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.
Deep neural networks' Jacobian spectrum becomes well-conditioned with orthogonal weights.
problem Understanding and handling the Jacobian spectrum of deep neural networks.
method Applying free probability theory to show almost sure asymptotic freeness of Jacobians in the wide limit.
result Layer-wise Jacobians of deep neural networks with orthogonal weights are almost surely asymptotically free.
KOOW method provides optimal covariate balance for continuous treatments.
problem Estimating effects of continuous treatments with robustness to model misspecification and extreme weights.
method Kernel Optimal Orthogonality Weighting (KOOW) using convex optimization.
result KOOW provides optimal covariate balance and controls for extreme weights.
Introduces new curvature concept for Kähler manifolds.
problem Optimizing curvature constraints for projective Kähler manifolds.
method Introduces weighted orthogonal Ricci curvature and proves vanishing theorems.
result Proves optimal curvature constraints for projective Kähler manifolds.
In the multiple linear regression setting, we propose a general framework, termed weighted orthogonal components regression (WOCR), which encompasses many known methods as special cases, including ridge regression and principal components regression. WOCR makes use of the monotonicity inherent in orthogonal components …
Pion optimizes LLMs by preserving weight matrix singular values.
problem Training large language models (LLMs) with standard optimizers leads to unstable weight matrices.
method Pion uses orthogonal transformations to update weight matrices, preserving their singular values.
result Pion offers a stable alternative to standard optimizers for LLM pretraining and finetuning.
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.
Orthogonal Wasserstein GANs improve image quality without gradient norm regularization.
problem Wasserstein-GANs' gradient norm regularization limits the distribution's fidelity.
method Substituted gradient norm regularization with orthogonality constraints on weight matrices.
result Orthogonal Wasserstein GANs achieve better image quality and generalization.
Deep networks with orthogonal weights show stable fluctuations, improving generalization and training speed.
problem Fluctuations in deep networks with Gaussian weights can impair training, especially in networks with depth comparable to width.
method Analytical and numerical studies of fully-connected networks with orthogonal weight initialization and tanh activations.
result Rectangular networks with orthogonal weights have stable fluctuations independent of network depth, leading to better generalization and training speed.
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 initializations speed up neural network training by preserving gradients and activations.
problem Understanding and optimizing the initialization of neural networks to speed up training.
method Connection between Fisher information matrix, spectral radius, and gradient smoothness.
result Orthogonal initializations ensure gradients and activations are preserved, leading to faster training.
A new classifier uses weighted orthogonal regression for robust classification with limited data.
problem Challenges in classification with insufficient training data.
method Exploits intrinsic structure of data through Eigen components with specific weights determined by eigenvalues.
result Robust learning in classification problems with limited data.
A new method selects features for better model performance.
problem Improving model performance by selecting effective features.
method Supervised orthogonal least square regression with feature weighting.
result The method reduces feature dimensionality and improves classification results.
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.
A new method improves continual learning by replaying pseudo data and using orthogonal weight modification.
problem Catastrophic forgetting in class incremental learning.
method Generative replay with orthogonal weight modification.
result Our method achieves substantial improvement over conventional generative replay and OWM.
OrthDNNs improve DNNs' generalization by ensuring equal singular values.
problem Improving deep learning models' generalization ability.
method Introducing OrthDNNs, proving local isometry, and establishing new generalization bounds.
result OrthDNNs achieve optimal generalization bounds with equal singular values.
Deep networks without non-linearities are equivalent to shallow ones.
problem Training deep orthogonal linear networks with no non-linearity.
method Riemannian gradient descent and gradient descent on factorization.
result Training deep overparametrized networks is equivalent to shallow ones.
Different neural networks learn similar mappings with different weights.
problem Understanding shared representations across neural networks with varying weights.
method Shared response model and orthogonal transformations.
result Different neural networks encode the same input examples as different orthogonal transformations of an underlying shared representation.
Study connects curvature to graph theory and reveals differences.
problem Exploring differences between Quadratic Orthogonal Bisectional Curvature and Real Bisectional Curvature.
method Real (1,1)--forms and Weitzenböck curvature operator used to represent graph Dirichlet energy.
result Curvature differences illuminated between Quadratic Orthogonal Bisectional Curvature and Real Bisectional Curvature.
Orthogonal initialization speeds up convergence in deep linear networks.
problem The impact of initialization on convergence speed and model performance in deep neural networks.
method Analysis of orthogonal initialization in deep linear networks, proving its superiority over Gaussian initialization.
result Orthogonal initialization speeds up convergence relative to Gaussian initialization in deep networks.
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.
In this short note we show the following result: Let (M2n+1,g) (n≥2) be a compact Sasaki manifold with positive transverse orthogonal bisectional curvature. Then π1(M) is finite, and the universal cover of (M2n+1,g) is isomorphic to a weighted Sasaki sphere. We also get some results in the case of n…
New LT-O-learners improve HLTE estimation with low overlap.
problem Challenges in estimating heterogeneous long-term treatment effects due to limited overlap.
method Introduces LT-O-learners that use custom overlap weights to downweight low-overlap samples.
result LT-O-learners provide robust HLTE estimates with lower variance in low-overlap regimes.
A new method for optimizing neural networks with orthogonal constraints.
problem Optimizing neural networks with orthogonal constraints.
method Parametrization using the exponential map to transform constrained optimization into unconstrained.
result Faster, more accurate, and stable convergence in RNNs with orthogonal recurrent weights.
Recurrent Neural Networks (RNNs) are designed to handle sequential data but suffer from vanishing or exploding gradients. Recent work on Unitary Recurrent Neural Networks (uRNNs) have been used to address this issue and in some cases, exceed the capabilities of Long Short-Term Memory networks (LSTMs). We propose a simp…
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.
