Normalization layers are widely used in deep neural networks to stabilize training. In this paper, we consider the training of convolutional neural networks with gradient descent on a single training example. This optimization problem arises in recent approaches for solving inverse problems such as the deep image prior…
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48 results for “normalized gradients”
Adapts Hölder smoothness with normalized gradients.
problem Improving smoothness adaptation methods.
method Black-box adaptation of Levy's method using normalized gradients.
result Bound depends on local Hölder smoothness.
Paper explores whether gradient normalization can replace clipping for SGD in heavy-tailed noise.
problem Ensuring convergence of SGD in heavy-tailed noise.
method Revisits gradient clipping and normalization, proving their sufficiency and effectiveness.
result Gradient normalization alone is sufficient for nonconvex SGD convergence under smoothness assumptions.
This note analyzes the normal form of gradient Ricci 4-solitons.
problem Understanding the curvature operator of gradient Ricci 4-solitons.
method Analyzing the normal form of the operator and curvature operator of Koiso-Cao soliton.
result The curvature operator of the Koiso-Cao soliton inherits a normal form relative to the space of algebraic Kähler curvature operators.
Gradient descent on normalized networks reveals sparsity preferences.
problem Understanding the inductive bias of gradient descent on normalized neural nets.
method Analysis of gradient descent on weight-normalized smooth homogeneous neural nets, focusing on SWN and EWN.
result EWN causes weights to be updated in a way that prefers asymptotic relative sparsity.
Improved KL divergence estimators for normalizing flows lead to faster convergence and better approximations.
problem Estimating KL divergences for normalizing flows efficiently and accurately.
method Path-gradient estimators for reverse and forward KL divergences.
result Path-gradient estimators lead to faster convergence and better approximation results.
New path-gradient estimator for continuous normalizing flows.
problem Limitation of simple Gaussian variational distributions in complex applications.
method Proposed a path-gradient estimator for continuous normalizing flows.
result Empirical evidence of superior performance of the new estimator.
New algorithm tackles nonconvex machine learning problems with adaptive normalization and independent sampling.
problem Nonconvex machine learning problems with generalized-smoothness.
method Adaptive gradient normalization, independent sampling, and gradient clipping.
result Achieves an O(ε^(-4)) sample complexity for fast convergence.
TaskNorm improves meta-learning performance by rethinking batch normalization.
problem Challenges in batch normalization for meta-learning with deep networks.
method Developed TaskNorm, a novel approach to batch normalization for meta-learning.
result TaskNorm consistently improves meta-learning performance across various datasets and meta-learning approaches.
GraN-GAN normalizes gradients for better GAN performance.
problem Improving image generation in GANs with piecewise linear discriminators.
method Piecewise Gradient Normalization (GraN) for input-dependent normalization.
result Significant performance gains in image generation across various datasets.
A method predicts GNS of transformer layers using normalization layer norms.
problem Estimating gradient noise scale with minimal variance.
method Simultaneously compute per-example gradient norms and parameter gradients.
result Total GNS is predicted well by normalization layer GNS.
The paper studies matrix normalization and graph balancing using a new functional and gradient descent.
problem Matrix normalization and graph balancing.
method A new functional called the non-normal energy, and gradient descent.
result Gradient descent of the non-normal energy converges to balanced graphs and preserves spectra and realness of weights.
In this paper we introduce a novel method of gradient normalization and decay with respect to depth. Our method leverages the simple concept of normalizing all gradients in a deep neural network, and then decaying said gradients with respect to their depth in the network. Our proposed normalization and decay techniques…
We conduct mathematical analysis on the effect of batch normalization (BN) on gradient backpropogation in residual network training, which is believed to play a critical role in addressing the gradient vanishing/explosion problem, in this work. By analyzing the mean and variance behavior of the input and the gradient i…
Gradient oversmoothing and expansion hinder deep GNN training, solved with normalization.
problem Gradient oversmoothing and expansion prevent deep GNN training.
method Proposed normalization method to constrain the Lipschitz bound of each layer.
result Residual GNNs with hundreds of layers can be efficiently trained with the proposed normalization.
A new path gradient estimator speeds up normalizing flows without sacrificing accuracy.
problem High computational cost and limited scalability of path gradient estimators for normalizing flows.
method Proposed a fast path gradient estimator that improves computational efficiency and scalability.
result The new estimator achieves superior performance and reduced variance across various applications.
