Weight decay stabilizes training dynamics by slowing progressive sharpening.
problem Understanding how weight decay affects training stability in deep learning models.
method Analyzing weight decay effects at the Edge of Stability, developing a mathematical framework.
result Weight decay dampens oscillations and stabilizes sharpness in CNNs, causing a phase transition in MLPs.
Three mechanisms of weight decay found for different optimizers and architectures.
problem Understanding the regularization effect of weight decay in neural networks.
method Empirical investigation of weight decay for SGD, Adam, and K-FAC with various network architectures.
result Identified three distinct mechanisms of weight decay effect.
Cautious Weight Decay modifies weight decay for better optimization.
problem Improving optimization in deep learning models.
method Applies weight decay selectively based on parameter sign alignment.
result Consistently improves model performance across various tasks and scales.
Study on optimal ReLU networks with weight decay for interpolation.
problem Interpolating data with radially symmetric distributions using shallow ReLU networks.
method Weight decay regularization in infinite neuron, infinite data limit; analysis of growth rates.
result Existence and growth rates of unique radially symmetric minimizers with weight decay.
Novel Adam-family method with decoupled weight decay for training neural networks.
problem Training nonsmooth neural networks with weight decay.
method Proposes a novel Adam-family method with decoupled weight decay, establishing convergence properties and demonstrating superior performance.
result Asymptotically approximates SGD and enhances generalization performance.
SGD and weight decay encourage neural networks to learn low-rank weight matrices.
problem The bias of SGD towards low-rank weight matrices in neural networks.
method The study investigates the effect of SGD and weight decay on the rank of weight matrices in neural networks, both theoretically and empirically.
result Training with SGD and weight decay induces a bias towards rank minimization in weight matrices, which becomes more pronounced with smaller batch sizes and stronger weight decay.
A new method to improve deep neural networks using weight rescaling.
problem Overfitting and sensitivity to hyperparameters in weight decay.
method Weight rescaling (WRS) to control weight norm and prevent overfitting.
result WRS outperforms weight decay and other methods in various applications.
This paper reveals periodic behavior in neural network training with BN and weight decay.
problem Understanding the dynamics of neural network training with BN and weight decay.
method Rigorous investigation of empirical and theoretical mechanisms.
result Periodic behavior in training is a generalization of previously opposing perspectives.
Weight decay outperforms adversarial training for robustness.
problem Improving machine learning model robustness to adversarial attacks.
method Weight decay vs adversarial training for robustness.
result Weight decay is superior to adversarial training in terms of robustness.
Adaptive weight-decay improves deep neural network performance.
problem Overfitting in deep neural networks.
method AdaDecay adjusts weight-decay adaptively based on gradient norms within each layer.
result AdaDecay improves generalization and accuracy across various datasets and models.
Analyzes minima of deep linear networks with weight decay.
problem Understanding the loss landscape of deep neural networks.
method Analytical solutions for global minima with weight decay and stochastic neurons.
result The origin is a special point with qualitatively different minima in networks with more than 1 hidden layer.
Adam's generalization performance is improved by batch size and weight decay in neural networks.
problem Understanding how batch size and weight decay affect Adam's generalization in neural networks.
method Theoretical analysis of two-layer over-parameterized CNNs on image data.
result Adam's mini-batch variants can achieve near-zero test error, unlike full-batch Adam.
Gradient flow with weight decay shows grokking effect in deep learning.
problem Understanding the grokking effect in deep learning.
method Analyzing gradient flow dynamics with weight decay.
result Weight decay causes slow norm reduction, explaining grokking.
Proposes volumization for neural networks to control bias-variance tradeoff.
problem Improving generalization and preventing memorization in neural networks.
method Defines a physical volume for weights, interpolating between L2 and L∞ regularization.
result Volumization interpolates between weight decay and clipping, improving generalization.
Weight Decay induces low-rank weight matrices in neural networks, improving generalization.
problem Improving generalization in neural networks.
method Training ReLU NN with Weight Decay and Stochastic Gradient Descent.
result The weight matrix of a trained NN is approximately rank-two.
We introduce a new weight-decay scaling rule to maintain sublayer gains across different widths in modern scale-invariant architectures.
problem In modern scale-invariant architectures, training quickly enters a steady state where normalization layers create backward scale sensitivity, degrading learning-rate transfer.
method We introduce a weight-decay scaling rule for AdamW that preserves sublayer gain across widths by equalizing the effective learning rate.
result Our empirical weight-decay scaling rule λ 2 ∝ d λ_2\propto \sqrt{d} λ 2 ∝ d approximately keeps sublayer gains width invariant, enabling zero-shot transfer of learning rate and weight decay. This paper analyzes convergence of large-scale Transformers with weight decay.
problem Understanding optimization guarantees in large-scale Transformer training.
method Construct mean-field limit, show gradient flow convergence to PDE, demonstrate global minimum consistency.
result Gradient flow reaches global minimum in large-scale Transformers with small weight decay.
