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.
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.
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. 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.
Proposes FOAGP for efficient orthogonal effect decomposition of black-box computer experiments.
problem Challenges in sensitivity analysis of black-box computer experiments with complex, nonlinear functional outputs.
method Functional-output orthogonal additive Gaussian process (FOAGP) with conditional orthogonality constraint.
result Demonstrates effectiveness in orthogonal effect decomposition and variance decomposition through simulations and real-world application.
Novel prior for orthogonal functions improves functional component estimation.
problem Improving orthogonality in functional principal component analysis.
method Sequential adaptive priors for orthogonal functions using hierarchical conditionally normal distributions.
result Proposed prior leads to nearly orthogonal posterior estimates.
Method constructs orthogonal curvilinear coordinates in constant curvature spaces.
problem Creating orthogonal coordinates in spaces of constant curvature.
method Modification of Krichever's method for Euclidean space, applied to constant curvature spaces.
result Examples of orthogonal coordinate systems on the sphere and hyperbolic plane constructed.
We study the Chern-Simons partition function of orthogonal quantum group invariants, and propose a new orthogonal Labastida-Mariño-Ooguri-Vafa conjecture as well as degree conjecture for free energy associated to the orthogonal Chern-Simons partition function. We prove the degree conjecture and some interesting cases o…
A Clifford algebra model for M"obius geometry is presented. The notion of Ribaucour pairs of orthogonal systems in arbitrary dimensions is introduced, and the structure equations for adapted frames are derived. These equations are discretized and the geometry of the occuring discrete nets and sphere congruences is disc…
DONUT improves treatment effect estimation by enforcing orthogonality constraints.
problem Estimating treatment effects from observational data is challenging due to unobserved outcomes.
method DONUT uses a regularization framework that formalizes unconfoundedness as orthogonality, leading to deep orthogonal networks.
result DONUT outperforms state-of-the-art methods in estimating average treatment effects.
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.
MuonEq improves training of matrix-valued parameters by rebalancing momentum before orthogonalization.
problem Training matrix-valued parameters with orthogonalized-update optimizers like Muon.
method MuonEq introduces three lightweight pre-orthogonalization equilibration schemes: two-sided row/column normalization (RC), row normalization (R), and column normalization (C).
result Row/column normalization acts as a zeroth-order surrogate for whitening and improves the geometry seen by orthogonalization.
Orthogonal initialization does not speed up training in ultra-wide neural networks.
problem Exploring the effect of orthogonal initialization on training speed in deep neural networks.
method Study of neural tangent kernel dynamics in FCNs and CNNs with orthogonal initialization.
result The NTK of orthogonally-initialized networks remains constant during training, suggesting no speedup in the NTK regime.
A new algorithm POGO optimizes thousands of orthogonal matrices efficiently.
problem Optimizing thousands of orthogonal constraints at scale is computationally expensive.
method Revisits Landing algorithm, uses modern adaptive optimizers, reduces hyperparameters.
result POGO optimizes thousands of orthogonal matrices in minutes, outperforming alternatives.
Batch normalization makes deep neural networks' representations increasingly orthogonal.
problem Orthogonality of deep neural network representations.
method Random linear transformations in successive batch-normalizations.
result Orthogonality of representations improves SGD performance.
The paper finds at least N orthogonal Finsler geodesic chords in a disk-like manifold.
problem Existence and multiplicity of orthogonal Finsler geodesic chords in a disk-like manifold.
method Study of Finsler geodesic chords under reversibility assumption.
result At least N orthogonal Finsler geodesic chords found in a disk-like manifold.
Optimizing over the set of orthogonal matrices is a central component in problems like sparse-PCA or tensor decomposition. Unfortunately, such optimization is hard since simple operations on orthogonal matrices easily break orthogonality, and correcting orthogonality usually costs a large amount of computation. Here we…
LOFT separates subspace rotation and transformation for orthogonal fine-tuning.
problem Conflating subspace rotation and transformation in orthogonal fine-tuning.
method LOFT explicitly separates subspace rotation and transformation, using task-aware support selection.
result LOFT recovers principal-subspace orthogonal adaptation and improves efficiency-performance trade-off.
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.
We propose orthogonality as a necessary condition for disentangling aleatoric and epistemic uncertainty.
problem Jointly estimating aleatoric and epistemic uncertainty is problematic and non-trivial.
method We propose orthogonality as a necessary condition for disentanglement and construct UDE to measure orthogonality and consistency.
result Orthogonality and consistency are necessary and sufficient criteria for disentanglement.
VRSGT algorithm reduces orthogonality constraints in decentralized optimization.
problem Decentralized optimization with orthogonality constraints.
method VRSGT algorithm with variance reduction and orthogonal techniques.
result VRSGT achieves convergence rate of O(1 / k) for orthogonality constraints.
We orthogonalize the NSS model to condition and diagnose its ill-conditioned parameters.
problem The ill-conditioning of the NSS model's design matrix.
method Exact orthogonal reparametrization via QR decomposition.
result Orthogonalization isolates the conditioning structure and maintains fit uncertainty.
Decomposing tensors into orthogonal factors is a well-known task in statistics, machine learning, and signal processing. We study orthogonal outer product decompositions where the factors in the summands in the decomposition are required to be orthogonal across summands, by relating this orthogonal decomposition to the…
New metrics improve landing algorithms for orthogonality constraints.
problem Optimizing landing algorithms with orthogonality constraints.
method Proposed a family of metrics over full-rank matrices to enhance landing algorithms.
result Natural extension of β-metric improves landing performance.
