Non-Linearly Separable Distributed Computing: A Sparse Tensor Factorization Approach

2026-01-22

AI Summary

This work addresses the high computational and communication overhead incurred when multiple users compute nonlinearly separable functions in distributed environments. To overcome the limitations of conventional approaches that rely on linear separability assumptions, the paper proposes an efficient computation framework based on sparse tensor representations. By introducing a fixed-support SVD-based sparse tensor decomposition method combined with a multidimensional sub-tensor partitioning strategy, the framework jointly optimizes task allocation and communication patterns. This integrated approach significantly reduces system resource consumption and achieves substantial improvements over state-of-the-art methods in both computational efficiency and communication cost.

Technology Category

• Machine Learning: Matrix & Tensor Methods
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Search and Optimization: Distributed Search

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments
• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

The work considers the $N$-server distributed computing setting with $K$ users requesting functions that are arbitrary multi-variable polynomial evaluations of $L$ real (potentially non-linear) basis subfunctions. Our aim is to seek efficient task-allocation and data-communication techniques that reduce computation and communication costs. Towards this, we take a tensor-theoretic approach, in which we represent the requested non-linearly decomposable functions using a properly designed tensor $\bar{\mathcal{F}}$, whose sparse decomposition into a tensor $\bar{\mathcal{E}}$ and matrix $\mathbf{D}$ directly defines the task assignment, connectivity, and communication patterns. We here design an achievable scheme, employing novel fixed-support SVD-based tensor factorization methods and careful multi-dimensional tiling of subtensors, yielding computation and communication protocols whose costs are derived here, and which are shown to perform substantially better than the state of art.

Problem

• Non-linearly separable functions
• Distributed computing
• Computation-communication tradeoff
• Sparse tensor factorization
• Task allocation

Innovation

• sparse tensor factorization
• non-linearly separable functions
• distributed computing
• fixed-support SVD
• multi-dimensional tiling