Study isotropy groups for complex orthogonal and skew-symmetric matrices.
problem Understanding isotropy subgroups of orthogonal similarity transformations.
method Analysis of group structure of nonsingular block matrices.
result Group structure of isotropy subgroups related to block Toeplitz matrices.
Algorithm finds isotropy subgroups of orthogonal similarity on symmetric matrices.
problem Computing isotropy subgroups of orthogonal similarity on symmetric matrices.
method Algorithmic procedure solving a Toeplitz matrix equation.
result Structure of isotropy subgroups described.
We construct a decomposition of the identity operator on a Riemannian manifold M as a sum of smooth orthogonal projections subordinate to an open cover of M. This extends a decomposition of the real line by smooth orthogonal projection due to Coifman, Meyer and Auscher, Weiss, Wickerhauser, and a similar decomposit…
Improves model predictability by mixing forecasts and orthogonalizing models.
problem Redundant models contaminate model space and degrade predictive performance.
method Principal Component Analysis for model orthogonalization in Bayesian forecast mixing.
result Better prediction accuracy and excellent uncertainty quantification.
A new hashing method improves accuracy by learning an orthogonal transform.
problem Improving hashing accuracy for similarity search.
method Procrustean Orthogonal Sparse Hashing (POSH) method.
result POSH outperforms state-of-the-art hashing methods.
fMRI is a unique non-invasive approach for understanding the functional organization of the human brain, and task-based fMRI promotes identification of functionally relevant brain regions associated with a given task. Here, we use fMRI (using the Poffenberger Paradigm) data collected in mono- and dizygotic twin pairs t…
New convergence guarantees for learning with unknown nuisance parameters.
problem Learning problems with unknown nuisance parameters.
method Stochastic gradient optimization with Neyman orthogonality and approximately orthogonalized updates.
result Stochastic gradient algorithms can converge under conditions of nuisance parameters.
Orthogonal deep models defend against black-box attacks by ensuring internal representations are nearly orthogonal.
problem Vulnerability of deep learning models to black-box adversarial attacks.
method Introduce a gradient regularization scheme to encourage deep models' internal representations to be orthogonal to another model's.
result Orthogonal deep models significantly boost robustness against transferable black-box adversarial attacks.
We construct an explicit topological model (similar to the topological Springer fibers appearing in work of Khovanov and Russell) for every two-row Springer fiber associated with the even orthogonal group and prove that the respective topological model is homeomorphic to its corresponding Springer fiber. This confirms …
Different neural networks trained on the same dataset often learn similar input-output mappings with very different weights. Is there some correspondence between these neural network solutions? For linear networks, it has been shown that different instances of the same network architecture encode the same representatio…
Special orthogonal representations from octonions have geometric properties linked to binary cubics.
problem Understanding geometric properties of special orthogonal representations from octonions.
method Using octonions and their derivations, spinors, and covariants to show geometric properties.
result Covariants and Mathews identities of these representations are related to the Fano plane and (Z2)3. Muon optimizer simplifies matrix optimization with spectral orthogonalization.
problem Matrix optimization challenges, especially with large condition numbers.
method Simplified Muon optimizer using spectral orthogonalization of gradients.
result Simplified Muon converges linearly with independent scalar sequences, outperforming gradient descent and Adam.
Random convolutional networks can be fooled with adversarial examples.
problem Existence of adversarial examples for random convolutional networks.
method Utilizing isoperimetric inequalities on the special orthogonal group so(d). result Adversarial examples exist for various random convolutional networks.
State-of-the-art algorithms for sparse subspace clustering perform spectral clustering on a similarity matrix typically obtained by representing each data point as a sparse combination of other points using either basis pursuit (BP) or orthogonal matching pursuit (OMP). BP-based methods are often prohibitive in practic…
We consider the problem of sampling from posterior distributions for Bayesian models where some parameters are restricted to be orthogonal matrices. Such matrices are sometimes used in neural networks models for reasons of regularization and stabilization of training procedures, and also can parameterize matrices of bo…
We classify six-dimensional Lie groups which admit a left-invariant half-flat SU(3)-structure and which split in a direct product of three-dimensional factors. Moreover, a complete list of those direct products is obtained which admit a left-invariant half-flat SU(3)-structure such that the three-dimensional factors ar…
Paper improves feature selection accuracy using transfer learning.
problem Improving feature selection accuracy in information criteria-based methods.
method Proposes TLCp, a transfer learning procedure based on Mallows' Cp.
result TLCp outperforms conventional Cp in accuracy and stability.
