Graph Neural Networks (GNNs) have become a topic of intense research recently due to their powerful capability in high-dimensional classification and regression tasks for graph-structured data. However, as GNNs typically define the graph convolution by the orthonormal basis for the graph Laplacian, they suffer from hig…
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48 results for “Haar convolutional features”
Haar Graph Poolingcs.LG
Deep Graph Neural Networks (GNNs) are useful models for graph classification and graph-based regression tasks. In these tasks, graph pooling is a critical ingredient by which GNNs adapt to input graphs of varying size and structure. We propose a new graph pooling operation based on compressive Haar transforms -- HaarPo…
Novel Haar-Laplacian for directed graphs enhances spectral graph applications.
problem Lack of suitable Laplacian for directed graphs in spectral graph theory.
method Inspired by Haar-like transformation, introduces a Hermitian matrix preserving direction and weight.
result HaarNet outperforms in weight prediction and denoising on directed graphs.
Paper introduces Laplace-HDC for better binary hyperdimensional computing.
problem Improving binary hyperdimensional computing for spatial information.
method Develops Laplace-HDC using the Laplace kernel and Haar convolutional features.
result Laplace-HDC outperforms previous methods in encoding spatial information.
QCNNs avoid barren plateaus, making them trainable.
problem Exponentially vanishing gradients in QNNs.
method Graph-based method to analyze Haar-distributed unitaries.
result QCNNs do not exhibit barren plateaus, implying trainability.
We define what it means for a proper continuous morphism between groupoids to be Haar system preserving, and show that such a morphism induces (via pullback) a *-morphism between the corresponding convolution algebras. We proceed to provide a plethora of examples of Haar system preserving morphisms and discuss connecti…
The abstract theorem extends a Lie group result to Lie groupoids.
problem Expressing functions on Lie groupoids as convolutions of two functions.
method Using a lemma from Dixmier-Malliavin, Lie algebroids, and exponential map.
result Every smooth, compactly-supported function on a Lie groupoid can be expressed as a finite sum of convolutions of two such functions.
Introduces new algebraic structures for relational groupoids and proves a reduction theorem.
problem Developing algebraic tools for relational groupoids.
method Introduces relational groupoids and convolution algebras, provides examples, and proves a reduction theorem.
result Establishes a reduction theorem recovering the usual convolution of Lie groupoids.
In this article we propose building general-purpose function approximators on top of Haar Scattering Networks. We advocate that this architecture enables a better comprehension of feature extraction, in addition to its implementation simplicity and low computational costs. We show its approximation and feature extracti…
The aim of this paper is to discuss the use of Haar scattering networks, which is a very simple architecture that naturally supports a large number of stacked layers, yet with very few parameters, in a relatively broad set of pattern recognition problems, including regression and classification tasks. This architecture…
Study convolution of invariant valuations on Lie groups.
problem Understanding convolution of valuations on Lie groups.
method Explicit formula for left-invariant valuations, showing existence of smooth bi-invariant valuations, defining convolution on arbitrary Lie groups.
result Unified convolution operations on Lie groups.
MathNet uses wavelets for graph representation and learning.
problem Graph Neural Networks (GNNs) for graph classification and regression.
method Multiresolution Haar-like wavelets, graph convolution, and pooling.
result MathNet achieves notable accuracy gains on graph classification and regression tasks.
This work proves the asymptotic freeness of layerwise Jacobians in MLPs with Haar orthogonal matrices.
problem Proving the asymptotic freeness of layerwise Jacobians in multilayer perceptrons (MLPs).
method Replacing each layer's parameter matrix with itself multiplied by a Haar orthogonal matrix, and using the invariance of the MLP.
result Proves the asymptotic freeness of layerwise Jacobians in MLPs with Haar orthogonal matrices.