The paper connects neural collapse and low-rank bias in networks with L2 regularization.
problem Understanding the emergence of low-rank bias and neural collapse in L2-regularized networks.
method Unified theoretical framework linking TCV and rank of weight matrices, proving global optimality of DNC1, and establishing a benign landscape property.
result Zero TCV across intermediate layers minimizes representation cost under natural architectural constraints, and DNC1 is globally optimal.
Study reveals dynamics of neural networks with normalization, weight decay, and SGD.
problem Understanding the equilibrium condition in Spherical Motion Dynamics (SMD).
method Investigates SMD by exploring the cause of equilibrium condition, introducing assumptions, proposing angular update, and verifying theoretical results.
result Proves weight norm and angular update can converge at linear rate under given assumptions.
OUI tool detects optimal Weight Decay for DNNs without validation data.
problem Optimal Weight Decay hyperparameter selection for DNNs.
method Overfitting-Underfitting Indicator (OUI) tool.
result OUI correlates with improved generalization and validation scores.
Generalizes neural tangent kernel analysis for two-layer networks with noise and regularization.
problem Limitations of NTK analysis in deep learning practice.
method Generalized NTK analysis for two-layer neural networks with weight decay and gradient noise.
result Noisy gradient descent with weight decay exhibits 'kernel-like' behavior and converges linearly.
Wide neural networks with weight decay exhibit neural collapse.
problem Proving neural collapse in wide neural networks trained with weight decay.
method Generic guarantees on neural collapse for wide networks with weight decay, proving low training error and balancedness, and bounded conditioning.
result First proof of neural collapse in end-to-end training of wide neural networks with weight decay.
New learning rate schedule improves deep learning performance.
problem Improving deep learning performance with varying learning rates.
method Exponential learning rate schedule with Batch Normalization.
result Exponential learning rate schedule with BN is equivalent to standard BN + SGD + Weight Decay + Momentum.
Regularization and data augmentation can be class-dependent, leading to poor performance on some classes.
problem Class-dependent effects of regularization and data augmentation.
method Evaluation of regularization and data augmentation techniques on Imagenet and INaturalist datasets.
result Regularization and data augmentation can lead to significant performance drops on some classes.
Regularizers change the geometric properties of loss functions in neural networks.
problem Understanding how different regularizers affect the geometric properties of loss functions in neural networks.
method Examined several regularizers, including weight decay, to determine if the regularized loss function becomes Morse.
result For certain regularizers, the regularized loss function becomes Morse, indicating a change in geometric properties.
This paper investigates the effectiveness of decoupled weight decay at the start of training.
problem The traditional approach to weight decay is not effective throughout training.
method The authors investigate decoupled weight decay, applying it only at the start of training.
result Applying weight decay only at the start of training stabilizes network weights and improves performance.
This work improves normalization methods in deep networks, enhancing stability and performance.
problem Shortcomings of Batch-Normalization hinder its use for certain tasks.
method Presented a novel view on normalization methods and weight-decay, suggesting alternatives like L 1 L^1 L 1 and L ∞ L^\infty L ∞ . result Improved normalization methods enable first batch-norm alternative for half-precision implementations.
Lion optimizer performs well in training AI models with memory efficiency.
problem Lion optimizer's theoretical basis is unclear.
method Continuous-time and discrete-time analysis of Lion updates with a new Lyapunov function.
result Lion is a novel and principled approach for constrained optimization.
Adversarial training effectiveness varies widely due to inconsistent training settings.
problem Variability in adversarial training effectiveness due to inconsistent training settings.
method Comprehensive evaluation of 10+ adversarial training methods and their hyperparameters.
result Basic training settings like weight decay can significantly impact adversarial robustness.
NovoGrad improves deep learning training with adaptive moments and layer-wise normalization.
problem Training deep neural networks efficiently and effectively.
method Layer-wise adaptive moments with gradient normalization and decoupled weight decay.
result NovoGrad outperforms well-tuned SGD with momentum and Adam/AdamW in various tasks.
Theoretical justification for deep networks' performance with regularization techniques.
problem Understanding the performance of deep networks trained with the square loss.
method Analysis of gradient flow and theoretical justification of regularization techniques.
result Convergence to solutions with smaller Frobenius norms leads to better classification error bounds.
Batch normalization makes neural networks more vulnerable to small adversarial perturbations.
problem Adversarial vulnerability of neural networks trained with batch normalization.
method Investigated the impact of batch normalization on adversarial robustness and compared it to weight decay.
result Substituting weight decay for batch norm nullifies adversarial vulnerability.
