# Demystifying MPNNs: Message Passing as Merely Efficient Matrix Multiplication

arXiv: https://arxiv.org/abs/2502.00140 · HTML: https://mlsanity.com/paper/2502.00140/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 31 Jan 2025.

## Built on by (most cited first, 1 of 1)

- [Position: Spectral GNNs Are Neither Spectral Nor Superior for Node Classification](https://mlsanity.com/paper/2603.19091/) (2026)

## Abstract (arXiv)

While Graph Neural Networks (GNNs) have achieved remarkable success, their design largely relies on empirical intuition rather than theoretical understanding. In this paper, we present a comprehensive analysis of GNN behavior through three fundamental aspects: (1) we establish that k-layer Message Passing Neural Networks efficiently aggregate k-hop neighborhood information through iterative computation, (2) analyze how different loop structures influence neighborhood computation, and (3) examine behavior across structure-feature hybrid and structure-only tasks. For deeper GNNs, we demonstrate that gradient-related issues, rather than just over-smoothing, can significantly impact performance in sparse graphs. We also analyze how different normalization schemes affect model performance and how GNNs make predictions with uniform node features, providing a theoretical framework that bridges the gap between empirical success and theoretical understanding.