Spectral normalization stabilizes GANs by controlling gradient explosion and vanishing.
problem Stability and sample quality issues in GAN training.
method Spectral normalization controls gradient explosion and vanishing, improving GAN training stability and sample quality.
result Bidirectional Scaled Spectral Normalization (BSSN) outperforms standard spectral normalization in sample quality and training stability.
Gradient Boosted Normalizing Flows improve flexibility of NFs without increasing complexity.
problem Improving flexibility of normalizing flows without increasing complexity.
method Gradient Boosting applied to normalizing flows to create a mixture model structure.
result GBNFs outperform non-boosted NFs and produce better results with simpler components.
Self Normalizing Flows improve normalizing flows by reducing computational complexity.
problem Efficient gradient computation in normalizing flows, especially in Jacobian determinant terms.
method Introducing Self Normalizing Flows that replace expensive terms with learned approximate inverses.
result Models can be trained more quickly and perform better than functionally constrained counterparts.
Batch normalization biases linear models towards uniform margins, improving performance in binary classification.
problem Understanding the implicit bias of batch normalization in linear models and neural networks.
method Analyzing gradient descent convergence on linear models and two-layer CNNs with batch normalization.
result Gradient descent with batch normalization in linear models converges to a uniform margin classifier with an exponential convergence rate.
Gradient control plays an important role in feed-forward networks applied to various computer vision tasks. Previous work has shown that Recurrent Highway Networks minimize the problem of vanishing or exploding gradients. They achieve this by setting the eigenvalues of the temporal Jacobian to 1 across the time steps. …
Lipschitz continuity recently becomes popular in generative adversarial networks (GANs). It was observed that the Lipschitz regularized discriminator leads to improved training stability and sample quality. The mainstream implementations of Lipschitz continuity include gradient penalty and spectral normalization. In th…
Stochastic gradient descent (SGD) has been the dominant optimization method for training deep neural networks due to its many desirable properties. One of the more remarkable and least understood quality of SGD is that it generalizes relatively well on unseen data even when the neural network has millions of parameters…
On the effect of normalization layers on Differentially Private training of deep Neural networkscs.LG
Normalization layers improve the accuracy of Differentially Private training of deep neural networks.
problem Reduced accuracy in deep neural networks with Differentially Private training.
method Proposed a novel method for integrating batch normalization with Differentially Private Stochastic Gradient Descent (DPSGD) without additional privacy loss.
result Training deeper networks with better utility-privacy trade-off is possible.
An algorithm is proposed for solving stochastic and finite sum minimization problems. Based on a trust region methodology, the algorithm employs normalized steps, at least as long as the norms of the stochastic gradient estimates are within a specified interval. The complete algorithm---which dynamically chooses whethe…
Paper explores weighted averaging schemes for SGD, achieving asymptotic normality and optimality.
problem Improving convergence of SGD in various settings.
method Develops a general weighted averaging scheme for SGD and establishes asymptotic normality.
result Establishes asymptotic normality and optimality of weighted averaged SGD solutions.
This research investigates if deep neural networks can be trained without batch normalization.
problem Training deep neural networks efficiently without batch normalization.
method Detailed study of batch normalization, comparison with other methods, and adaptation of training process.
result It is possible to train deep neural networks effectively without batch normalization.
New gradient estimator improves training for normalizing flows.
problem Training normalizing flows for complex models.
method Developed a new gradient estimator for Stochastic Gradient Descent.
result Significantly faster and more precise training for φ^4 model.
Recently, researchers proposed various low-precision gradient compression, for efficient communication in large-scale distributed optimization. Based on these work, we try to reduce the communication complexity from a new direction. We pursue an ideal bijective mapping between two spaces of gradient distribution, so th…
New theory explains why normalization is preferred in SGD under heavy-tailed noise.
problem Understanding why normalization is preferred in stochastic gradient descent (SGD) under heavy-tailed noise.
method Developed a worst-case complexity theory for stochastically preconditioned SGD and its variants.
result Normalization guarantees convergence at optimal rates, while clipping may fail in the worst case.
Study on neural networks' performance under different normalizations as N grows.
problem Characterizing neural networks' performance under various normalizations.
method Developed an asymptotic expansion to analyze statistical output of shallow neural networks.
result No bias-variance trade-off exists to leading order in N, and variance decreases as normalization approaches mean field.
This study evaluates different normalizing flow architectures for MCMC.
problem Lack of systematic comparison of normalizing flow architectures in MCMC.
method Extensive evaluation of various normalizing flow architectures on different MCMC methods and target distributions.
result Contractive residual flows are the best general-purpose models for MCMC.