AdamW optimizes a constrained loss with ℓ ∞ \ell_\infty ℓ ∞ norm constraint.
problem Understanding the optimization behavior of AdamW with ℓ ∞ \ell_\infty ℓ ∞ norm constraint. method Analyzing AdamW as a smoothed version of SignGD and connecting it to Frank-Wolfe optimization.
result AdamW implicitly performs constrained optimization with ℓ ∞ \ell_\infty ℓ ∞ norm constraint. New regularizer improves neural network robustness and generalization.
problem Ineffective weight decay for networks with homogeneous activation functions.
method Proposes an invariant regularizer to penalize intrinsic weight norms.
result Improves generalization and adversarial robustness on various datasets.
Regularization timing affects deep network performance, not just its presence.
problem The timing of regularization in deep networks impacts their performance.
method Analysis of different datasets, architectures, regularization methods, and learning rate schedules.
result The critical period for regularization in deep networks is decisive of final performance.
Develops exact convex optimization formulations for neural networks.
problem Training two-layer neural networks with rectified linear units.
method Uses semi-infinite duality and minimum norm regularization to develop exact convex optimization formulations.
result Shows equivalence of ReLU networks trained with weight decay to block ℓ 1 \ell_1 ℓ 1 penalized convex models. Residual Continual Learning prevents forgetting in sequential tasks.
problem Preventing catastrophic forgetting in sequential learning of multiple tasks.
method ResCL reparameterizes network parameters by combining original and fine-tuned networks, keeping network size constant.
result ResCL achieves state-of-the-art performance in various continual learning scenarios.
Convex dual network improves neural network reconstruction for medical imaging.
problem Non-convex nature of neural networks hinders their use in sensitive applications.
method Introduces a convex duality framework for a two-layer fully-convolutional ReLU denoising network.
result Training neural networks with weight decay regularization induces path sparsity and piecewise linear filtering.
Framework models supervised learning in non-stationary data.
problem Non-stationary data in supervised learning.
method Statistical physics methods applied to LVQ and neural networks.
result LVQ and ReLU have different sensitivity to concept drift.
Hybrid regularization avoids double descent in random feature models.
problem Avoiding the double descent phenomenon in random feature models.
method Combines early stopping and weight decay, using GCV for hyperparameter selection.
result Hybrid method successfully avoids double descent and achieves comparable generalization.
Variational Laplace improves Bayesian neural networks performance.
problem Improving Bayesian neural networks performance.
method Develops variational Laplace for BNNs, exploiting curvature of likelihood.
result Variational Laplace outperforms other inference methods.
We analyze dropout in deep networks with rectified linear units and the quadratic loss. Our results expose surprising differences between the behavior of dropout and more traditional regularizers like weight decay. For example, on some simple data sets dropout training produces negative weights even though the output i…
We study deep Bayesian neural networks with Gaussian priors, revealing heavy-tailed unit activations.
problem Characterizing regularization effects in deep Bayesian neural networks.
method Investigation of deep Bayesian neural networks with Gaussian weight priors and ReLU-like nonlinearities.
result The prior distribution on units becomes increasingly heavy-tailed with depth, influencing activation patterns.
Variational Laplace improves Bayesian neural network performance without sampling.
problem Improving Bayesian neural network performance and calibration.
method Develops a new variational Laplace method for BNNs, exploiting curvature of likelihood.
result Variational Laplace outperforms standard VI methods in test performance and calibration.
Analyzes why neural networks generalize beyond training data.
problem Understanding why neural networks generalize beyond training data.
method Examined loss landscapes of neural networks to identify the mismatch between training and test losses.
result Identified the 'LU mechanism' explaining grokking in various tasks.
New method for training deep neural networks with regularization, converging to better generalization.
problem Improving generalization of deep neural networks through explicit regularization.
method Regularizer Mirror Descent (RMD) method, inspired by convergence properties of stochastic mirror descent (SMD).
result RMD converges to a point close to the minimizer of the cost function, leading to better generalization performance.
Paper introduces vector-valued variation spaces for multi-output neural networks.
problem Understanding and optimizing multi-output neural networks.
method Development of vector-valued variation spaces and representer theorem.
result Novel bounds for layer widths in deep networks and a convex optimization method for compression.
New method trains neural networks with threshold activation functions efficiently.
problem Training neural networks with threshold activation functions is challenging due to zero gradients.
method We study weight decay regularized training problems of deep neural networks with threshold activations, showing they can be formulated as convex optimization problems.
result Regularized deep threshold network training problems can be formulated as standard convex optimization problems, paralleling the LASSO method.