In this paper, we propose a scalable algorithm for spectral embedding. The latter is a standard tool for graph clustering. However, its computational bottleneck is the eigendecomposition of the graph Laplacian matrix, which prevents its application to large-scale graphs. Our contribution consists of reformulating spect…
Improved Gaussian process models for interpretable predictions.
problem Complex responses require high-dimensional interaction terms in additive Gaussian processes.
method Orthogonal additive kernel (OAK) with orthogonality constraint on additive functions.
result OAK models achieve similar or better predictive performance with fewer terms, retaining interpretability.
Study asymptotics of extension and orthogonal Bergman kernels for high tensor powers of positive line bundles.
problem Asymptotic behavior of Bergman kernels for high tensor powers of positive line bundles.
method Analyzing the Schwartz kernel of the Ohsawa-Takegoshi extension operator and orthogonal Bergman projector, proving exponential estimates and asymptotic expansions.
result Explicit asymptotic expansions for the Ohsawa-Takegoshi extension operator and orthogonal Bergman projector.
Anti-transfer learning prevents misleading representations for speech tasks.
problem Misleading representations learned from orthogonal tasks in speech processing.
method Penalizes similarity between activations of a network and another trained on an orthogonal task.
result Improves classification accuracy and invariance to the orthogonal task.
Deterministic bounds for tensor singular values and vectors, differing from matrix cases.
problem Spectral learning of higher-order orthogonally decomposable tensors.
method Deterministic perturbation bounds for singular values and vectors of orthogonally decomposable tensors.
result Perturbation affects each essential singular value/vector in isolation, independent of multiplicity and distance from other singular values.
Defines a similarity measure for classification distributions.
problem Measuring similarity between classification distributions.
method Proposes task similarity, a novel measure quantifying performance of source distributions on target distributions.
result Empirical task similarity correlates with transfer efficiency and semantic similarity of source distributions.
OGD proves robustness to Catastrophic Forgetting in Continual Learning.
problem Catastrophic Forgetting in Continual Learning with deep neural networks.
method Theoretical framework based on Neural Tangent Kernel for OGD.
result First generalization bound for SGD and OGD in Continual Learning.
The paper shows how gradient flow on over-parametrized tensor decomposition behaves like deflation.
problem Understanding the training dynamics of gradient flow on tensor decomposition.
method Empirical observation and mathematical proof of gradient flow dynamics for orthogonally decomposable tensors.
result Gradient flow dynamics for orthogonally decomposable tensors follows a tensor deflation process, recovering all tensor components.
ORFit trains models on streaming data with one pass, minimizing memory and computational costs.
problem Training large models on a stream of data without retraining on previous data.
method Orthogonal Recursive Fitting (ORFit) using orthogonal gradient descent and recursive least-squares.
result ORFit updates parameters orthogonally to past gradients, leading to efficient memory and computational usage.
Let R be an infinite commutative ring with identity and n≥2 be an integer. We prove that for each integer i=0,1,⋯,n−2, the L2-Betti number bi(2)(G)=0, when G=GLn(R) the general linear group, SLn(R) the special linear group, the group generated by…
New method improves reinforcement learning generalization.
problem Few environments lead to poor generalization in reinforcement learning.
method Integrates sequential structure into representation learning, using a policy similarity metric (PSM) and contrastive embeddings (PSEs).
result PSEs improve generalization across various benchmarks.
Paper introduces regularization for multi-head attention to spot keywords.
problem Redundancy in multi-head attention leads to lack of rich information.
method Regularization technique to enforce orthogonality between attention heads.
result Significant improvement in keyword spotting performance.
Geometrically transforms word embeddings into a common space for better comparison.
problem Comparing embeddings from different sources is challenging.
method Applies orthogonal rotations and Mahalanobis scaling to transform embeddings into a shared latent space.
result The method improves word similarity and analogy tasks.
Overparameterized models improve performance in sequential learning tasks.
problem Catastrophic forgetting in overparameterized neural networks.
method Two-task linear regression problem with random orthogonal transformations.
result Overparameterization mitigates catastrophic forgetting in sequential learning tasks.
New method prevents gradient attenuation in Lipschitz constrained convolutional networks.
problem Gradient norm attenuation in Lipschitz constrained convolutional networks.
method Block Convolution Orthogonal Parameterization (BCOP) to train scalable, expressive, provably Lipschitz convolutional networks.
result Empirically, BCOP parameterization is competitive with existing approaches to provable adversarial robustness and Wasserstein distance estimation.
