Recent work has highlighted a surprising alignment between gradients and the top eigenspace of the Hessian -- termed the Dominant subspace -- during neural network training. Concurrently, there has been growing interest in the distinct roles of sharp and flat directions in the Hessian spectrum. In this work, we study Bulk-SGD, a variant of SGD that restricts updates to the orthogonal complement of the Dominant subspace. Through ablation studies, we characterize the stability properties of Bulk-SGD and identify critical hyperparameters that govern its behavior. We show that updates along the Bulk subspace, corresponding to flatter directions in the loss landscape, can accelerate convergence but may compromise stability. To balance these effects, we introduce interpolated gradient methods that unify SGD, Dom-SGD, and Bulk-SGD. Finally, we empirically connect this subspace decomposition to the Generalized Gauss-Newton and Functional Hessian terms, showing that curvature energy is largely concentrated in the Dominant subspace. Our findings suggest a principled approach to designing curvature-aware optimizers.

The process of training a deep neural network is characterized by significant time requirements and associated costs. Although researchers have made considerable progress in this area, further work is still required due to resource constraints. This study examines innovative approaches to expedite the training process of deep neural networks (DNN), with specific emphasis on three state-of-the-art models such as ResNet50, Vision Transformer (ViT), and EfficientNet. The research utilizes sophisticated methodologies, including Gradient Accumulation (GA), Automatic Mixed Precision (AMP), and Pin Memory (PM), in order to optimize performance and accelerate the training procedure. The study examines the effects of these methodologies on the DNN models discussed earlier, assessing their efficacy with regard to training rate and computational efficacy. The study showcases the efficacy of including GA as a strategic approach, resulting in a noteworthy decrease in the duration required for training. This enables the models to converge at a faster pace. The utilization of AMP enhances the speed of computations by taking advantage of the advantages offered by lower precision arithmetic while maintaining the correctness of the model. Furthermore, this study investigates the application of Pin Memory as a strategy to enhance the efficiency of data transmission between the central processing unit and the graphics processing unit, thereby offering a promising opportunity for enhancing overall performance. The experimental findings demonstrate that the combination of these sophisticated methodologies significantly accelerates the training of DNNs, offering vital insights for experts seeking to improve the effectiveness of deep learning processes.

In the rapidly advancing domain of deep learning optimization, this paper unveils the StochGradAdam optimizer, a novel adaptation of the well-regarded Adam algorithm. Central to StochGradAdam is its gradient sampling technique. This method not only ensures stable convergence but also leverages the advantages of selective gradient consideration, fostering robust training by potentially mitigating the effects of noisy or outlier data and enhancing the exploration of the loss landscape for more dependable convergence. In both image classification and segmentation tasks, StochGradAdam has demonstrated superior performance compared to the traditional Adam optimizer. By judiciously sampling a subset of gradients at each iteration, the optimizer is optimized for managing intricate models. The paper provides a comprehensive exploration of StochGradAdam's methodology, from its mathematical foundations to bias correction strategies, heralding a promising advancement in deep learning training techniques.