NeuMatC: A General Neural Framework for Fast Parametric Matrix Operation

TL;DR

NeuMatC is a neural framework that efficiently performs parametric matrix operations by learning a low-rank, continuous mapping, significantly reducing computation time in applications like wireless communication.

Contribution

NeuMatC introduces a novel neural approach to handle general parametric matrix operations by exploiting low-rankness and continuity, enabling fast computations across parameters.

Findings

Over 3x speedup in parametric inversion

10x speedup in parametric SVD

Maintains acceptable accuracy

Abstract

Matrix operations (e.g., inversion and singular value decomposition (SVD)) are fundamental in science and engineering. In many emerging real-world applications (such as wireless communication and signal processing), these operations must be performed repeatedly over matrices with parameters varying continuously. However, conventional methods tackle each matrix operation independently, underexploring the inherent low-rankness and continuity along the parameter dimension, resulting in significantly redundant computation. To address this challenge, we propose \textbf{\textit{Neural Matrix Computation Framework} (NeuMatC)}, which elegantly tackles general parametric matrix operation tasks by leveraging the underlying low-rankness and continuity along the parameter dimension. Specifically, NeuMatC unsupervisedly learns a low-rank and continuous mapping from parameters to their corresponding matrix operation results. Once trained, NeuMatC enables efficient computations at arbitrary parameters using only a few basic operations (e.g., matrix multiplications and nonlinear activations), significantly reducing redundant computations. Experimental results on both synthetic and real-world datasets demonstrate the promising performance of NeuMatC, exemplified by over $3\times$ speedup in parametric inversion and $10\times$ speedup in parametric SVD compared to the widely used NumPy baseline in wireless communication, while maintaining acceptable accuracy.