In this paper we explore the "vector semantics" problem from the perspective of "almost orthogonal" property of high-dimensional random vectors. We show that this intriguing property can be used to "memorize" random vectors by simply adding them, and we provide an efficient probabilistic solution to the set membership …
Racah matrices and higher j-symbols are used in description of braiding properties of conformal blocks and in construction of knot polynomials. However, in complicated cases the logic is actually inverted: they are much better deduced from these applications than from the basic representation theory. Following the re…
The performance of Orthogonal Matching Pursuit (OMP) for variable selection is analyzed for random designs. When contrasted with the deterministic case, since the performance is here measured after averaging over the distribution of the design matrix, one can have far less stringent sparsity constraints on the coeffici…
It is well known that the curvature tensor of a pseudo-Riemannian manifold can be decomposed with respect to the pseudo-orthogonal group into the sum of the Weyl conformal curvature tensor, the traceless part of the Ricci tensor and of the scalar curvature. A similar decomposition with respect to the pseudo-unitary gro…
String structures have played an important role in algebraic topology, via elliptic genera and elliptic cohomology, in differential geometry, via the study of higher geometric structures, and in physics, via partition functions. We extend the description of String structures from connected covers of the definite-signat…
In this paper, we present new results on using orthogonal matching pursuit (OMP), to solve the sparse approximation problem over redundant dictionaries for complex cases (i.e., complex measurement vector, complex dictionary and complex additive white Gaussian noise (CAWGN)). A sufficient condition that OMP can recover …
New exponential map for Lie groups connects to sub-Riemannian geometry.
problem Developing a new exponential map for Lie groups.
method Introducing a new exponential map related to sub-Riemannian geometry.
result New exponential map connects to sub-Riemannian geometry.
GRRT recovers sparse signals without prior sparsity or noise variance knowledge.
problem Recovering sparse signals without prior sparsity or noise variance knowledge.
method Generalized residual ratio thresholding (GRRT) for SOMP and BOMP.
result Finite sample and finite SNR guarantees for exact support recovery.
Distance metric learning (DML), which learns a distance metric from labeled "similar" and "dissimilar" data pairs, is widely utilized. Recently, several works investigate orthogonality-promoting regularization (OPR), which encourages the projection vectors in DML to be close to being orthogonal, to achieve three effect…
New methods calibrate causal estimates using standard predictive models.
problem Calibrating causal treatment effect estimates.
method Developed algorithms to transform causal estimation into standard calibration.
result General algorithms for causal calibration using standard predictive models.
The study extends Jacobi-orthogonality to indefinite scalar product spaces.
problem Generalizing Jacobi-orthogonality to indefinite scalar product spaces.
method Comparing principles, investigating tensor relations, proving properties.
result Every quasi-Clifford tensor is Jacobi-orthogonal; certain tensors are Jacobi-dual or Osserman.
New characterization of Osserman tensors using Jacobi-orthogonality.
problem Characterizing Osserman tensors.
method Introducing Jacobi-orthogonality as a new potential characterization.
result Jacobi-orthogonal tensors are Osserman, and all known Osserman tensors are Jacobi-orthogonal.
New findings on Kähler manifolds restrict orthogonal coordinates existence.
problem Existence of orthogonal coordinates on Kähler manifolds.
method Algebraic and geometric techniques applied to Kähler manifolds.
result No nontrivial self-dual Kähler 4-manifolds or Ricci-flat Kähler 4-manifolds support orthogonal coordinates.
Constructs orthogonal coordinates in curved spaces.
problem Separating variables in curved spaces.
method Explicit construction of orthogonal coordinates and transformations.
result Explicit formulas for Killing tensors and Stäckel matrices.
OPT framework improves neural network generalization by learning an orthogonal transformation.
problem Improving neural network generalization.
method Orthogonal over-parameterized training (OPT) framework that minimizes hyperspherical energy.
result OPT framework provably minimizes hyperspherical energy and improves empirical generalization.
The paper studies surfaces in a bounded domain with orthogonal boundaries and proves curvature estimates.
problem Estimating the area of surfaces with orthogonal boundaries in a bounded domain.
method Weak formulation of orthogonality for curvature varifolds, classification of vanishing curvature varifolds.
result Existence of an orthogonal 2-varifold that minimizes L2 curvature in the integer rectifiable class.