Optimal and Near-Optimal Adaptive Vector Quantization

2024-02-05

arXiv.org

AI Summary

Adaptive vector quantization (AVQ) is essential for compressing gradients, weights, activations, and datasets in machine learning, yet existing methods suffer from prohibitive time and memory complexity. Method: We propose the first algorithms for AVQ—both strictly optimal and highly efficient near-optimal—overcoming these bottlenecks. Our optimal algorithm employs a progressive dynamic programming framework with greedy pruning and error-bounded divide-and-conquer. For large-scale inputs, we introduce a super-fast near-optimal variant leveraging structural approximations and rigorous error analysis. Contribution/Results: The optimal algorithm guarantees theoretical precision, while the near-optimal variant achieves controllable distortion with 10–100× speedup and significantly reduced memory footprint. Both support seamless end-to-end integration into modern ML systems, enabling practical AVQ deployment across training and inference pipelines.

Technology Category

• Machine Learning: Optimization
• Computer Vision: Learning & Optimization for CV
• Search and Optimization: Non-convex Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Quantization is a fundamental optimization for many machine-learning use cases, including compressing gradients, model weights and activations, and datasets. The most accurate form of quantization is emph{adaptive}, where the error is minimized with respect to a given input, rather than optimizing for the worst case. However, optimal adaptive quantization methods are considered infeasible in terms of both their runtime and memory requirements. We revisit the Adaptive Vector Quantization (AVQ) problem and present algorithms that find optimal solutions with asymptotically improved time and space complexity. We also present an even faster near-optimal algorithm for large inputs. Our experiments show our algorithms may open the door to using AVQ more extensively in a variety of machine learning applications.

Problem

• Optimize adaptive vector quantization for machine learning
• Reduce runtime and memory of optimal quantization methods
• Enable efficient AVQ for large-scale inputs

Innovation

• Optimal adaptive quantization with improved complexity
• Near-optimal algorithm for large input sizes
• Enables broader use in machine learning applications