# Adaptive Weight Decay for Deep Neural Networks

arXiv: https://arxiv.org/abs/1907.08931 · HTML: https://mlsanity.com/paper/1907.08931/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Jul 2019.

## Built on by (most cited first, 13 of 13)

- [Improving Robustness with Adaptive Weight Decay](https://mlsanity.com/paper/2210.00094/) (2022)
- [AlphaDecay: Module-wise Weight Decay for Heavy-Tailed Balancing in LLMs](https://mlsanity.com/paper/2506.14562/) (2025)
- [Cyclical Focal Loss](https://mlsanity.com/paper/2202.08978/) (2022)
- [FedLWS: Federated Learning with Adaptive Layer-wise Weight Shrinking](https://mlsanity.com/paper/2503.15111/) (2025)
- [OUI Need to Talk About Weight Decay: A New Perspective on Overfitting Detection](https://mlsanity.com/paper/2504.17160/) (2025)
- [General Cyclical Training of Neural Networks](https://mlsanity.com/paper/2202.08835/) (2022)
- [Improving Deep Learning Optimization through Constrained Parameter Regularization](https://mlsanity.com/paper/2311.09058/) (2023)
- [Evaluating Deep Learning in SystemML using Layer-wise Adaptive Rate Scaling(LARS) Optimizer](https://mlsanity.com/paper/2102.03018/) (2021)
- [Learning to Forget: Continual Learning with Adaptive Weight Decay](https://mlsanity.com/paper/2604.27063/) (2026)
- [Random Linear Projections Loss for Hyperplane-Based Optimization in Neural Networks](https://mlsanity.com/paper/2311.12356/) (2023)
- [A Computer Vision-Based Quality Assessment Technique for the automatic control of consumables for analytical laboratories](https://mlsanity.com/paper/2404.10454/) (2024)
- [OUIDecay: Adaptive Layer-wise Weight Decay for CNNs Using Online Activation Patterns](https://mlsanity.com/paper/2605.10161/) (2026)
- [Bigger Text Encoders Can Hurt CLIP Zero-Shot Performance](https://mlsanity.com/paper/2609.05730/) (2026)

## Abstract (arXiv)

Regularization in the optimization of deep neural networks is often critical to avoid undesirable over-fitting leading to better generalization of model. One of the most popular regularization algorithms is to impose L-2 penalty on the model parameters resulting in the decay of parameters, called weight-decay, and the decay rate is generally constant to all the model parameters in the course of optimization. In contrast to the previous approach based on the constant rate of weight-decay, we propose to consider the residual that measures dissimilarity between the current state of model and observations in the determination of the weight-decay for each parameter in an adaptive way, called adaptive weight-decay (AdaDecay) where the gradient norms are normalized within each layer and the degree of regularization for each parameter is determined in proportional to the magnitude of its gradient using the sigmoid function. We empirically demonstrate the effectiveness of AdaDecay in comparison to the state-of-the-art optimization algorithms using popular benchmark datasets: MNIST, Fashion-MNIST, and CIFAR-10 with conventional neural network models ranging from shallow to deep. The quantitative evaluation of our proposed algorithm indicates that AdaDecay improves generalization leading to better accuracy across all the datasets and models.