A notion of orthogonality in multisymplectic geometry has been developed by Cantrijn, Ibort and de León and used by many authors. In this paper, we review this concept and propose a new type of orthogonality in multisymplectic geometry; we prove a number of results regarding this orthogonality and its associated subspa…
New algorithms reduce orthogonality constraint enforcement time in machine learning.
problem Efficiently solving orthogonality constraints in machine learning.
method Extending the landing algorithm to Stiefel manifold, incorporating stochastic and variance reduction techniques.
result All proposed methods achieve the same convergence rate as Riemannian counterparts enforcing constraints.
Study removes bias from chest X-ray embeddings using orthogonalization.
problem Reduces bias in chest X-ray embeddings due to protected features.
method Orthogonalization technique to remove protected feature effects.
result Orthogonalization removes bias and makes predictions of protected attributes infeasible.
We present an intriguing discovery related to Random Fourier Features: in Gaussian kernel approximation, replacing the random Gaussian matrix by a properly scaled random orthogonal matrix significantly decreases kernel approximation error. We call this technique Orthogonal Random Features (ORF), and provide theoretical…
AuON is a linear-time optimizer that improves upon Muon's performance without approximate orthogonal matrices.
problem High memory and computational costs of orthogonal momentum updates.
method AuON uses normalized nonlinear scaling and a 'emergency brake' to handle exploding attention logits.
result AuON achieves strong performance without approximate orthogonal matrices, preserving structural alignment and reconditioning.
Paper links set derivatives to its orthogonal projections.
problem Understanding the relationship between set derivatives and projections.
method Derives equations from topological link between Minkowski functional partial derivatives and set boundary.
result System of equations for orthogonal projections derived.
In this paper, we prove that any complete shrinking gradient Kähler-Ricci solitons with positive orthogonal bisectional curvature must be compact. We also obtain a classification of the complete shrinking gradient Kähler-Ricci solitons with nonnegative orthogonal bisectional curvature.
Study diameter bounds on Kähler and quaternionic Kähler manifolds with positive curvature.
problem Determine diameter bounds for Kähler and quaternionic Kähler manifolds under curvature positivity.
method Define orthogonal Bakry-Émery tensor, study diameter theorems, and derive Bonnet-Myers type bounds.
result Sharper diameter bounds than in Riemannian case under specific curvature assumptions.
Random orthogonalization improves FL in massive MIMO systems without CSI.
problem Efficient model aggregation in FL with minimal channel estimation overhead.
method Combining FL with massive MIMO's channel hardening and favorable propagation, random orthogonalization reduces channel estimation overhead.
result Achieves model aggregation without CSI, significantly reducing channel estimation overhead.
We develop the idea of using an algebraic-geometry approach to classical differential geometry problems. Consider an orthogonal net constructed according to algebraic-geometric data we obtain a set of smooth orthogonal nets that are Ribaucour transformations of the initial orthogonal net.
Formula for Laplace-Beltrami on orthogonal group in Euclidean coords.
problem Computing Laplace-Beltrami on constrained submanifolds.
method Embedded gradient vector field method, explicit formula derivation.
result Explicit formula for Laplace-Beltrami on orthogonal group.
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.
New method relaxes PCA orthogonality constraints using explained variance of correlated components.
problem Difficulty in using PCA for sparse design due to orthogonality constraints and non-differentiable penalty.
method Introduce expvar(Y) to measure variance explained by correlated components, relax orthogonality constraints.
result Two expvar(Y) definitions suitable for block PCA formulations without orthogonality constraints.
Computes isotropy subgroups of orthogonal matrices acting on Hermitian matrices.
problem Computing isotropy subgroups of orthogonal matrices acting on Hermitian matrices.
method Algorithm for solving a matrix equation to compute isotropy subgroups.
result Computed isotropy subgroups of orthogonal matrices acting on Hermitian matrices.
Local classification of 4D Ricci solitons with specific algebra properties.
problem Classifying 4D Ricci solitons with a 2D Abelian Killing algebra.
method Local classification under specific curvature and symmetry conditions.
result Classification of Ricci solitons with orthogonally intransitive 2D Abelian Killing algebra.
The paper proves integral formulas for manifolds with multiple orthogonal distributions.
problem Understanding geometric properties of manifolds with multiple orthogonal distributions.
method Develops integral formulas for Riemannian manifolds with k>2 orthogonal complementary distributions. result Generalizes known formulas for k=2 and applies to manifold splitting and immersions. New differential geometry perspective on orthogonal RNNs.
problem Mitigating exploding and vanishing gradients in RNNs.
method Using tools from differential geometry, parameterizing vector fields via directional derivatives of scalar functions.
result Our approach achieves comparable or better results on benchmark tasks.
Conformal vector fields on LCP manifolds are orthogonal and Killing.
problem Understanding conformal vector fields on specific geometric manifolds.
method Analyzing properties of conformal vector fields on compact locally conformally product manifolds.
result Conformal vector fields are orthogonal to the flat distribution and Killing.
A new method reduces bootstrap simulation cost and improves accuracy.
problem Efficiently simulating input uncertainty with large sample sizes.
method Orthogonal Bootstrap: Decomposes into Infinitesimal Jackknife and orthogonal parts.
result Significantly reduces computational cost and maintains accuracy.
One reflection suffices for orthogonal weights, reducing GPU usage.
problem Efficiently computing orthogonal weight matrices without high GPU utilization.
method Use an auxiliary neural network to compute one reflection instead of many.
result One reflection is sufficient for orthogonal weights, improving GPU utilization.