We present a powerful new loss function and training scheme for learning binary hash functions. In particular, we demonstrate our method by creating for the first time a neural network that outperforms state-of-the-art Haar wavelets and color layout descriptors at the task of automated scene matching. By accurately rel…
Hyperbolic groups' infinite orbits spread evenly in spaces.
problem Equidistribution of hyperbolic groups in homogeneous spaces.
method Averaging measures along spheres in Cayley graphs converges to Haar measure.
result Infinite orbits of hyperbolic groups equidistribute in homogeneous spaces.
This paper proposes a new methodology to compute Value at Risk (VaR) for quantifying losses in credit portfolios. We approximate the cumulative distribution of the loss function by a finite combination of Haar wavelets basis functions and calculate the coefficients of the approximation by inverting its Laplace transfor…
Sums of Adjoint Orbitsmath.GR
Let G be a real compact connected simple Lie group, and g its Lie algebra. We study the problem of determining, from root data, when a sum of adjoint orbits in g, or a product of conjugacy classes in G, contains an open set. Our general methods allow us to determine exactly which sums of adjoint orbits in su(m) and pro…
Orthogonal random features approximate a Bessel kernel, offering sharper bounds than random Fourier features.
problem Approximating Gaussian kernel efficiently for large datasets.
method Use of Haar orthogonal matrices to construct orthogonal random features and analyze their bias and variance.
result Orthogonal random features approximate a Bessel kernel, not the Gaussian kernel, with sharper bounds.
Explicit Taylor series for the volume of tubes in Lie groups
problem Computing the volume of tubes in riemannian manifolds
method Using bi-invariant metrics
result Explicit Taylor series for the volume of a tube in a Lie group
Quantum walks blend patterns into splines when averaged.
problem Understanding the asymptotic patterns of quantum random walks.
method Averaging over quantum coins using the Haar measure.
result Patterns blend into splines, showing a unified behavior.
Motivated by an abstract notion of low-level edge detector filters, we propose a simple method of unsupervised feature construction based on pairwise statistics of features. In the first step, we construct neighborhoods of features by regrouping features that correlate. Then we use these subsets as filters to produce n…
We compute the Riemannian volume on the moduli space of flat connections on a nonorientable 2-manifold, for a natural class of metrics. We also show that Witten's volume formula for these moduli spaces may be derived using Haar measure, and we give a new proof of Witten's volume formula for the moduli space of flat con…
In this letter we exhibit the relation between the isometries of a Riemannian contraction of a sub-Riemannian manifold and those of the sub-Riemannian metric, for to use this relation with two goals: establishing a result about the existence of fixed points of isometries groups; and the other, defining a Multiresolutio…
We analyze in this paper a random feature map based on a theory of invariance I-theory introduced recently. More specifically, a group invariant signal signature is obtained through cumulative distributions of group transformed random projections. Our analysis bridges invariant feature learning with kernel methods, as …
New MHSNs extract multiscale features from complex data for robust classification.
problem Signal classification and domain classification on complex data.
method Layered structure with multiscale basis dictionaries, pooling operations, and invariant features.
result High-accuracy classification with fewer parameters than traditional graph neural networks.
Quantum neural networks converge to Gaussian processes as they grow.
problem Understanding the convergence of quantum neural networks to Gaussian processes.
method Analyzing Haar random unitary and orthogonal deep QNNs, considering input states, measurement observables, and non-independence of unitary matrix entries.
result Quantum neural networks outputs converge to Gaussian processes in the limit of large Hilbert space dimension.
This paper presents a basic property of region dividing of ReLU (rectified linear unit) deep learning when new layers are successively added, by which two new perspectives of interpreting deep learning are given. The first is related to decision trees and forests; we construct a deep learning structure equivalent to a …
DropCluster clusters features in convolutional layers to prevent overfitting.
problem Dropout's effectiveness in convolutional layers is limited due to feature spatial correlation.
method DropCluster clusters features in convolutional layers and randomly drops clusters during training.
result DropCluster controls overfitting better than other approaches on various datasets.
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.
