A Distributed Data-Parallel PyTorch Implementation of the Distributed Shampoo Optimizer for Training Neural Networks At-Scale (2309.06497v1)

Abstract: Shampoo is an online and stochastic optimization algorithm belonging to the AdaGrad family of methods for training neural networks. It constructs a block-diagonal preconditioner where each block consists of a coarse Kronecker product approximation to full-matrix AdaGrad for each parameter of the neural network. In this work, we provide a complete description of the algorithm as well as the performance optimizations that our implementation leverages to train deep networks at-scale in PyTorch. Our implementation enables fast multi-GPU distributed data-parallel training by distributing the memory and computation associated with blocks of each parameter via PyTorch's DTensor data structure and performing an AllGather primitive on the computed search directions at each iteration. This major performance enhancement enables us to achieve at most a 10% performance reduction in per-step wall-clock time compared against standard diagonal-scaling-based adaptive gradient methods. We validate our implementation by performing an ablation study on training ImageNet ResNet50, demonstrating Shampoo's superiority over standard training recipes with minimal hyperparameter tuning.

• The paper introduces a data-parallel PyTorch adaptation of the Shampoo optimizer, using block-diagonal preconditioners for efficient parameter updates.
• It demonstrates that the distributed implementation incurs less than a 10% overhead compared to conventional diagonal preconditioners while speeding up convergence.
• Empirical evaluations on ImageNet with ResNet50 confirm improved learning speed and final accuracy with minimal hyperparameter tuning.

Distributed Data-Parallel PyTorch Implementation of Distributed Shampoo

The paper presents a meticulous implementation of the Distributed Shampoo Optimizer in PyTorch, aimed at training neural networks at scale. Shampoo, an adaptive gradient optimization method, is distinguished by its use of block-diagonal preconditioners, featuring a Kronecker product approximation for calculating the preconditioner for each neural network parameter. This paper offers a comprehensive exploration of the algorithm, elucidating its theoretical underpinnings, practical optimizations, and the empirical performance enhancements achieved through the use of distributed computing resources.

Technical Summary

Shampoo emerges from the AdaGrad family, adapting the full-matrix AdaGrad's superior theoretical properties to be applicable in modern large-scale settings. Unlike full-matrix AdaGrad, whose computational demands are quadratic in storage and cubic in compute, Shampoo utilizes a block-diagonal preconditioner for each network layer. This approach ensures a practical balance between computational cost and the adaptive efficacy of the optimizer. The parameter updates follow a reduced complexity structure that accommodates the massive scale of contemporary neural networks.

The primary contribution of this paper is its PyTorch adaptation, which leverages multi-GPU architectures to distribute the heavy computational load across processors. It employs PyTorch's DTensor data structure, allowing blocks associated with each parameter to be distributed. Consequently, it achieves substantial computational efficiency with a marginal increase in per-step execution time (up to 10%) compared to conventional diagonal preconditioners like Adam(W) and RMSProp.

Numerical Results

The implementation is shown to effectively train large models with less than a 10% performance penalty over standard methods based on diagonal scaling. This is underscored by empirical evaluations where the Shampoo optimizer, in concert with standard training practices, demonstrates its capacity to accelerate convergence and thus reduce overall compute time in achieving desired accuracy levels.

In an ablation paper on the ImageNet dataset with the ResNet50 architecture, the data-parallel, distributed implementation of Shampoo outperformed diagonal-scaling approaches in both learning speed and final accuracy. Furthermore, these improvements were realized with minimal hyperparameter tuning, showcasing Shampoo’s operational robustness and adaptability.

Implications and Future Work

The research brings into focus several implications, both practical and theoretical. Practically, the distributed implementation's efficiency can significantly benefit deep learning applications requiring large-scale training, such as those encountered in big tech companies' recommendation systems. Theoretically, the work invites further analysis of adaptive methods featuring structured preconditioners beyond block-diagonal approximations, potentially exploring more sophisticated tensor restructuring or hierarchical layering strategies.

Looking forward, this work lays groundwork for future extensions where innovative numerical linear algebra techniques, potentially leveraging lower precision computations, could be explored to further reduce the overhead of matrix operations without sacrificing convergence properties. Moreover, the interplay between learning rate strategies and various forms of momentum in conjunction with structured optimizers like Shampoo warrants deeper investigation to maximize performance gains across diverse model architectures and application domains.

In summary, the paper provides a detailed blueprint for implementing a highly efficient, distributed adaptive optimizer. It positions Distributed Shampoo as a viable and potentially superior alternative to existing methods for large-scale neural network training. The dual emphasis on robust theoretical foundations and practical performance optimizations exemplifies a well-engineered approach to tackling modern computational challenges in machine learning.