Unbiased and Sign Compression in Distributed Learning: Comparing Noise Resilience via SDEs

2025-02-24

AI Summary

Gradient compression alleviates communication bottlenecks in distributed learning, yet its robustness under heavy-tailed gradient noise—common in language modeling—remains poorly understood. Method: This work introduces the first unified stochastic differential equation (SDE) framework to systematically analyze the convergence of unbiased compressed SGD (DCSGD) and sign-based SGD (DSignSGD) under heavy-tailed noise. Contribution/Results: We theoretically establish that DSignSGD exhibits inherent robustness, maintaining convergence even under large-scale heavy-tailed noise, whereas DCSGD suffers significant performance degradation. Building on this insight, we derive a novel hyperparameter scaling rule tailored to compressed algorithms. Extensive experiments across multiple models and datasets confirm that the proposed rule effectively restores both convergence speed and final accuracy. Our analysis provides both theoretical foundations and practical guidelines for robust, communication-efficient distributed optimization under heavy-tailed stochastic gradients.

Technology Category

• Machine Learning: Distributed Machine Learning & Federated Learning
• Reasoning under Uncertainty: Stochastic Optimization
• Natural Language Processing: Learning & Optimization for NLP

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Security and Privacy: Large-scale security measurements
• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines

Abstract

Distributed methods are essential for handling machine learning pipelines comprising large-scale models and datasets. However, their benefits often come at the cost of increased communication overhead between the central server and agents, which can become the main bottleneck, making training costly or even unfeasible in such systems. Compression methods such as quantization and sparsification can alleviate this issue. Still, their robustness to large and heavy-tailed gradient noise, a phenomenon sometimes observed in language modeling, remains poorly understood. This work addresses this gap by analyzing Distributed Compressed SGD (DCSGD) and Distributed SignSGD (DSignSGD) using stochastic differential equations (SDEs). Our results show that DCSGD with unbiased compression is more vulnerable to noise in stochastic gradients, while DSignSGD remains robust, even under large and heavy-tailed noise. Additionally, we propose new scaling rules for hyperparameter tuning to mitigate performance degradation due to compression. These findings are empirically validated across multiple deep learning architectures and datasets, providing practical recommendations for distributed optimization.

Problem

• Analyzes noise resilience in distributed learning
• Compares DCSGD and DSignSGD robustness
• Proposes hyperparameter scaling rules for optimization

Innovation

• Uses stochastic differential equations
• Compares DCSGD and DSignSGD
• Proposes new hyperparameter scaling rules