A new convolution method stabilizes GANs by learning coarse structures first.
problem Mode collapse in GANs during training.
method Soft octave convolutions that split filters into high and low frequency parts, shifting weight updates.
result Reduces mode collapse and artifacts in generated images.
The article describe the model, derivation, and implementation of variational Bayesian inference for linear and logistic regression, both with and without automatic relevance determination. It has the dual function of acting as a tutorial for the derivation of variational Bayesian inference for simple models, as well a…
In this paper we study almost complex and almost para-complex Cayley structures on six-dimensional pseudo-Riemannian spheres in the space of purely imaginary octaves of the split Cayley algebra Ca′. It is shown that the Cayley structures are non-integrable, their basic geometric characteristics are calculate…
In this paper there is proposed a generalized version of the SVM for binary classification problems in the case of using an arbitrary transformation x -> y. An approach similar to the classic SVM method is used. The problem is widely explained. Various formulations of primal and dual problems are proposed. For one of t…
Paper proposes a bijective approach for signal/symbol translation using variational auto-encoders.
problem Extracting symbolic information from signals, especially in music, is challenging and non-generic.
method Turned into a density estimation task, using two variational auto-encoders with additive constraint.
result Bijective signal/symbol translation achieved, allowing both signal-to-symbol and symbol-to-signal inference.
Gaussian processes (GP) are powerful tools for probabilistic modeling purposes. They can be used to define prior distributions over latent functions in hierarchical Bayesian models. The prior over functions is defined implicitly by the mean and covariance function, which determine the smoothness and variability of the …
In this paper, we present the optimization formulation of the Kalman filtering and smoothing problems, and use this perspective to develop a variety of extensions and applications. We first formulate classic Kalman smoothing as a least squares problem, highlight special structure, and show that the classic filtering an…
We introduce a novel implementation in ANSI C of the MINE family of algorithms for computing maximal information-based measures of dependence between two variables in large datasets, with the aim of a low memory footprint and ease of integration within bioinformatics pipelines. We provide the libraries minerva (with th…
LIBS2ML is a fast, scalable library for second order machine learning.
problem Large-scale machine learning problems in big data.
method Scalable second order learning algorithms using MEX files.
result Efficient solution for large-scale learning problems.
ragamAI uses machine learning to create concert recitals for Carnatic music.
problem Creating a comprehensive listening experience for Carnatic music concerts.
method Playlist and session-based recommender models, leveraging mathematical structure in past concerts.
result ragamAI generates concert recitals that perform 25%-50% better than baseline models.
A musical instrument based on moduli spaces lets users hear geometric concepts.
problem Understanding geometric structures through auditory means.
method Developed a plastic hormonica based on Farey tessellations and Poincaré disk decorations.
result Users can audibly experience paths in Riemann moduli spaces and listen to mapping classes.
DeepCAM learns convolutional dictionaries for image processing.
problem Processing high-dimensional signals like images efficiently.
method Introduces a Deep Convolutional Analysis Dictionary Model (DeepCAM) using convolutional dictionaries.
result DeepCAM achieves performance comparable to other methods on single image super-resolution.
Introduces Finslerian convolution metrics and their properties.
problem No specific problem stated; focuses on new metric concept.
method Definition and study of Finslerian convolution metrics.
result Characterization of Finslerian convolution metrics of Riemannian, Minkowskian, and Randers types.
Improved generative models using flexible convolutions.
problem Generating high-quality images efficiently.
method Generalized 1 x 1 convolutions to d x d convolutions, chaining autoregressive and periodic convolutions.
result Flexible d x d convolutions significantly improve generative flow models' performance.
Spectral graph convolutional neural networks (CNNs) require approximation to the convolution to alleviate the computational complexity, resulting in performance loss. This paper proposes the topology adaptive graph convolutional network (TAGCN), a novel graph convolutional network defined in the vertex domain. We provi…
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.
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…
ConvNets can be translated into CKNs that perform similarly.
problem The distinction between ConvNets and kernel-based methods.
method Translation of ConvNets into CKNs using a new gradient algorithm.
result CKNs perform as well as ConvNets, supporting the translation.
Convolution Neural Network (CNN) has gained tremendous success in computer vision tasks with its outstanding ability to capture the local latent features. Recently, there has been an increasing interest in extending convolution operations to the non-Euclidean geometry. Although various types of convolution operations h…
Enhances group convolutional networks with attention to learn meaningful relationships.
problem Lack of explicit means to learn meaningful relationships among symmetry patterns.
method Introduces attentive group equivariant convolutions, applying attention during convolution.
result Consistently outperforms conventional group convolutional networks on benchmark datasets.
