# Adaptive Weight Decay for Deep Neural Networks

## TL;DR

This paper introduces AdaDecay, an adaptive weight decay method that adjusts regularization for each parameter based on gradient norms, improving generalization in deep neural networks across various datasets.

## Contribution

The paper proposes a novel adaptive weight decay approach that dynamically determines regularization strength per parameter, unlike traditional constant decay methods.

## Key findings

- AdaDecay outperforms state-of-the-art optimization algorithms.
- Improves accuracy on MNIST, Fashion-MNIST, and CIFAR-10.
- Enhances generalization across shallow and deep models.

## Abstract

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.