Distributed Mean Estimation With Rotated Vector Quantization
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Existing distributed computing systems face significant communication costs, particularly when dealing with low-power and low-bandwidth devices, which can hinder efficient distributed mean estimation and machine-learned model updates.
Innovation Solution
The implementation of a computing system that uses random rotation and probabilistic quantization techniques to reduce communication costs. Specifically, client devices rotate vectors by a random rotation matrix, perform probabilistic quantization, and then transmit the quantized rotated updates to a centralized server.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If vectors are transmitted directly from client devices to the centralized server, then the mean estimation can be performed accurately, but the communication bandwidth and cost increase significantly
Solution Approach 1:
The patent extracts only the essential information needed for mean estimation by performing probabilistic quantization on rotated vectors. Instead of transmitting full-precision vectors, the system quantizes the rotated vectors to a limited number of bits (e.g., 3-5 bits), extracting only the most significant directional information while discarding redundant precision, thus reducing communication bandwidth while preserving estimation accuracy.
Solution Approach 2:
The patent applies random rotation matrices to transform the original vectors into a rotated coordinate system before quantization. This parameter transformation redistributes the vector information across different dimensions, allowing probabilistic quantization to capture the essential directional information more efficiently. The rotation parameter changes enable the system to achieve the same estimation accuracy with fewer bits per vector.
2Measurement precision
If full-precision vectors are transmitted to ensure accurate mean estimation, then the estimation accuracy is maintained, but the communication cost becomes prohibitive for low-power and low-bandwidth devices
Solution Approach 1:
The patent employs probabilistic quantization that maps continuous vector values to a discrete set of quantization levels using random sampling. This approach uses simple, computationally inexpensive quantization operations that can be performed on low-power devices without requiring complex compression algorithms or high-precision arithmetic, making it suitable for resource-constrained environments while maintaining acceptable estimation accuracy.
3Quantity of substance
If probabilistic quantization is applied directly to original vectors, then communication bandwidth is reduced, but the mean square error of mean estimation increases
Solution Approach 1:
The patent performs random rotation of vectors before applying probabilistic quantization. This preliminary transformation aligns the vector information in a way that makes the subsequent quantization more effective. By rotating the vectors first, the system ensures that the quantization process captures the most significant directional information, thereby reducing the mean square error of the mean estimation while still achieving bandwidth reduction.
Data Source
AI summary
The present disclosure provides systems and methods for communication efficient distributed mean estimation. In particular, aspects of the present disclosure can be implemented by a system in which a number of vectors reside on a number of different clients, and a centralized server device seeks to estimate the mean of such vectors. According to one aspect of the present disclosure, a client computing device can rotate a vector by a random rotation matrix and then subsequently perform probabilistic quantization on the rotated vector. According to another aspect of the present disclosure, subsequent to quantization but prior to transmission, the client computing can encode the quantized vector according to a variable length coding scheme (e.g., by computing variable length codes).