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 recent times, the use of separable convolutions in deep convolutional neural network architectures has been explored. Several researchers, most notably (Chollet, 2016) and (Ghosh, 2017) have used separable convolutions in their deep architectures and have demonstrated state of the art or close to state of the art pe…
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.
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.
Functor connects Lie groupoid algebras to bornological structures.
problem Establishing a functorial relationship between Lie groupoid convolution algebras and bornological structures.
method Developed a monoidal functor from differentiable stacks to Morita 2-category of complete bornological algebras.
result Convolution algebras are self-induced and convolution modules are smooth.
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…
New method enforces orthogonality in convolutional layers for improved robustness.
problem Improving adversarial robustness in deep learning models.
method Applying the Cayley transform to skew-symmetric convolutions in the Fourier domain.
result The proposed method preserves orthogonality and enhances adversarial robustness compared to existing techniques.
New method improves grouped convolutions on edge devices.
problem Efficiently implementing grouped convolutions on edge devices.
method Grouped Spatial Pack Convolutions (GSPC) in TVM.
result GSPC outperforms existing implementations by 3.4x, 8x, and 4x on average.
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.
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.
Convolutional networks outperform fully-connected ones in certain tasks.
problem Understanding the computational advantage of convolutional networks over fully-connected networks.
method Demonstrated a computational advantage through a specific problem class.
result Convolutional networks can solve certain problems that fully-connected networks cannot, even with gradient descent.
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.
Proposes a fixed smooth convolutional layer to reduce checkerboard artifacts in CNNs.
problem Checkerboard artifacts in CNNs during upsampling and strided convolution.
method Fixed convolutional layer with adjustable smoothness, applied to four CNNs and GANs.
result Significantly improves classification performance and image generation quality.
New bounds for CNNs show better generalization than previous models.
problem Improving understanding of CNNs' generalization ability.
method Proposed tighter generalization bounds for CNNs by exploiting the sparse and permutation structure of weight matrices and spectral norms of convolution operations.
result Theoretical and experimental results show tighter bounds for CNNs than existing bounds.
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.
New linear flows using exponential of linear transformations improve generative models.
problem Improving generative models in machine learning.
method Developed convolution exponentials and generalized Sylvester Flows using the exponential of linear transformations.
result Convolution exponentials and Convolutional Sylvester Flows outperform other models in log-likelihood.
The paper detects amateur drones using acoustic signals, overcoming interference.
problem Detection of unmonitored UAVs (amateur drones) for security and safety.
method Machine learning approach using Independent Component Analysis (ICA) for acoustic signal detection.
result The RMS values of PSD with KNN outperform other methods in detecting AmDr.
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.
We describe convolutional networks using harmonic functions.
problem Understanding the function space and smoothness of convolutional networks.
method Using reproducing kernel Hilbert spaces and functional ANOVA decomposition.
result Convolutional networks can be decomposed into a sum of elementary functions.
Alternative to convolutions using decision trees for neural networks.
problem Replacing complex convolutions with simpler decision-based layers.
method Binary decisions as indices to conditional distributions, trained using backpropagation.
result Performance similar to conventional neural networks, with runtime improvements.
Convolutional networks can denoise images without training data.
problem Denoising and regularization of images without labeled data.
method Exploiting the structural bias of convolutional generators through gradient descent.
result Early-stopped gradient descent denoises/regularizes images effectively.
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.
New method bounds singular values of convolutional kernels to stabilize gradients.
problem Stable gradients in convolutional neural networks.
method Frobenius norm regularization for convolutional kernels.
result Bounded singular values of transformation matrices.
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.
Coordinate-independent convolutions on manifolds avoid reference frame ambiguity.
problem Applying convolutions on non-Euclidean manifolds without reference frame ambiguity.
method Developed coordinate-independent and gauge-equivariant convolutions on Riemannian manifolds.
result Coordinate-independent convolutions are equivariant under local gauge transformations.
Adaptive graph convolution improves attributed graph clustering performance.
problem Joint modeling of graph structures and node attributes is challenging.
method Adaptive graph convolution that captures global cluster structure and selects appropriate order for different graphs.
result Empirical results show our method compares favorably with state-of-the-art methods.
FCC-GAN combines fully connected and convolutional layers for improved GAN performance.
problem Lack of understanding in choosing GAN network architectures.
method Proposes FCC-GAN, a hybrid architecture combining fully connected and convolutional layers.
result FCC-GAN outperforms traditional GAN architectures in terms of learning speed and sample quality.
Recently, many researchers have been focusing on the definition of neural networks for graphs. The basic component for many of these approaches remains the graph convolution idea proposed almost a decade ago. In this paper, we extend this basic component, following an intuition derived from the well-known convolutional…