Overflow-Avoiding Memory AMP

TL;DR

This paper introduces overflow-avoiding and complexity-reduced variants of the GD-MAMP algorithm, enhancing numerical stability and efficiency in high-dimensional signal recovery tasks.

Contribution

It proposes two novel modifications to the GD-MAMP algorithm: one to prevent overflow issues and another to reduce computational complexity without sacrificing convergence.

Findings

Overflow-avoiding GD-MAMP effectively prevents numerical overflow.

Complexity reduction decreases matrix-vector products by one-third with minimal impact on convergence.

The methods maintain the original algorithm's performance while improving stability and efficiency.

Abstract

Approximate Message Passing (AMP) type algorithms are widely used for signal recovery in high-dimensional noisy linear systems. Recently, a principle called Memory AMP (MAMP) was proposed. Leveraging this principle, the gradient descent MAMP (GD-MAMP) algorithm was designed, inheriting the strengths of AMP and OAMP/VAMP. In this paper, we first provide an overflow-avoiding GD-MAMP (OA-GD-MAMP) to address the overflow problem that arises from some intermediate variables exceeding the range of floating point numbers. Second, we develop a complexity-reduced GD-MAMP (CR-GD-MAMP) to reduce the number of matrix-vector products per iteration by 1/3 (from 3 to 2) with little to no impact on the convergence speed.