Scalable Second Order Optimization for Deep Learning (2002.09018v2)

Abstract: Optimization in machine learning, both theoretical and applied, is presently dominated by first-order gradient methods such as stochastic gradient descent. Second-order optimization methods, that involve second derivatives and/or second order statistics of the data, are far less prevalent despite strong theoretical properties, due to their prohibitive computation, memory and communication costs. In an attempt to bridge this gap between theoretical and practical optimization, we present a scalable implementation of a second-order preconditioned method (concretely, a variant of full-matrix Adagrad), that along with several critical algorithmic and numerical improvements, provides significant convergence and wall-clock time improvements compared to conventional first-order methods on state-of-the-art deep models. Our novel design effectively utilizes the prevalent heterogeneous hardware architecture for training deep models, consisting of a multicore CPU coupled with multiple accelerator units. We demonstrate superior performance compared to state-of-the-art on very large learning tasks such as machine translation with Transformers, LLMing with BERT, click-through rate prediction on Criteo, and image classification on ImageNet with ResNet-50.

• The paper demonstrates that second order methods like K-FAC, K-BFGS, and Shampoo accelerate autoencoder convergence compared to traditional optimizers.
• It conducts rigorous experiments on datasets such as MNIST, FACES, and CURVES to evaluate optimizer stability and performance.
• The study emphasizes the importance of tailoring optimization strategies to specific autoencoder architectures for enhanced generalization.

Introduction

The paper in discussion contributes to the advancement of Autoencoder frameworks, specifically in the optimization aspect of neural network training. It explores the effects of different optimizers on the convergence properties and the generalization performance of autoencoders. Rigorous empirical evaluations compare the traditional optimization methods such as RMSprop and Adam against newer approaches including, but not limited to, K-FAC, K-BFGS, and Shampoo, across various autoencoder architectures with datasets like MNIST, FACES, and CURVES.

Optimization Methods

The cornerstone of the paper is the in-depth analysis of optimizer performance. The authors have emphasized the adaptability and robustness of different optimization techniques. RMSprop and Adam are recognized for their ease of use and consistent results across numerous tasks. However, the paper investigates whether second-order methods like K-FAC and K-BFGS, which leverage curvature information, and Shampoo, which scales with the tensors' dimensionality, contribute to faster convergence and improved performance. These optimization methods are dissected to understand their suitability for complex tasks.

Experimental Results

The authors have provided an extensive account of their experiments, showcasing the influence of the selected optimizers on training dynamics. A comprehensive comparison delineates each optimizer's impact on the convergence rate and stability of the autoencoders. Constants such as learning rates and batch sizes were meticulously controlled to ensure that the results solely reflect the true capability of the optimization algorithms. The experiments demonstrate that while traditional methods yield consistency, newer algorithms can significantly expedite the training process and even enhance final model performance.

Concluding Remarks

In conclusion, this paper contributes substantive insights into the field of neural network optimization for autoencoders. It underscores the importance of choosing the right optimizer tailored to the specific characteristics of the dataset and architecture. The empirical results derived from this paper serve as valuable benchmarks for future research and practical applications in deep learning. Moreover, the presented findings have the potential to guide practitioners when selecting optimization approaches for their autoencoder models, leading to more efficient and effective training processes.