New algorithm speeds up group equivariant neural networks computations.
problem Challenging computations in group equivariant neural networks.
method Diagrammatic framework based on category theory for matrix multiplication.
result Exponential improvement in time complexity for matrix multiplication.
The paper proposes new ways to enforce orthogonality in deep CNNs training.
problem Enforcing orthogonality in deep CNNs training.
method Developed novel orthogonality regularizations using analytical tools like mutual coherence and restricted isometry property.
result Consistent performance gains in final accuracies and convergence speed after applying regularizations.
An algorithm for efficient computation of equivariant neural network layers.
problem Efficiently computing with Brauer's group equivariant neural network layers.
method Category theoretic constructions and Kronecker product matrices.
result Significant reduction in computational cost compared to naive implementation.
The paper proves smoothness of almost-minimizers' boundaries near the free boundary.
problem Minimizing degenerate area functionals with weighted boundary conditions.
method Epsilon-regularity theorem applied to almost-minimizers.
result Almost-minimizers' boundaries are C1,γ0-smooth, orthogonal to the boundary Ω. 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.
New survival learners estimate heterogeneous treatment effects from time-to-event data.
problem Estimating HTEs from time-to-event data with censoring outcomes.
method Orthogonal survival learners with theoretical guarantees and custom weighting functions.
result Orthogonal survival learners provide robust and model-agnostic HTE estimation.
Paper refines Alesker-Bernig-Schuster theorem, proving Hodge-Riemann relations for Euclidean balls.
problem Understanding translation-invariant valuations and their geometric implications.
method Explicit construction of highest weight vectors and analysis of natural operations on these vectors.
result Proof of Hodge-Riemann relations for Euclidean balls, extending geometric inequalities.
GAIT-prop derives a biologically plausible learning rule from backpropagation.
problem Biological implausibility in traditional backpropagation for neural networks.
method GAIT-prop uses a top-down model to convert output error into plausible targets for weight updates.
result GAIT-prop and backpropagation give identical weight updates under certain conditions.
OPAA estimates probability densities using functional analysis.
problem Estimating probability density functions efficiently and accurately.
method OPAA uses a parallelizable algorithm based on functional analysis to estimate probability distributions.
result OPAA provides an efficient method to estimate probability density functions and normalizing weights.
The paper computes characteristic classes for Lie group representations.
problem Computing characteristic classes for Lie group representations.
method The paper outlines a procedure to compute characteristic classes of irreducible representations of Lie groups, expressing them as polynomial functions in the highest weight.
result The paper expresses characteristic classes of Lie group representations as polynomial functions in the highest weight.
New unitary RNN architecture using complex Cayley transform outperforms existing methods.
problem Vanishing or exploding gradient problem in RNNs.
method Developed a unitary RNN architecture based on a complex scaled Cayley transform.
result scuRNN achieves comparable or better results than existing unitary RNNs.
The paper analyzes and improves a deep learning optimization technique using matrix gradient orthogonality.
problem Improving deep learning training through more effective optimization methods.
method Develops a stochastic non-Euclidean trust-region gradient method for deep learning optimization.
result Proves state-of-the-art convergence results for the proposed algorithm in various scenarios.
Gradient-enhanced GSA uses Poincaré chaos expansions for accurate sensitivity analysis.
problem Accurately estimating Sobol' indices with limited data.
method Integrates sparse, gradient-enhanced regression with Poincaré chaos expansions for derivative-based sensitivity analysis.
result Accurately estimated Sobol' indices using limited data.
New method optimizes matrix denoising for weighted loss functions and heterogeneous signals.
problem Estimating low-rank matrices from noisy observed matrices.
method Developed a family of weighted loss functions and derived optimal spectral denoisers.
result A new denoiser exploiting heterogeneity in signal matrices improves estimation.
Boosts neural network performance by improving weight separability.
problem Improving the separability of weight vectors in neural networks.
method Proposes a new evaluation metric and feed-backward reconstruction loss to encourage weight separability.
result Improves visual recognition performance across various tasks.
Recently, Neural networks have seen a huge surge in its adoption due to their ability to provide high accuracy on various tasks. On the other hand, the existence of adversarial examples have raised suspicions regarding the generalization capabilities of neural networks. In this work, we focus on the weight matrix learn…
AON improves neural network generalization by making weights approximately orthogonal.
problem Improving generalization of deep neural networks.
method Approximated orthonormal normalisation (AON) technique to make weight vectors approximately orthogonal.
result AON yields promising validation performance compared to orthonormal regularisation.
OrthoGrad improves neural calibration by constraining gradient updates orthogonally.
problem Overconfidence in neural networks, leading to poor uncertainty estimates.
method Orthogonal gradient updates to optimize for decision boundaries and reduce overconfidence.
result Significant improvements in test loss, predictive entropy, and confidence measures.
It is well known that the initialization of weights in deep neural networks can have a dramatic impact on learning speed. For example, ensuring the mean squared singular value of a network's input-output Jacobian is O(1) is essential for avoiding the exponential vanishing or explosion of gradients. The stronger condi…
DFRot improves LLMs by reducing outlier and massive activation effects.
problem Reducing outlier and massive activation effects in rotated LLMs.
method Weighted loss function and orthogonal Procrustes transforms for rotation matrix refinement.
result DFRot achieves dual free (Outlier-Free and Massive Activation-Free) with significant improvements in perplexity.
New bound for neural networks with full-rank weights, independent of network width.
problem Understanding generalization of neural networks with full-rank weight matrices.
method Using Koopman operators to derive a tighter generalization bound for full-rank weight matrices.
result The bound is tighter than existing norm-based bounds when condition numbers are small.