Deep neural networks (DNNs) have achieved great success in the last decades. DNN is optimized using the stochastic gradient descent (SGD) with learning rate annealing that overtakes the adaptive methods in many tasks. However, there is no common choice regarding the scheduled-annealing for SGD. This paper aims to present empirical analysis of learning rate annealing based on the experimental results using the major data-sets on the image classification that is one of the key applications of the DNNs. Our experiment involves recent deep neural network models in combination with a variety of learning rate annealing methods. We also propose an annealing combining the sigmoid function with warmup that is shown to overtake both the adaptive methods and the other existing schedules in accuracy in most cases with DNNs.

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 L2 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.

Continual learning aims to enable neural networks to learn new tasks without catastrophic forgetting of previously learned knowledge. Orthogonal Gradient Descent algorithms have been proposed as an effective solution to mitigate catastrophic forgetting. However, these algorithms often rely on the Neural Tangent Kernel regime, which imposes limitations on network architecture. In this study, we propose a novel method to construct an orthonormal basis set for orthogonal projection by leveraging Catastrophic Forgetting Loss. In contrast to the conventional gradient-based basis that reflects an update of model within an infinitesimal range, our loss-based basis can account for the variance within two distinct points in the model parameter space, thus overcoming the limitations of the Neural Tangent Kernel regime. We provide both quantitative and qualitative analysis of the proposed method, discussing its advantages over conventional gradient-based baselines. Our approach is extensively evaluated on various model architectures and datasets, demonstrating a significant performance advantage, especially for deep or narrow networks where the Neural Tangent Kernel regime is violated. Furthermore, we offer a mathematical analysis based on higher-order Taylor series to provide theoretical justification. This study introduces a novel theoretical framework and a practical algorithm, potentially inspiring further research in areas such as continual learning, network debugging, and one-pass learning.