Expected centre of mass for random embeddings is constant.
problem Understanding the expected centre of mass for random embeddings.
method Analyzing the Haar measure and Gaussian unitary ensemble on SL(N, C).
result The expectation of the centre of mass is a constant multiple of the identity matrix.
The paper improves on existing algorithms for minimizing different types of regret in online learning.
problem Minimizing external, internal, and swap regret in online learning with multiple experts.
method Develops a single algorithm using φ-regret minimization and Haar-wavelet-inspired matrix features to achieve optimal bounds in various scenarios.
result Achieves optimal bounds for external, internal, and swap regrets in different expert scenarios.
Eigenvalue Distribution of Large Random Matrices Arising in Deep Neural Networks: Orthogonal Casestat.ML
The paper proves a distribution claim for neural network Jacobians.
problem Distribution of singular values in deep neural networks.
method Free probability and random matrix theory techniques.
result Singular value distribution matches for specific cases.
CatGCN improves GCNs by modeling feature interactions for categorical node features.
problem Suboptimal initial node representations in GCNs due to lack of feature interaction modeling.
method Integrates explicit interaction modeling (local and global) into initial node representation learning for categorical node features.
result CatGCN enhances initial node representations through feature interaction modeling, leading to improved model performance.
Automatic continuity of polynomial maps and cocycles proved.
problem Proving continuity of polynomial maps and cocycles.
method The approach involves proving continuity of polynomial maps and cocycles.
result Automatic continuity of polynomial maps and cocycles.
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…
In this paper we discuss general properties of geodesic surfaces that are locally biLipschitz homogeneous. In particular, we prove that they are locally doubling and that there exists a special doubling measure analogous to the Haar measure for locally compact groups.
Multivariate time series classification is a high value and well-known problem in machine learning community. Feature extraction is a main step in classification tasks. Traditional approaches employ hand-crafted features for classification while convolutional neural networks (CNN) are able to extract features automatic…
Generative model uses random convolutional features to create financial time series.
problem Generating realistic financial time series with limited data and avoiding overfitting.
method Train generators by matching random convolutional features of real and generated time series, using SOCK (SOft Competing Kernels) feature map.
result Generators trained with random SOCK features outperform baselines across various financial datasets.
Random representations of surface groups approach asymptotic freeness in large limit.
problem Asymptotic freeness of Haar unitary matrices for surface groups.
method Interplay between Dehn's work and classical invariant theory.
result Expected value of trace of a fixed non-identity element is bounded as .
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.
Though Convolutional Neural Networks (CNNs) have surpassed human-level performance on tasks such as object classification and face verification, they can easily be fooled by adversarial attacks. These attacks add a small perturbation to the input image that causes the network to misclassify the sample. In this paper, w…
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.
This paper presents a novel approach to exploit the distinctive invariant features in convolutional neural network. The proposed CNN model uses Scale Invariant Feature Transform (SIFT) descriptor instead of the max-pooling layer. Max-pooling layer discards the pose, i.e., translational and rotational relationship betwe…
A new convolutional spectral kernel network learns hierarchical and local features.
problem Lack of deep learning in non-stationary spectral kernels.
method Introduces convolutional filters and deep architectures into non-stationary spectral kernels, derives generalization error bounds, and introduces regularizers.
result Validated the effectiveness of the convolutional spectral kernel network on real-world datasets.
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.
New method compresses deep learning layers using tensor decomposition.
problem Reduction of computation cost and interpretability for tensor data.
method CP-decomposition to compress convolutional layers in deep learning.
result Reduces model complexity and maintains prediction performance.
A new neural network model reduces features in high-dimensional sequential data.
problem Exponential growth in features of truncated signature transform in high-dimensional data.
method Proposes a neural network model inspired by Convolutional Neural Networks to address feature growth.
result Reduces the number of features efficiently in a data-dependent way.
Deep learning with Convolutional Neural Networks has shown great promise in various areas of image-based classification and enhancement but is often unsuitable for predictive modeling involving non-image based features or features without spatial correlations. We present a novel approach for representation of high dime…