Distributed Mean Estimation with Random Rotation and Quantization
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Solution Overview
Problem
Distributed computing systems face significant communication costs, particularly when low-power and low-bandwidth devices like mobile phones or embedded devices need to transmit data to a centralized server, making it challenging to efficiently estimate the mean of vectors in applications like neural network training and k-means clustering.
Innovation Solution
The system employs a random rotation technique followed by probabilistic quantization and variable length coding to reduce communication costs, where client devices rotate vectors with a random rotation matrix and perform probabilistic quantization before transmitting them to a server, which then decodes and aggregates the data, significantly reducing mean square error and communication bits required.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If clients transmit full-precision model updates to the server, then the accuracy of mean estimation is improved, but the communication cost increases
Solution Approach 1:
The system applies random rotation to the model update vectors before quantization. This preliminary transformation redistributes the vector energy across all dimensions, ensuring that subsequent low-bit quantization preserves more essential information. The rotation is performed once before communication, enabling accurate mean estimation without transmitting full-precision data.
Solution Approach 2:
The system changes the representation parameters of model updates by applying random rotation matrices and performing probabilistic quantization. This transforms the data from high-dimensional floating-point vectors to rotated and quantized representations that maintain estimation accuracy while significantly reducing the number of bits required for transmission.
2Quantity of substance
If clients use low-precision quantization to reduce communication bits, then communication cost is reduced, but the mean square error of estimation increases
Solution Approach 1:
Random rotation is applied as a preliminary step before quantization to redistribute vector information. This ensures that when low-precision quantization is subsequently applied, the essential variance and structure of the original vectors are preserved in the quantized representation, minimizing mean square error despite reduced precision.
Solution Approach 2:
The system transforms the problem from directly quantizing original vectors to quantizing rotated vectors in a transformed coordinate system. This dimensional transformation allows the quantization process to capture more essential information at lower precision levels, reducing the trade-off between communication bits and estimation accuracy.
3Adaptability or versatility
If distributed learning is performed on low-power devices, then accessibility and deployment are improved, but communication bandwidth requirements become prohibitive
Solution Approach 1:
Low-power devices perform random rotation and quantization locally before transmission. This preliminary processing reduces the data size that needs to be communicated over bandwidth-constrained channels, enabling distributed learning deployment on resource-constrained devices without prohibitive communication requirements.
Solution Approach 2:
The system replaces the mechanical approach of transmitting large amounts of raw data with a computational approach where preprocessing (rotation and quantization) is performed locally. This substitution transforms the communication burden from network transmission to local computation, which is more feasible on low-power devices.
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).