial transformations.
method Randomly transform feature maps during training to learn invariant representations.
result Significant improvements on benchmark tasks, including image recognition and retrieval.
A new method for comparing image probability measures using convolution operators.
problem Efficiently comparing images using conventional sliced Wasserstein methods.
method Proposed convolution sliced Wasserstein (CSW) methods with stride, dilation, and non-linear activation.
result CSW demonstrates favorable performance over conventional sliced Wasserstein in image comparison and deep generative modeling.
We study the challenges of applying deep learning to gene expression data. We find experimentally that there exists non-linear signal in the data, however is it not discovered automatically given the noise and low numbers of samples used in most research. We discuss how gene interaction graphs (same pathway, protein-pr…
Paper introduces signal processing on cell complexes.
problem Processing signals on non-Euclidean domains.
method Signal processing on abstract regular cell complexes.
result Hodge Laplacians for cell complexes enable convolutional filters.
We consider the problem of discrete-time signal denoising, focusing on a specific family of non-linear convolution-type estimators. Each such estimator is associated with a time-invariant filter which is obtained adaptively, by solving a certain convex optimization problem. Adaptive convolution-type estimators were dem…
Complex-valued neural networks improve seismic data analysis by preserving phase information.
problem Low-frequency aliasing in seismic data due to discarded phase information.
method Developed complex-valued deep convolutional networks to leverage phase information in deterministic physical data.
result Complex-valued networks outperform real-valued networks in training and inference from deterministic physical data.
A scattering transform defines a signal representation which is invariant to translations and Lipschitz continuous relatively to deformations. It is implemented with a non-linear convolution network that iterates over wavelet and modulus operators. Lipschitz continuity locally linearizes deformations. Complex classes o…
Linear RNNs exhibit a bias towards shorter memory due to initialization variance.
problem Understanding the performance limitations of RNNs, especially linear ones.
method Kernel regime analysis to show equivalence to 1D-convolutional networks and analyze weightings.
result Linear RNNs with random initialization have a bias towards shorter memory periods.
Diffuse optical tomography (DOT) has been investigated as an alternative imaging modality for breast cancer detection thanks to its excellent contrast to hemoglobin oxidization level. However, due to the complicated non-linear photon scattering physics and ill-posedness, the conventional reconstruction algorithms are s…
Local unsupervised learning outperforms end-to-end training for image classification.
problem Local unsupervised learning is believed to be inferior to end-to-end training.
method Designing a local algorithm to learn convolutional filters at scale on large image datasets using local Hebbian learning.
result Convolutional networks with patch normalization significantly outperform standard networks on image classification tasks.