Paper proves properties of minimal hypersurfaces in specific solitons.
problem Characterizing minimal hypersurfaces in shrinking gradient Ricci solitons.
method Analyzes stable minimal hypersurfaces with specific curvature conditions.
result Minimal hypersurfaces in these solitons have zero second fundamental form and normal Ricci curvature.
Paper introduces geometry-aware normalizing flows for improved causal inference.
problem Disparity between sample and population distributions in causal inference.
method Integrates continuous normalizing flows with parametric submodels, employing Wasserstein gradient flows and optimal transport.
result Significantly reduces parameter estimation bias and variance in finite-sample settings.
Improved sampling efficiency for molecular systems using path gradients after Flow Matching.
problem Improving sampling efficiency for complex molecular systems.
method Hybrid approach combining Flow Matching and path gradients.
result Up to a threefold increase in sampling efficiency for molecular systems.
Muon dynamics study uses spectral Wasserstein flow for optimization stability.
problem Optimizing deep learning models with gradient normalization.
method Introduces Spectral Wasserstein distances for matrix flows, proving equivalence with Benamou--Brenier formulation.
result Gradient-flow interpretation of mean-field normalized training dynamics.
A new method for categorical variational inference using discrete normalizing flows.
problem Challenges in optimizing variational approximations for discrete latent variables.
method Differentiable reparameterization using a mixture of discrete normalizing flows.
result Improves optimization of evidence lower bound and reduces sensitivity to hyperparameters.
Layer normalization placement affects training stability and warm-up stage necessity.
problem Training instability and the necessity of a learning rate warm-up stage in Transformers.
method Theoretical analysis and mean field theory to prove gradient behavior at initialization.
result Removing the warm-up stage for Pre-LN Transformers can achieve comparable results with less time and tuning.
We formulate the problem of neural network optimization as Bayesian filtering, where the observations are the backpropagated gradients. While neural network optimization has previously been studied using natural gradient methods which are closely related to Bayesian inference, they were unable to recover standard optim…
SAM optimizer benefits from normalization, stabilizing and guiding optimization.
problem Improving deep neural network performance with SAM optimizer.
method Theoretical and empirical study of normalization in SAM for convex and non-convex functions.
result Normalization helps SAM in stabilizing and guiding optimization along a continuum of minima.
Algorithm improves online canonical correlation analysis.
problem Online canonical correlation analysis.
method Stochastic Scaled-Gradient Descent (SSGD) for minimizing expectation over Riemannian manifolds.
result Achieved optimal one-time-scale algorithm with explicit rate of local asymptotic convergence.
New method trains normalizing flows using entropy-regularized transport.
problem Training continuous normalizing flows efficiently.
method Formulates flows as gradients of scalar potentials, training only these potentials.
result Trains normalizing flows without explicit flow computation during training.
The paper proves convergence of normalized Ricci flow on compact manifolds.
problem Convergence of normalized Ricci flow on compact manifolds.
method Gradient inequality of Łojasiewicz type to show convergence to steady-states.
result Convergence of normalized Ricci flow to steady-states on compact manifolds.
We study the negative gradient flow of the spinorial energy functional (introduced by Ammann, Weiß, and Witt) on 3-dimensional Berger spheres. For a certain class of spinors we show that the Berger spheres collapse to a 2-dimensional sphere. Moreover, for special cases, we prove that the volume-normalized standard 3-sp…
Extends normalizing flows to arbitrary smooth manifolds.
problem Current normalizing flows are limited to basic geometries and cannot handle complex real-world data.
method Uses Neural ODEs and geometric control theory to extend flows to arbitrary smooth manifolds.
result Demonstrates scalable unbiased estimator for divergence in generalized setting.
In recent years, plenty of metrics have been proposed to identify networks that are free of gradient explosion and vanishing. However, due to the diversity of network components and complex serial-parallel hybrid connections in modern DNNs, the evaluation of existing metrics usually requires strong assumptions, complex…
New method trains deep ResNets without normalization, achieving state-of-the-art performance.
problem Training deep ResNets without normalization layers leads to instability and lower accuracy.
method Adaptive gradient clipping and Normalizer-Free ResNets design.
result Normalizer-Free ResNets achieve 86.5% top-1 accuracy on ImageNet, matching EfficientNet-B7.
BatchNorm helps train quantized networks by avoiding gradient explosion.
problem Training quantized neural networks is difficult due to gradient issues.
method Investigated the impact of BatchNorm on both full-precision and quantized networks.
result BatchNorm avoids gradient explosion in quantized networks, contrary to expectations.